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

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

Propolis was widely used in health preservation and disease healing, it contains many ingredients. The previous study had been revealed that the propolis has a wide range of efficacy, such as antiviral, immune enhancement, anti-inflammatory and so on, but its antiviral components and underlying mechanism of action remain unknown. In this study, we investigated the chemical composition, and anti-PPV and immunological enhancement of Propolis Flavonoid(PF). Chemical composition of PF was distinguished by UPLC-Q/TOF-MS/MS analysis.The presence and characterized of 26 major components was distinguished in negative ionization modes.To evaluate the effects of PF used as adjuvant on the immune response porcine parvovirus (PPV). Thirty Landrace-Yorkshire hybrid sows were randomly assigned to 3 groups, and the sows in adjuvant groups were intramuscular injected PPV vaccine with 2.0 mL PF adjuvant (PA), oilemulsion adjuvant (OA), respectively. After that, serum hemagglutination inhibition antibody titers, IgM and IgG subclasses, eripheral lymphocyte proliferation activity, and concentrations of cytokines were measured. Results indicated an enhancing effect of PA on IgM, IL-2, IL-4, IFN-γ and the IgG subclass responses. These findings suggested that PA could significantly enhance the immune responses. Furthermore, we screened the chemical components the effective of anti-PPV, Ferulic acid have an excellently anti-PPV effective.

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

Petri nets are a graphical notation for describing a class of discrete event dynamic systems whose behaviours are charaterised by concurrency, synchronisation, mutual exclusion and conflict. They have been used over the years for the modelling of various distributed systems applications. With the advent of pervasive systems and the Internet of Things, the Calculus of Context-aware Ambients (CCA) emerged as a suitable formal notation for analysing the behaviours of these systems. In this paper, we are interested in comparing the expressive power of Petri nets to that of CCA. That is, can the class of systems represented by Petri nets be modelled in CCA? To answer this question, an algorithm is proposed that maps any Petri net onto a CCA process. We show that a Petri net and its corresponding CCA process behave the same way through experiments. It follows that CCA is at least as expressive as Petri nets, i.e. any system that can be specified in Petri nets can also be specified in CCA. Moreover, tools developed for CCA can also be used to analyse Petri nets.

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual tank device are precisely formulated by fractional calculus. Using the accurate model, multivariable Fractional-Order Controller is designed for the nonlinear device. The merits of the fractional-order design include: 1) Control of multivariable nonlinearities, 2) Compensation of uncertainties, 3) Elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control design.

We present a summary of the main results within the Scale Invariant Vacuum (SIV) paradigm based on the Weyl Integrable Geometry (WIG) as an extension to the standard Einstein General Relativity (EGR). After a brief review of the mathematical framework, where we also highlight the connection between the weak-field SIV equations and the notion of un-proper time parametrization within the reparametrization paradigm, we continue with the main results related to early Universe; that is, applications to inflation, Big Bang Nucleosynthesis, and the growth of the density fluctuations within the SIV. In the late time Universe the applications of the SIV paradigm are related to scale-invariant dynamics of galaxies, MOND, dark matter, and the dwarf spheroidals where one can find MOND to be a peculiar case of the SIV theory. Finally, within the recent time epoch, we highlight that some of the change in the length-of-the-day (LOD), about 0.92 cm/yr, can be accounted for by SIV effects in the Earth-Moon system.

We present a summary of the main results within the Scale Invariant Vacuum (SIV) paradigm as related to the Weyl Integrable Geometry. After a brief review of the mathematical framework, we will highlight the main results related to inflation within the SIV [9], the growth of the density fluctuations [8], and the application of the SIV to scale-invariant dynamics of Galaxies, MOND, Dark Matter, and the Dwarf Spheroidals [7]. The connection of the weak-field SIV results to the un-proper time parametrization within the reparametrization paradigm is also discussed [14].

Four discrete models using the exact spectral derivative discretization finite difference (ESDDFD) method are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index , the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is in part an artifact of the CEFD method as it is absent from the ESDDFD models.

The complete-lattice approach to optimization problems with a vector- or even set-valued objective already produced a variety of new concepts and results and was successfully applied in finance, statistics and game theory. For example, the duality issue for multi-criteria and vector optimization problems could be solved using the complete-lattice approach, compare [11]. So far, it has been applied to set-valued dynamic risk measures (in the stochastic case), as discussed in Feinstein, Rudloff etc. (see [11], for example), but it has not been applied to deterministic calculus of variations and optimal control problems. In this paper, the following problem of set-valued optimization is considered: minimize the functional $$ \overline J_t[y]=\int_0^t \overline L(s,y(s),\dot y(s))\ ds + U_0(y(0)) $$ over all admissible arcs $y$, where $\overline L$ is the associated multifunction to a vector-valued Lagrangian $L$, the integral is in the Aumann sense and $U_0$ is the initial cost. A new concept of \emph{value function}, for which a Bellman's optimality principle holds, is introduced. Also the classical result of the Hopf-Lax formula holds for the generalized value function. Finally, a derivative with respect to the time $t$ and a directional derivative with respect to $x$ of the value function are defined, based on ideas close to the concepts in [12]. The value function is proved to be solution of a suitable Hamilton-Jacobi equation.

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.

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.

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.

