Exploring therapeutic options is crucial in the ongoing COVID-19 pandemic caused by SARS-CoV-2. Nirmatrelvir, a potent inhibitor targeting the SARS-CoV-2 Mpro, shows promise as an antiviral treatment. Additionally, Ivermectin, a broad-spectrum antiparasitic drug, has demonstrated effectiveness against the virus in laboratory settings. However, its clinical implications are still debated. Using computational methods such as molecular docking and 100 ns molecular dynamics simulations, we investigated how Nirmatrelvir and Ivermectin interact with SARS-CoV-2 Mpro(A). Calculations using density functional theory have been instrumental in elucidating the behavior of isolated molecules, primarily by analyzing the frontier molecular orbitals. Our analysis revealed distinct binding patterns: Nirmatrelvir formed strong interactions with amino acids like MET49, MET165, HIS41, HIS163, HIS164, PHE140, CYS145, GLU166, and ASN142, showing stable binding with a root mean square deviation (RMSD) of around 2.0 Å. On the other hand, Ivermectin interacted with THR237, THR239, LEU271, LEU272, and LEU287, displaying an RMSD of 1.87 Å, indicating enduring interactions. Both ligands stabilized Mpro(A), with Ivermectin showing stability and persistent interactions despite forming fewer hydrogen bonds. These findings offer detailed insights into how Nirmatrelvir and Ivermectin bind to the SARS-CoV-2 main protease, providing valuable information for potential therapeutic strategies against COVID-19.

Ménière's disease (MD) has an unclear cause. The microvascular dysregulation of the inner ear has been increasingly pointed as a potential contributor. This study investigates the prevalence of cardiovascular risk factors (CVRFs) in MD patients compared to those with posterior circulation cerebral infarction (POCI). CVRFs like hypertension, diabetes, dyslipidemia, obesity, coronary heart disease, and smoking were assessed in both MD and POCI patients. Brain MRI identified POCI etiology as "small vessel occlusion" (SVO) or "other etiology" (OE). The study included 64 MD and 84 POCI patients. Compared to MD, POCI OE showed a higher prevalence of CVRFs across various age groups, including hypertension, diabetes, dyslipidemia, and smoking. Notably, the odds of having POCI OE were significantly higher for individuals with hypertension and smoking. On the other hand, POCI SVO showed similar prevalence of CVRFs compared to MD. This study reveals no significant difference in CVRF prevalence between MD and smaller vessel POCI. However, a clear distinction emerges when comparing MD to POCI with involvement of larger blood vessels. Further research is needed to confirm these findings and explore potential shared risk factors between POCI (SVO) and MD.

Build a special identical equation, use its calculation characters to prove and search for solution of any odd converging to 1 equation through (*3+1)/2^k operation, change the operation to (*3+2^m-1)/2^k, and get a solution for this equation, give a specific example to verify. Thus prove the Collatz Conjecture is true. Furthermore, analysis the sequences produced by iteration calculation during the procedure of searching for solution, build a weight function model, prove it decrease progressively to 0, build a complement weight function model, prove it increase to its convergence state. Build a (*3+2^m-1)/2^k odd tree, prove if odd in (*3+2^m-1)/2^k long huge odd sequence can not converge, the sequence must outstep the boundary of the tree after infinite steps of (*3+2^m-1)/2^k operation.

The predatory mirids Macrolophus pygmaeus Ramber and Nesidiocoris tenuis Reuter (Heteroptera: Miridae) are used for the biological control of Tuta absoluta Meyrick (Lep.: Gelechiidae) and other pests in tomato greenhouses. The functional response of 1 (young) and 10 (old) days old adult females and males of M. pygmaeus and N. tenuis on eggs of T. absoluta, was determined on tomato at two temperatures (20° and 25°C) and LD 16:8 and found to be Type II. M. pygmaeus females exhibited higher predation efficiency, than males at both tested temperatures. Young M. pygmaeus females had a higher efficiency than old ones, whereas males had a low efficiency irrespective of age. The predation efficiency of N. tenuis was high (but lower than M. pygmaeus) in both young females and males, although old females had a higher efficiency than the respective males. Our results show that the two predatory species have different functional response characteristics to their prey depending mainly on sex and age which may affect their role as biological control agents.

P versus NP is considered as one of the most fundamental open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, a precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is NP-complete. It is well-known that P is equal to NP under the assumption of the existence of a polynomial time algorithm for some NP-complete. We show that the Monotone Weighted Xor 2-satisfiability problem (MWX2SAT) is NP-complete and P at the same time. Certainly, we make a polynomial time reduction from every directed graph and positive integer k in the K-CLOSURE problem to an instance of MWX2SAT. In this way, we show that MWX2SAT is also an NP-complete problem. Moreover, we create and implement a polynomial time algorithm which decides the instances of MWX2SAT. Consequently, we prove that P = NP.

The pervasive presence of atmospheric pollution, particularly polycyclic aromatic hydrocarbons such as 7,12-dimethylbenz(a)anthracene, instigates aberrant cellular and tissue conditions, precipitating oxidative damage and inflammatory cascades conducive to the onset of cancer, notably mammary cancer. Given the hepatic metabolism of 7,12-dimethylbenz(a)anthracene, the imperative of employing natural antioxidants becomes apparent. In this study, we delve into the antioxidant and hepato-protective properties of Pistacia lentiscus against 7,12-dimethylbenz(a)anthracene-induced toxicity, alongside exploring its potential anticancer attributes. Our investigations unveil Pistacia lentiscus's anti-proliferative efficacy against human breast cancer cell lines. Notably, 7,12-dimethylbenz(a)anthracene-intoxication escalates body weight, disrupts lipid profiles, and incites serum oxidative damage. Concurrently, hepatic and renal oxidative stress ensue, accompanied by heightened antioxidant enzyme activity in the 7,12-dimethylbenz(a)anthracene-exposed-group compared to controls (p<0.05). Nonetheless, Pistacia lentiscus co-administration rectifies biochemical imbalances, significantly attenuates oxidative stress aberrations, and augments antioxidant enzyme responses (p<0.05). Importantly, histological analysis evinces Pistacia lentiscus's shielding effect against 7,12-dimethylbenz(a)anthracene induced hepatocyte injury and steatosis. Our findings underscore Pistacia lentiscus's robust anti-proliferative, antioxidant, and hepato-protective capacities, mitigating metabolic disturbances, oxidative stress propagation in liver and kidney functions, and potential histological alterations, thereby impeding 7,12-dimethylbenz(a)anthracene-induced mammary cancer initiation. We posit that Pistacia lentiscus may serve as a prophylactic agent against breast cancer instigated by this carcinogen.

This study delves into the performance evaluation of an avant-garde technology in mobile communications known as Large Intelligent Surface (LIS), poised to be an integral component of the sixth-generation (6G) networks. This groundbreaking technology has the potential to markedly augment the Signal-to-Interference plus Noise Ratio (SINR) by orchestrating signals originating from the base station through a network of digitally controlled reflectors meticulously engineered to modulate the phase of incoming electromagnetic waves. A LIS can establish a Line of Sight (LoS) within channels that inherently do not have a LoS. In addition, it can also be optimized to increase transmission security by ensuring that the signal reaches only the target users of the message with better quality. In this study, analytical expressions were derived to calculate the distribution parameters, the bit error probability, and the secrecy outage probability. These calculations consider the presence of an eavesdropper link, highlighting the potential of the LIS to increase the confidentiality of digital communication systems. The accuracy of the proposed formulas was demonstrated by showing how the performance of the LIS varies with different design parameters and environmental fading.

In the quest for robust and efficient digital communication, this paper introduces cutting-edge key exchange protocols leveraging tropical semirings’ computational prowess and block matrices’ structural resilience. Moving away from the conventional use of finite fields, these protocols deliver markedly faster processing speeds and heightened security. We present two implementations of our concept, each utilizing a different platform for the set of commuting matrices: one employing tropical polynomials of matrices and the other employing Linde-de la Puente matrices. The inherent simplicity of tropical semirings leads to a decrease in operational complexity, and using block matrices enhances our protocols’ security profile. The security of these protocols relies on the Matrix Decomposition Problem. We also provide a comparative analysis of our protocols against existing matrix block-based protocols in finite fields. This research marks a significant shift in cryptographic protocol design, specifically tailored for demanding engineering applications, and sets a new standard in secure and efficient digital communication.

Here we will electrically-quantum model the neutron and proton as a three-phase alternating current electric generator, for this, we will use the theory of three-phase electric generators and vector or phasor diagrams. We will use this model to hypothesize how the quarks that form neutrons and protons with a combined mass of 10 MeV/c², can generate, through quarks-antiquarks-gluon interactions, a mass of 939.56 MeV/c² for the neutron and a mass of 938.27 MeV/c² for the proton. Using quantum mechanics and the theory of the generalization of the Boltzmann constant in curved space-time we will calculate the number of quarks-antiquarks-gluons and gravitons inside a neutron. We will also analyse βˉ decay using vector diagrams, we will calculate the tension of the string T₀ and the length of the string ℓs between quarks-antiquark and finally, we will model a black hole using a neutron equivalent model. In version 2 of this article, we will update the vector diagrams of the βˉ decay and theoretically calculate the energy of the W⁻ boson, the Z⁰ boson, and the Θ angle, Θ = arc cos (W⁻/Z⁰). We will demonstrate, through vector diagrams, that quarks-antiquarks-gluon interactions are the cause of the origin of the W⁻ boson and the Z⁰ boson. We will also demonstrate how the fine structure constant α originates. It is important to make clear, in future updates, we will describe the relationship that exists between the theory described in this paper and the Isospin theory, flavour and colour theory

The ceramic sherds from approximately 20 samples of lead-glazed tableware, recovered from diverse archaeological sites, including three repurposed storage pits transformed into dumpsters within the medieval city of Santarém (13th-14th century), underwent a meticulous examination. This investigation utilized techniques such as micro-Raman, ground state diffuse reflectance absorption, and X-ray fluorescence spectroscopies, in addition to X-ray diffraction and stereomicroscopy. A parallel study was conducted on contemporaneous European ceramics (glazed sherds) sourced from archaeological sites dating back to the 13th-15th centuries in Saintonge (France), Ardenne, Zomergem, and Bruges (Belgium), as well as Surrey-Hampshire, Kingston, and Cheam (England). The colour of the ceramic bodies is predominantly white or whitish, with a few exhibiting a vivid red hue. Ceramic sherds with a light paste composition were likely crafted using kaolin clays as raw materials. Analyses of fabric, mineralogical, and elemental composition of the sherds suggest that the majority of Santarém's glazed ceramics were locally or regionally produced, potentially derived from a Pliocene kaolin-rich sand formation. However, this conclusion is not supported by the absence of discovered lead glaze kilns or workshops in Santarém for the late Middle Ages. A distinctive feature from the European workshop ceramics lies in the quartz temper content and fabric.

Cucurbitacin phytonematicides consistently suppress population densities of plant nematodes, but have no effect against bacteria, fungi and insects. This study investigates the mechanism through which cucurbitacin phytonematicides consistently exert nematicidal properties on nematodes. Post 72-h exposure of second-stage juveniles (J2) of Meloidogyne enterolobii to geometric concentration of Nemafric-BL phytonematicide, J2 total proteins were measured using TruspecCHNS Macro. Total proteins versus phytonematicide exhibited a negative quadratic relation (R² = 0.97), with the minimum total proteins achieved at x = 4.9% phytonematicide. Beyond the minimum, total proteins increased gradually, depicting the existence of both isoprenylation (breakdown) and farnesylation (biosynthesis) of total proteins. In conclusion, cucurbitacins and nematode cuticles are both chemically structured, which provides the mechanism through which the test chemicals consistently decrease population densities of plant nematodes.

This investigation introduces an efficient method for assessing the reliability of semi-rigid steel frame connections in existing buildings, explicitly targeting the Top Angle and Seat Pad (TA-SP) semi-rigid connection commonly used in Australian cities' high-rise buildings. The moment capacity of these connections was examined through parameter power model testing, meticulously considering the bending, shear, and prying forces actions to determine the weakest elements in the connection system. A plastic hinge model was applied to ensure computational efficiency and accuracy in assessing the connections' ultimate strength. Comparatively, the finite element (F.E) method M−θ curves were introduced to scrutinise the nonlinear behaviour of the connection, providing validation for the predicted analytical approach. Further emphasis was placed on identifying the reliability of the weakest elements in the connection system, employing the First-Order and Second-Order Reliability Methods models to estimate their reliability index. The correlation between the model's failure probability and a percentile error was also explored, utilising Monte Carlo simulation reference for refined validation. Novel formulas and methodologies were introduced to compute the locked-chain-series system reliability, which accounts for the inherent material and geometric variability. The findings highlight the critical significance of the weakest element in determining the overall reliability of the existing TA-SP connection.

