Fatty acids and glucose are the main bioenergetic substrates in mammals that are alternatively used during the transition between fasting and feeding. Impairment of mitochondrial fatty acid oxidation causes mitochondrial myopathy leading to decreased physical performance. Here, we report that haploinsufficiency of ADCK2, a member of the aarF domain-containing mitochondrial protein kinase family, in human is associated with liver dysfunction and severe mitochondrial myopathy with lipid droplets in skeletal muscle. In order to better understand the etiology of this rare disorder, we generated a heterozygous Adck2 knockout mouse model to perform in vivo and cellular studies using integrated analysis of physiological and omics data (transcriptomics-metabolomics). The data show that Aldh2+/- mice exhibits impaired fatty acid oxidation, liver dysfunction, and mitochondrial myopathy in skeletal muscle resulting in lower physical performance. Significant decrease in CoQ biosynthesis was observed and supplementation with CoQ partially rescued the phenotype both in the human subject and mouse model. These results indicate that ADCK2 is involved in organismal fatty acid metabolism and in CoQ biosynthesis in skeletal muscle. We propose that patients with isolated myopathies and myopathies involving lipid accumulation be tested for possible ADCK2 defect as they are likely to be responsive to CoQ supplementation.

Cinnamomum tamala leaf (CTL), also known as tejpat and Indian bay leaf, is used all over the world for seasoning, flavouring, and medicinal purposes. Numerous researchers are interested in exploring the nutritional and medicinal benefits of CTL due to their potential as nutraceuticals. These characteristics could be explained by the presence of several essential bioactive substances and lipid derivatives. There are no reports available on this species about its metabolites profile. In this work, rapid screen and identify chemical compounds in supercritical (SC)-CO2 extracts of CTL by use of UPLC-Q-TOF-MSE with multivariate statistical analysis approach was established in both negative and positive mode. As a results, a total of 166 compounds, including 66 monocarboxylic fatty acids, 52 dicarboxylic fatty acids, 27 fatty acid amides, and 21 others were tentatively identified based on accurate mass, and the mass spectrometric fragmentation pattern, out of which 142 compounds are common and found in all five CTL extracts. They displayed robust [M+H]+ and/or [M-H]- ions in both low- and high-energy collision-induced dissociations (CIDs). Based on chemical profiling and chemometric analysis, CTL4 (300bar/55°C) extract was found significantly more potent in other CTL’s extracts. A new mono- and di-carboxylic fatty acids, fatty acid amides and other essential bioactive compounds were separated within 20 min runtime and identified in CTL for the first time. The combination of UPLC-Q-TOF-MSE and chemometric analysis is a powerful method to rapidly screen the metabolites profile for the quality control of C. tamala leaf.

In this paper we deal with the resolution of a fuzzy multiobjective programming problem using the level sets optimization. We compare it to other optimization strategies studied until now and we propose an algorithm to identify possible Pareto efficient optimal solutions.

A novel effective vibrational mode was discovered in the conventional transducer with an array of orthogonal (square) regular piezoelectric rods in 1-3 piezocomposite, containing the damping backing and front matching layers. The operational resonance in the structure was determined as the Surface Acoustic Wave (SAW) on the backing boundary excited by the adjacent piezo-rods, with its frequency typically near 3 times lower the fundamental half-lambda conventional piezocomposite resonance. Pulse-echo sensitivity and transmitting sound-pressure-level (SPL) in air showed that the signal strength is roughly comparable to the industrial similar air transducers at the frequency range 100…700 kHz, where at these frequencies the lateral and longitudinal piezoelement dimensions in the conventional transducer design are typically close to each other causing interference with unwanted coupling modes. As was determined theoretically and proved in experiments, the backing SAW resonance effect in the transducer performance is inherent just to the regular periodic 1-3 piezocomposite structure, and does occur neither with randomly located/oriented piezo-rods, nor in the homogeneous piezo-plate at least with the same lateral cross-section as the connected to it backing. The purpose of the article is to investigate a newly discovered operational vibrational mode of a SAW type in 1-3 regular piezocomposite, other than piezoelectric resonance. The investigated phenomena can improve the transceiver sensitivity, bandwidth, providing lower drive voltage, and smaller and lighter weight ultrasonic transducers. Based on the piezocomposites with thickness’ 1…1.5 mm (rod resonance near 2…3 MHz), pillar width 0.2…0.8 mm, kerf width 0.1…0.4 mm, the transceivers with an operating frequency from 140 kHz to 650 kHz were designed and fabricated with a conventional backing of a mixture of high-density tungsten powder and epoxy, and a matching layer of a mixture of low-density glass bubbles and epoxy. Experimental evaluation of their acoustical performance showed expected characteristics suitable for practical applications.

As modern systems are becoming more complex their control strategy cannot longer relay only on measurement information that usually comes from probes but also from mathematical models. Those systems models can lead to unbearable computation times due to their own complexity, turning the control process non-viable, which leads to the implementation of surrogate models that enable to achieve estimates within acceptable time to take decisions. A control trained with Deep Reinforcement Learning algorithm, using a Physics-Informed Neural Network to obtain the temperature map on the following time step, replaces the need of running Direct Numerical Simulations. On this work we considered an 1D heat conduction problem, which temperature distribution feeds a control system to activate a heat source aiming to obtain a constant, previously defined, temperature value. With this approach, control training becomes much faster without the need of performing numerical simulations or laboratory measurements, as well the control is taken based on Neural Network enabling its implementation on simple processors to edge computing.

