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.

Recent technological advancements in produced water for the oil and gas industry have a long history that spreads over centuries and has roots with many mathematicians, physicists, engineers, and inventors. Working to understand the many ideas and questions has helped to bring the produced water technologies to where we are today. Fluid mechanics is an essential factor in the world of engineering because it comes with significant benefits when designing the necessary equipment to overcome the challenging endeavors of daily operations. Many of us believe certain ideas or products were developed within a specific year not fully understanding the idea or concept might be hundreds of years old. For example, when we think of fluid mechanics, we do not think of Archimedes' immersing King Hiero II crown in water. Archimedes did this to determine the displacement of the water as he knew gold was denser than silver. Archimedes was one of the pioneers who was part of the beginning of fluid mechanics. Another interesting fact is the first valve invented was in 1 AD by Heron of Alexandria. This valve can be described as the very first hydraulic valve. The evolution of technology over hundreds of years has made considerable innovations benefiting engineers all over the world. These innovations come in the form of PLCs, RTUs, PIDs, mathematical formulas, processing methods, and SCADA systems.

Modification of electrode surface with a selective layer gives the possibility to detect target ana-lytes of forensic interest. 3-(4-trifluoromethyl)-phenyl)-thiophene (ThPhCF3) was deposited on a graphite (G) electrode by electrochemical oxidation and characterized as a receptor for the recognition of synthetic stimulants (2-aminoindane, buphedrone, naphyrone). First, the structural characterization of the polymeric layer were obtained from Raman spectroscopy. Second, the electrochemical profiles of selected synthetic stimulants and their affinity to ThPhCF3/G-modified electrodes were studied using square wave voltammetry and electrochemical impedance spec-troscopy. The values of the adsorption constant show the importance of – PhCF3 groups in the interaction with synthetic stimulants, namely recognition by the formation of hydrogen bonds (Kads (buphedrone) < Kads (2-AI)) and interaction with aromatic H atoms (Kads (buphedrone) < Kads (naphyrone)). It was demonstrated that the polymeric layer derived from thiophene with – PhCF3 group is capable to increase the intensity of the electrochemical signal.

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.

In this study, the microbial strain was isolated from the humus soil to ferment Sophora flavescens and Eleutherococcus sessiliflorus extracts. The isolated microbial was identified as Bacillus genus by 16S rRNA sequence analysis. The fermented plant extracts exhibited the antifungal effects against four types of the plant pathogens such as P. carotorum, B. cinerea, C. fructicola Sau-3, and C. gloeosporioides according to incubation time. Especially, the fermented plant extracts showed the most active activities for Colletotrichum genus to inhibit mycelium growth. Metabolite changes in fermented S. flavescens and E. sessiliflorus extracts were confirmed through LC-Q-TOF/MS. Flavonoid and peptide derivatives were improved in fermented S. flavescens and E. sessiliflorus extracts compared to their unfermented one, respectively. This study suggested that the isolated Bacillus microbial fermentation could be a valuable tool in improving the bioactivity of S. flavescens and E. sessiliflorus extracts to have potential with more environmentally-friendly antifungal agents.

Metal-organic frameworks (MOFs) have been subject of extensive scientific investigation in the last three decades and, currently, are one of the type of compounds most studied to be potentially applied in a wide range of distinct catalytic processes. Pristine MOF compounds provide several intriguing benefits for catalytic applications, including high interior surface areas and densities of active sites, allowing high catalytic reaction rates per volume, post-synthesis modified with com-plementary catalytic groups, enabling multiple functional groups to catalyze the reaction. Most of large-scale catalytic applications, including those in fuel processing, gas emission reduction and chemical synthesis, nevertheless the pristine MOFs often reveal limited stabilities and opportuni-ties for regeneration at high temperatures. As a result, the real applications of MOFs in these tech-nologies are likely to be constrained, and their controlled thermal modification aiming the prepa-ration of MOF-derivative compounds has been applied to induce crystalline structural changes and increase their structural stability, enhancing its potential applicability in more severe catalytic processes. Recent advances concerning the use of this strategy to boost the catalytic potential of the MOF-derivative compounds are outlined in this short-review article.

Given the landscape of intricate and constantly evolving cyber threats, organizations demand refined strategies to deploy a Security Information and Event Management to support the management of a Cyber Security Operations Center. The dynamic nature of cyber threats complicates the efficient allocation of the location of network intrusion detection sensors, a critical component of a robust cybersecurity framework. Our research introduces an approach that integrates the precision of biomimetic optimization algorithms with the adaptability of Deep Q–Learning. By employing different biomimetic algorithms enhanced with deep learning, we aim to refine the deployment of sensors in network infrastructures, balancing the network security imperative against deployment costs. The results of computational tests demonstrate that the improved iterations leveraging Deep Q–Learning have outperformed their native counterparts. These findings underscore the importance of reinforcement learning, specifically through Deep Q–Learning, as a powerful tool to enhance the effectiveness of metaheuristics in addressing optimization challenges.

We investigate a singularly perturbed q-difference differential Cauchy problem with polynomial coefficients in complex time and space with quadratic nonlinearity. We construct local holomorphic solutions on sectors in the complex plane with respect to the perturbation parameter with values in some Banach space of formal power series in space with analytic coefficients on shrinking domains in time. Two aspects of these solutions are addressed. One feature concerns asymptotic expansions in the parameter for which a Gevrey type structure is unveiled. The other fact deals with confluence properties as q tends to 1. In particular the built up Banach valued solutions are shown to merge in norm to a fully bounded holomorphic map in all its arguments that solves a nonlinear partial differential Cauchy problem.

The fungus Xylaria sp. Z184, harvested from the leaves of Fallopia convolvulus (L.) Á. Löve, has been isolated for the first time. Chemical investigation of the methanol extract of this strain’s culture broth led to the discovery of three new pyranone derivatives fallopiaxylaresters A-C (1–3) and a new bisabolane-type sesquiterpenoid named fallopiaxylarol A (4), along with the first complete set of spectroscopic data for the previously-reported pestalotiopyrone M (5). Known pyranone derivatives (6–11), sesquiterpenoids (12–14), isocoumarin derivatives (15–17), and an aromatic allenic ether (18) were co-isolated. Their structures were elucidated by the interpretation of HRESIMS, 1D, 2D NMR spectroscopy and quantum chemical computation method. The antimicrobial, anti-inflammatory, and α-glucosidase inhibitory activities of selected compounds and crude extract were evaluated in vitro. The extract inhibited nitric oxide (NO) production induced by lipopolysaccharide (LPS) in murine RAW264.7 macrophage cells, with an inhibition rate of 77.28 ± 0.82% at a concentration of 50 μg/mL. The compounds 5, 7 and 8 displayed weak antibacterial activity against Staphylococcus areus subsp. aureus at a concentration of 100 μM.

The design of a mixed-mode proportional-integral-derivative (PID) controller circuit using current-feedback operational amplifiers (CFOAs) as active components is proposed. With the same circuit topology, the proposed configuration of three CFOAs, four resistors, and two capacitors is capable of performing the PID controller in all four operation modes: namely voltage mode, trans-admittance mode, current mode, and trans-impedance mode. Numerous mathematical analyses are conducted to determine the controller performance under ideal and non-ideal conditions. Additionally, the mixed-mode second-order lowpass filter is suggested, and also used to examine the workability of the proposed mixed-mode PID controller in a feedback control structure. The proposed PID controller is implemented with the commercially available IC-type CFOA AD844, and the simulation results are presented to illustrate the functionality of the controller and its closed-loop control system.

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

Many corporations have now revised their value statements to showcase their commitment to sustainable development and green business due to the pressing issues of climate and environmental damage. Despite the importance of value statements that can direct companies to achieve sustainable goals, what kind of values can be perceived as organizational orientations to sustainability remains unknown. This study explores how the general public views the inclusion of sustainable components in value statements from the listed companies in Hong Kong by using Q-sort methodology (n = 30). Analyzing the final sample of 40 value statements extracted from 27 listed companies, we identified three factors related to sustainability, namely, Empowering business process management, Empowering customer-centric excellence, and Empowering sustainable progress. This study provides an additional component to the traditional triple bottom line by suggesting that internal operation of a company is an emerging idea to understand corporate sustainability.

The Fourier Continuous Derivative ($D_C$) offers a unique perspective on fractional differentiation grounded in the theory of Fourier series. This approach has the potential to address problems across various disciplines, including physics, engineering, and mathematics. The primary insight underpinning this approach is that a convex function defined on $\mathbb{Z}$ retains its convexity on $\mathbb{R}$. This paper delves into the Fourier Continuous Derivative, compares it with traditional fractional derivatives, and outlines its possible real-world applications, such as modeling viscoelastic materials, solving wave equations, and financial data analysis.