In this paper we present two ways to solve the Jacobian conjecture. The first way is an equivalent statement to the Jacobian conjecture using idempotent ideals. The second way is to use an equivalent thesis to the thesis of the Jacobian conjecture. In both cases we will show that the Jacobian conjecture is true.

Let R be a commutative ring and m, n be positive integers. We define a proper submodule N of an R-module M to be (m,n)-closed if for r∈R and b∈M, r^{m}b∈N implies rⁿ∈(N:_{R}M) or b∈N. This class of submodules lies properly between the classes of prime and primary submodules. Many characterizations, properties and supporting examples concerning this class of submodules are provided. The notion of (m,n)-modules is introduced and characterized. Furhermore, the (m,n)-closed avoidance theorem is proved. Finally, the (m,n)-closed submodules in amalgamated modules are studied.

We investigate the shear quasinormal modes (QNMs) in the context of electron stars, focusing on the Lifshitz geometry and exploring the behavior in the small star limit. The study begins by analyzing the shear sector modes in the infrared (IR) Lifshitz limit, where the geometry approaches that of a pure Lifshitz space. We derive and solve the differential equations governing the shear modes, revealing the asymptotic behavior in terms of the Lifshitz exponent. In the special case of integer values of the exponent, we obtain analytic corrections to the solutions to extract hydrodynamical QNMs. We then explore the cases with a Lifshitz exponent equal to or greater than three, providing analytical corrections to the Lifshitz IR solutions. A special case with an exponent of two is also considered, leading to modified solutions. The study extends to finding hydrodynamical QNMs, emphasizing the role of the Lifshitz geometry. Further investigations involve the flux with real and complex frequencies, considering the off-shell Lagrangian and deriving conserved flux expressions. Our analysis focuses on the exterior of the star, modeled by the Reissner-Nordström-AdS geometry. The small star limit is examined, revealing interesting features in the behavior of fermionic excitations. In summary, we provide a detailed exploration of shear quasinormal modes in electron stars, shedding light on their behavior in Lifshitz geometry, small star limits, and the interplay between real and complex frequencies. Our findings contribute to our understanding of the dynamics of electron stars and their gravitational properties.

This article studies electrostatic fields and potentials in the presence of conductors and point charges under the framework of solving Laplace’s equation with specifi ed boundary conditions. The results demonstrate that many problems posed and solved in elementary electrostatics through various heuristics such as the method of images, can be more rigorously treated under the solution framework of Laplace’s equation.

In this paper, we introduce and investigate a new family of sequences called the generalized Fibospinomials (or the generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we handle with $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomial spinors. After a short history on spinors and quaternions, we present Binet's formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some identities of generalized Fibonacci polynomial spinors, $(r,s)$-Fibonacci polynomial spinors and $(r,s)$-Lucas polynomial spinors. Moreover, we give some special identities such as Catalan's and Cassini's identities and we present matrices related with these polynomials.

A substantial spike in the need for quality healthcare has resulted from people being more cognizant of health issues. With blockchain, healthcare providers may safely share patient information electronically, which is especially important given the sensitive nature of the data contained inside them. However, flaws in the current blockchain design have surfaced since the dawn of quantum computing systems. The study proposes a novel quantum inspired blockchain system (Qchain) and constructs a unique entangled quantum medical record (EQMR)system with an emphasis on privacy and security. This Qchain relies on entangled states to connect its blocks. Automated production of the chronology indicator reduces storage capacity requirements by connecting entangled BloQ (blocks with quantum properties) with controlled activities. One qubit is used to store the hash value of each block. A lot of information regarding quantum internet is included in the protocol for the entangled quantum medical record (EQMR). EQMR can be accessed in Medical Internet of Things (M-IoT) systems may be kept private and secure, and their where-abouts can be monitored in the event of an emergency. The protocol also uses quantum authentication in place of more conventional methods like encryption and digital signatures. Mathematical research shows that the quantum converged blockchain (QCB) is highly safe against attacks such as the External attack, Intercept-Measure-Repeat attack, and Entanglement-Measure attack. The reliability and auditability evaluations of the entangled BloQ, as well as the quantum circuit design for computing the hash value, are presented. There's also a comparison between the suggested approach and several other quantum blockchain designs.

Chronic fatigue syndrome (CFS) is a disease in which fatigue that interferes with daily life persists for six months or longer. The number of patients with CFS is increasing, as CFS-like symptoms have been reported to occur in the sequelae of both COVID-19 infection and the SARS-CoV-2 vaccine, both of which have become significant issues in recent years. While the pathogenesis mechanism is not yet fully understood, research suggests that oxidative stress (OS) may play a role in the development of CFS. In this paper, we discuss the antioxidant potential of the antioxidant formulation Twendee M® (TwM) and the results of a questionnaire that monitored changes in symptoms before and after TwM in a total of 23 men and women diagnosed with CFS. TwM is a supplement containing 15 different ingredients, and has a strong antioxidant capacity that cannot be achieved with a single antioxidant ingredient. The results of the questionnaire showed that TwM significantly improved all of the major symptoms of CFS, including fatigue, muscle pain, joint pain, sleep disturbance, decreased memory and concentration, and headache. TwM was shown to alleviate various symptoms of CFS and improve quality of life.

The current study characterizes the transient M/M/1 queue manifold info-geometrically, through devising Fisher Information matrix(FIM) and its inverse(IFIM). Additionally, the impact of stability on the existence of IFIM and explore the geodesic equations of motion has been revealed. More potentially, the paper discusses the relationship between stability and the Gaussian curvature, as well as the connections between queueing theory, information geometry, , Riemannian geometry, and the Theory of Relativity.

The current work reports the upper bound of the state variable of the of the Pointwise Steady Fluid Flow Approximation (PSFFA) model of non-stationary M/Ek/1 queueing system.

The theory of Ismail's non-extensive maximum entropy solution (NME) is described in detail. It is used as an inductive inference technique for heavy-tailed queues with a non-robust mean queue length and a non-extensive "long-range" interaction. In our novel method, we substitute the non-robust mean queue length for the conventional Pollaczeck-Khinchin mean queue length. In other words, the new non-extensivity parameter q will be included in the resulting state probability function. Numerical portraits are provided to capture the influential effect of the derived formalism, , on the stable M//1 queue with heavy tails. More potentially, some applications of Hurst Exponent to social computing and connected health are provided. Conclusion with some challenging open problems and possible future research pathways are given.

The current paper provides a cutting-edge information data length- theoretic approach to the transient M/M/Infinity queueing system. This is a first time ever investigation that unifies information data length and queueing theories. The significant impact of both time and the number of states for the transient M/M/ Infinity queue on both the upper and lower bounds of the obtained information data length is observed and noted. The paper concludes with some challenging open problems, combined with concluding remarks and future research pathways.

The current study characterizes the transient M/M/1 queue manifold info-geometrically, through devising Fisher Information matrix(FIM) and its inverse(IFIM). Additionally, the impact of stability on the existence of IFIM and explore the geodesic equations of motion has been revealed. More potentially, the paper discusses some info-geometric applications to Machine Learning are highlighted. Closing remarks with some challenging open problems combined with the next phase of research are given.

From a differential geometric perspective, information geometry (IG) aims to characterise the structure of statistical geodesic models. The research done for this paper offers a novel method for modelling the information geometry of a queuing system. From the perspective of IG, the manifold of the transient M/M/infinity queue is described in this context. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of transient M/M/infinity QM are devised. In addition to that, new results that uncovered the significant impact of stability of QM on the existence of (IFIM) are obtained. Moreover, the Geodesic equations of motion of the coordinates of the underlying transient are obtained. Also, it is revealed that stable QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of transient M/M/iInfinity queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability(instability) phases of M/M/Infinity QM. Furthermore, a new discovery that presents the significant impact of stability of queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. Also, it is shown that stability of the devised (IME) enforces the instability of M/M/ Infinity QM. More interestingly, novel relativistic info-geometric queueing theoretic links are revealed .

In this paper, we first define the concepts of r-fuzzy soft α-open (semi-open and δ-open) sets on fuzzy soft topological spaces based on the article Aygunoglu et al. (Hacet. J. Math. Stat., 43 (2014), 193-208), and the relations of these sets with each other are established. In addition, we introduce the concepts of fuzzy soft δ-closure (δ-interior) operators, and study some properties of them. Also, the concept of r-fuzzy soft δ-connected sets is introduced and studied with help of fuzzy soft δ-closure operators. Thereafter, we define the concepts of fuzzy soft α-continuous (β-continuous, semi-continuous, pre-continuous and δ-continuous) functions, which are weaker forms of fuzzy soft continuity, and some properties of these functions along with their mutual relationships are discussed. Moreover, a decomposition of fuzzy soft α-continuity and a decomposition of fuzzy soft semi-continuity is obtained. Finally, as a weaker form of a fuzzy soft continuity, the concepts of fuzzy soft almost (weakly) continuous functions are defined, and some properties are specified. Additionally, we explore the notion of continuity in a very general setting called, fuzzy soft (L, M, N, O)-continuous functions and a historical justification is introduced.

This study aimed to determine the correlation of colour M-mode velocity propagation in the assessment of left ventricular diastolic function among acute decompensated heart failure patients with preserved ejection fraction (HFpEF). This research is an observational analytical study using a cross–sectional study design conducted from April to June 2022. The subjects of this study were patients diagnosed with acute HFpEF and treated at Dr. Soetomo General Academic Hospital, Surabaya. Patients with heart rhythm disturbances, moderate to severe valvular heart disease, and congenital heart defects were excluded from this study. Patients were measured for diastolic function including mitral valve early mitral inflow velocity (MV E Velocity), mitral peak velocity of early filling (E’) (E' Septal and E' Lateral), left atrial volume index (LAVI), The maximal tricuspid regurgitation velocity (TR V Max), Vp, the ratio of early diastolic mitral inflow velocity to early diastolic mitral annulus velocity (E/E'), the ratio between early and late ventricular filling velocity (E/A) and E/Vp Ratio. N-terminal-pro hormone B-type natriuretic peptide (NT–ProBNP) examination was also performed on study subjects as an additional diagnosis of acute heart failure. There were 33 patients who met the inclusion and exclusion criteria and were included in our study. There were 26 patients (78.8%) with grade I diastolic dysfunction, 4 patients (12.1%) with grade II diastolic dysfunction, and 3 patients (9.1%) with grade III diastolic dysfunction. There is a strong positive correlation between Vp with parameters E' Septal (p = < 0.001; r = 0.636) and E' Lateral (p = < 0.001; r = 0.650). Vp is negatively correlated with the ratio E/E' (p = 0.029; r = –0.37). The PCWP estimate with E/Vp ratio had a strong correlation with the NT–Pro BNP value > 300 pg/ml in acute HFpEF patients (p = < 0.001; r = 0.726) compared to the PCWP estimate with E/E' (p = < 0.001; r = 0.549). There is no correlation between Vp value and degree of diastolic dysfunction in patients with acute HFpEF.

It has been more than a century since Erlang published his paper in 1909. The classical queueing system for the M/D/c queue has been investigated by many authors. The key is to find the roots of an equation using explicit or numerical methods. We present an alternate form of explicit solution(s) of this/these root(s) using the Lambert-W function in this paper. In addition, the unsaturated probabilities of the number of customers in the system is derived explicitly in terms of this/these root(s). Finally, the mean number of customers in the system and the mean queueing delay are obtained from these probabilities. The exact queueing delay formula for the M/D/c queue is expressed in closed-form in terms of the root(s). Numerical results show that they are in excellent agreement with the numerical results published by Seelen, Tijms and Van Hoorn.

Partial negative allosteric modulators (NAM) of the mGlu5 receptor are an excellent alternative to full antagonists and NAMs because they retain some therapeutic effects and, at the same time, have a much broader therapeutic window. Here, we investigated whether partial mGlu5 NAM, M-5MPEP induced a fast and sustained antidepressant-like effect, characteristic of rapid-acting antidepressant drugs (RAADs) like ketamine, in C57BL/6J mice. M-5MPEP caused a rapid, dose-dependent antidepressant-like action in the tail suspension test (TST) 60 min after injection. This effect was antagonized by an AMPA receptor antagonist (NBQX) and a TrkB receptor antagonist (ANA-12) but not by 5HT1A and 5HT2A/2C receptor antagonists. Furthermore, M-5MPEP (30 mg/kg) induced sustained antidepressant-like effects 24 h after the last of four administrations. These effects were revealed in the splash test, designed to measure apathy-like state, and in the TST. Western blot and ELISA analyses indicated the involvement of the TrkB/BDNF pathway in the sustained M-5MPEP effects. Additionally, prolonged effects of M-5MPEP were entirely reversed by the TrkB receptor antagonist ANA-12 in both the splash test and the TST, confirming the critical role of TrkB receptor activation in the sustained antidepressant-like effect of M-5MPEP. Importantly, M-5MPEP enhanced the subthreshold dose of (R)-ketamine in the TST, indicating both substances' convergent mechanisms of action and the possibility of their practical use in treating depression.