The asymptotic behavior of the analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain is studied. Different asymptotic expansions with respect to the perturbation parameter and to the time variable are provided: one of Gevrey nature, and another of mixed type Gevrey and q-Gevrey. This asymptotic phenomena is observed due to the modification of the norm established on the space of coefficients of the formal solution. The techniques used are based on the adequate path deformation of the difference of two analytic solutions, and the application of several versions of Ramis-Sibuya theorem.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

Rhenium Disulfide (ReS2) has evolved as a novel 2D transition-metal dichalcogenide (TMD) material which has promising applications in optoelectronics and photonics because of its distinctive anisotropic attributes. In this review, we emphasize on formulating saturable absorbers (SAs) based on ReS2 to produce Q-switched and mode-locked pulsed lasers of diverse operation wavelengths like 1 μm, 1.5 μm, 2 μm, and 3 μm. We outline ReS2 synthesis techniques and integration platforms concerning solid-state and fiber-type lasers. We discuss the laser performance based on SAs attributes. Lastly, we draw conclusions and outlook by recommending additional improvements for SA devices so as to advance the domain of ultrafast photonic technology.

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

Collatz conjecture (3x+1 problem) is a natural phenomenon in set theory that may be reconstructed using known combinatorics and order theory. Construction begins by selecting a specific order isomorphism with a bijectional order-embedding. Mapping by 3x+1 induces a unique property to only members of the mapped embedding. Under selective congruence from recursive division by two, that complex controls sequence behavior. This demonstration uses an order isomorphism consisting of two linear orders: the (1) odd positive integers and the always odd (2) Rule 50 Jacobsthal numbers, as the embedding. The argument proceeds by cardinality. When the order isomorphism is mapped under 3x+1, all Rule 50 Jacobsthal numbers are mapped to all the powers of four. This one-to-one correspondence guarantees that every odd integer is assigned to a Rule 50 Jacobsthal number, and subsequently, to a power of four. To align this construction with the conjecture, expand the set to all positive integers by showing that: (1) the powers of four embed the powers of two, in a natural way, and (2) the unique factorization of any positive even integer, not congruent to a power of two, is simply an odd integer, once the factorized power of two is divided out. In other words, if the initial choice for a positive integer is not congruent to a power of two, then recursion continues until a Rule 50 Jacobsthal number (guaranteed by cardinality) is attained. Since this value mapped by 3x+1 is always a power of four, repeated division by two will always send the sequence to one. Because this same process occurs for any choice of positive integer, Collatz conjecture is true.

The paper deals with exploration of subsequences of polygonal numbers of different sides derived through step-by-step elimination of terms of the original sequences. Eliminations are based on special rules similarly to how the classic sieve of Eratosthenes was developed through the elimination of multiples of primes. These elementary number theory activities, appropriate for technology-enhanced secondary mathematics education courses, are supported by a spreadsheet, Wolfram Alpha, Maple, and the Online Encyclopedia of Integer Sequences. General formulas for subsequences of polygonal numbers referred to in the paper as polygonal number sieves of order k that include base-two exponential functions of k have been developed. Different problem-solving approaches to the derivation of such and other sieves based on the technology-immune/technology-enabled framework have been used. The accuracy of computations and mathematical reasoning is confirmed through the technique of computational triangulation enabled by using more than one digital tool. A few relevant excerpts from the history of mathematics are briefly featured.

In this work, Gaussian Tribonacci functions are defined and investigated on the set of real numbers $\mathbb{R},$ \textit{i.e}., functions $f_{G}$ $:$ $\mathbb{R}\rightarrow \mathbb{C}$ such that for all $% x\in \mathbb{R},$ $n\in \mathbb{Z},$ $f_{G}(x+n)=f(x+n)+if(x+n-1)$ where $f$ $:$ $\mathbb{R}\rightarrow \mathbb{R}$ is a Tribonacci function which is given as $f(x+3)=f(x+2)+f(x+1)+f(x)$ for all $x\in \mathbb{R}$. Then the concept of Gaussian Tribonacci functions by using the concept of $f$-even and $f$-odd functions is developed. Also, we present linear sum formulas of Gaussian Tribonacci functions. Moreover, it is showed that if $f_{G}$ is a Gaussian Tribonacci function with Tribonacci function $f$, then $% \lim\limits_{x\rightarrow \infty }\frac{f_{G}(x+1)}{f_{G}(x)}=\alpha \ $and\ $\lim\limits_{x\rightarrow \infty }\frac{f_{G}(x)}{f(x)}=\alpha +i,$ where $% \alpha $ is the positive real root of equation $x^{3}-x^{2}-x-1=0$ for which $\alpha >1$. Finally, matrix formulations of Tribonacci functions and Gaussian Tribonacci functions are given. In the literature, there are several studies on the functions of linear recurrent sequences such as Fibonacci functions and Tribonacci functions. However, there are no study on Gaussian functions of linear recurrent sequences such as Gaussian Tribonacci and Gaussian Tetranacci functions and they are waiting for the investigating. We also present linear sum formulas and matrix formulations of Tribonacci functions which have not been studied in the literature.