The article is devoted to the research of economic cycles and crises, which are studied within the framework of the theory of long waves by N. D. Kondratiev (K-waves) using the mathematical apparatus of fractional calculus. The object of the study is the mathematical model of S.V. Dubovsky 3 and some of its modifications, which describe the dynamics of the economic system, characterizing the interaction between the efficiency of new technologies and the efficiency of capital productivity. Modifications in the model are determined by the following points: the mathematical model takes into account the dependence of the rate of accumulation on capital productivity, there is an external harmonic influence - the influx of investments and new technological solutions, the economic system has heredity, including time-dependent, which leads to a delayed effect - the system’s response to impact. The property of heredity in the mathematical model is taken into account using fractional derivatives of constant and variable orders. Mathematical model S.V. Dubovsky and its modifications are studied numerically using the Adams-Bashforth-Moulton algorithm. Oscillograms and phase trajectories are constructed, and an interpretation of the simulation results is given.

Coenzyme Q (CoQ) is a lipidic compound widely distributed in nature with crucial functions in metabolism, protection against oxidative damage and ferroptosis, and other processes. CoQ biosynthesis is a conserved and complex pathway involving several proteins. COQ2 is a member of the UbiA family of transmembrane prenyltransferases that catalyzes the condensation of the head and tail precursors of CoQ, a key step in the process because its product is the first intermediate that will be modified in the head by the next component of the synthesis process. Mutations in this protein have been linked to primary CoQ deficiency in humans, a rare disease predominantly affecting organs with a high energy demand. The reaction catalyzed by COQ2 and its mechanism are still unknown. Here we aimed at clarifying COQ2 reaction by exploring possible substrate binding sites using a strategy based on homology, comprising the identification of ligand-bound homologs with solved structures available in the Protein Data Bank (PDB) and their subsequent structural superposition to the AlphaFold predicted model for COQ2. The results highlight some residues located on the central cavity or the matrix loops that may be involved in substrate interaction, some of them mutated in primary CoQ deficiency patients. Furthermore, we analyze the structural modifications introduced by the pathogenic mutations found in humans. These findings shed new light on the understanding of COQ2 function and, thus, CoQ biosynthesis and pathogenicity of primary CoQ deficiency.

The polysaccharide-based chiral stationary phase (CSP) columns for high-performance liquid chromatography (HPLC) were applied in the separation of liquid crystalline racemic mixtures obtained based on (R,S)-2-octanol and were found to be highly effective in recognizing isomers of minor structural differences. The mobile phase (MP), which consists of acetonitrile (ACN)/water (H2O) at different volume ratios, was used. All measurements were made at room temperature. The order of the elution was also determined. The chromatographic parameters such as resolution - (Rs), selectivity - (α), and the number of theoretical plates, i.e., column efficiency - (N), were determined. The polysaccharide-based CSP columns have unique advantages in separation technology, and this study has shown the potential usefulness of the CSP columns in separating liquid crystalline racemic mixtures belonging to the same homologous series.

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.

Ensuring precise electric locomotive stopping is pivotal for achieving intelligent and unmanned auxiliary transportation systems. Currently, human drivers' expertise plays a central role in the stopping process, posing challenges for automation and cargo location accuracy, particularly in coal mining. This paper focuses on achieving accurate electric locomotive stopping under diverse conditions by utilizing permanent magnet synchronous motor-driven locomotives. This technique introduces a novel stopping control method that combines a fuzzy Proportional-Integral-Derivative (F-PID) controller and a vector control model for permanent magnet synchronous motors (PMSM). After this, we design the F-PID using the PMSM technique based on the new fuzzy rules for each sub-system. In the end, extensive simulations and real-world experiments are conducted on an electric locomotive stopping test bed, which demonstrate the effectiveness of the proposed control method. From the simulation results, it confirming that the ability to achieve precise stopping under various working conditions.

The development of saltiness enhancement peptides is important in reducing salt intake and promoting dietary health. Our study aimed to analyze and identify straw mushroom enzymatic peptides with salty taste enhancing effects. The taste-related peptides within the straw mush-room extract were isolated via ultrafiltration and identified using UPLC-Q-TOF-MS/MS. Sub-sequent, E-tongue and sensory analyses unveiled that the ultrafiltration fraction (500-2000 Da) of straw mushroom peptides exhibited a saltiness enhancement effect. The UPLC-Q-TOF-MS/MS analysis identified 220 peptides within the ultrafiltration fractions (500-2000 Da), which were then assessed for their interaction with the T1R1/T1R3 receptor. The investigation underscored the significant involvement of Asp223, Gln243, Leu232, Asp251, and Pro254 in the binding of peptides from triple enzymatically hydrolyzed straw mushrooms to T1R1/T1R3. Based on the binding energy and active site analysis, three peptides were selected for synthesis: DFNALPFK (-9.2 kcal/mol), YNEDNGIVK (-8.8 kcal/mol), and VPGGQEIKDR (-8.9 kcal/mol). Notably, 3.2 mmol of VPGGQEIKDR enhanced a 0.05% NaCl solution to the saltiness level of a 0.15% NaCl solution. Also, 0.8 mmol of YNEDNGIVK elevated a 0.05% NaCl solution to the saltiness of a 0.1% NaCl solution.

Price markups and firm Tobin’s Q ratios are widely believed to have been increasing in the past several decades. Various models for the calculation of price markups have been developed, but each have methodological drawbacks and some results are poorly reflective of the near past wider macroeconomic experience. This paper defines an approach for the definition and measurement of markup pricing using the measure of Economic Rent and The Capital Asset Pricing Model. The results show limited markup pricing for The UK’s FTSE 100 companies (2018-2023), but that that certain Real Estate, Technology/Media and Financial Services/Equity Investment firms have enjoyed higher price markup levels. An analysis of the business models of these firms is used to qualitatively propose explanations for such markups. Finally, this work offers a formal proof that that expected price markup is equal to Tobin’s Q and finds that the empiric market level of markup is near equivalent to the market Tobin’s Q; differences between the markup and Tobin’s Q at the level of the firm are equally assessed.

In the paper, a study of the performance of unmanned ground vehicle (UGV), establishes numerical simulation model of the chassis system by three-dimensional software and finite element analysis software. Based on the numerical modelling and analysis, the work focuses on study of the strength and stiffness of the vehicle's chassis and researched the distribution of stress and deformation under the extremal condition. The paper also presents an autopilot design with new cascade control system for an autonomous motion of an unmanned ground vehicle based on Proportional-Integral-Derivative (PID) and Feed-Forward (FF) control. The PID-FF controller is a part of dedicated for presented UGV used in a hybrid control system for precise control and stabilization, necessary to increase the vehicle motion stability and maneuvers precision. The hybrid PID-FF control system proposed for the ground vehicle model gives a satisfactory quality of control, while maintaining the simplicity of the control system. Presented tests performed in area of mechanical design and control analysis gives good results and proves usefulness of designed unmanned device.

Towards smart batteries for electric vehicles (EVs) smart algorithms to control battery packs, mainly reconfigurable batteries, have to be developed. This work proposes a reinforcement learning (RL) algorithm to balance the State of Charge (SoC) of reconfigurable batteries based on the topologies half-bridge and battery modular multilevel management (BM3). As RL algorithm, Amortized Q-learning (AQL) is implemented, which allows enourmous numbers of possible configurations of the reconfigurable battery to be controlled, as well as the combination of classical controlling approach and machine learning methods. This enables safety mechanisms in control. As a neural network of the AQL a Feedforward Neuronal Network (FNN) is implemented consisting of three hidden layers. The experimental evaluation using a 12-cell hybrid cascaded multilevel converter illustrates the applicability of the method to balance the SoC and maintain the balanced state during discharge. The evaluation shows a 20.3% slower balancing compared to the classical. Nevertheless, AQL shows great potential to be applied for multiobjective optimizations as an applicable RL algorithm for control in power electronics.

Lifestyle interventions halt the progression of prediabetes to frank type 2 diabetes (T2D). However, the feasibility of a diabetes prevention program promoting tailored interventions on a national scale and conducted by primary care physicians is unclear. To explore this issue, general practitioners dislocated in ten different regions throughout Italy enrolled random subjects without known metabolic diseases to identify individuals with prediabetes and prescribe them an intervention based on physical activity. Using a simple stepwise approach, people referring to their primary care physician for any reason were screened for their diabetes risk with a web-based app of the Findrisc questionnaire. Those at risk for T2D, i.e. with a Findrisc score > 9, were invited to come back after overnight fasting to measure fasting glycaemia (FG). Those with 100 ≤ FG < 126 mg/dL were considered as people with prediabetes and compiled the Physical Activity Readiness Questionnaire (PAR-Q) to then receive a personalized prescription of physical activity. Overall, 5928 people were enrolled and compiled the questionnaire. Of these, 2895 (48.8 %) were at risk for T2D. Among these, FG was measured in 2168 subjects (participation rate 75%). The numbers of individuals with undetected prediabetes and T2D according to FG were 755 and 79 (34.8% and 3.6% of those assessing FG), respectively. Of the 755 subjects in the prediabetes range, 739 compiled the PAR-Q and started a personalized program of physical activity (participation rate 97%). Physicians involved in the study reported a mean of 6 minutes to perform the screening. Overall, these data suggest the feasibility of a national diabetes prevention program developed by general practitioners using a simple stepwise approach starting from a web-app to intercept individuals with prediabetes.