Here, applying the theory of the generalization of the Boltzmann constant in curved space-time, we will model the mechanism by which elementary particles are formed. We will determine the relationship between gravity and each of the elementary particles that form the standard model following analogies to that of stellar bodies. In order to achieve our goal, we will propose new models for photons, quarks and gluons; with this, we will demonstrate why there are stable and unstable elementary particles; why the first family of elementary particles forms hadrons and why the second and third families cannot form hadrons; why the fermions comply with the Pauli exclusion principle and why the bosons do not comply with the Pauli exclusion principle, etc. Finally, we will analyse the generalization of the ADS/CFT correspondence and propose a theory of everything (T.O.E.).

Let R be a commutative ring with identity and m, n be positive integers. In this paper, we introduce the class of (m,n)-prime ideals which lies properly between the classes of prime and (m,n)-closed ideals. A proper ideal I of R is called (m,n)-prime if for a,b∈R, a^{m}b∈I implies either aⁿ∈I or b∈I. Several characterizations of this new class with many examples are given. Analougus to primary decomposition, we define the (m,n)-decomposition of ideals and show that every ideal in an n-Noetherian ring has an (m,n)-decomposition. Furthermore, the (m,n)-prime avoidance theorem is proved.

Oncostatin M (OSM), an inflammatory cytokine belonging to interleukin-6 superfamily, is recognized as an essential factor secreted by osteal macrophages to orchestrate bone remodelling. Osteoprotegerin (OPG) produced by osteoblasts regulates osteoclastogenesis. We previously demonstrated that bone morphogenetic protein-4 (BMP-4) stimulates OPG synthesis in osteoblast-like MC3T3-E1 cells, and that SMAD1/5/8(9), p38 mitogen-activated protein kinase (MAPK), and p70 S6 kinase positively regulates the OPG synthesis. The present study is aimed to investigate the effect of OSM on BMP-4-stimulated OPG synthesis in osteoblasts. OSM suppressed the release and the mRNA expression of OPG upregulated by BMP-4 in MC3T3-E1 cells.  Neither the BMP-4-induced phosphorylation of SMAD1/5/9 nor that of p38 MAPK affected by OSM. On the other hand, the BMP-4-stimulated phosphorylation of p70 S6 kinase was considerably suppressed by OSM. These results strongly suggest that OSM suppresses the BMP-4-stimulated OPG synthesis via inhibition of the p70 S6 kinase-mediated pathway in osteoblasts.

The Bessel function of the first kind J_N(kx) is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind I_N(kx) . Known polynomial approximations for the range −3≤x≤3 (having five-digit accuracy) are compared with those arising from this Legendre series and substitute versions are given with twice the number of terms and range (with five-digit accuracy or having fifteen-digit accuracy over −3≤x≤3). It is shown that infinite series of like-powered contributors (involving _2F_3 hypergeometric functions) extracted from the Fourier-Legendre series may be summed, having values that are inverse powers of the first five primes 1/(2^i 3^j 5^k 7^l 11^mm) for powers of order x24.

We report on the occurrence of natural Magnesium Alumina Silicate Hydrate (M-(A)-S-H) cement at Feragen and Leka in eastern and western Trøndelag Norway, respectively. Both occurrences are located in the sub-arctic climate zone and form in glacial till and moraine material deposited on ultramafic rock during the Weichselian glaciation. Weathering of serpentinized peridotite dissolve brucite and result in a relative high pH alkaline fluid that subsequently reacts with the felsic minerals of the till (quartz, plagioclase, K-feldspar) to form a cement consisting of an amorphous material or a mixture of nanocrystalline Mg-rich phyllosilicates, including illite. The presence of plagioclase in the till results in the enrichment of alumina in the cement, i.e., forms M-A-S-H instead of the M-S-H cement. Dissolution of quartz results in numerous etch-pits and negative quartz crystals filled with M-A-S-H cement. Where the quartz dissolution is faster that the cement precipitation, a honeycomb-like texture is formed. Compositionally the cemented till (tillite) contains more MgO and has a higher loss of ignition than the till, suggesting that the cement is formed by a MgO fluid that previously reacted with the peridotite. The M-(A)-S-H cemented till represent a new type of duricrust, coined magsilcrete. The study of natural Mg-cement provides information on peridotites as a Mg-source for Mg-cement and as a feedstock for CO2 sequestration.

Level index was introduced in 2017 for rooted trees which is a component of Gini index. In the origin, Gini index is a tool for economical investigations but Balaji and Mahmoud defined the graph theoretical applications of this index for statistical analysis of graphs. Level index is an important component of Gini index. In this paper we define a new graph polynomial which is called level polynomial and calculate the level polynomial of some classes of trees. We obtain some interesting relations between the level polynomials and some integer sequences.

Nuclear fusion reactors are composed by several complex components whose behaviour may be not certain a priori. This uncertainty may have a significant importance in the evolution of fault transients in the machine, causing unexpected damages to its components. For this reason a suitable method for the uncertainty propagation during those transient is required. The Monte Carlo method would be the reference option, but it is, in most of the cases, not applicable due to the large amount of required simulations to be repeated. In this context the Polynomial Chaos Expansion has been considered as a valuable alternative. It allows to create a surrogate model of the original one in terms of orthogonal polynomials. Then, the uncertainty quantification is performed repeatedly calling this much simpler and faster model. Using the fast current discharge in the Divertor Tokamak Test Toroidal Field (DTT TF) coils as a reference scenario, this method has been applied: the uncertainty on the parameters of the Fast Discharge Unit (FDU) varistor disks is propagated to the simulated electrical and electro-magnetic relevant effects. Eventually two worst case scenarios have been analyzed from the thermal-hydraulic point of view with the 4C code, simulating a fast current discharge as a consequence of a coil quench. Eventually it has been demonstrated that the uncertainty on the inputs (varistor parameters) strongly propagates obtaining a wide range of possible scenarios in case of accidental transients. This result underlines the necessity to take into account and propagate all possible uncertainties in the design of a fusion reactor, according to the Best Estimate Plus Uncertainty approach.

: Poultry products in Zambia form an integral part of the human diet in many households, as they are cheap and easy to produce. The burden of poultry diseases has, however, remained a major challenge. Growing consumer demand for poultry products in Zambia has resulted in non-prudent antimicrobial use on farms, intending to prevent and treat poultry diseases for growth optimization and maximising profits. This cross-sectional study aimed to identify the different types of bacteria causing diseases in chickens in Lusaka and to detect the extended-spectrum-lactamase (ESBL)-encoding genes. We collected 215 samples from 91 diseased chickens at three post-mortem facilities and screened them for gram-negative bacteria. Of these samples, 103 tested positive for various clinically relevant Enterobacteriaceae, including Enterobacter (43/103, 41.7%), Escherichia coli (20/103, 19.4%), Salmonella (10/103, 9.7%), and Shigella (8/103, 7.8%). Other isolated bacteria included Yersinia, Morganella, Proteus, and Klebsiella, which accounted for 21.4%. E. coli, Enterobacter, Salmonella, and Shigella were subjected to antimicrobial susceptibility testing. The results revealed that E. coli, Enterobacter, and shigella were highly resistant to tetracycline, ampicillin, amoxicillin, and trimethoprim-sulfamethoxazole, while Salmonella showed complete susceptibility to all antibiotics. The observed resistance patterns correlated with antimicrobial usage estimated from sales data from a large-scale wholesale and retail company. Six (6/14, 42.9%) E. coli isolates tested positive for bla_CTX-M, whilst eight (8/14, 57.1%) Enterobacter samples tested positive for bla_TEM. Interestingly, four (4/6, 66.7%) of the E. coli isolates carrying bla_CTX-M-positive strains were also positive for bla_TEM. Sanger sequencing of the PCR products revealed that five (5/6,83.3%) of the abovementioned isolates possessed the bla_CTX-M-15 allele. The results suggest the presence of potentially pathogenic ESBL-producing Enterobacteriaceae in poultry, threatening public health. Keywords:. Enterobacteriaceae, bla_CTX-M, bla_TEM

A new method for the synthesis of azido-propargyloxy derivatives of 1,3,5-triazine has been developed. The antibacterial activity against E. coli bacteria of propargyloxy substituted 1,3,5-triazines - 2,4,6-trispropargyloxy-1,3,5-triazine, 2-azido-4,6-bispropargyloxy-1,3,5-triazine and 2,4-diazido-6-propargyloxy-1,3,5-triazine and their hyperbranched polymers. It has been shown that the presence of an azide group in the compound directly affects the antibacterial activity. The cytotoxicity of these compounds against the M-HeLa, FetMSC and Vero cell lines was studied. The IC50 value was determined for low molecular weight compounds. It has been shown that hyperbranched polymers without azide groups don’t exhibit pronounced cytotoxicity and can be used in biomedical applications.

Crop digital twin is redefining traditional farming practices, offering unprecedented opportunities for real-time monitoring, predictive and simulation analysis, and optimization. This research embarks on an exploration of the synergy between precision agriculture, crop modeling, and regression algorithms to create a digital twin for augmenting farmers the concentration and composition prediction-based crop nutrient recovery. This captures the holistic representation of crop characteristics, considering the intricate relationships between environmental factors, nutrient concentrations, and crop compositions. However, the complexity arising from diverse soil and environmental conditions makes nutrient content analysis expensive and time-consuming. This paper presents the result of a predictive digital twin case study that employs six regression algorithms namely Elastic Net, Polynomial, Stepwise, Ridge, Lasso, and Linear Regression to predict rice nutrient content efficiently, particularly considering the coexistence and composition of multiple nutrients. Our research findings highlight the superiority of the Polynomial Regression model in predicting nutrient content, with a specific focus on accurate nitrogen percentage prediction. This insight can be used for nutrient recovery intervention by knowing the precise amount of nutrient to be added into the crop medium. The adoption of the Polynomial Regression model offers a valuable tool for nutrient management practices in the crop digital twin, potentially resulting in higher-quality rice production and a reduced environmental impact. The proposed method can be replicable in other low-resourced crop digital twin system.

Background: Polycystic ovary syndrome is a common reproductive and endocrinological disease characterized by ovulatory dysfunction, polycystic ovaries, and hyperandrogenism. Adipokines are believed to contribute to developing polycystic ovary syndrome and its accompanying metabolic complications such as dyslipidemia, insulin resistance, and cardiovascular diseases. Oncostatin M, a novel adipokine, plays a role in oogenesis, lipogenesis, and inflammation and may contribute to polycystic ovary syndrome pathogenesis and its related metabolic problems. Methods: In this case-control study, the patients were grouped in a 1:1 ratio into either the polycystic ovary syndrome (n = 32) or the control group (n = 32). Blood samples were obtained between the third and fifth days of the menstrual cycle. Serum levels of fasting glucose, insulin, C-reactive protein, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, triglyceride, white blood cell count, thyroid-stimulating hormone, luteinizing hormone, follicle-stimulating hormone, total testosterone, prolactin, estradiol, homeostasis model assessment of insulin resistance and oncostatin M were analyzed. Results: Oncostatin M levels were significantly lower, but C-reactive protein levels were substantially higher in the polycystic ovary syndrome group than in the control group (p = 0.002, p = 0.001, respectively). Oncostatin M was inversely correlated with total cholesterol, non-high-density lipoprotein cholesterol, fasting glucose, and the luteinizing hormone/follicle-stimulating hormone ratio (ρ = -0.329, p =0 .017; ρ = -0.386, p = 0.005; ρ = -0.440, p = 0.001; ρ = -0.316, p = 0.023, respectively). Conversely, there was no correlation between oncostatin M and total testosterone level (ρ = 0.220; p = 0.118). In the context of inflammation and metabolic parameters, oncostatin M was inversely correlated with C-reactive protein, homeostatic model assessment for insulin resistance score, and low-density lipoprotein cholesterol (ρ = -0.353, p = 0.019; ρ = -0.275, p = 0.048; ρ = -0.470, p < 0.001, respectively). The diagnostic performance of oncostatin M, C-reactive protein, homeostasis model assessment of insulin resistance, and non-high-density lipoprotein cholesterol for polycystic ovary syndrome is as follows: Oncostatin M, sensitivity: 50%, specificity: 75%, Accuracy: 63%, p = 0.009; C-reactive protein, sensitivity: 84%, specificity: 61%, Accuracy: 74%, p = 0.004; homeostasis model assessment of insulin resistance, sensitivity: 72%, specificity: 81%, Accuracy: 77%, p < 0.001; and non-high-density lipoprotein cholesterol; sensitivity: 72%, specificity: 75%, accuracy: 73%, p < 0.001. Conclusions: Plasma oncostatin M levels were considerably lower in patients with polycystic ovary syndrome than in the control group, and this was inversely correlated with the hormonal and metabolic parameters of polycystic ovary syndrome. Thus, oncostatin M may be a novel therapeutic target for polycystic ovary syndrome and its metabolic complications.