In this paper, we generalize Fibonacci quaternion, octonion, sedenion, trigintaduonion, etc. and define Horadam 2^{k}-ions and investigate their properties. Each Horadam (such as Fibonacci, Lucas, Pell) quaternions, octonions and sedenions are Horadam 2^{k}-ions. We also present connection to some earlier works.

Assuming a two component, positive and negative mass, superfluid/supersolid for space (the Winterberg model), we model the Higgs field as a condensate made up of a positive and a negative mass, planckion pair. The connection is shown to be consistent (compatible) with the underlying field equations for each field, and the continuity equation is satisfied for both species of planckions, as well as for the Higgs field. An inherent length scale for space (the vacuum) emerges, which we estimate from previous work to be of the order of,

Let be a power function $f_{r,M}(s)$ defined for every $s$ within the finite set $M$ as follows $$f_{r,M}(s)= \begin{cases} s^r, \ &s\in M,\\ 0, \ &\mathrm{otherwise}. \end{cases} $$ Let a discrete convolution of $f_{r,M}(s)$ be denoted as follows $\mathrm{Conv}_{r,M}[n]=(f_{r,M}*f_{r,M})[n]$. Let a real coefficients $A_{m,j}$ be given by the following recurrence $$ A_{m,j} = \begin{cases} 0, & \mathrm{if } \ j<0 \ \mathrm{or } \ j>m, \\ (2j+1)\binom{2j}{j} \sum_{d=2j+1}^{m} A_{m,d} \binom{d}{2j+1} \frac{(-1)^{d-1}}{d-j} B_{2d-2j}, & \mathrm{if } \ 0 \leq j < m, \\ (2j+1)\binom{2j}{j}, & \mathrm{if } \ j=m. \end{cases} $$ In this paper we show that for every $n>0$ the following odd-power identities involving coefficients $A_{m,j}$ and convolution transform $\mathrm{Conv}_{r,M}[n]$ hold $$ \begin{split} n^{2m+1}+1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{N}}[n],\\ n^{2m+1}-1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{Z}_{>0}}[n],\\ n^{2m+1}&=\sum_{r=0}^{m}A_{m,r}\sum_{k=1}^{n} k^r(n-k)^r\\ &=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1} k^r(n-k)^r. \end{split} $$

INTRODUCTION: Breast sensibility following reconstruction surgery, though often overlooked, holds significant importance due to its widespread occurrence and profound effects on patients’ well-being and safety. Our objective is to compare the sensory outcomes between DIEP flap microsurgery reconstruction and implant-based reconstruction. Additionally, we explored the potential influence of sociodemographic and clinical factors on sensory recovery, along with assessing temperature discrimination abilities and evaluating quality of life. MATERIAL AND METHODS: We conducted an ambispective descriptive-analytical study, involving women who underwent mastectomy with reconstruction using either DIEP flap and implants at our hospital between 1990 and 2021. Data were collected from medical records, patient histories, physical examination, and validated quality of life questionnaires (BREAST-Q). RESULTS: A total of 99 women with breast reconstruction were included, 47 with DIEP flap and 52 with implants. Sensory recovery in implant-based reconstruction was found to be superior to DIEP flap reconstruction (5.03 and 5.18 respectively, p-value &lt;0.005). A direct correlation was observed between sensory improvement and thermal discrimination (Spearman coefficient 0.9, p-value &lt;0.001). Factors such as radiotherapy, delayed reconstruction with DIEP flap, and height with implants were associated with poorer sensory recovery in the breast. Women experiencing better breast sensibility reported higher satisfaction with their surgeon, medical team, and psychosocial quality of life. CONCLUSION: Women reconstructed with implants or DIEP abdominal flap exhibit suboptimal overall sensory recovery of the reconstructed breast, with slightly better outcomes observed in women reconstructed with implants.

This article deals with a finite-source stock-dependent stochastic inventory system with heterogeneous servers and retrial facility. The system can store up to S number of items, and the lifetime of each item follows an exponential distribution. The primary customers arrive in a finite waiting hall from a finite source and get service from the multi-channel (c-heterogeneous servers). The customer’s arrival rate depends on the present stock level. Those customers who arrive while the waiting hall is full enter into the finite orbit. Also, customers in the waiting hall can become impatient and enter the orbit. The (s,Q) ordering policy is adopted for the replenishment of stocks. In the steady state, the joint probability distribution of a number of items in the inventory, busy servers, customers in the waiting hall, and orbit is computed. The comparative numerical analysis of heterogeneous and homogeneous servers on the expected total cost, the average number of customers in the waiting hall and orbit, the fraction of successful retrial rate, and the average impatient customer rate are also carried out.

A family of singularly perturbed q-difference-differential equations under the action of a small complex perturbation parameter is studied. The action of the formal monodromy around the origin is present in the equation, which suggests the construction of holomorphic solutions holding logarithmic terms in both, the formal and the analytic level. We provide both solutions and describe the asymptotic behavior relating them by means of q-gevrey asymptotic expansions of some positive order, with respect to the perturbation parameter. On the way, the development of a space product of Banach spaces in the Borel plane is needed to provide a fixed point for a coupled system of equations.