Given the AdS/CFT relationship, the study of higher-dimensional AdS black holes is extremely important. Furthermore, since the restriction derived from $f(Q)$'s field equations which prevents it from deriving spherically symmetric black hole solutions, the result is either $Q'=0$ or $f_{QQ}=0$. We derive static anti-de-Sitter black holes in $D$-dimensions using the cylindrical coordinate in the framework of the cubic form of $f(Q)$ gravity, where the coincident gauge condition is imposed \cite{Heisenberg:2023lru,Maurya:2023muz}. Within this study we are going to use the power-law ansatz which is the most viable according to observations where $f(Q)=Q+\frac{1}2\gamma Q^2+\frac{1}3\gamma Q^3-2\Lambda$, and the condition $D \geq 4$ is satisfied. Since these solutions lack a general relativity limit, they belong to a brand-new solution class, the characteristics of which are derived only from the non-metricity $Q$ modification. We investigate the singularities of the solutions by computing the values of different curvature and non-metricity invariants. We discover that the solutions indeed have a central singularity, but because of the f(Q) impact, it is softer than in the typical general relativity case. In conclusion, we compute thermodynamic parameters such as Gibbs free energy, Hawking temperature, and entropy. These thermodynamic calculations confirm that our model is stable.

Recently, Shehata et al. [37] introduced the r+1Rs(B;C; z) matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, dierential properties, new integral representations, k- Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the k-Riemann{Liouville and k-Weyl fractional integral and derivative operators an extended version of r+1Rs;k matrix function. We establish its relationships with other well known special matrix functions which have some particular cases in the context of three parametric Mittag-Leer matrix function, k- Konhauser and k-Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed.

In option pricing, we often deal with options whose payoffs depend on multiple factors such as foreign exchange rates, stocks, etc. Usually, it leads to a knowledge of the joint distributions and complicated integration procedures. The paper develops an alternative approach that converts the option pricing problem to a dual one and presents a solution to the problem in the optional semimartingale setting. The paper contains several examples which illustrate results in terms of the parameters of models and options.

Intermediate CAG expansions in the gene ataxin-2 (ATXN2) are a known risk factor for ALS, but little is known about their role in FTD risk. Moreover, their contribution to the risk and phenotype of patients might vary in populations with different genetic background. The aim of this study was to assess the relationship of intermediate CAG expansions in ATXN2 with the risk and phenotype of ALS and FTD in the Spanish population. Repeat-Primed PCR was performed in 620 ALS and 137 FTD patients in three referral centers of Spain to determine the exact number of CAG repeats. In our cohort, ≥27 CAG repeats in ATXN2 was associated with a higher risk of developing ALS (odds ratio [OR] = 2.666 [1.471-4.882]; p = 0.0013), but not FTD (odds ratio [OR] = 1.446 [0.558-3.574]; p = 0.44). Moreover, ALS patients with ≥27 CAG repeats in ATXN2 showed shorter survival rate compared to those with &lt;27 repeats (hazard ratio [HR] 1.74 [1.18, 2.56], p = 0.005), more frequent limb onset (odds ratio [OR] = 2.34 [1.093-4.936]; p = 0.028), as well as family history of ALS (odds ratio [OR] = 2.538 [1.375-4.634]; p = 0.002). Intermediate CAG expansions of ≥27 repeats in ATXN2 are associated with ALS risk, but not with FTD, in the Spanish population. ALS patients carrying an intermediate expansion in ATXN2 show more frequent limb onset, but worse prognosis than those without expansions. In patients carrying C9orf72 expansions, the intermediate ATXN2 expansion might increase the penetrance and modify the phenotype.

Here, we describe the bicomplex (p,q)- Fibonacci numbers and the bicomplex (p,q)- Fibonacci quaternions that are based on these numbers and give some of their equations, including the Binet formula, generating function, Catalan, Cassini, d’Ocagne’s identities, and some summation formulas for both of them. Finally, we create a matrix for bicomplex (p,q)- Fibonacci quaternions, and we obtain a determinant of a special matrix that gives the terms of that quaternion.

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.

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.

We propose a new hierarchy of the vector derivative nonlinear Schr{\"o}dinger equations and consider the simplest multiphase solutions of this hierarchy. The study of the simplest solutions of these equations led to the following results. First, the three-leaf spectral curves $\Gamma=\{(\mu,\lambda)\}$ of the simplest multiphase solutions have a quite simple symmetry. They are invariant with respect to holomorphic involution $\tau$. The type of this involution depends on the genus of the spectral curve. Or the involution has the form $\tau:(\mu,\lambda)\to(\mu,-\lambda)$, or $\tau:(\mu,\lambda)\to(-\mu,-\lambda)$. The presence of symmetry leads to the fact that the dynamics of the solution is determined not by the entire spectral curve $\Gamma$, but by its factor $\Gamma/\tau$, which has a smaller genus. Secondly, it turned out that the dynamics of the two-component vector $\bp=(p_1,p_2)^t$ is determined, first of all, by the dynamics of its length $\abs{\bp}$. Independent equations determine the dependence of the direction of the vector $\bp$ from its length. In cases where the direction of the vector $\bp$ is fixed, the corresponding spectral curve splits into separate components. In conclusion, we note that, as in the case of the Manakov system, the equation of the spectral curve is invariant with respect to the orthogonal transformation of the vector solutions. I.e., the solution can be found from the spectral curve up to the orthogonal transformation. This fact indicates that the spectral curve does not depend on the individual components of the solution, but on their symmetric functions. Thus, the spectral data of multiphase solutions have two symmetries. These symmetries make it difficult to reconstruct signals from their spectral data. The work contains examples illustrating these statements.

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.

The development and use of highly automated vehicles (HAV) in agriculture is a highly important task because of the lack of machine drivers and unsatisfactory level of their qualifications, reducing the impact of harmful factors on employees of agricultural enterprises. HAVs allow to avoid these problems: increase productivity and the efficiency of seasonal use of equipment, and reduce the impact of harmful factors on people. Modern HAVs in agriculture are based on the following methods: parallel driving according to geo coordinates without automatic turning and without obstacles tracking, and on technical vision without the use of a geographic information system (for example Cognitive AgroPilot) and a digital field map, which makes it impossible to generate the optimal path around the field.

This paper introduces new improvements to the modified version of the BIRECT (BI secting RECTangles) algorithm referred to as BIRECTv. We explore various approaches, by first including a grouping strategy for hyper-rectangles having almost the same sizes by categorizing them into different classes. Therefore constraining them not to exceed a certain pre-defined threshold (a small positive value to define the tolerance level). This approach allows for more efficient computation and can be particularly useful when dealing with a large number of hyper-rectangles with varying sizes. To avoid over-sampling, and preventing redundant or excessive sampling, at some shared vertices in descendant subregions, a particular vertex database is used to limit the number of samples taken within each subregion to two. The experimental investigation shows that these improvements have a positive impact on the performance of the BIRECTv(imp.) algorithm and the proposal is a promising global optimization algorithm compared to the original BIRECTv algorithm and its variants. Additionally, the BIRECTv(imp.) algorithm showed particular efficacy in solving high-dimensional problems.

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.

We present atomic structures and nonequilbrium synthesis of new class of materials, where the basic structural unit is a diamond tetrahedron. When units of one, two, and three tetrahedra are randomly packed, we create distinct phases of amorphous Q-carbon. Four tetrahedra in two adjacent layers lead to crystalline diamond lattice, which has four missing tetrahedra alternately. When these four missing tetrahedra are filled, we create subunit cell of crystalline Q-diamond. Theoretical calculations show that superconducting transition temperature (Tc) in 50 atomic % B-doped Q-diamond can reach near room temperature at ambient pressures. This is consistent with our earlier results using low-loss EELS measurements in 50 atomic % B-doped Q-carbon, which had mostly amorphous QB3 phase mixed with some crystalline Q-diamond phase. These EELS results showed that the Tc for these samples was in between 90K and 300K. Theoretical calculations of density of states, Eliashberg function, electron-phonon interaction parameter, and root-mean-square and logarithmic average of frequency in crystalline Q-diamond show Tc in the range of 268K to 300K, which is in a complete agreement with our EELS results in QB3.