Quantum Gravity is not sufficient to predict the properties of particles (baryonic and non-baryonic) to a great extent. So, we develop General Quantum Gravity (GQG), which is a renormalizable formalization of quantized gravity that emerges from General Relativity through a new scenario of Quantum Mechanics. Inside every observable $(3+1)D$ spacetime in this new scenario of Quantum Mechanics, there must contain an internal hidden $(n+1)D$ spacetime, which immediately yields extra hidden dimensions by a closed continuous mapping, so that the overall spacetime must acquire Supersymmetry. We have also found that Superstrings are inevitably natural and universal but hidden inside every $(3+1)D$ observable spacetime. Superstrings are found eleven-dimensional (rather than lower dimensional) within this quantum spacetime. Consequently, eleven-dimensional Supergravity is necessarily a natural phenomenon within the GQG spacetime. GQG is formalized here in two different aspects. The first one gives an Einstein field equation in a semi-quantum Minkowski spacetime with semi-quantum Lorentzian metric tensor, whereas, the second one yields a purely Quantum Mechanical Einstein field equation in a quantum non-Minkowski spacetime with non-Lorentzian metric tensor. Dark Energy (as well as Dark Matter) appears from GQG quite naturally. We develop here Gravitational Electroweak Dark Energy interactions, where gravity and Dark Energy are allowed to combine with electroweak symmetry. Likewise, in Gravitational Chromodynamic Dark Energy interactions, we combine QCD with gravitational and Dark Energy symmetries. In a Dark Matter gauge symmetry model, we combine Dark matter with all possible gauge symmetries. A Universal Model $SU(7)_{UM}$ combines entire baryonic and non-baryonic particle interactions all together.

When it is in the template RNA, the naturally occurring m¹A epitranscriptomic RNA modification was recently reported to be able to stop the RNA polymerization reaction catalyzed by the RNA dependent RNA polymerase (RdRp) of SARS-CoV-2. In this report, we report that m¹A via its triphosphate form (m¹ATP) can be incorporated into RNA by the same RdRp. These two findings point a new direction for antiviral drug development based on m¹A for combatting COVID-19. More broadly, it is possible that the large pool of epigenetic RNA as well as DNA modifications could serve as a treasury for drug discovery aimed at combating various infectious and other diseases.

Using the method of the beta function, Sun has recently evaluated some series of the type $\sum_{k=0}^{\infty}(ak+b)x^k/\binom{mk}{nk}$. By factorization of the polynomial $t^{m-n}(1-t)^n-x$, we will give a general method to find new $\pi$-series.

Many probability-based uncertainty quantification (UQ) schemes require a large amount of sampled data to build credible probability density function (PDF) models for uncertain parameters. Unfortunately, the data collected in compressor blades of aero-engine are mostly limited due to expensive and time-consuming tests. In this paper, we develop a preconditioner-based data-driven polynomial chaos (PDDPC) method that can efficiently deal with uncertainty propagation of limited sampled data. The calculation accuracy of PDDPC method is closely related to the sample size of collected data. Therefore, the influence of sample size on PDDPC method is investigated using a nonlinear test function. Subsequently, we consider the real manufacturing errors of stagger angle for compressor blades. Under three different operating conditions, PDDPC method is applied to investigate the effect of stagger angle error on UQ results of multiple aerodynamic parameters of a two-dimensional compressor blade. The results show that as the sample size of measured data increases, UQ results of aerodynamic performance obtained by PDDPC method gradually converge. There exists a critical sample size that ensures accurate UQ analysis of compressor blades. The probability information contained in the machining error data is analyzed through Kullback-Leibler divergence, and the critical sample size is determined. The research results can make a valuable reference for the fast and cheap UQ analysis of compressor blades in practical engineering.

Background: Polycystic ovary syndrome (PCOS) is a common reproductive and endocrinological disease characterized by ovulatory dysfunction, polycystic ovaries, and hyperandrogenism. Adipokines are believed to contribute to developing PCOS and its accompanying metabolic complications such as dyslipidemia, insulin resistance, and cardiovascular diseases. Oncostatin M (OSM), a novel adipokine, plays a role in oogenesis, lipogenesis, and inflammation and may contribute to PCOS pathogenesis and its related metabolic problems. Methods: In this case-control study, the patients were grouped in a 1:1 ratio into either the PCOS (n = 32) or the control group (n = 32). Blood samples were obtained between the 3rd and 5th days of the menstrual cycle. Serum levels of fasting glucose, insulin, C-reactive protein (CRP), low-density lipoprotein, high-density lipoprotein, triglyceride, white blood cell count, thyroid-stimulating hormone, luteinizing hormone, follicle-stimulating hormone, total testosterone, prolactin estradiol, and OSM were analyzed. Results: OSM levels were significantly lower, but CRP levels were substantially higher in the PCOS group than in the control group (p = .002, p = .001, respectively). OSM was inversely correlated with total cholesterol, non-high-density lipoprotein cholesterol, fasting glucose, and the luteinizing hormone/follicle-stimulating hormone ratio (ρ = .329, p = .017; ρ = .386, p = .005; ρ = .440, p = .001; ρ = .316, p = .023, respectively). Conversely, there was no correlation between OSM and total testosterone level (ρ = .220; p = .118). In the context of inflammation and metabolic parameters, OSM was inversely correlated with CRP, Homeostatic Model Assessment for Insulin Resistance score (HOMA-IR), and low-density lipoprotein cholesterol (LDL) (ρ = .353, p = .019; ρ = .275, p = .048; ρ = .470, p < .001, respectively). The performance of Oncostatin M for diagnosing PCOS showed 50% sensitivity, 75% specificity, and 63% accuracy (p = .009) in ROC curve analysis. Conclusions: Plasma OSM levels were considerably lower in patients with PCOS than in the control group, and this was inversely correlated with the hormonal and metabolic parameters of PCOS. Thus, OSM may be a novel therapeutic target for PCOS and metabolic complications.

The migration from MATLAB to Python (M-to-PY) has gained significant traction in recent computational research. While MATLAB has long served as a linchpin in myriad scientific endeavors, there's an emerging trend to rejuvenate these projects using Python's extensive AI tools and libraries. This study presents a semi-automated process for M-to-PY conversion, using a detailed case study of an image skeletonization project comprising fifteen MATLAB files and a 1404-image dataset. Skeletonization is foundational for ongoing 3D motion detection research using AI transformers, predominantly developed in Python. The utilization of ChatGPT-4, acting as an AI co-programmer, is pivotal in this conversion. By leveraging the public OpenAI API, we developed an M-to-PY converter prototype, evaluated its efficacy using test cases from the Bard bot, and subsequently employed the converted code in an AI application. The dual contributions encompass a well-tested M-to-PY converter and a Skeleton App capable of sketching and skeletonizing any given image, enriching the AI toolset. This study accentuates how AI resources, like ChatGPT-4, can simplify code transitions, opening doors for innovative AI implementations using primarily MATLAB-coded scientific research.

We introduce a special vector field ω on a Riemannian manifold (N^m, g), such that the Lie derivative of the metric g with respect to ω is equal to ρRic, where Ric is the Ricci curvature of (N^m, g) and ρ is a smooth function on N^{m} and call this vector field a ρ-Ricci vector field. We use ρ-Ricci vector field on a Riemannian manifold (N^m, g) and find two characterizations of m-sphere S^m(α). In first result, we show that an m-dimensional compact and connected Riemannian manifold (N^m, g) with nonzero scalar curvature admits a ρ-Ricci vector field ω such that ρ is nonconstant function and the integral of Ric(ω,ω) has a suitable lower bound is necessary and sufficient for (N^m, g) to be isometric to m-sphere S^m(α). In second result, we show that an m-dimensional complete and simply connected Riemannian manifold (N^m, g) of positive scalar curvature admits a ρ-Ricci vector field ω such that ρ is a nontrivial solution of Fischer-Marsden equation and the squared length of the covariant derivative of ω has an appropriate upper bound, if and only if, (N^m, g) to be isometric to m-sphere S^m(α).

The behaviour and bifurcations of solutions to three-dimensional (three-phase) quadratic polynomial dynamical systems (DSs) are considered. The integrability in elementary functions is proved for a class of autonomous polynomial DSs. The occurrence of bifurcations of the type twisted fold is discovered on the basis and within the frames of the elements of the developed DS qualitative theory. The discriminant criterion applied originally to two-phase quadratic polynomial DSs is extended to three-phase DSs investigated in terms of their coefficient matrices. Specific classes of D- and S-vectors are introduced and complete description of the symmetry relations inherent to the DS coefficient matrices is performed using the discriminant criterion.

We classify all the topologically non-equivalent phase portraits of the quadratic polynomial differential system dx/dt = (1-2x)(y-x), dy/dt =y (2-g y-(5g-4)x/(g-1)), in the Poincaré disc for all the values of the parameter g in R\{1}. The differential system dx/dt = y-x, dy/dt =y (2-g y-(5g-4)x/(g-1))/(1-2x), when the parameter g in (1,2] models the structure equations of a static star in general relativity in the case of the existence of a homologous family of solutions, being x = m(r)/r where m(r)>= 0 is the mass inside the sphere of radius r of the star, y = 4pi r^2 rho where rho is the density of the star, and t = ln (r/R) where R is the radius of the star. We classify the possible values of m(r)/r and 4pi r^2 rho when r-->0.

ABSTRACT: Objectives: Oncostatin M (OSM), a member of the interleukin (IL)-6 family of cytokines, is known to elicit pathogenic effects involving disruption of the epithelial barrier function as a part of immunological response networks. It is not yet known how these integrated cytokine signals influence inflammation and other physiological processes in the pathology of chronic rhinosinusitis (CRS). We investigated the expression and distribution of OSM and OSM receptor (OSMR) in sinonasal specimens of CRS patients, and we compared the results with a panel of inflammatory cytokine levels and clinical features. Materials and Methods: We classified CRS patients as eosinophilic (ECRS, n=36) or non-eosinophilic (non-ECRS, n=35) based on the Japanese Epidemiological Survey of Refractory Eosinophilic Chronic Rhinosinusitis (JESREC) phenotypic criteria, and we compared their cases with those of 68 non-CRS subjects. We also examined stimulatory effects of OSM on the expression levels of cytokine receptors by using the human bronchial epithelium cell line BEAS-2B. Results: An RT-PCR showed that the OSM mRNA levels were significantly increased in the ethmoid sinus mucosa of the CRS patients. The OSM mRNA levels were positively correlated with those of TNF-α, IL-1β, IL-13, and OSMR-β. In BEAS-2B cells, OSM treatment induced significant increases in the OSMR-β, IL-1R1, and IL-13Ra mRNA levels. Conclusions: Our findings indicate that OSM is involved in the pathogenesis of CRS in both type 1 and type 2 inflammation, suggesting the OSM signaling pathway as a potential therapeutic target for modulating epithelial stromal interactions.

Formal Calculation uses an auxiliary form to calculate various nested sums and provides results in three forms. In addition to computation, it is also a powerful tool for analysis, allowing one to study various numbers in a unified way. This article contains many results of two types of Stirling numbers, associated Stirling numbers, and Eulerian numbers, making a great generalization of Euler polynomials, Wilson's theorem, and Wolstenholme's theorem, showing that they are just special cases. Formal Calculation provides a novel method for obtaining combinatorial identities and analyzing q-binomial.This article has obtained a large number of results in q-analogues, including inversion formulas for q-binomial coefficients. This article also introduces a theorem on symmetry.

The fatigue crack growth rate (FCGR) of aluminium alloys under the combined influence of temperature and humidity remains a relatively unexplored area, receiving limited attention due to its intricate nature and challenges in predicting the combined impact of these factors. The challenge was to investigate and address the specific mechanisms and interactions between temperature and humidity, as in coastal environment conditions, on the FCGR of aluminium alloy. The present study conducts a comprehensive investigation on the combined influence of temperature and humidity on the FCGR of Al6082 alloy. The fatigue pre-cracked compact tension specimens were corroded for 7 days and then subjected to various temperature and humidity conditions in a thermal chamber for 3 days to simulate coastal environments. The obtained data were analysed to determine the influence of temperature and humidity on the FCGR of Al6082 alloy. An empirical model was also established to predict fatigue life cycle values under these environmental conditions precisely. The correlation between FCGR and fracture toughness models was also examined. The Al6082 alloy exhibits a 34% increase in the Paris constant C, indicating reduced FCGR resistance due to elevated temperature and humidity levels. At the same time, fatigue, corrosion, moisture-assisted crack propagation, and hydrogen embrittlement lead to a 27% decrease in threshold fracture toughness. The developed model exhibited accurate predictions for fatigue life cycles, and the correlation between fracture toughness and FCGR showed less than 10% error, indicating a strong relationship between these parameters.