The proliferation of mobile and IoT devices, coupled with the advances in the wireless communication capabilities of these devices, have urged the need for novel communication paradigms for such heterogeneous hybrid networks. Researchers have proposed opportunistic routing as a means to leverage the potentials offered by such heterogeneous networks. While several proposals for multiple opportunistic routing protocols exist, only a few have explored fuzzy logic to evaluate wireless links status in the network to construct stable and faster paths towards the destinations. We propose FQ-AGO, a novel Fuzzy Logic Q-learning Based Asymmetric Link Aware and Geographic Opportunistic Routing scheme that leverages the presence of long-range transmission links to assign forwarding candidates towards a given destination. The proposed routing scheme utilizes fuzzy logic to evaluate whether a wireless link is useful or not by capturing multiple network metrics, the available bandwidth, link quality, node transmission power, and distance progress. Based on the fuzzy logic evaluation, the proposed routing scheme employs a Q-learning algorithm to select the best candidate set toward the destination. We implement FQ-AGO on the NS-3 simulator and compare the performance of the proposed routing scheme with three other relevant protocols: AODV, DSDV, and GOR. For precise analysis, we consider various network metrics to compare the performance of the routing protocols. Our simulation result validates our analysis and demonstrates remarkable performance improvements in terms of total network throughput, packet delivery ration, and end-to-end delay.

Transient receptor potential melastatin-8 (TRPM8) is a cation channel that is activated by cold and “cooling agents” such as menthol and icilin, which induce a cold sensation. Stimulation of TRPM8 activates an intracellular signaling cascade that ultimately leads to a change in the gene expression pattern of the cells. Here, we investigated the TRPM8-induced signaling pathway that links TRPM8 channel activation to gene transcription. Using a pharmacological approach, we show that inhibition of phosphatidylinositol 4-phosphate 5 kinase alpha (PIP5K), an enzyme essential for the biosynthesis of phosphatidylinositol 4,5-bisphosphate, attenuated TRPM8-induced gene transcription. Analyzing the link between TRPM8 and Gq proteins, we show that pharmacological inhibition of the beta gamma subunits impairs TRPM8 signaling. In addition, genetic studies showed that TRPM8 requires an activated Galpha subunit for signaling. In the nucleus, the TRPM8-induced signaling cascade triggers an activation of the transcription factor AP-1, a complex consisting of a dimer of basic region leucine zipper (bZIP) transcription factors. Here, we identified the bZIP protein c-Jun as an essential component of AP-1 within the TRPM8-induced signling cscade. In summary, with PIP5K, Gq subunits and c-Jun we have identified key molecules in the TRPM8-induced signaling from the plasma membrane to the nucleus.

The current research examines the many characteristics of the $\ell_{p}(\widetilde{F}(\widetilde{r},\widetilde{s}))$ $(1\leq p<\infty)$ and $\ell_{\infty}(\widetilde{F}(\widetilde{r},\widetilde{s}))$ spaces which are the generalized forms of those by Candan in 2024 using Fibonacci numbers and two non-zero real numbers in accordance with a predetermined rule, we have made an effort to go through all the characteristics and features which the author of earlier versions thought are the most valuable. This manuscript contains all the information required to describe the matrix class $(\ell_{1},\ell_{p}(\widetilde{F}(\widetilde{r},\widetilde{s})))$ $(1\leq p<\infty)$ which are going to be given in detail in the following sections of the manuscript. We are going to offer estimates for the norms of the bounded linear operators $L_{A}$ formed by those matrix transformations utilizing the Hausdorff measure of non-compactness and identify prerequisites to derive the relevant subclasses of compact matrix operators. When the findings of the current study are compared to those found in the literature, it can be said that the newly found ones are more inclusive and comprehensive.

Several life contingency agreements are based on the assumption that policyholders have impaired life expectancy attributable to factors such as lifestyle, social class, or preexisting health issues. Quantifying two crucial variables, augmented death probabilities and the discount rate of projected cash flows, is essential for pricing such agreements. Information regarding the correct values of these parameters is subject to vagueness and imprecision, which further intensifies if impairments must be considered. This study proposes modelling mortality and interest rates using a generalization of fuzzy numbers (FNs), known as intuitionistic fuzzy numbers (IFNs). Consequently, this paper extends the literature on life contingency pricing with fuzzy parameters, where uncertainty in variables, such as interest rates and death probabilities, is modelled using FNs. While FNs introduce epistemic uncertainty, the use of IFNs adds bipolarity to the analysis by incorporating both positive and negative information regarding actuarial variables. Our analysis focuses on two agreements involving policyholders with impaired life expectancy: determining the annuity payment in a substandard annuity and pricing a life settlement over a whole life insurance policy. In particular, we emphasize modelling interest rates and survival probabilities using triangular intuitionistic fuzzy numbers (TIFNs) owing to their ease of interpretation and implementation.

We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only absorption of particles can occur. The asymptotic behavior of the integer moments of both the total number of particles and the number of particles at a lattice point is studied depending on the relationship between the model parameters. In the case of the existence of an isolated positive eigenvalue of the evolution operator of the average number of particles, a limit theorem is obtained on the exponential growth of both the total number of particles and the number of particles at a lattice point.

Amid to the COVID-19 pandemic, digital health literacy (DHL) has become a significant public health concern. This research aims to assess information seeking behavior, as well as the ability to find relevant information and deal with DHL among university students in Pakistan. An online-based cross-sectional survey, using a web-based interviewing technique, was conducted to collect data on DHL. Simple bivariate and multivariate linear regression was performed to assess the association of key characteristics with DHL. The results show a high DHL related to COVID-19 in 54.3% of students. Most of the Pakistani students demonstrated ~50% DHL in all dimensions, except of reliability. Multivariate findings showed that gender, sense of coherence and importance of information were found to be significantly associated with DHL. However, a negative association was observed with students’ satisfaction with information. This led to the conclusion that critical operational and navigations skills are essential to achieve COVID-19 DHL and cope with stress, particularly to promote both personal and community health. Focused interventions and strategies should be designed to enhance DHL amongst university students to combat the pandemic.