This study investigates the therapeutic potential of new compound, potassium 2-[2-(2-oxo-4-phenylpyrrolidin-1-yl) acetamido]ethanesulfonate (Compound I), in depression. Willner's chronic unpredictable mild stress model of depression in 48 male Wistar rats was used a depression model. The rats were randomized into four groups, including an intact group, a Compound I group, a Fluoxetine group, and a control group receiving saline. Behavioral tests, such as the Porsolt forced swim test, hole-board test, elevated plus maze test, and light-dark box, were used to assess the animals' conditions. Our results demonstrated that Compound I effectively reduced the immobilization time of rats in the forced swim test, increased orientation and exploratory behavior, and decreased the latency period of going into the dark compartment compared to the control group. Hippocampal and striatal serotonin concentrations were increased in the Compound I group, and the compound also reduced the level of corticosterone in the blood plasma of rats compared to intact animals. These results suggest that Compound I has a reliable antidepressant activity, comparable to that of the reference antidepressant Fluoxetine.

This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially we develop a binary data matrix to record variables' values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle oriented coordinate and generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar field in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of cumulative probability function defined on Riemannian manifold also gives the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and gives the formal definition of joint probabilities by partial derivatives of cumulative distribution function. The equivalence between symmetrized covariant derivative and generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.

By utilizing a generalized version of the Madelung quantum-hydrodynamic framework that incorporates noise, we derive a solution using the path integral method to investigate how a quantum superposition of states evolves over time. This exploration seeks to comprehend the process through which a stable quantum state ultimately emerges in the presence of fluctuations induced by the noisy gravitational background. The model defines the conditions that give rise to a limited range of interaction for the quantum potential, allowing for the existence of coarse-grained classical descriptions at a macroscopic level. The theory uncovers the smallest attainable level of uncertainty in an open quantum system and examines its consistency with the localized behavior observed in large-scale classical systems. The research delves into connections and similarities with decoherence theory and the Copenhagen interpretation of quantum mechanics. Additionally, it assesses the potential consequences of wave function decay on the measurement of photon entanglement. To validate the proposed theory, an experiment involving entangled photons transmitted between detectors on the Moon and Mars is discussed. Finally, the findings of the theory are applied to the creation of larger Q-bits systems at elevated temperatures.

In this paper, existence and stability results of non-local integro-differential equation with Hilfer derivative of order ω∈(1,2) have been investigated. In this derivative is applied in RLC circuit equation of various fractional order. To proposed problem the existence solutions are derived using Schaefer’s fixed point theorem and the Banach contraction principle is using for uniqueness results. To demonstrate the effectiveness and applicability of our theoretical conclusions and two-step Lagrange polynomial interpolation were used to solve four numerical results.

This article deals with the queueing-inventory system, composed of c junior servers, a senior server, two finite waiting halls, and an infinite orbit. On occasion, junior servers encounter challenges during customer service. In these instances, they approach the senior server for guidance in resolving the issue. Suppose the senior server is engaged with another junior server. The approaching junior servers await their turn in a finite waiting area with a capacity of c for consultation. Concerning this, we study the performance of junior servers approaching the senior server in the retrial queueing-inventory model with the two finite waiting halls dedicated to the primary customers and the junior servers for consultation. We formulate a level-dependent QBD process and solve its steady-state probability vector using Neuts and Rao’s truncation method. The stability condition of the system is derived, and the R matrix is computed. Optimum total cost has been obtained, and sensitivity analyses, which include expected total cost, waiting time of customers in waiting hall and orbit, number of busy servers, and fraction of successful retrial rate of the model, are done numerically.

Dermal pigmentation is a challenging condition due to relative resistance to medical treatment and requirement of multiple sessions with modalities like chemical peels and lasers. There is inadequate literature regarding the efficacy and safety of lasers for dermal pigmentation in Indian skin. One hundred and twenty two patients were enrolled and divided into 4 groups: a) Dermal melasma b) Acquired dermal macular hyperpigmentation c) Nevus and d) Tattoo. Sequential combination of various lasers were used with different protocols for 4 different groups like ablative pixel Er:YAG, intense pulse light based technologies, Q-Switched and Alma Hybrid lasers for treatment of dermal pigmentation. A total of 4-10 sessions were conducted at three weekly intervals. Results were evaluated by comparing photographs at baseline, one month after the last session and then at 6 months interval to assess the relapse. All groups showed a statistically significant reduction in pigmentation. The mean treatment duration was 5-7 months for tattoo, lichen planus pigmentosus and melasma with 6-8 number of sessions. The mean treatment duration for nevus was 7-9 months with 8-10 sessions. Lasers are safe and effective modalities in Indian skin type for treatment of dermal pigmentation. Treatment period and relapse of dermal pigmentation may be reduced by combining resurfacing and chromophore selective lasers along with adequate dietary and lifestyle modifications to minimize complications and recurrence rates.

The duality is one of the most interesting properties of the Laplace and Fourier transforms associated to the integer order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier transforms. The scale and nabla derivatives are used.

Abstract: — management of the Continuous Stirred Tank Reactor (CSTR) operation has proven to be a difficult undertaking due to the complex and ever-changing nature of its behavior, which is both nonlinear and dynamic, which is further compounded by its instability. Attempts have been made to use Proportional-Integral-Derivative (PID) controllers for such processes, but the performance is often poor due to the inherent limitations of the controllers. In contrast, heuristic algorithms have been employed to tune the controllers, but these methods can only provide optimal performance for a restricted range of parameter variations. This paper presents a novel approach that involves using a conventional gain scheduling PID controller in combination with a fuzzy gain scheduling (FGS) controller method to calibrate set-point weighted PID controllers for the CSTR process. The paper outlines the design of the controllers and evaluates their performance by subjecting them to varying input signals within the given bandwidth.

To verify the concept of the metasurfaced reverberation chamber (MRC) which was proposed. This paper reports on measurements in the reverberation chamber (RC) performance by using a 1-bit random coding metasurfaced stirrer. The measurement results are validated and compared with that from two mechanical stirrers (horizontal stirrer and vertical stirrer). Figures of merit such as quality factor (Q factor), number of samples, standard deviation, angle autocorrelation, average K-factor, total scattering cross section (TSCS) and the enhanced back scattering coefficient (eb) are presented. Results indicate the feasibility of the MRC technique in the operation frequency of the RC. And it is possible to enlarge the test volume of the RC by using the 1-bit random coding metasurface stirrer.

The resonance spectrum of surface resistance derivative in quasi-two dimensional layered organic conductors has been calculated numerically for the out-of-plane and in-plane magnetic field. Not all but some of the resonances in a given series of transitions are present in the spectra. They are observed at the positions corresponding to the maxima in the surface resistance derivative curve and are in a good agreement with previously calculated magnetic field resonance positions. For tilted magnetic fields, there are more resonances present in the spectrum than in the case of a non-tilted field. Apart from the resonances corresponding to the transitions between the adjacent surface states there also appear resonances involving the transitions between the more distant surface states. This is correlated with the specific topology of Fermi surface of the organic conductors. The presented calculations will allow correct interpretation of the experimental curves for the resonance spectrum, and also to obtain information on the surface properties of these materials for their possible implementation in fabrication of devices based on organic molecular conductors.

In the particular configuration of the scalar field K-essence in the Wheeler-DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is $\beta=\frac{2\alpha}{2\alpha - 1}$. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; when $\omega_{X} \in [0,1]$, the order belongs to the interval $1\leq \beta \leq 2$, and when $\omega_{X}\in[-1,0)$, the order belongs to the interval $0<\beta \leq 1$. In the quantum scheme, we introduce the factor ordering problem in the variables $(\Omega,\phi)$ and its corresponding momenta $(\Pi_\Omega, \Pi_\phi)$, obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time $T(\tau)$, however in the dust era we found a closed solution in the gauge time $\tau$.

In this study, we investigate the existence of positive solutions within a system of Riemann-Liouville fractional differential equations that incorporate the (r1,r2,r3)-Laplacian operator while being subject to three-point boundary conditions. These equations incorporate various fractional derivatives and are influenced by parameters represented as (ψ1,ψ2,ψ3). Our approach involves employing techniques such as cone expansion and compression of the functional type, in conjunction with the Leggett-Williams fixed point theorem, to establish the existence of positive solutions. To emphasize the practical significance of our findings in the realm of fractional differential equations, we provide two illustrative examples.

An all-dielectric metasurface composed of orthogonal-slit silicon disks is proposed in this study. By modifying the unit structure of the metasurface with the bound states in the continuum (BIC) theory, a sharp Fano resonance can be generated. The resonance properties of the metasurface are investigated by analyzing the effects of the structural parameters on the resonance using the eigenmode analysis method. The Q factor and the resonance wavelength can be adjusted by varying the slit width, the disk thickness, and the disk radius. The electromagnetic characteristics and mechanism of the toroidal dipole-BIC (TD-BIC) are explored in depth through an analysis of the multipole expansion of the scattered power, along with the electromagnetic field and the current distribution at resonance. This research provides a novel approach for excitation of a strong TD-BIC resonance and proposes potential applications in optical switches, high-sensitivity optical sensors, and related areas.