This research paper is about to obtain new soliton solutions to the M-fractional (1+1)-dimensional nonlinear Westervelt model by utilizing $\exp_a$ function and modified simplest equation techniques. The gained solutions involving dark, bright, periodic, dark-bright and other solitons. These results have many applications in wave propagation of sound waves, high amplitude in medical imaging and therapy. Achieved results are verified by Mathematica tool and the effect of M-fractional derivative on the solutions is explained through 2-Dimensional, 3-Dimensional and contour plots. At the end, these techniques are simple, fruitful and effective to deal with nonlinear FPDEs.

Positive recurrence for a single-server queueing system is established under generalised intensity conditions of service which does not assume existence of the density distribution function of service but a certain integral type lower bound as a sufficient condition. Positive recurrence implies existence of the invariant distribution and a guaranteed slow convergence to it in the total variation metric.

Clarifying the impact mechanism of digital transformation of enterprises on the M&A efficiency of listed companies can provide a factual basis for improving capital market regulatory policies. Taking the mergers and acquisitions of listed companies from 2007 to 2021 as a research sample, the influence mechanism of the digital transformation degree of companies on their M&A efficiency was studied. The research results show that the digital transformation of listed companies will improve their M&A efficiency. Digital transformation will reduce the degree of mispricing of stocks of M&A companies, curb conflicts between managers and agents of M&A companies, and improve their M&A efficiency. Further research finds that the promotion effect of digital transformation on M&A efficiency is more significant in non-state-owned companies, with a higher degree of financing constraint and high analyst attention. In the future, regulatory authorities should actively promote the digital transformation of listed companies, curb mispricing and management agency problems in the capital market with digital governance, and improve the efficiency of mergers and acquisitions in the capital market.

Advanced composite materials have drawn significant interest in the last years as an alternative to traditional materials due to their higher performance. However, industry struggle to provide low-cost, higher occupational safety, lower footprint with composites, making them suitable for holistic analyses. Therefore, the material design becomes an essential element that can impact the competitiveness, particularly in terms of productivity, circularity, safety, sustainability, and quality of the value chain. The Material Design-for-eXcellence is a state-of-art methodology for material performance multi-dimensional assessment along its life cycle phases, either useful to support ma-terial selection for new products or also to new material design support optimizing resource effi-ciency. In this methodology, the material behaviour and its multiple characteristics assessment, and the manufacturing processes efficiency are evaluated. The framework considers the analogy of product design holistic approaches, as Lean Design-for-X, to organize and assess the mul-ti-dimensional performance for each “X” Material Property. In this work, it was possible to observe that the bio-based composites solutions could be a good sustainable alternative for several sectors. Every day researchers are creating more new materials, having a diversity of properties at different scales, Material Design-for-eXcellence must also in the near future consider other factors. Hence, additional studies are thus foreseen to explore and develop this new tool.

Log collection and storage is a crucial process for enterprises around the globe. Log analysis helps identify potential security breaches and, in some cases, is required by law for compliance. However, enterprises often delegate these responsibilities to third-party Cloud Service Providers (CSPs), where the logs are collected and processed for anomaly detection and stored in a data warehouse for archiving. Prevalent schemes rely on plain (unencrypted) data for anomaly detection. More often, these logs can reveal sensitive information about an organization or the customers of that organization. Hence, it is best to keep it encrypted at all times. This paper presents "SigML++," an extension of work done in "SigML." We utilize Fully Homomorphic Encryption (FHE) with the Cheon-Kim-Kim-Song (CKKS) scheme for supervised log anomaly detection on encrypted data. We use an Artificial Neural Network (ANN) based probabilistic polynomial approximations using a Perceptron with linear activation. We probabilistically approximate the Sigmoid activation function (σ(x)) in the encrypted domain for the intervals [−10,10] and [−50,50]. Experiments show better approximations for Logistic Regression (LR) and Support Vector Machine (SVM) for low-order polynomials.

In this paper, the new optical wave solutions of truncated M-fractional perturbed Kundu-Eckhaus model with full non-linearity are obtained by utilizing the expa function technique and modified extended tanh expansion function technique. The solutions are in the form of dark soliton, bright soliton, singular solitons and other form of solutions. The gained solutions are helpful for the further development of concerned model. The obtained results have also been presented graphically in both two-dimensional and three-dimensional formats to discuss the dynamical features as well as the parametric dependence of the constructed solutions. The study offers a highly spectacular and acceptable techniques to combine various intriguing wave demonstrations for more sophisticated models of the modern day.

ntroduction: Respiratory tract Infections are the greatest cause of death worldwide. Since its outbreak in 2019, the coronavirus pandemic (COVID-19) has been a challenge to humans in terms of treatment and prevention of this respiratory viral infection. The re-emergence of respiratory viral infections like influenza, pose a serious hazard to global public health because they occur seasonally. Creating broad-spectrum antiviral compounds for rapid action in the case of an outbreak crisis, as well as bioweapon defences, is critical. Human galectin-3 is found in high concentrations in activated T lymphocytes, epithelial and endothelial cells, and fibroblasts. ProLectin -I and ProLectin -M are both galectin antagonists. Blocking viral entry with a complex polysaccharide component "ProLectin-M" has downstream effects on viral reproduction enabling it to be used as a therapeutic tool and a safe alternative to conventional anti-viral medicines. Methods: In total, 3 cell based assays have been conducted to evaluate antiviral efficacy of ProLectin–I and ProLectin-M against SARS-CoV-2 virus, Influenza-A (H1N1), and human respiratory syncytial virus (hRSV) strain A2. ProLectin-M and ProLectin-I were evaluated for their anti-viral potency using SARS-CoV2 virus strain by viral RNA Extraction and qRT-PCR assays. The plaque assays were carried out to determine the antiviral activity of the test products (ProLectin-I and ProLectin-M) against ‘Influenza-A (H1N1)-A/PR/8/34 (TC adapted)’ and ‘Human respiratory syncytial virus (hRSV) strain A2’ in a cell based in vitro setting. As eference standard, "Oseltamivir Phosphate" and "Remdesivir" were used to determine antiviral activity of test products against H1N1 and hRSV strains respectively.Results: The IC_{50 of} ProLectin-M and ProLectin-I against SARS-CoV-2 virus was found to be 6248 ng/ml (6.2µg/ml) and 4207 ng/ml (4.2μg/ml) respectively. The CC₅₀ value was similar in both the test products i.e. >100 µg/ml. Against Influenza A (H1N1) strain, ProLectin-M exhibited 95 % reduction in the viral load at the test concentration of 21.8 µg/mL with an IC₅₀ value of 5.4 µg/mL whereas, ProLectin-I did not show any cytotoxicity till 250 µg/mL concentration. Against 'human respiratory syncytial virus (hRSV) strain A2, ProLectin-M exhibited 65 % reduction in the viral load at the test concentration of 43.75 µg/mL with an IC₅₀ value of 27.41 µg/mL whereas, ProLectin- I did not show any cytotoxicity till 250 µg/mL concentration. Conclusion: Both ProLectin-I and ProLectin-M have been reported to exhibit broad-spectrum antiviral activity in ‘in-vitro’ setting. ProLectin-M reducing influenza-A virus by 95% and hRSC strain A2 by 65%. To better understand broad spectrum antiviral activity of ProLectin-I and ProLectin-M, further pre-clinical research is warranted.

ESBL-producing E. coli is a growing public problem in healthcare settings and the community. Between 2009 and 2018, a total of 187 ESBL-producing pathogenic E. coli isolates were confirmed, and clonal complex (CC) 10 was the predominant clone. This study aimed to characterize ESBL-producing pathogenic E. coli CC10 strains obtained from diarrheal patients to improve the understanding of CC10 distribution in the Republic of Korea. A total of 57 CC10 strains were selected for molecular characterizations, such as the identification of serotype, antibiotic resistance genes, genetic environments, plasmid profiles, and the genetic correlation between CC10 strains. In the CC10 isolates, the most prevalent serotype was O25:H16, followed by O6:H16. ESBL genes were identified as blaCTX-M, and the most dominant ESBL gene was blaCTX-M-15 (56%) and blaCTX-M-14 (30%). Most blaCTX-M genes were located on plasmids, and these plasmid profiles were confirmed as IncB/O/K/Z, IncF, IncI1 and IncX1. The mobile elements located up-and down-stream mainly included ISEcp1 (complete or incomplete) and IS903 or orf477 were found, respectively. Phylogenetic analysis showed that the CC10 strains were genetically diverse and divided into several distinct lineages. In this study, we found that CC10 ESBL-producing pathogenic E. coli has been steadily isolated; particularly, CTX-M-15-producing E. coli O25:H16 isolates were the major type related with distribution in CC10 clones during the last decade. Identification of ESBL-producing pathogenic E. coli CC10 isolates highlights the possibility of the emergence of resistant isolates with epidemic potential within this CC. Therefore, continuous monitoring will be conducted to prevent further spread of resistant ESBL-producing E. coli CC10 strains.

The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the following steps: 1) Lax representation $[L,M]=0$; 2)~construction of fundamental analytic solutions (FAS); 3) reducing the inverse scattering problem (ISP) to a Riemann-Hilbert problem (RHP) $\xi^+(x,t,\lambda) =\xi^-(x,t,\lambda) G(x,t\lambda)$ on a contour $\Gamma$ with sewing function $G(x,t,\lambda)$; 4) soliton solutions and possible applications.Step 1) involves several assumptions: the choice of the Lie algebra $\mathfrak{g}$ underlying $L$, as well as its dependence on the spectral parameter, typically linear or quadratic in $\lambda$. In the present paper we propose another approach which substantially extends the classes of integrable NLEE.Its first advantage is that one can effectively use any polynomial dependence in both $L$ and $M$. We use the following steps: A) Start with canonically normalized RHP with predefined contour $\Gamma$; B) Specify the $x$ and $t$ dependence of the sewing function defined on $\Gamma$; C) Introduce convenient parametrization for the solutions $ \xi^\pm(x,t,\lambda)$ of the RHP and formulate the Lax pair and the nonlinear evolution equations (NLEE); D) use Zakharov-Shabat dressing method to derive their soliton solutions. This needs correctly taking into account the symmetries of the RHP. E) Define the resolvent of the Lax operator and use it analyze its spectral properties.

The degradation of Proton-exchange membrane fuel cell (PEMFC) gasket materials is crucial in electric vehicles as it can cause hazardous hydrogen fuel leaks, which are usually due to high temperatures, pressures, and hydrogen fuel exposure. Degradation of gasket materials in PEMFC presents a critical concern for electric vehicle safety due to potential hydrogen fuel leaks. This study utilizes finite element analysis (FEA) to assess the suitability of gasket materials for PEMFC applications, focusing on aging and tensile conditions. The dual degradation framework, incorporating contact pressure and von Mises stress, is employed to evaluate Liquid Silicon Rubber (LSR) and Ethylene Propylene Diene Monomer (EPDM) materials. Under aging techniques, the Yeoh model exhibits the least Mean Absolute Percentage Error (MAPE) and computational cost of 0.27 seconds, while the Ogden model records the highest computational cost of 0.89 seconds. In evaluating MAE, Root Mean Square Error (RMSE), and R-squared metrics, LSR and EPDM materials demonstrate respective averages of 0.25%, 0.275%, 0.945%, and 0.815%, 0.685%, 0.77%. Tensile testing (Uniaxial) reveals RMSE and MAE values of 0.30%, 0.40%, and 0.50%, 0.40%, respectively. FEA proves instrumental in identifying suitable gasket materials for PEMFC applications. LSR emerges as the superior choice, demonstrating enhanced FEA modelling performance under aging and tensile conditions. These findings contribute valuable insights to the design and development of improved gasket materials, bolstering the safety and reliability of electric vehicles.