Integrated ultra-low-loss waveguides are highly desired for integrated photonics to enable applications that require long delay lines, high-Q resonators, narrow filters, etc. Here we present an ultra-low-loss silicon waveguide on 500 nm thick SOI platform. Meter-scale delay lines, million-Q resonators and tens of picometer bandwidth grating filters are experimentally demonstrated. We design a low-loss low-reflection taper to seamlessly integrate the ultra-low-loss waveguide with standard heterogeneous Si/III-V integrated photonics platform to allow realization of high-performance photonic devices such as ultra-low-noise lasers and optical gyroscopes.

In this paper, we introduce the bicomplex Tetranacci and Tetranacci-Lucas quaternions. Moreover, we present Binet's formulas, generating functions, and the summation formulas for those bicomplex quaternions.

Hamacher operation which is generalization of the Algebraic and Einstein operation, can widely provide a large number of arithmetical operation with respect to uncertainty information, and Heronian mean can deal with correlations of the input arguments or different criteria and don’t make calculation redundancy, meanwhile, the normal intuitionistic fuzzy numbers (NIFNs) can depict distinctively normal distribution information in practical decision making. In this paper, a multi-criteria group decision-making (MCGDM) problem is researched under the NIFNs environment, and a new MCGDM approach is introduced on the basis of the Hamacher operation. Firstly, according to Hamacher t-conorm and t-norm, some operational laws of NIFNs are presented. Secondly, it is noticed that Heronian mean can’t only once take into account mutual relation between attribute values once, but also consider the correlation between input argument and itself. Therefore, we develop some operators and study their properties in order to aggregate normal intuitionistic fuzzy numbers information, these operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM) and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we apply the proposed operators to the MCGDM problem and present a new method. The main characteristics of this new method involve that: (1) it is suitable to make decision under the normal intuitionistic fuzzy numbers environment and more reliable and reasonable to aggregate the normal distribution information. (2) it utilizes Hamacher operation which can provide more reliable and flexible decision-making results and offer an effective and powerful mathematic tool for the MAGDM under uncertainty. (3) it uses the Heronian mean operator which can considers relationships between the input arguments or the attributes and don’t brings subsequently about redundancy. Lastly, an application is given for showing the feasibility and effectiveness of the presented method in this paper.

The following system of equations {x_1 \cdot x_1=x_2, x_2 \cdot x_2=x_3, 2^{2^{x_1}}=x_3, x_4 \cdot x_5=x_2, x_6 \cdot x_7=x_2} has exactly one solution in ({\mathbb N}\{0,1})^7, namely (2,4,16,2,2,2,2). Hypothesis 1 states that if a system of equations S \subseteq {x_i \cdot x_j=x_k: i,j,k \in {1,...,7}} \cup {2^{2^{x_j}}=x_k: j,k \in {1,...,7}} has at most five equations and at most finitely many solutions in ({\mathbb N}\{0,1})^7, then each such solution (x_1,...,x_7) satisfies x_1,...,x_7 \leq 16. Hypothesis 1 implies that there are infinitely many composite numbers of the form 2^{2^{n}}+1. Hypotheses 2 and 3 are of similar kind. Hypothesis 2 implies that if the equation x!+1=y^2 has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(4,5),(5,11),(7,71)}. Hypothesis 3 implies that if the equation x(x+1)=y! has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(1,2),(2,3)}. We describe semi-algorithms sem_j (j=1,2,3) that never terminate. For every j \in {1,2,3}, if Hypothesis j is true, then sem_j endlessly prints consecutive positive integers starting from 1. For every j \in {1,2,3}, if Hypothesis j is false, then sem_j prints a finite number (including zero) of consecutive positive integers starting from 1.

Aiming at the problem of hypersonic morphing vehicle avoiding no-fly zones and reaching the target, an improved predictor-corrector guidance method is proposed. Firstly, the aircraft motion model and the constraint model are established. Then, the basic algorithm is given, the Q-learning method is used to design the attack angle and sweep angle scheme to ensure that the aircraft can fly over the low-altitude zones. The B-spline curve is used to design the location of flight path points and the bank angle scheme is designed according to the predictor-corrector method, so that the aircraft can fly around to avoid high-altitude zones. Next, Monte Carlo reinforcement learning(MCRL) method is used to improve predictor-corrector method and Deep Neural Network(DNN) is used to fit reward function. The improved method can generate trajectory with better performance. Simulation results verify the effectiveness of the proposed algorithm.