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

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.

Sirtuins are a family of Class III epigenetic modifying enzymes involved in regulating cellular processes through the removal of acetyl groups from proteins. They rely on NAD+ as a coenzyme in contrast with classical HDACs (Class I, II, and IV) that depends on Zn+ for their activation, linking their function to cellular energy levels. There are seven mammalian sirtuin isoforms (SIRT1-7), each located in different subcellular compartments. Sirtuins act as master regulators of cellular homeostasis, responding to changes in nutrient availability and energy status. They play vital roles in diverse physiological and pathological conditions, making them promising therapeutic targets for various diseases, including cancer, neurodegenerative disorders, and metabolic diseases. High levels of SIRT6 are involved in the cancer progression of many tumor types and our previous studies revealed that sirtuin 6 was highly expressed in NSCLC cells and its inhibition potentially favored apoptosis and cell cycle arrest. Sirt6 emerged as a promising target and inhibitors of natural and synthetic sources are highly warranted. Imidazole derivatives are often investigated as sirtuin regulators due to their ability to interact with the binding site and modulate their activity. Imidazole bestows many possible substitutions on its ring and neighboring atoms, to design and synthesize derivatives with specific target selectivity and improved pharmacokinetic properties, optimizing drug development. We recently developed imidazole-based derivatives that potentially inhibited classical HDAC enzymes. Therefore, we evaluated the Sirtuin inhibition activity of our in-house compound comprised of imidazole derivatives and the strongest inhibition was observed with Ethyl 2-[5-(4-chlorophenyl)-2-methyl-1-H-Imidazole-4-yl) acetate against Sirt6 by in-silico and protein expression studies. Our results suggested that Ethyl 2-[5-(4-chlorophenyl)-2-methyl-1-H-Imidazole-4-yl) acetate could be a potential novel sirt6 inhibitor.

TThis paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann-Liouville fractional integral and fractional Caputo derivatives, enabling a comprehensive understanding of these functions. Additionally, we introduce a secondary characterization based on the Bernstein characterization of completely monotone functions. The practical significance of our study is showcased through an examination of the positivity of the fundamental solution of the space-fractional Bessel diffusion equation, highlighting the real-world applicability of the developed concepts. Through this work, we contribute to the broader understanding of radial positive definite functions and their utility in diverse mathematical and applied contexts.

The present analysis deals with the study of the $f(Q, T )$ theory of gravity which was recently considered by many cosmologists. In this theory of gravity, the action is taken as an arbitrary function $f(Q, T )$ where $Q$ is non-metricity and $T$ is the trace of energy-momentum tensor for matter fluid. In this study, we have taken three different forms of the function $f(Q, T )$ as $f(Q,T)=a_1Q+a_2 T$ and $f(Q,T)=a_3 Q^2+a_4 T$ and discussed some physical properties of the same. Also, we have obtained the various cosmological parameters towards Friedmann-Lemaitre-Robertson-walker (FLRW) Universe by defining the transit form of scale factor which yields the Hubble parameter in redshift form as $H(z)=\frac{H_{0}}{(\lambda+1)} \left(\lambda+ (1+z)^{\delta}\right)$. %We have obtained the approx best-fit values of model parameters using the least square method for observational constraints on available datasets like Hubble dataset $H(z)$, Supernova dataset SNe-Ia, etc., by applying the Root Mean Squared Error formula (RMSE). By applying the Root Mean Squared Error formula (RMSE), we were able to determine the approximate best-fit values of model parameters using the least square approach for observational constraints on the datasets Hubble dataset $H(z)$, Supernova dataset SNe-Ia, etc. We have observed that the deceleration parameter $q(z)$ exhibits a signature-flipping (transition) point within the range $0.623 \le z_{0} \le 1.668$ through which it changes its phase from the decelerated to the accelerated expanding universe with $\omega = -1$ at $z=-1$ for the approximate best-fit values of the model parameters. %For obtained approx best-fit values of model parameters we have observed that the deceleration parameter $q(z)$ shows a signature-flipping (transition) point within the range $0.623 \le z_{0} \le 1.668$ through which it changes its phase from decelerated to the accelerated expanding universe with $\omega = -1$ at $z=-1$.

In this study, we construct a new Atangana-Baleanu fractional model for whooping cough disease to predict future dynamics of the disease, as well as to suggest strategies to eliminate the disease in an optimal way. We prove that the proposed model has a unique solution which is positive and bounded. To measure contagiousness of the disease, we determine the reproduction number R0 and use it to examine the local and global stability at equilibrium points that have symmetry. Through sensitivity analysis, we determine parameters of the model that are most sensitive to R0. The ultimate aim of this research is to analyze different disease prevention approaches in order to find the most suitable one. For this, we include the vaccination and quarantine compartments in the proposed model and formulate an optimal control problem to assess the effect of vaccination and quarantine rates on disease control in three distinct scenarios. Firstly, we study the impact of vaccination strategy and conclude findings with presentation of graphical results. Secondly, we examine the impact of quarantine strategy on whooping cough infection with possible elimination from the society. Lastly, we implement vaccination and quarantine strategies together to visualize their combine effect on infection control. In addition to the study of an optimal control problem, we examine the effect of fractional order on disease dynamics as well as the impact of constant vaccination and quarantine rates on disease transmission and control. We determine that the optimal control strategy with the three controls is more effective in reducing the spread of whooping cough infection. Implementation of Toufik-Atangana type numercial scheme both for the state and adjoint equations is another contribution of this article.

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.

Currently, two-component integrable nonlinear equations from the hierarchies of the vector nonlinear Schrodinger equation and the vector derivative nonlinear Schrödinger equation are being actively investigated. Usually, such two-component integrable nonlinear evolutionary equations are considered, the form of which does not depend on the replacement of one component with another. In this paper, we propose for consideration and usage a new hierarchy of two-component integrable nonlinear equations, which have an important difference from the already known equations. Among the hierarchy equations there are analogues of the two-component nonlinear Schrödinger equation (second equation from hierarchy) and the two-component modified Korteweg-de Vries equation (fourth equation from hierarchy). The third equation of the hierarchy is a combination of the nonlinear Schrödinger equation for one component and the modified Korteweg-de Vries equation for the second component. The equations for the individual components are very different from each other, even if they have the same order. Let us note that even hierarchy equations can be reduced to well-known variants of the scalar derivative nonlinear Schrödinger equations, and odd equations can’t be reduced. To construct the hierarchy equations, we use the monodromy matrix method, first proposed by B.A. Dubrovin. Knowledge of the monodromy matrix makes it possible to construct spectral curves of multiphase solutions, as well as to find stationary equations that these solutions satisfy. The last section presents the simplest solutions in the form of solitons and periodic one-phase waves, as well as spectral curves corresponding to these solutions.

The high-speed railway operation environment monitoring network system has a wide variety of sensors and inconsistent business requirements, which have certain requirements for data transmission delay and network life. Most of the previous research focuses only on prolonging network lifetime or reducing data transmission delays when designing or optimizing routing protocols, without co-designing the two. In addition, due to the harsh operating environment of high-speed railways, when the network changes dynamically, the traditional routing algorithm will generate unnecessary redesigns and lead to high overhead. Based on the actual needs of high-speed railway operation environment monitoring, this paper proposes a novel Double Q-values adaptive model combined with the existing reinforcement learning method, which considers the energy balance of the network and real-time data transmission, and constructs energy saving and delay. The two-dimensional reward avoids the extra overhead of maintaining a global routing table while capturing network dynamics. In addition, the adaptive weight coefficient is used to ensure the adaptability of the model to each business of the high-speed railway operation environment monitoring system. Finally, simulations and performance evaluations are carried out and compared with previous studies.Finally, simulations and performance evaluations are carried out and compared with previous studies. The results show that the proposed routing algorithm successfully extends the network’s life cycle and gets good real-time data performance. It also saves energy and has fewer delays than the other three routing protocols in different situations.

Limited availability of expensive alloying elements elevates low-alloyed steels to a unique position in the field of lightweight construction and mass production. Quenching and partitioning (Q&P) heat treatments of low-alloyed steels with exceptional property combinations are particularly promising. In this study, we characterize for the first time a new low-alloyed steel to be processed by Q&P heat treatments. In combined experimental and numerical studies, we design a novel approach that effectively combines the short cycle times of press hardening with the excellent property profiles of Q&P-treated steels. We identify appropriate transformation parameters for Q&P heat treatments by dilatometric studies and we adjust a number of reference conditions with different isothermal holding times. By means of SEM analysis and XRD measurements, we show that different fractions of retained austenite result in different mechanical properties. Initial numerical designs of the process can identify varying temperature profiles and cooling rates depending on the position in the die. The results show that the geometry of the part plays a minor role, but the die temperature is the dominant factor for successful partitioning directly in the press hardening process.