The predominance of traffic lights in urban settings often induces fluctuations in traffic patterns and energy utilization among vehicles. To counteract the adverse effects of traffic lights on the energy efficiency of electric vehicles (EVs), a Multi-Intersections-Based Eco-Approach and Departure strategy (M-EAD) is proposed. This strategy aims to enhance vehicle energy efficiency, traffic flow, and battery longevity, all while upholding satisfactory driving comfort. The M-EAD strategy unfolds in two distinct stages: the optimization of an eco-friendly green signal window and the refinement of speed trajectories. The initial stage tackles the optimization of traffic light green signal windows, underpinned by the minimization of travel delays via solving the shortest path problem. In the subsequent stage, a receding horizon framework takes center stage, leveraging an iterative dynamic programming algorithm to tackle the speed optimization challenge. The objective here is to curtail energy consumption and reduce battery wear by finding an optimal speed trajectory. Furthermore, the real-world efficacy of this approach is substantiated through on-road vehicle tests, attesting to its viability in actual road scenarios.

This paper presents a design and performance analysis of a 10-element 5G massive MIMO antenna array for sub-6GHz mobile handsets, specifically for LTE bands 42 (3400-3600 MHz), 43 (3600-3800 MHz), 48/49 (3550-3700 MHz) applications. The proposed antenna array consists of 10 closely spaced linearly polarized inverted-F antennas with a compact size of 20 × 9 mm2 of a single element. The proposed antenna array provides high gain, high efficiency, and low correlation between the antenna elements, which results in improved channel capacity, increased data rate, and enhanced signal quality. The performance of the antenna array is evaluated in terms of the radiation pattern, gain, efficiency, and correlation coefficient. The simulation and measured results show that the proposed antenna array achieves an approximate peak gain of 3.1 dBi at the resonance frequency, a total efficiency of 65 %, and a low correlation coefficient of 0.06 between the antenna elements. Therefore, the proposed 5G massive MIMO antenna array is a promising candidate for sub-6 GHz mobile handsets, particularly for LTE bands 42/43/48/49 applications.

The inherent non-smoothness of vibroimpact system leads to complex behaviors as well as strong sensitive dependence on parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, the investigations of dynamical behaviors for vibroimpact systems with stochastic parameters are highly essential. The present study aims to analyze the dynamical characteristics of the three-degree-of-freedom vibroimpact system with an uncertain parameter by means of the Chebyshev polynomial approximation method. Specifically, the vibroimpact system model considered is one with unilateral constraint. Firstly, the three-degree-of-freedom vibroimpact system with an uncertain parameter is transformed into an equivalent deterministic form by the Chebyshev orthogonal approximation. Then, the ensemble means responses of the stochastic vibroimpact system are derived. Numerical simulations are performed to verify the effectiveness of the approximation method. Furthermore, the periodic and chaos motions under different system parameters are investigated, and the bifurcations of the vibroimpact system are analyzed by the Poincaré map. The results demonstrate that both the restitution coefficient and the random factor can induce the appearance of the periodic bifurcation. It is worth noting that the bifurcations fundamentally differ between the stochastic and deterministic systems. The former has a bifurcation interval, while the latter occurs at a critical point.

In this study, based on frost formation data provided by Harbin Meteorological Bureau, combined with geographical factors, temperature and population density, linear fitting, Mann-Kendall mutation test, pettitt method and sliding T test were used to analyze the spatio-temporal variation characteristics of frost date in Harbin Municipality and the effects of geographical factors, temperature and population density on frost regularity. The results showed that (1) The earliest year of FSD appeared was 1966 and 1967, on the 255th, i.e., August 18th, and the latest was 283 days, i.e., October 10th, 2006. The earliest year in which the FED appeared was April 24th of 2015, the 114th day of that year, and the latest was April 21st of 1974, the 141st day of that year. The year with the most frost was 2012, with 161 days, and the year with the shortest was 1966, with 123 days. (2) Throughout the study period, FSD increased by 7.8 days at a rate of -1.27d/10a, FED increased by 10.9 days at a rate of 1.77d/10a, and FFS increased by 18.9 days at a rate of 3.05d/10a. The tendency rate of FSD and FFS at each site in Harbin showed an increasing trend. For FED, the tendency rate of some sites showed an increasing trend. In general, FSD showed a delayed trend, FED showed an advanced trend, and FFS showed a prolonged trend. Using the method of unary linear regression, FSD of each site showed an increasing trend, FFS showed an increasing trend, and FED showed a decreasing trend in general. (3) Throughout the study period, FSD was mutated in 2000, and the arrival time of it in the study area averaged the 265th, i.e., September 22nd, and after that, the arrival time of it changed to the 272nd, i.e., September 29th of that year. FED was mutated in 2006, and the arrival time of it in the study area averaged 128th, i.e., April 8th. After the mutation, the arrival time of FED changed to 121st, i.e., April 1st of that year. FFS was mutated in 2004. Before the mutation, with an average arrival time of 137days in the study area .But after that, the time changed to 150 days.(4) FSD and FFS in Harbin Municipality were negatively correlated with latitude and positively correlated with temperature, while FED was positively correlated with latitude and negatively correlated with temperature. The FSD, FED and FFS in the central part of Harbin Municipality were the earliest, the latest and the longest, respectively, so the Pearson correlation coefficient method and the influence of longitude could not be reflected in the multiple regression. Several factors were judged by grey correlation analysis method. The longitude is significantly related to FSD, FED and FFS.

Today electricity is distributed to the individual users via physical Copper connections. From the power stations, the energy is transported through transmission lines where the electricity, sinusoidally modulated at a fixed frequency of about 50 Hz, is raised up to a voltage in a range approximately variating between 30, and 110 kV. When electrons, aligned at this voltage, pass through the transmission lines, they cause coherent vibrations, sometimes even audible in the acoustic frequencies. In the spectrum of movements to which electric cables are subjected, there are also unexpected and sporadic movements caused by winds and rain. The problem of carrying out persistent, precise and spatially distributed monitoring of transmission line health is to use a large number of sensors physically distributed everywhere and somehow transmit the results to a control station. The use of synthetic aperture radar (SAR) data could be a viable solution of persistent and wide-area high-voltage vibration monitoring. In this paper we produce a comprehensive survey on how to monitor both movements in terms of vibrational displacement, due to weathering, and those due to electricity transmission, normally fixed at about 50 Hz. The results demonstrate the technical feasibility of an operational use of SAR for these purposes in the very short term. This would allow the possibility of monitoring malfunctions such as black-outs or other frequency anomalies.

Here we mathematically model black holes and the early universe following dynamics similar to RLC electrical models, focusing on their similarities at the singularity. We use this mathematically modelling to hypothesize the evolution of an expanding universe as the result of a black hole collapse followed by its evaporation. Or model consists of several steps defined by: (1) the formation of a black hole following general relativity equations; (2) growth of the black hole modelled as a resistance-capacitance-like electrical circuit; (3) expansion of space-time following the disintegration of the black hole, modelled by RLC-like dynamics. In updating this article, version 2, we will expand by presenting three additional examples related to the theory of the generalization Boltzmann's constant in curved space-time and the theory of general and especial relativity. We will calculate the critical mass to produce a black hole in the LHC, the existence of a high temperature Bose-Einstein condensate and finally we will demonstrate the existence of a tangential force to the repulsion force in the disintegration of subatomic particles. In the update of this article, version 3, we will expand to develop two examples. First, we will present the relationship between M-theory, extra dimensions with the theory of the generalization of Boltzmann's constant in curved space-time. Secondly, we will propose the idea of ​​updating the Lambda-CDM model, considering the primordial gravitational waves to correctly describe the evolution of the universe.

Microarray patches (MAPs) have the potential to be a safer, more acceptable, easier to use, and more cost-effective means for the administration of vaccines than injection by needle and syringe. Here, we report findings from a randomized, partially double-blind, placebo-controlled Phase I trial using the Vaxxas high-density MAP (HD-MAP) to deliver a measles rubella (MR) vaccine. Healthy adults (N = 63, age 18–50 years) were randomly assigned 1:1:1:1 to four groups: uncoated (placebo) HD-MAPs, low-dose MR HD-MAPs (~3,100 median cell-culture infectious dose [CCID50] measles, ~4,300 CCID50 rubella); high dose MR-HD-MAPs (~9,300 CCID50 measles, ~12,900 CCID50 rubella); or a sub-cutaneous (SC) injection of an approved MR vaccine, MR-Vac (≥1,000 CCID50 per virus). The MR vaccines were stable and remained viable on HD-MAPs when stored at 2–8°C for at least 24 months. When MR HD-MAPs stored at 2–8°C for 24 months were transferred to 40°C for 3 days in a controlled temperature excursion, loss of potency was minimal, and MR HD-MAPs still met World Health Organisation (WHO) specifications. MR HD-MAP vaccination was safe and well-tolerated; any systemic or local adverse events (AEs) were mild or moderate. Similar levels of binding and neutralizing antibodies to measles and rubella were induced by low-dose and high-dose MR HD-MAPs and MR-Vac. The neutralizing antibody seroconversion rates at day 28 after vaccination for the low-dose HD-MAP, high-dose HD-MAP and MR-Vac groups were 37.5%, 18.8% and 35.7% respectively for measles and 37.5%, 25.0% and 35.7% respectively for rubella. Most participants were seropositive for measles and rubella antibodies at baseline, which appeared to negatively impact the number of participants that seroconverted to vaccines delivered by either route. The data reported here suggest HD-MAPs could be a valuable means for delivering MR-vaccine to hard-to-reach populations and support further development. Clinical trial registry number: ACTRN12621000820808.

A major route for influx of calcium ions into neurons uses the STIM-Orai1 voltage-independent channel. Once cytosolic calcium ([Ca2+]i) elevates, it activates mitochondrial and endoplasmic calcium stores, to affect downstream molecular pathways. In the present study we employed a novel drug, Carbonyl Cyanide Chlorophenylhydrazone (CCCP), a mitochondrial uncoupler, to explore the role of mitochondria in cultured neuronal morphology. CCCP caused a sustained elevation of [Ca2+]i and, quite surprisingly, a massive increase in density of dendritic filopodia and spines in the affected neurons. This morphological change can be prevented in cultures ex-posed to calcium-free medium, to Orai1 antagonist 2APB, or to cells transfected with domi-nant-negative Orai1 plasmid. It is suggested that CCCP activates mitochondria through influx of calcium, to cause a rapid growth of dendritic processes

In this paper, a short survey of the existed results concerning the Jacobian Conjecture is first given. Then the 3-fold linear type polynomial map will be analyzed in detail. The expansion of the Jacobian condition is deduced to obtain its equivalent algebraic equations, and the Jacobian condition will be analyzed to derive two coordinate transformations that can maintain the invariance of the Jacobian condition. Finally, it is proved by mathematical induction method that one general chain expression presented in this paper is just the inverse polynomial map of 3-fold linear type polynomial map, i.e. LJC(n,[3]) holds such that the Jacobian Conjecture holds.

Systematic results of lattice dynamical calculation are reported for the novel (SiC)m/(GeC)n superlattices (SLs) by exploiting a modified-linear chain model (M-LCM) and a realistic rigid-ion- model (RIM). By employing the bond polarizability method in the framework of M-LCM, we have simulated Raman intensities for the graded (SiC)10-D/(Si0.5Ge0.5C)D/(GeC)10-D/(Si0.5Ge0.5C)D SLs by carefully integrating interfacial layer thickness D (≡ 0, 1, 2, 3 monolayers (MLs)). The variation of D has initiated considerable up (down) shifts of GeC-, (SiC)-like Raman peaks in the middle of the optical phonon frequency region. With D = 3 MLs, the maximum energy shift (by ~ 47 cm-1) of SiC-like modes has caused substantial changes in the Raman intensity profiles linked to the localization of atomic displacements at the interfacial transition regions. This effect can be considered as a vital tool for authenticating the interfacial structures in technologically important SLs. By using a RIM, we have reported SL phonon dispersions along the growth [001] as well as in the plane [100], [110] perpendicular to the growth. Our simulations of phonons in the acoustic mode region have not only confirmed the formation of minigaps at the zone center and zone edges but also provided evidence of anti-crossing and phonon confinement. Besides examining angular dependence of zone-center optical modes, we have also discussed phonon folding, confinement and anisotropic behavior in (SiC)m/(GeC)n SLs.

The main aim of this study was to determine the prevalence of plasmid-mediated colistin resistance mcr-1 to mcr-5 genes among colistin and multi-drug resistant Enterobacterales, Pseudomonas aeruginosa and Acinetobacter sp strains isolated from patients in a tertiary hospital in the city of Toluca, Mexico. 241 strains were included in the study. The presence of mcr genes among these strains was assessed by PCR and sequencing. In the case of mcr-carrying E. coli, further PCR tests were performed to determine the presence of blaCTX-M and whether the strains belonged to the O25b-ST131 clone. Conjugation experiments were carried to assess plasmid-mediated colistin resistance horizontal transmission. 12 strains (5.0%), of which four were E. coli; four, P. aeruginosa; three, K. pneumoniae and one, E. cloacae, were found to be resistant to colistin. Of these strains, two E. coli isolates were found to carry mcr-1. Both mcr-1-carrying E. coli strains were found to co-express blaCTX-M, belong to the O25b-ST131 clone and horizontally transmit their colistin resistance. The results of this study confirm the presence of plasmid-mediated colistin resistance in hospitalized patients in Mexico and demonstrated that the multidrug-resistant O25b-ST131 E. coli clone can acquire mcr genes and transmit such resistance trait to other bacteria.