As a critical transmitter, the compact 532 nm lasers operating on high repetition and narrow pulse widths have been used widely for airborne or space-borne laser active remote sensing. We developed a free space pumped TEM₀₀ mode sub-nanosecond 532 nm laser that occupied a volume of less than 125 mm × 50 mm × 40 mm (0.25 liters). The fundamental 1064 nm laser consists of a passively Q-switched composite crystal microchip laser and an off-axis, two-pass power amplifier. The pump sources were two single-emitter semiconductor laser diodes (LD) of 808 nm with a maximum continuous wave (CW) power of 10 W each. The average power of fundamental 1064 nm laser was 1.26 W with the laser operating at 16 kHz repetition rates, and 857ps pulse widths. Since the beam distortion would be severe in microchip lasers in terms of the increase in heat load, for obtaining a high beam quality of 532 nm, the beam distortion was compensated by adjusting the distribution of pumping beam in our experiment of fundamental amplification. Furthermore, better than 0.6 W average power, 770 ps, beam quality of M² ＜1.2, and 16 kHz pulse output at 532 nm was obtained by a Type I LiB₃O₅ (LBO) crystal in the critical phase matching (CPM) regime for second harmonic generation (SHG).

We propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.

We discuss what we believe could be an improvement in future discussions of the ever-changing brain. We do so by distinguishing different types of brain variability and outlining methods suitable to analyse them. We argue that, when studying brain and behaviour data, classical methods such as regression analysis and more advanced approaches both aim to decompose the total variance into sensible variance components. In parallel, we argue that a distinction needs to be made between innate and acquired brain variability. For varying high-dimensional brain data, we present methods useful to extract their low-dimensional representations. Finally, to trace potential causes and predict plausible consequences of brain variability, we discuss how to combine statistical principles and neurobiological insights to make associative, explanatory, predictive, and causal enquires; but cautions are needed to raise association- or prediction-based neurobiological findings to causal claims.

In this paper, we mainly show that generalized hyperharmonic number sums with reciprocal binomial coefficients can be expressed in terms of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.

In the heterogeneous wireless networked control system (WNCS), age of information (AoI) of the actuation update and actuation update cost are important performance metrics. To reduce the monetary cost, the control system can wait for the availability of WiFi network of the actuator and then conduct the update by using WiFi network in an opportunistic manner, but it leads to the increased AoI of the actuation update. To assess this problem, this paper proposes a priority-aware actuation update scheme (PAUS) where the control system decides whether to deliver or delay the actuation update to the actuator by considering the control priority (i.e., robustness of AoI of the actuation update). For the optimal decision, we formulate a Markov decision process model and derive the optimal policy based on Q-learning. Simulation results demonstrate that PAUS outperforms the comparison schemes in terms of the expected reward.

(1) Background: This work aimed to conduct the first comparative study providing long-term data about patient reported outcome measures as well as donor-site scar assessment and aesthetic evaluation of the reconstructed breasts in patients with DIEP versus PAP flap breast reconstruction. (2) Methods: This prospective, single-center, matched cohort study included a total of 36 patients after DIEP and PAP flap breast reconstruction. Evaluation was done using the Breast-Q and POSAS questionnaire as well as the Breast Aesthetic Scale for cosmetic analysis by four plastic surgeons. (3) Results: Post-operative Breast-Q evaluation revealed no significant differences between both patient groups for the categories physical well-being donor-site, physical well-being breast and satisfaction with the breast. Scar evaluation of the donor-site region showed equivalent results for the thigh and the abdomen concerning the overall opinion of patients and observers. There was no significant difference between both methods of reconstruction for all aspects of breast aesthetics. (4) Conclusions: Similar results of donor-site morbidity, scar quality and aesthetic outcome of the breast in both the DIEP and PAP patient group have been demonstrated. Hence, in cases suitable for both types of reconstruction, the decision can be based on factors such as patients’ lifestyle, leisure activities and preferences.

The aim of the present work is to explore a different non-traditional approach to higher dimensional spacetime which differs from the usual approaches such as large extra space dimensions, warped extra space dimensions and multiple extra time dimensions. This approach will be referred to as "Dynamic" higher dimensional spacetime. By this term will be introduced a new kind of higher dimensional spacetime (more than the usual 3+1 dimensions), which behaves dynamically in the sense that time is not a fixed dimension but is the extra plus one dimension to the spatial dimensions of the phenomenon we are studying. For a higher dimensional phenomenon, the lower dimensional time will behave as space and the new time will be a plus one dimension, meaning if we study a 3-dimensional phenomenon then time is the usual 4th dimension but if we are studying a 4-dimensional phenomenon then its time will be an extra 5th dimension and for this phenomenon the 4th dimension will behave as space. All spatial dimensions are indistinguishable from each other and behave in the exact same way, which means that the important parameter is not the dimension we are studying (for example the 4th or the 5th) but the number of dimensions in which a phenomenon can interact and how higher dimensional phenomena interact with lower ones. This non-traditional approach to higher dimensional spacetime may appear confusing at first but will become clearer in the rest of the paper. For this reason, we will first associate the time dimension with propagation relative to space dimensions and change orthogonal to them in order to give the reader a better intuition. Following that, we will describe how higher - dimensional phenomena would appear to us, the 3 - dimensional observer and try to set some guidelines on how we should mathematically model higher - dimensional phenomena in order for us to make accurate predictions of their behaviour. Then we will express the general framework of a "Dynamic" higher - dimensional spacetime and turn our gaze to 4+1 – dimensional phenomena. We will explore how a mass term arises for 4 – dimensional waves by generalizing the frequency – speed – wavelength relation of 3D waves and give a basic description on a possible way to describe a 4+1 – dimensional disturbance in a scalar Energy Field in order to make accurate predictions on our 3+1 dimensional plane. In this framework we will derive the Klein – Gordon equation by generalizing the wave equation and ignoring all lower than 4+1 - dimensional disturbances and compere our mass term findings with the Klein – Gordon equation mass term and with results from gravity – induced quantum interference experiments. Lastly, we will describe how a "Dynamic" 5 - dimensional spacetime would appear in a 3D observer and examine whether our findings are compatible with quantum mechanics and the special theory of relativity.