We establish certain modular equations of degree three based on some results of Ramanujan's theta functions.

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 continuing public health issue known as COVID-19 (the 2019 Novel Corona virus infection) has a global emphasis. Despite (or perhaps because of) the fact that there are significant gaps in our understanding of COVID-19 epidemiology, transmission dynamics, research methods, and management breakout poses a new kind of global hazard. The good news is that there is currently enough knowledge about the epidemic process to allow for the creation of mathematical forecasting models. We modify a conventional SEIR epidemic model to the unique dynamic compartments and epidemic features of COVID 19 as it spreads in a population with a diverse age structure. Although many US states and other nations around the world followed lockdown and reopening processes, we perform some analysis on using some techniques of the epidemic course. A new perspective of fractional calculus known as piecewise derivatives of fractional order is used to study the proposed model. Sufficient conditions are established to show the existence theory. In addition, a numerical scheme based on Newton’s polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Some real data results are also shown with comparison of the numerical results.

NAD⁺ is known classically as a metabolite that participates in catabolic and anabolic pathways throughout the metabolism that is taught to students in introductory biochemistry courses. However, non-classical studies starting over a decade ago found that NAD⁺ is also involved in higher order functions, in part because of its involvement in the activation of SIRTs and the support of the mitochondrial unfolded protein response. Many studies since have suggested that NAD⁺ is involved in an extensive spectrum of human pathologies, including neurodegenerative disorders, cardiomyopathy, obesity, and diabetes, Further, healthy aging and longevity appear to be closely related to NAD⁺ and its related metabolites, including NAR and NMN. Together, these studies show that this system has value as a dietary supplement to improve general health overall, as well as mitigating specific disease conditions. Accordingly, many are now recommending the consumption of materials in this system as dietary supplements. Nicotinamide riboside (NAR) appears to have special value in this regard. It appears to be better tolerated than other molecules in this system, as well as better pharmacodynamics and greater potency. Unfortunately, NAR is a reactive molecule, often unstable during its manufacturing, transport, and storage. Indeed, HPLC analyses of many commercial samples of NAR shows that they contain substantial amounts of material that are not, in fact, NAR. In some of these commercial preparations, NAR is a minority component. Therefore, more stable derivatives of NAR that are easily converted upon consumption into NAR are therefore desired. Recently work related to prebiotic chemistry provided the borate derivative of NAR. NARB is considerably more stable than NAR itself. However, immediately upon consumption, the borate dissociates from NARB, and is lost in the body through dilution and binding to other species, notably carbohydrates such as fructose and glucose. The NAR left behind is expected to behave pharmacologically in ways identical to NAR itself. This review provides a comprehensive summary (through Q1 of 2023) of literature that makes the case for the consumption of NAR as a dietary supplement. It then summarizes the challenges of delivering quality NAR to consumers using standard synthesis, manufacture, shipping, and storage approaches. It concludes by outlining the advantages of NAR-borate in these processes.

In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.

As an option to deal with the insulin-dependent disease, a recent commuted PD control strategy is designed and carefully analyzed for different clinic diabetic patients. This controller approach is mainly conceived to stabilize the glucose blood concentration in a diabetic patient around its basal value, hence avoiding extreme situations such as hypoglycemia and hyperglycemia. This control strategy receives two inputs carefully tuned to actuate when the measured variable is out of a prescribed healthy zone. Therefore, one of these variables is invoked to decrease the glucose concentration to insulin injection, and the other is employed to increase the glucose absorption, both by using a proper PD controller. According to our numerical experiments, our controller approach performs well, even when there is an external disturbance in the controlled system.

This article focuses on developing a continuous authentication system using behavioral biometrics to recognize users accessing computing devices. The user’s distinct behavioral biometric is captured through keystroke dynamics, and reward-based reinforcement learning (RL) ideas are applied to recognize them throughout the session. The suggested system adds an extra layer of security to traditional authentication methods, forming a robust continuous authentication system that can be added to static authentication systems. The methodology involves training a RL model to detect unusual user typing patterns and flag suspicious activity. Each user has an agent trained on their historical data, which is preprocessed and used to create episodes for the agent to learn from. The environment involves fetching observations and randomly corrupting them to learn out-of-order behavior. The observation vector includes both running features and summary features. The re-ward function is binary and minimalistic. The Principal Component Analysis (PCA) model is used to encode the running features, and the Double Deep Q-Network (DDQN) algorithm with a fully connected neural network is used as the policy net. The evaluation achieved an average training accuracy and EER (equal error rate) of 94.7% and 0.0126 and test accuracy and ERR of 81.06% and 0.0323 for all users when the number of encoder features was increased. Therefore, it is concluded that by continuously learning and adapting to changing behavior patterns, this approach can provide more secure and personalized authentication, lowering the possibility of unauthorized access and cyberattacks. Overall, the use of reinforcement learning and behavioral biometrics for continuous authentication has the potential to significantly enhance security in the digital age and are effective in identifying each user.

In this study, we introduce a new class of bi-univalent functions using q-Janowski Function. We derive the Fekete-Szegö functional problems for functions in this new subclass, as well as estimates for the Taylor-Maclaurin coefficients |α2| and |α3|. Furthermore, a collection of fresh outcomes are3 presented by customizing the parameters employed in our initial discoveries.

Black ginseng is a type of processed ginseng that is traditionally used as herbal medicine in East Asian countries. It is prepared from fresh, white, or red ginseng by undergoing a process of steaming and drying nine times. However, the chemical differentiation of black ginseng with different processing levels is not well understood. The aim of this study is to propose a new method for discriminating and quantifying black ginseng. Six ginsenosides from black ginseng were accurately quantified, and based on this, the black ginseng samples were divided into uncompleted and completed black ginseng. Ultra-high-performance liquid chromatography-quadrupole-time of flight/mass spectrometry (UPLC-Q-TOF/MS) combined with a multivariate statistical analysis strategy was then employed to differentiate the two groups. A total of 141 ions were selected as analytical markers of black ginseng, with 45 of these markers being annotated by matching precise m/z and MS/MS data from prior studies.

Epilepsy is a neurological disorder that affects approximately 1% of the world's population. To diagnose and estimate the occurrence of epilepsy, the analysis of recorded brain activity is performed by a neurologist, which is not only time-consuming and tedious but also occasionally accompanied by human error. Therefore, in recent decades, researchers have aimed to unravel an approach for designing and building an automated method for diagnosing and estimating the occurrence of epilepsy. Accordingly, the present study proposed two new-fangled ways based on brain signals and a convolutional neural network (CNN). Moreover, this research implements a CNN with a sequential three-layer structure. Numerous experiments were performed, and the accuracy of estimating epilepsy using the developed methods was achieved at 95% without feedback and 97% with feedback. The proposed methods were proven to be more accurate than the previous techniques and can be employed as a physician's assistant once entering the field of operation.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

The main goal of the paper is to use a generalized proportional Riemann-Liouville fractional derivative (GPRLFD) to model BAM neural networks and to study some stability properties of the equilibrium. Initially, several properties of the GPRLFD are proved such as the fractional derivative of a squared function. Also some comparison results for GPRLFD are provided. Two types of equilibrium of the BAM model with GPRLFD are defined. In connection with the applied fractional derivative and its singularity at the initial time the Mittag-Leffler exponential stability in time of the equilibrium is introduced and studied. An example is given illustrating the meaning of the equilibrium as well as its stability properties.

The gradient descent algorithm has become the standard algorithm for computing the extreme values of functions, but for multivariate functions this algorithm is mostly ineffective. This is because the convergence rate of each element is inconsistent in most cases. However, in this paper, we found that the gradient sign is a self-optimizing operator, ensuring that the convergence rate is consistent across all elements. This also explains, from an optimization perspective, the success of the Fast Gradient Sign Method (FGSM) in generating adversarial samples that are indistinguishable from the normal input, but can easily fool neural networks. We also found that the fractional order gradient is also self-optimizing, and that the convergence speed of this algorithm can be controlled by adjusting the order of the gradient. Experiments suggest that this algorithm not only generates adversarial samples faster than other algorithms, but that a single source image can generate many such samples. This algorithm is also more effective than others at generating adversarial samples from simple images.

This study seeks to determine how economic policy uncertainty (EPU) influences investment decisions and the market value of the Pakistan Stock Exchange. The study examines investment and operational data from 249 energy and petroleum companies between 2015 and 2020, in addition to macroeconomic variables such as EPU. This study investigates the moderating effects of EPU on investments in fixed and intangible assets, as well as its effect on Tobin's Q and the market price per share. The outcomes demonstrate that EPU reduces the costs of both tangible and intangible assets for businesses. In addition, companies with a greater Tobin's Q and market price per share are more impacted by uncertain corporate investment policies. However, financial leverage is found to be negatively correlated with share price and positively correlated with earnings per share and earnings per unit. Tobin's Q is positively correlated with financial leverage, indicating that firms that raise capital through debt are more likely to create value for investors. The research indicates that market-dependent enterprises are more susceptible to the unpredictability of monetary policy. Eventually, the findings suggest that consistent and transparent economic policies may increase the efficiency of corporate investment.