The literature lacks consensus on the minimum microbial density required for diagnosing urinary tract infections (UTIs). This study categorized the microbial densities of urine specimens from symptomatic presumptive UTI patients and correlated them with detected levels of immune response biomarkers NGAL, IL-8, and IL-1β. The objective was to identify changes in immune response at different microbial densities and determine an optimal threshold for diagnosing symptomatic UTIs. Midstream clean-catch urine samples were analyzed for microbial identification and quantification using SUC and M-PCR, while NGAL, IL-8, and IL-1β levels were measured with ELISA. NGAL, IL-8, and IL-1β levels were all significantly higher in symptomatic subjects with microbial densities ≥ 10,000 cells/mL by M-PCR (p < 0.0069) or equivalent CFUs/mL by SUC (p < 0.0104) compared to samples with no detectable microbes. With both PCR and SUC, a consensus of two or more elevated biomarkers correlated well with microbial densities > 10,000 cells/mL or CFU/mL, respectively. The association between ≥ 10,000 cells and CFU per mL with elevated biomarkers in symptomatic patients suggests that this lower threshold may be more suitable for diagnosing UTIs. These findings challenge the widely used threshold of 100,000 CFU per mL, which may overlook many active UTI cases.

Ptolemy’s Theorem in Euclidean geometry, named after the Greek astronomer and mathematician Claudius Ptolemy, is well known. We translate Ptolemy’s Theorem from analytic Euclidean geometry into the Poincar´e ball model of analytic hyperbolic geometry, which is based on M¨obius addition. The translation of Ptolemy’s Theorem from Euclidean geometry into hyperbolic geometry is achieved by means of the hyperbolic trigonometry, called gyrotrigonometry, to which the Poincar´e ball model gives rise, and by means of the duality of trigonometry and gyrotrigonometry.

In this paper, chaos sequence is used to replace the traditional Spread Spectrum sequence. From the perspective of the communication partner, a new method of generating the initial value of chaotic sequence is proposed, which is more suitable for the multi-base Spread Spectrum System and easy to extract. In order to further improve the error performance of the system and ensure the integrity of the system, an improved suboptimal soft information extraction method based on log-likelihood ratio (LLR) is proposed in the channel coding module, which can further improve the error performance of the system. On this basis, we choose the synchronization mode of multiple transmission of one reference signal to solve the problem that chaotic sequence is difficult to obtain synchronization because of its aperiodic characteristics. Finally, the system is simulated in the channel with low SNR. The simulation results show that chaotic sequence as Spread Spectrum code can make the signal transmit accurately in the worse channel environment. The performance gain of applying soft information decoding decision in the M-ary Spread Spectrum System with chaotic sequence as Spread Spectrum code can reach 5.2dB compared with the traditional Direct Spread Spectrum System.

The paper analyzes the phenomenon that condition the durability and reliability of a type of dental bur based on the wear of the active part and with effect on its quality. For the experimental study, a conical-cylindrical dental bur and a sample dental material in cobalt-chromium alloy, cylindrical shape, tested on a specially made experimental installation were used. The paper was limited to the consideration of a single parameter (loss of mass, mw by wear of the active part of the dental bur tested) for the establishment the durability and reliability, useful for the extension of the lifetime or even optimization of its operation. The wear phenomenon of the active part of dental bur is studied based on the results and experimental data obtained in the work process that was validated by interpolation and led to polynomial functions which approximate very well the dependent parameter, mw, considered in the experimental program. The results of the interpolation showed that in the first 11 h of work, the dental bur works with high efficiency, after which it can be easily decommissioned (optimizing operation, possibly constructive solutions); i.e., it should be replaced with a new one (criterion for replacing of worn dental bur).

Polynomial recurrence bounds for a class of stochastic differential equations with a gradient type drift and an additive Wiener process are studied without Lyapunov functions.

This article introduces ten similarity measures that utilize cosine and cotangent functions to compare (m,n)-rung orthopair fuzzy sets, this a super class of q-rung orthopair fuzzy sets. Further, we applied our established weighted similarity measures to medical diagnosis, pattern recognition,and building material problems and also presented the comparison between established measures with the existing cosine and cotangent measures of q-rung orthopair, pythagorean and intuitionistic fuzzy sets. Lastly, we considered a numerical example that demonstrates the effective and scientific application of these similarity measures in plant leaf disease classification. Furthermore, we present graphical interpretations to demonstrate the effectiveness of our established measures.

Suppose G is a graph with vertex-orbits O1,1 O2, . . . ,Ot, and jOi j denotes the cardinallity of Oi. Then OG (x) = åt 2 i=1 xjOi j is called as orbit polynomial. It is well-known that this polynomial 3 has a unique positive zero d in the interval [0, 1]. The aim of this paper is to study the specific 4 properties of this polynomial and then we determine the location of this root for several classes of 5 complex networks to compare with other graphical measures. Besides, we compare the unique 6 positive zero measure with several well-known centrality graph measures.

Acute and chronic bone infections, especially those caused by methicillin-resistant Staphylococcus aureus (MRSA), remains a major complication and therapeutic challenge. It is documented that local administration of vancomycin offers better results than the usual routes of administration (e.g. intravenous) when ischemic areas are present. In this work, we evaluate the antimicrobial efficacy against S. aureus and S. epidermidis and analyzed the potential cytotoxic effect of a novel hybrid 3D-printed scaffold based on poly(caprolactone) and chitosan loaded with different vancomycin concentrations (1, 5, 10 and 20%). For this purpose, vancomycin release was measured by means of HPLC, and the biological response of ah-BM-MSCs in the presence of the scaffolds was evaluated in terms of cytotoxicity (LDH activity), proliferation (AlamarBlueⓇ) and osteogenic differentiation (ALP activity, Alizarin Red staining). In addition, two cold plasma treatments were evaluated to improve the adhesion of hydrophobic polymers to hydrogels. The hybrid PCL/CS/Van scaffolds tested were found to be biocompatible, bioactive, and bactericide, as demonstrated by no cytotoxicity or functional alteration and by bacterial inhibition. Our results suggest that the scaffolds developed would be excellent candidates to be used in a wide range of biomedical fields such as drug delivery systems or tissue engineering applications.

This paper discusses a passive control issue for Nonlinear Time-Varying (NTV) systems subject to stability and attenuation performance. Based on the modeling approaches of Takagi-Sugeno (T-S) fuzzy model and the Linear Parameter-Varying (LPV) model, a Parameter-Dependent Polynomial Fuzzy (PDPF) model is constructed to represent the NTV systems. According to Parallel Distributed Compensation (PDC) concept, a parameter-dependent polynomial fuzzy controller is built to achieve robust stability and passivity of PDPF model. Furthermore, the passive theory is applied to achieve the performance constraining the disturbance effect on the PDPF systems. To develop the stability criteria, by introducing a parameter-dependent polynomial Lyapunov function, one can derive some stability conditions which belong to the term of Sum-Of-Squares (SOS) form. Based on the Lyapunov function, two stability criteria are proposed to design the corresponding PDPF controller such that the NTV system is robustly stable and passive. Finally, a numerical example is applied to demonstrate the effectiveness of the proposed stability criterion.

Extended-spectrum β-lactamase (ESBL) mediating resistance in Enterobacterales is a global public health issue, especially in low-and middle-income countries (LMICs) such as Cameroon. ESBL-producing Enterobacterales reduce therapeutic options and lead to the use of last resort drugs such as carbapenems even in vulnerable populations like children under five years. This study aims at determining the phenotypic and genotypic characteristics of ESBL-producing Escherichia coli (ESBL-Ec) isolated from children under five years with and without diarrhoea in two health care facilities in Dschang. A cross-sectional study was conducted from 3 February to 19 May 2022 in two hospitals in the city of Dschang, Cameroon. Stool collected were cultured on Eosine Methylen Blue (EMB) medium. Enterosystem 18 R kit was used for bacterial identification. Evaluation of the resistance patterns and detection of ESBL production were performed with, the Kirby Bauer disk diffusion method and CHROMagar® ESBL medium, respectively. The genomic DNA of ESBL-Ec was extracted using the boiling method and subjected to conventional and multiplex PCRs for detection of blaSHV, blaCTX-M and blaTEM genes. Data were entered into ExcelTM 2016. Epi info and R software were used for statistical analyses with a p-value <0.05 considered statistically significant. Out of the 125 children enrolled, 67.2% (84/125) were colonized by E. coli. Among these, 57.14% (48/84) were colonized by ESBL-Ec. ESBL- Ec isolates showed high levels of resistance to amoxicillin-clavulanic acid (96.22%), cefotaxime (75.47%), ceftriaxone (73.58%), ofloxacin (67.92%), levofloxacin (56.6%) and ciprofloxacin (54.71%). Children aged between 1-3 years (47.62%, p=0.09) and those who had taken an antibiotic one week prior to collection (70.83%, p=0.04) had a higher prevalence of ESBL-Ec with statistical significance. The majority of ESBL-Ec isolates (52.83%; 28/53) were co-producers of blaCTX-M and blaTEM. Infection prevention and control measures coupled with antimicrobial stewardship strategies need to be strengthened to reduce emergence and dissemination of ESBL-Ec among this vulnerable population.

In an $m$-person symmetric game, all players are identical and indistinguishable. In this paper, we find that the payoff tensor of the player $k$ in an $m$-person symmetric game is $k$-mode symmetric, and the payoff tensors of two different individuals are the transpose of each other. Furthermore, we reformulate the $m$-person symmetric game as a tensor complementary problem and demonstrate that locating a symmetric Nash equilibrium is equivalent to finding a solution to the resulting tensor complementary problem. Finally, we use the hyperplane projection algorithm to solve the resulting tensor complementary problem, and we present some numerical results to find the symmetric Nash equilibrium.

Exact sequential state estimation of orbiting objects in space can be found by predicting the state using Fokker Planck Kolmogorov Equation (FPKE) and measurement correction using Bayes’ conditional/posterior Probability Density Function (PDF). Posterior PDF can be expressed as Gaussian density expanded in terms of Hermite polynomials named as Gram Charlier Series (GCS). This research is an extension of an earlier work on second order linearized solution to nonlinear Bayesian filtering using Taylor series and third order GCS expansion of posterior PDF. In this new extension, Bayes’ posterior PDF is approximated by a mixture of GCS functions for which the parameters are propagated using linear propagation theory. The update of weights of different components of GCS mixture model uses the FPKE error as feedback to adapt for the amplitude of different GCS components while solving a quadratic programming problem earlier used for Gaussian Mixture Model (GMM) PDF. Proposed filtering method is applied on tracking of space debris. The simulation results for the filter shows performance is moderately better than single GCS filter, Extended Kalman Filter (EKF) and Gaussian Sum Filter (GSF) under space debris’ highly uncertain initial conditions and sparse measurement availability.

This paper analyzes the potential strategies for a bank merger from a Sustainable Development Goals (SDG) perspective, focusing on three key criteria: profitability, market share, and service quality. In the short-term, the merged bank should prioritize optimizing financial performance through cost management, revenue stream identification, and risk management practices. Market share expansion can be achieved through targeted customer acquisition and retention efforts, market research, and competitive analysis. Service quality can be enhanced through improved customer service, efficient complaint resolution processes, and leveraging technology. These short-term plans align the merged bank's operations with the identified criteria and promote responsible banking practices that contribute towards the SDGs. In the long-term, the merged bank should focus on diversifying revenue streams, expanding its customer base, and optimizing cost structure. Long-term strategies should include establishing a strong brand presence, customer loyalty programs, and continuous improvement in service quality. The paper emphasizes the importance of monitoring progress, making necessary adjustments, and aligning with SDGs for sustained profitability and long-term success in the marketplace. The findings of this study provide valuable insights for banks considering a merger and highlight the significance of considering SDGs in their strategic planning.