We consider a multitude of topics in mathematics where unification constructions play an important role: the Yang–Baxter equation and its modified version, Euler’s formula for dual numbers, means and their inequalities, topics in differential geometry, etc. It is interesting to observe that the idea of unification (unity and union) is also present in poetry. Moreover, Euler’s identity is a source of inspiration for the post-modern poets.

This paper is a continuation of previous papers on unification theories publishes in AXIOMS. We present results about the (modified) Yang-Baxter equation, Euler’s formula, dual numbers, coalgebra structures, non-associative structures, differential geometry, and (mean) inequalities. We will also attempt to relate our discussion to some Brain Studies and Machine Learnig.

We consider several unification problems in mathematics. We refer to transcendental numbers. Also, we present some ways to unify the main non-associative algebras (Lie algebras and Jordan algebras) and associative algebras.

This study explores the properties and behavior of bi-close-to-convex functions, introducing new subclasses defined by their relationship with fractional differential operator and bi-univalent functions. Using the Faber polynomial technique, we derive upper bounds for the n^{th} coefficient of functions in these classes. We also investigate the erratic behavior of initial coefficients in bi-close-to-convex functions, as characterized by the (λ,q)-fractional differintegral operator. Furthermore, we address Fekete-Szegö problems and present notable findings from our investigation, contributing to the continued growth and refinement of geometric function theory, yielding new insights and practical uses.

The steep rise in reinforcement learning (RL) in various applications in energy as well as the penetration of home automation in recent years are the motivation for this article. It surveys the use of RL in various home energy management system (HEMS) applications. There is a focus on deep neural network (DNN) models in RL. The article provides an overview of reinforcement learning. This is followed with discussions on state-of-the-art methods for value, policy, and actor–critic methods in deep reinforcement learning (DRL). In order to make the published literature in reinforcement learning more accessible to the HEMS community, verbal descriptions are accompanied with explanatory figures as well as mathematical expressions using standard machine learning terminology. Next, a detailed survey of how reinforcement learning is used in different HEMS domains is described. The survey also considers what kind of reinforcement learning algorithms are used in each HEMS application. It suggests that research in this direction is still in its infancy. Lastly, the article proposes four performance metrics to evaluate RL methods.

The aim of this work is to study generalizations of the notion of mean. Kolmogorov proposed a generalization based on an improper integral with a decay rate for the tail probabilities. This weak or Kolmogorov mean relates to the Weak Law of Large Numbers in the same way that the ordinary mean relates to the Strong Law. We propose a further generalization, also based on an improper integral, called the doubly weak mean, applicable to heavy-tailed distributions such as the Cauchy distribution and the other symmetric stable distributions, We also consider generalizations arising from Abel-Feynman type mollifiers that damp the behavior at infinity and alternative formulations of the mean in terms of the cumulative distribution and the characteristic function.

Artificial Intelligence (AI) and Deep Reinforcement Learning (DRL) have revolutionised e-learning by creating personalised, adaptive, and secure environments. However, challenges such as privacy, bias, and data limitations persist. E-FedCloud aims to address these issues by providing more agile, personalised, and secure e-learning experiences. This study introduces E-FedCloud, an AI-assisted adaptive e-learning system that automates personalised recommendations and tracking, thereby enhancing student performance. It employs federated learning-based authentication to ensure secure and private access for both course instructors and students. Intelligent Software Agents (ISAs) evaluate weekly student engagement using the Shannon Entropy method, classifying students into either engaged or not-engaged clusters. E-FedCloud utilises weekly engagement status, demographic information, and an innovative DRL-based early warning system, specifically ID2QN, to predict the performance of not-engaged students. Based on these predictions, the system categorises students into three groups: risk of dropping out, risk of scoring lower in the final exam, and risk of failing the end exam. It employs a multi-disciplinary ontology graph and an attention-based capsule network for automated, personalised recommendations. The system also integrates performance tracking to enhance student engagement. Data is securely stored on a blockchain using the LWEA encryption method.

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.

This paper focuses on enhancing the object detection and decision-making capabilities of Autonomous Emergency Medical Response Systems (AEMRS). Using advanced sensors, Convolutional Neural Networks (CNN), and reinforcement learning, we propose a model that processes environmental data to identify obstacles and make optimal navigation decisions. The integration of these technologies aims to minimize response time and improve the efficiency of emergency medical services. The perception system utilizes radar, LiDAR, and camera inputs to create a comprehensive understanding of the environment. These data are processed through a series of CNN layers to detect and classify objects such as vehicles, pedestrians, and road signs. On the decision-making front, a Q-learning algorithm is employed to enable the ambulance to learn from its interactions with the environment, continuously improving its route planning and collision avoidance strategies. By combining these advanced AI techniques, the proposed AEMRS can significantly enhance the speed and reliability of emergency responses, ultimately saving more lives. This paper presents the design, implementation, and simulation results of the proposed system, demonstrating its potential to revolutionize emergency medical services.