Bio-based packaging materials and efficient drug delivery systems are gaining attention, carboxymethyl cellulose (CMC) is one of the most soluble cellulose derivatives, is a good candidate material due to its biocompatibility, biodegradability, and reproducibility. However, CMC-based films are lack of sufficient mechanical properties, limiting its widespread application. In this paper, the molecular interactions between CMC and additives with different molecular structures have been studied with rheological method. The additives are chitosan and cellulose derivatives including O-carboxymethylated chitosan (O-CMCh), N-2-hydroxypropyl-3-trimethylammonium-O-carboxymethyl chitosan (HTCMCh), hydroxypropyltrimethyl ammonium chloride chitosan (HACC), cellulose nanofibers (CNC), and cellulose nanofibers (CNF). The influencing factors, such as molecular structure, concentration of additives and temperature on the rheological properties were studied, which results revealed the information intermolecular interactions. Based on the rheological properties, several systems were selected to prepare films, which show very good transparency, wettability, mechanical properties, biodegradability, and cytotoxicity. These good characteristics of the selected films also proved the good biocompatibility of CMC and chitosan and cellulose derivatives. This work will provide an idea to prepare CMC-based food packaging and effective drug delivery materials with specific properties.

Chronoamperometric curves of the oxidation of a ferrocenyl derivative by the potential step showed diffusion controlled-like currents less than the Cottrell's equation at a platinum wire electrode. The lower deviation cannot be explained by the Butler-Volmer heterogeneous kinetics, but was ascribed to the negatively capacitive current associated with the redox reaction. The deviation at the fully oxidized potential corresponds to the non-zero concentration at the electrode surface, which cannot be predicted from the Nernst equation. The Nernst equation expresses the relationship of the potential with the activity at the electrode surface rather than the concentration. The diffusion equation provides the relation of the current with the surface concentration rather than the activity. The negative capacitance or the non-zero concentration may arise from structure formation on the electrode owing to the dipole-dipole interaction, which is similar to the generation of the double layer capacitance including frequency dispersion. On this concept, we derive here expressions for the lowered diffusion-controlled current and the time-dependent surface concentration. The negatively capacitive current shows the time-dependence of t-0.9, which is similar to the decay of the double layer capacitive currents. The surface concentration decays with the t-0.4-dependence.

Firstly, we present a more explicit formulation of the complete system $D(N)$ of representatives of Manin's symbols over $\mathbb{Q}$, which was initially given by Shimura. Then we establish a bijection between $D(M)\times D(N)$ and $D(MN)$ for $(M,N)=1$, which reveals a recursive structure between Manin's symbols of different levels. Based on Manin's complete system $\Pi (N)$ of representatives of cusps on $X_0(N)$ and Cremona's characterization of the equivalence between cusps, we establish a bijection between a subset $C(N)$ of $D(N)$ and $\Pi (N)$, and then establish a bijection between $C(M)\times C(N)$ and $C(MN)$ for $(M,N)=1$. We also provide a recursive structure for elliptical points on $X_0(N)$. Based on these recursive structures, we obtain recursive algorithms for constructing Manin symbols over $\mathbb{Q}$, cusps and elliptical points on $X_0(N)$. This gives rise to a more efficient algorithms for modular elliptic curve. As direct corollaries of these recursive structures, we present a recursive version of the genus formula and an elementary proof of formulas of the numbers of $D(N)$, cusps and elliptical points on $X_0(N)$.

This paper aims to unify q-derivative/q-integral and h-derivative/h-integral in a single definition, this will be called q−h-derivative/q−h-integral. These notions are further extended on finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities are studied for q−h-integrals which are directly connected with well known results. In diverse fields of science and engineering the theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified by using the concept of q−h-derivative/q−h-integral.

Rice false smut caused by Ustilaginoidea virens is one of the most devastating diseases on rice worldwide, which results in serious reduction of rice quality and yield. As an airborne fungal disease, early diagnosis of rice false smut, monitoring the epidemics and distribution of its pathogens, is particularly important to management the infection. In this study, a quantitative loop-mediated isothermal amplification (q-LAMP) method for the U. virens detection and quantifying was developed. This method has higher sensitivity and efficiency compared to quantitative real-time PCR (q-PCR) method. The species-specific primer sets UV-2 used was design based on the unique sequence of U. virens ustiloxins biosynthetic gene (NCBI accession number: BR001221.1). The q-LAMP assay was able to detect a concentration of 6.4 spores/mL at an optimal reaction temperature of 63.4℃ within 60 min. Moreover, the q-LAMP assay can even achieve accurate quantitative detection when there were only 9 spores on the tape. A linearized equation for the standard curve, y =-0.2866x + 13.829 (x is the amplification time, the spore number = 100.65y), was established for detection and quantifying of U. virens. In field detection applications, this q-LAMP method is more accurate and faster than traditional observation method. Collectively, this study has established a powerful and simple monitoring tool for U. virens, which provide valuable technical supports for forecast and management of rice false smut, and theoretical basis for precise fungicide application.

Based on the marine natural products piperafizine B, X334 and our previously reported compound 4m, fourteen novel 3,6-diunsaturated 2,5-diketopiperazine (2,5-DPK) derivatives (1-2, 4-6, 8-16), together with two known ones (3 and 7), were designed and synthesized as anticancer agents against cell lines A549 and Hela. The MTT assay results showed that the derivatives 6, 8-12 and 15 had moderate to good anticancer capacities with the IC50 values ranging from 0.7 to 8.9 μM. Among them, compound 11 with naphthalen-1-ylmethylene and 2-methoxybenzylidene functions at the 3- and 6-positions of 2,5-DPK ring, respectively, displayed good inhibitory activities to both cancer cells A549 (IC50 = 1.2 μM) and Hela (IC50 = 0.7 μM). It could also induce apoptosis and obviously block the cell cycle progression at G2/M phase in both cells at 1.0 μM. The electron withdrawing functions might not be favorable for the derivatives with high anticancer activities. Additionally, compared to piperafizine B and X334, these semi-N-alkylated derivatives have high liposolubilities (&gt; 1.0 mg•mL-1). Compound 11 can be further developed aiming to the discovery of novel anticancer candidate.

Background: This literature review investigates qualitative and quantitative uses of indocyanine green (ICG) in surgical treatment, as this novel technique has become increasingly popular in ORs (operating rooms) worldwide due to its many advantages. Method: An extensive literature review was performed by searching for relevant terms in 5 international databases (www.pubmed.gov, www.sciencedirect.com, www.scopus.com, www.Oxfordjournals.com, www.reaxys.com). The results of this search were summarized into the main advantages of employing ICG in colorectal surgery as follows: a) intraoperative fluorescence angiography capability; b) fluorescence-guided identification of lymph node involvement in colorectal cancer and the sentinel lymph node method; c) positive fluorescence flagging of a liver tumour as small as "only" 200 tumour cells; d) facilitation of fistula diagnosis; and e) tumour tattooing. Moreover, in addition to qualitative intraoperative ICG use, this technique can be combined with quantitative methods and parameters, such as maximum intensity, relative maximum intensity, and different inflow parameters (time-to-peak, slope, and t1/2max). The conclusion of this article is that fluorescence surgery with ICG aided by near-infrared (NIR) light is a relatively recent technology, an advantage of which is improving the specific anatomic and functional information provided, thus allowing more comprehensive and safer tumour removal as well as preservation of important structures.

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.

We propose a new statistical analysis of the Acoustic Emissions (AE) produced in a series of triaxial deformation experiments leading to fractures and failure of two different rocks, namely, Darley Dale Sandstone (DDS) and AG Granite (AG). By means of q-statistical formalism, we are able to characterize the pre-failure processes in both types of rocks. In particular, we study AE inter-event time and AE inter-event distance distributions. Both of them can be reproduced with q-exponential curves, showing universal features which are observed here for the first time and could be important in order to understand more in detail rock fractures dynamics.

The time interval set approach depends on results for radiation propagation from star sources, ie spherically symmetric, where properties relate to propagation sphere surfaces, finite for any realistic event and measurement. In contrast the usual vector and one moment time set approach from Newton’s laws, applies to stationary parallel radiation. A time interval only description necessarily has to start from it's own definitions, and properties for time intervals have to be defined with time intervals. This paper is devoted to deriving time interval only set properties commutation, addition and multiplication and derivative, and to define how these can correspond consistently to one moment time set properties. Time development within the time interval description equilibrium depends on the well-known ‘mean velocity theorem’ (MVT) and the time interval version of the Legendre transform, defined in earlier papers. Radiation propagation ‘away from’ and gravitation ‘towards’ the star source can be part of the description. In the discussion parts these properties are applied within astrophysics. Included is a integral derivation of star source radiation energy for both zero and non zero wave particle mass. The time interval set is not one of the usual sets encountered. However it’s non-linearity or non-commutativity property can be related to Noether charges and structure constants, that equal the radiation wave group-velocity, for photons the light velocity c, and, different from the usual derivative to one moment time, to specifics of the time interval only set derivative to time intervals.