This study explores the implications of merging two fundamentally different types of banks: Islamic and conventional banks. The research aims to provide insight into such a merger's unique opportunities and challenges and offer strategic guidance for future mergers. A balanced scorecard-based strategic analysis using Quantum Spherical Fuzzy Decision-Making Approach was used to develop the merged bank's short- and long-term strategic plans. The balanced scorecard included 12 key performance indicators (KPIs) in 4 groups, and the methodology also incorporated several questions to guide the analysis. The study results offer valuable insights into the potential opportunities and challenges of merging these two types of banks and strategic recommendations for stakeholders at all levels. The study is a valuable guideline for future mergers between similar or different types of banks. Overall, the findings suggest that a well-planned merger strategy is essential for avoiding challenges and maximizing the benefits of merging Islamic and conventional banks. By integrating the strengths of both types of banks, a merged entity could create a competitive advantage and potentially improve financial performance. However, this requires careful consideration of cultural differences, regulatory challenges, and other factors that could impact the merger's success.

This paper presents the symmetries of differential equations associated with one-variable and Bivariate Hermite polynomials by proposing a representation of Lie algebra for these differential operators. Applying the Baker-Campbell-Hausdorff formula to these algebras, results in new relations and generating functions in one-variable and Bivariate Hermite polynomials. A general form of representation for other orthogonal polynomials such as Laguerre polynomials is introduced.

Using a simple model for internal heat evolution and mass-internal heat relations found for rocky exo planetary objects in the inner solar system we have inferred the phases of volcanism at earth ( EA) or host star ages (SA) in 52 potentially habitable rocky exo planets. We have also calculated the internal tidal heat contributions and magnetic moments of these exo planets. Based on these results we have inferred the probability of existence of life favouring geophysical conditions in the above exo planets at EA and SA. In M star associated exo planets, occurrences of super flares and long night periods may pose problems for the development of advanced life

A new set of basis functions is presented. The foundation in mathematics is established. To reconstruct a signal, it is compared to the Fourier basis functions. The M-basis functions' potential applications are also presented.

In present paper, spatial Minkowski Pythagorean Hodograph (MPH) curves are characterized with Rational Rotation Minimizing Frames (RRMFs). We define Euler-Rodrigues Frame (ERF) for MPH curves and by means of this concept, we reach the definition of MPH curves of type (n, m). Expressing the conditions provided by these curves in the form of Minkowski-Hopf map that we define, it is aimed to establish a connection with the Lorentz force which occurs during the process of Computer Numerical Control (CNC) type sinker Electronic Discharge Machines (EDMs). This approach is reinforced by split quaternion polynomials. Finally, we give conditons satisfied by MPH curves of low degree to be type (n, m) and construct illustrative examples.

Background: Multidrug-resistant bacteria present resistance mechanisms against β-lactam antibiotics, such as Extended-Spectrum Beta-lactamases (ESBL) and Metallo-β-lactamases enzymes (MBLs) operon encoded in Gram-negative species. Likewise, Gram-positive bacteria have evolved other mechanisms through mec genes, which encode modified penicillin-binding proteins (PBP2). This study aimed to determine the presence and spread of β-lactam antibiotic resistance genes and the microbiome circulating in Quito’s Public Transport (QTP). Methods: A total of 29 station turnstiles were swabbed to extract the surface environmental DNA. PCRs were performed to detect the presence of 13 antibiotic resistance genes and to identify 16S rDNA barcoding, followed by clone analysis, Sanger sequencing and BLAST search. Results: ESBL genes blaTEM-1 and blaCTX-M-1 and MBL genes blaOXA-181 and mecA were detected along QPT stations. Two subvariants were found for blaTEM-1, blaCTX-M-1, and blaOXA-181. Almost half of the circulating bacteria found at QPT stations were common human microbiota species including those classified by the WHO as pathogens of critical and high-priority surveillance. Conclusions: β-lactam antibiotic resistance genes are widely spread throughout QPT. This is the first report of blaOXA-181 in environmental samples in Ecuador. Moreover, we detected a new putative variant of this gene. Some commensal coagulase-negative bacteria may have a role as mecA resistance reservoirs

The Subtropical Front (STF) plays a key role in the ecology of Chilean jack mackerel Trachurus murphyi. Nonetheless, there are few remote sensing studies of the STF in the open Southeast Pacific Ocean, and almost all of them have been conducted by satellite oceanographers in Russia and Ukraine to support respective large-scale fisheries of jack mackerel in this region. We reviewed these studies that documented long-term seasonal and interannual variability of the STF from sea surface temperature (SST) and sea surface height (SSH) data. We also mapped the STF from satellite sea surface salinity (SSS) data of the SMOS mission (2012-2019). The Subtropical Front consists of two fronts -- North and South STF about 500 km apart -- that border the Subtropical Frontal Zone (STFZ) in-between. The STF is density-compensated, with spatially divergent manifestations in temperature and salinity. In the temperature field, the STF extends in the WNW to ESE direction in the Southeast Pacific. In the salinity field, the STFZ appears as a broad frontal zone, extending zonally between 30-35°S across the entire South Pacific. Three major types of satellite data – SST, SSH, and SSS – can be used to locate the STF. The SSH data is most advantageous with regard to the jack mackerel fisheries owing to the all-weather capability of satellite altimetry and the radical improvement of the spatial resolution of SSH data in the near future. Despite the dearth of dedicated in situ studies of the South Pacific STFZ, there is a broad consensus regarding the STFZ being the principal spawning and nursing ground of T. murphyi as well as a major migration corridor between Chile and New Zealand.

Ante-mortem bovine tuberculosis (bTB) tests for buffaloes include the single comparative intradermal tuberculin test (SCITT), interferon-gamma (IFN-γ) release assay (IGRA) and IFN-γ-inducible protein 10 release assay (IPRA). Although parallel test interpretation increases detection of Mycobacterium bovis-infected buffaloes, these algorithms may not be suitable for screening buffaloes in historically bTB-free herds. In this study, the specificities of three assays were determined using M. bovis unexposed herds, and a high specificity diagnostic algorithm developed. Serial test interpretation using the IGRA and IPRA showed significantly greater specificity (98.3%) than individual tests or parallel testing (73%). When the SCITT was added, the algorithm had a 100% specificity. Since the cytokine assays had imperfect specificity, potential cross-reactivity with nontuberculous mycobacteria (NTM) was investigated. No association was found between NTM presence (in oronasal swab cultures) and positive cytokine assay results. As a proof-of-principle, serial testing was applied to high-value buffaloes (n=153) in a historically bTB-free herd. Buffaloes positive on a single test (n=28) were regarded as test negative. Four buffaloes were positive on IGRA and IPRA, and M. bovis infection was confirmed following culling. These results demonstrate the value of using IGRA and IPRA in series to screen buffalo herds with no previous history of M. bovis infection.

Generating long-lived mucosal and systemic antibodies through respiratory immunization with protective antigens encapsulated in nanoscale biodegradable particles could potentially decrease or eliminate the incidence of many infectious diseases but requires incorporation of a suitable mucosal immunostimulant. We previously found that respiratory immunization with a model protein antigen (LPS-free OVA) encapsulated in PLGA 50:50 nanoparticles (~380 nm diameter) surface modified with complement peptide-derived immunostimulant 02 (CPDI-02; formerly EP67) through 2kDa PEG linkers increases mucosal and systemic OVA-specific memory T-cells with long-lived surface phenotypes in young, naïve female C57BL/6 mice. Here, we determined if respiratory immunization with LPS-free OVA encapsulated in similar PLGA 50:50 microparticles (~1 μm diameter) surface modified with CPDI-02 (CPDI-02-MP) increases long-term OVA-specific mucosal and systemic antibodies. We found that, compared to MP surface modified with inactive, scrambled scCPDI-02 (scCPDI-02-MP), intranasal administration of CPDI-02-MP in 50 μL sterile PBS greatly increased titers of short-term (14 days post-immunization) and long-term (90 days post-immunization) antibodies against encapsulated LPS-free OVA in nasal lavage fluids, bronchoalveolar lavage fluids, and sera of young, naïve female C57BL/6 mice. Thus, surface modification of biodegradable microparticles with CPDI-02 is likely to increase long-term mucosal and systemic antibodies against encapsulated protein antigen after respiratory and possibly other routes of mucosal immunization.

The Musa textilis var. Abuab has high fiber quality (FQ) but has low resistance against abaca bunchy top virus (AbBTV); the Musa balbisiana var. Pacol, has low FQ but high resistance against AbBTV. Their backcrosses (BC2 and BC3) possess both desirable traits. Analysis using RNA-seq showed that the regulatory divergence of Abuab and Pacol is largely explained by cis differences with 27.4% and 22.3% if we are to assess it using BC2 and BC3, respectively. Cis differences between the two genotypes are significantly reduced from BC2 to BC3 due to changes in genomic constitution. Trans, on the other hand, is robust to changes in allelic composition. All these are attributed to the loss of heterozygosity in the BC3 relative to BC2. Further analysis showed that both backcrosses exhibited genome-wide preferential expression of Pacol- over Abuab-specific alleles, despite the wider genetic presence of the latter in the hybrids. The ratio of the two genotype-specific expressed transcripts and the ratio of their corresponding genetic make-up are significantly disproportionate, a phenomenon which we refer here as “genome–transcriptome incongruence”. We also observed preferential expression switching in which several genes prefer Abuab- (or Pacol-) specific allele in the BC2 but switched to Pacol- (or Abuab-) specific allele in the BC3 genome.

Studies have previously described the occurrence of multidrug-resistant (MDR) Escherichia coli in human and veterinary medical settings, livestock, and, to a lesser extent, in the environment and food. While they mostly analyzed foodborne E. coli regarding phenotypic and sometimes genotypic antibiotic resistance and basic phylogenetic classification, we have limited understanding of the in vitro and in vivo virulence characteristics and global phylogenetic contexts of these bacteria. Here, we investigated an E. coli strain (PBIO3502) isolated from a pork sausage in Germany in 2021 in-depth. Whole-genome sequence analysis revealed sequence type (ST)58, which is an emerging international high-risk clonal lineage. In addition to its MDR phenotype that mostly matched the genotype, PBIO3502 demonstrated pronounced virulence features, including in vitro biofilm formation, siderophore secretion, serum resilience, and in vivo mortality in Galleria mellonella larvae. Along with the genomic analysis indicating close phylogenetic relatedness of our strain with publicly available, clinically relevant representatives of the same ST, these results suggest the zoonotic and pathogenic character of PBIO3502 with the potential to cause infection in humans and animals. Also, our study highlights the necessity of the One Health approach while integrating human, animal, and environmental health, as well as the role of meat products and food chains in the putative transmission of MDR pathogens.

Abstract: Due to their rapid evolution and their impact on health care, be-ta-lactamases, protein degrading beta-lactam antibiotics, are used as generic model of protein evolution. Therefore, we investigated the mutation effects in two distant beta-lactamases TEM-1 and CTX-M-15. Interestingly we found a site with a complex pattern of genetic interactions. Mutation G251W in TEM-1 is in-activating the protein’s function just as the reciprocal mutation W251G in CTXM-15. Phylogenetic analysis revealed that mutation G has been entrenched in TEM-1 background: while rarely observed throughout the phylogeny it is es-sential in TEM-1. Using a rescue experiment in TEM-1 G251W mutant, we could identify sites that alleviates the deviation from G to W. While few of these muta-tions could potentially involve local interactions, most of them were found on distant residues in the 3D structure. Many well-known mutations having an impact on protein stability, such as M182T, were recovered. Our results there-fore suggest that entrenchment of an amino acid may rely on diffuse interactions among multiple sites with a major impact on protein stability.

In this note we study the computation of the minimum polynomial of a matrix $A$ and how we can use it for the computation of the matrix $A^n$. We also describe the form of the elements of the matrix $A^{-n}$ and we will see that it is closely related with the computation of the Drazin generalized inverse of $A$. Next we study the computation of the exponential matrix and finally we give a simple proof of the Leverrier - Faddeev algorithm for the computation of the characteristic polynomial.

The global pandemic caused by the new coronavirus has largely changed established business practices. The aim of the study is to present the results of eighteen-month intensive research into the effects of the pandemic on e-consumer behavior. In one of the most active e-commerce markets in Europe, the Czech Republic, we analyzed a sample of more than one and a half million Facebook users in terms of their C2B interactions on the B2C activities of the five major e-commerce market players. The measurements were carried out in three periods, which corresponded to the onset of the first wave, peak, and fading of the second wave of the pandemic. This enabled us to monitor the effect of seasonality and the stabilization of patterns of consumer behavior during the coronavirus crisis. The results suggest that a specific panic pattern of e-consumer behavior was developed at the time of the onset of the pandemic. However, as the pandemic progressed, the market has adapted to a new normal, which, as evidenced by the change in trends, appears to be a combination of the pre-pandemic and pandemic behavioral patterns. Using a statistical analysis, it was possible to identify delta of changes within the patterns of consumer behavior, thus fulfilling the final condition for creating an empirical model of the COVID-19 pandemic impacts on e-consumer behavior presented in this study.