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to Poisson process and upon arrival of a catastrophe all inventory in the system is instantly destroyed. But consumer customers in the system (in the server or in the buffer) continue still waiting for the replenishment of the stock. The arrivals of the consumer customers follow a Markovian Arrival Process (MAP) and they can be queued in an infinite buffer. Service time of a consumer customer follows a phase-type distribution. The system receives negative customers whose have Poisson flows to service facility and upon arrival of a negative customer one consumer customer is pushed out from the system, if any. One of two replenishment policies can be used in the system: either (s,S) or (s,Q). If upon arrival of the consumer customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or join the queue (backorder sale scheme). The system is formulated by a four-dimensional continuous-time Markov chain. Steady state distribution is obtained using the matrix-geometric method. A comprehensive numerical study is performed on the performance measures under various replenishment policies. Finally, an optimization study is presented.

The compound, C27H23N3 (1), crystallizes in the triclinic system of the P-1 space group. The unit cell comprises a dimer of 1, in which the monomers are linked by two complementary hydrogen bonds between N1 and H1-C1 of another molecule. The dimers form chains along the a-axis through intermolecular interactions between the N2 acceptor atoms and C17 donors from molecules in the nearest neighbouring dimer. These interactions form extended sheets of the dimers of 1, along the ab plane. The quinolinylmeth-2-yl groups of 1 lie in almost orthogonal planes and their N1/2(q) donor atoms being away from the apical amino N3 atom.

Matiyasevich's theorem states that there is no algorithm to decide whether or not a given Diophantine equation has a solution in non-negative integers. Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. We prove: (1) Smorynski's theorem easily follows from Matiyasevich's theorem, (2 ) Hilbert's Tenth Problem for Q has a negative solution if and only if the set of all Diophantine equations with a finite number of rational solutions is not recursively enumerable.

In this article, two elliptical-ovel-shaped cylindrical dielectric resonator based wideband Graphene inspired reconfigurable metasurface absorber is designed on diffused quartz substrate having a relative permittivity of 3.75 and conductivity 2200Kg/m3 with height of 25μm. This metasurface having gold plated ground in microstrip with 5μm which is essential by calculating skin depth at 2.0THz frequency. Two elliptical ovel shaped patches with Graphene plated having built in potential varies 0-2.5eV and relaxation time 1.0ps at 290oK. By changing the relaxation time of Graphene 0.1ps-0.3ps its resonance frequency also varies i.e., reconfigurable property they provide without adding any active i.e., PIN diode components. The proposed MS is designed having a dimension of 100×100μm2 is designed on a microstrip. This MS works in the range of 1.6-2.38THz having more than 90% absorbance with two transmission zero at 2.1THz and 2.3THz having high Q ˃ 50 which is used to determine the sensitivity where the proposed MS used as a sensor to determine hemoglobin (Blood Glucose level) and urine (Uric acid) by changing their refractive index from 1.34-1.43. Maximum sensitivity achieved at 2000GHz/RIU and average sensitivity for hemoglobin and urine sensing achieved 833.33GHz/RIU, FOM-8.33 and 4277.7733GHz/RIU, FOM-555.55 respectively.

In real-life scenario, there are many mathematical tools to handle the incomplete and imprecise data. One of them is the fuzzy approach. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named as enhancing decomposition approach, is presented for achieving a subset for the parametric space that contains the sameα-pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

Mereology stands for the philosophical concept of parthood and is based on a sound set of fundamental axioms and relations. One of these axioms relates to the existence of a universe as a thing having part all other things. The present article formulates this logical expression first as an algebraic inequality and eventually as an algebraic equation reading in words: The universe equals the sum of all things. “All things” here are quantified by a “number of things”. Eventually this algebraic equation is normalized leading to an expression The whole equals the sum of all fractions. This introduces “1” or “100%” as a quantitative – numerical - value describing the “whole”. The resulting “basic equation” can then be subjected to a number of algebraic operations. Especially squaring this equation leads to correlation terms between the things implying that the whole is more than just the sum of its parts. Multiplying the basic equation (or its square) by a scalar allows for the derivation of physics equations like the entropy equation, the ideal gas equation, an equation for the Lorentz-Factor, conservation laws for mass and energy, the energy-mass equivalence, the Boltzmann statistics, and the energy levels in a Hydrogen atom. It further allows deriving a “contrast equation” which may form the basis for the definition of a length and a time scale. Multiplying the basic equation with vectors, pseudovectors, pseudoscalars and eventually hypercomplex numbers opens up the realm of possibilities to generate many further equations.

Soft-Core architecture for Analogue to Digital Converter (ADC) sampling is useful for mixed signal applications. Soft-core architecture for cutting edge odd or even ADC sampling with interface to block RAM memory has not been found. Soft-core architecture as a concept has become popular due to the advantage of customization for different applications as compared to general-core architecture suited for single application. The latest generation of piece wise sampling is odd sampling and was introduced in the second decade of the 20th century. Odd and even order sampling techniques are analogue in nature driven by a tuned (tuned for odd or even) mixer. This paper proposes a third-generation piece wise sampling with soft-core architecture that enables an option to select both odd and even while interfacing to memory mapping. The proposed odd/even has superior SNR performance of 6 dB as compared to existing architecture such as Mod-∆ which recorded worst performance of 18 dB. Advances in soft-core technology have allowed a niche odd/even switching field to be identified and studied, the study has also been extended to include memory architecture.