In this paper, the stabilization and high efficiency of an unstable Second Harmonic Generation (SHG) of a Nd : YVO4 laser with a KTP intracavity is carried out by using a passive Q-switching crystal and a parametric modulation method (harmonic modulation) is shown. The harmonic modulation was defined as um(t) = Amsin(2π fmt), with modulation amplitude as Am(Vpp), and modulation frequency as fm(Hz), applied to the pumping of the Nd : YVO4 -KTP laser to control the amplitude and frequency of the emission, thus stabilizing the dynamic states of this laser. The promising application of this green light source is materialized when such light is necessary for high-density optics, such as in the treatment materials industry or in some aesthetic applications.

Abstract The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here we generalize this MBF to include a fractional parameter, such that the exponential in the previously mentioned integral is replaced by a Mittag-Leffler function. The necessity for this generalization arises from a problem of communication in networks. We find the power series representation of the fractional MBF of the first kind, as well as some differential properties. We give some examples of its utility in graph/networks analysis and mention some fundamental open problems for further investigation.

In tunnel excavation with boring machines, the tunnel face is supported to avoid collapse and minimise settlement. This article proposes the use of reinforcement learning, specifically the Deep Q-Network algorithm, to predict the face support pressure. The approach is tested both analytically and numerically. By using the soil properties ahead of the tunnel face and the overburden depth as the input, the algorithm is capable of predicting the optimal tunnel face support pressure, adapting to changes in geological and geometrical conditions.

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

In this paper, the 1st level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and then specify a set of the kernels that satisfy this condition and posses an integrable singularity of power law type at the origin. The 1st level general fractional derivatives of arbitrary order are integro-differential operators of convolution type with the kernels from this set. They contain both the general fractional derivatives of arbitrary order of the Riemann-Liouville type and the regularized general fractional derivatives of arbitrary order considered in the literature so far. For the 1st level general fractional derivatives of arbitrary order, some important properties including the 1st and the 2nd fundamental theorems of Fractional Calculus are formulated and proved.

Discretization is the process of converting a continuous function or model or equation into discrete steps. In this work, adaptive and learning methods are implemented to control DC motors that are used for actuating control surfaces of unmanned underwater vehicles. Adaptive control is a method in which the controller is designed to adapt the system with parameters which vary or are uncertain. Parameter estimation is the process of computing the parameters of a system using a model &amp; measured data. Adaptive methods have been used in conjunction with different parameter estimation techniques. Deterministic artificial intelligence, a learning-based approach that uses the process dynamics defined by physics, is also applied to control the output of the DC motor to track a specified trajectory. This work goes further to evaluate the performance of the adaptive &amp; learning techniques based on different discretization methods. The results are evaluated based on the absolute error mean between the output &amp; the reference trajectory and the standard deviation of the error. The first order-hold method of discretization and surprisingly large sample time of seven tenths of a second yields over sixty percent improvement over the results presented in the prequel literature.

Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning &amp; fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

(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.

Enterococcus faecalis is a bacterium that can develop a multidrug resistance profile associated with the community as well as nosocomial-acquired infections. Among the treatment options for these infections are aminoglycosides combined with bacterial cell wall inhibitors such as beta-lactams, since E. faecalis is intrinsically resistant to aminoglycosides. One of its most representative resistance mechanisms is the expression of aminoglycoside-modifying enzymes, such as the aminoglycoside phosphotransferase type IIIa of E. faecalis (EfAPH(3')-IIIa). This enzyme acts by phosphorylating aminoglycosides in an ATP-dependent reaction, modifying the 3' position of hydroxyl groups of these antibiotics. Considering this scenario, 3,092 natural products obtained from the ZINC22 database were analyzed to select molecules with the highest affinity for the nucleotide-binding pocket of EfAPH(3')-IIIa, which could be potential aminoglycoside adjuvants. The molecules that showed the best-score results obtained from ensemble docking-based virtual screening were ZINC000000952700 (BS-1), ZINC000014793040 (BS-2) and ZINC000015498603 (BS-3). The most promising results were for BS-2, a flavone derivative, due to its improved stability profile in molecular dynamics simulation (average values of RMSD of 0.23 nm, and Rg of 1.94 nm), binding free energy calculations (average ΔG total of -35.3 nm), as well as better toxicological profile (lower probability of hepatotoxicity, carcinogenic, immunotoxicity, mutagenicity, and cytotoxicity effects), compared to BS-1 and BS-3. These results allow us to propose that a flavone derivative may act as an adjuvant to aminoglycosides in the treatment of E. faecalis infections, acting as an inhibitor in the nucleotide-binding pocket of EfAPH(3')-IIIa.

Read-Across Structure-Activity Relationship (RASAR) is an emerging cheminformatic approach that combines the usefulness of a QSAR model and similarity-based Read-Across predictions. In this work, we have generated a simple, interpretable, and transferable quantitative-RASAR (q-RASAR) model which can efficiently predict the cytotoxicity of TiO2-based multi-component nanomaterials. The data set involves 29 TiO2-based nanomaterials which contain specific amounts of noble metal precursors in the form of Ag, Au, Pd, and Pt. The data set was rationally divided into training and test sets and the Read-Across-based predictions for the test set were generated using the tool Read-Across-v4.1 available from https://sites.google.com/jadavpuruniversity.in/dtc-lab-software/home. The hyperparameters were optimized based on the training set data and using this optimized setting, the Read-Across-based predictions for the test set were obtained. The optimized hyperparameters and the similarity approach, which yields the best predictions, were used to calculate the similarity and error-based RASAR descriptors using the tool RASAR-Desc-Calc-v2.0 available from https://sites.google.com/jadavpuruniversity.in/dtc-lab-software/home. These RASAR descriptors were then clubbed with the physicochemical descriptors and were subjected to features selection using the tool Best Subset Selection v2.1 available from https://dtclab.webs.com/software-tools. The final set of selected descriptors was used to develop multiple linear regression based q-RASAR models, which were validated using stringent criteria as per the OECD guidelines. Finally, a random forest model was also developed with the selected descriptors. The final machine learning model can efficiently predict the cytotoxicity of TiO2-based multi-component nanomaterials superseding previously reported models in the prediction quality.

Attitude control of a novel regional truss-braced wing aircraft with low stability characteristics is addressed in this paper using Reinforcement Learning (RL). In recent years, RL has been increasingly employed in challenging applications, particularly, autonomous flight control. However, a significant predicament confronting discrete RL algorithms is the dimension limitation of the state-action table and difficulties in defining the elements of the RL environment. To address these issues, in this paper, a detailed mathematical model of the mentioned aircraft is first developed to shape an RL environment. Subsequently, Q-learning, the most prevalent discrete RL algorithm will be implemented in both the Markov Decision Process (MDP), and Partially Observable Markov Decision Process (POMDP) frameworks to control the longitudinal mode of the air vehicle. In order to eliminate residual fluctuations that are a consequence of discrete action selection, and simultaneously track variable pitch angles, a Fuzzy Action Assignment (FAA) method is proposed to generate continuous control commands using the trained Q-table. Accordingly, it will be proved that by defining an accurate reward function, along with observing all crucial states (which is equivalent to satisfying the Markov Property), the performance of the introduced control system surpasses a well-tuned Proportional–Integral–Derivative (PID) controller.

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.

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

The quest for accurate and more efficient methods for solving periodic/oscillatory problems is gaining more attention in recent time. This paper presents the construction and implementation of a family of exponentially–fitted Obrechkoff methods. A single–step Obrechkoff method involving terms up to the fourth derivatives was used as the base method. We also present the stability and convergence properties of the constructed family of methods. Two numerical examples were use to illustrate the performance of the constructed methods.

For solving the fractional differential equations in computational fluid dynamics (CFD), it’s complicated and difficult by the Laplace and Fourier transforms. Based on the Caputo fractional derivative, the analytical solutions for unsteady unidirectional flows of a generalized Oldroyd-B fluid are deduced by the separation of variables method. Results show that the analytical solutions are given easily, and have good university. For some specific parameter values, the well-known analytical solutions for the generalized second grade fluid, the generalized Upper-Convected Maxwell (UCM) fluid as well as the ordinary Oldroyd-B fluid can be obtained.

Power series expansions are useful in approximation theory and mathematical physics. The manuscript presents several types of fractional Taylor expansions of sufficiently smooth functions. This is achieved by employing an incremental regularization procedure to the computation of the derivative. The series are constructed in an algorithmic way, which allows for its implementation in computer algebra systems.

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models