This present work explores the performance of a thermal-magnetic engine of Otto type, considering as a working substance an effective interacting spin model corresponding to the q− state clock model. We obtain all the thermodynamic quantities for the q = 2, 4, 6, 8 cases in a small lattice size (3×3 with free boundary conditions) by using the exact partition function calculated from the energies of all the accessible microstates of the system. The extension to bigger lattices was performed using the mean-field approximation. Our results indicate that the total work extraction of the cycle is highest for the q=4 case, while the performance for the Ising model (q=2) is the lowest of all cases studied. These results are strongly linked with the phase diagram of the working substance and the location of the cycle in the different magnetic phases present, where we find that the transition from a ferromagnetic to a paramagnetic phase extracts more work than one of the Berezinskii–Kosterlitz–Thouless to paramagnetic type. Additionally, as the size of the lattice increases, the extraction work is lower than smaller lattices for all values of q presented in this study.

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

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

The paper discusses the design and modeling of a simple and illustrative hardware kit for teaching the basics of quantum cryptography to engineering students. The novel solution differs from those already on the market in that it is focused on familiarising trainees with the physical principles of quantum key distribution, as well as with the basics of mathematical formalism in quantum mechanics. This is achieved by using a minimally sufficient set of optical elements with a simple mathematical description in the Jones formalism. This composition of the kit is targeted mostly at engineering students and does not require advanced training in physics as a prerequisite. The configurable architecture of the hardware educational kit contributes to the deeper involvement of students. By independently changing the modular configuration of the system, students can conduct experiments that were not directly provided by the developers. For instance, students can assess the impact of choosing the basic settings of phase retarders on the course of a man-in-the-middle attack. The proposed amount of mathematical and informational support, as well as ready-made formal models, is sufficient to reasonably put forward hypotheses for experimental verification and interpret the obtained empirical data. At this moment, the hardware kit is being replicated, distributed and successfully applied at universities and companies in the communications industry. The accumulated experience of educational use testifies to the high efficiency of the kit as a tool for basic QKD training for people without prior knowledge of quantum mechanics. A discrete event model simulating the operation of the hardware kit is implemented in the non-commercial modeling software CPN Tools and is openly distributed.

The (numerical) solution of Ordinary Differential Equations (ODEs) problems is of paramount relevance, ODEs system being an ubiquitous mathematical formulation of many physical phenomena (such as those involved in fluid dynamics, chemistry, biology, evolutionary-anthropology, ...): almost every dynamici phenomenon can be modeled by means of an ODEs system. The present paper is the first manifesto of FOODIE, a library aimed to numerically solve ODEs problems by means of a clear, concise and efficient abstract interface. FOODIE, meaning Fortran Object oriented Ordinary Differential Equations integration library, has manifolds aims: to provide a set to built-in numerical schemes that are accurate, robust, validated and efficient and to allow easy application of these schemes to (almost) all ODEs problems by means of an effective Abstract Calculus Pattern. The key idea is to allow the same solver-implementation to be applied to all ODEs problems thus avoiding the re-implementation of the ODEs solver for each different ODEs problem: code re-usability is consequently maximized, FOODIE being a general robust framework. Besides, the same framework also allows rapid development of new ODEs solvers due to the high abstraction level of the library itself. The present paper is the first announcement of FOODIE project: the current implementation is extensively discussed and its capabilities are proved by means of tests and examples.

This article presents a hybrid approach to assessing students’ foreign language proficiency in a cyber-physical educational environment. It focuses on the advantages of integrated assessment of student knowledge by considering the impact of automatic assessment, learners’ independent work, and their achievements to date. An assessment approach is described using the mathematical theory of fuzzy functions, which are employed to ensure fair evaluation of students. The largest possible number of students, whose re-evaluation of test results will not affect the overall performance of the student group, is automatically determined. The study also models the assessment process in the cyber-physical educational environment through the formal semantics of calculus of context-aware ambients (CCA).

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.

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.

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.

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

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

We introduce the lower chaos grade of a real-valued function F defined on the Markov triple (E,μ,Γ), where μ is a probability measure and Γ is the carré du champ operator. As an application of this concept, we obtain the better estimate of the four moments theorem for Markov diffusion generators worked by Bourguin et al (2019). For our purpose, we need to find the largest number except zero in the set of eigenvalues corresponding to its eigenfunction in the case where the square of a random variable F, coming from a Markov triple structure, can be expressed as a sum of eigenfunctions, We give some examples of eigenfunctions of the diffusion generators such as Ornstein-Uhlenbeck, Jacobi and Romanovski-Routh. In particular, two bounds, called the four moments theorem and fourth moment theorem respectively, will be provided for the normal approximation of the case where a random variable F comes from eigenfunctions of a Jacobi generator.

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 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.

The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is presented and applied to selected theoretical models of the population dynamics. The role of the derived Lagrangians and the energy-like terms in the population dynamics is investigated, and it is shown that the obtained standard Lagrangians can be used to study oscillatory behavior of the models and the period of their oscillations, which may have ecological and environmental implications. These and other physical and biological insights gained from the derived standard Lagrangians are discussed.

A new type of ordinary differential equation is introduced and discussed, namely, the time-dependent order ordinary differential equations. These equations can be solved via fractional calculus and are mapped into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equations smoothly deforms solutions of the classical integer order ordinary differential equations into one-another, and can generate or remove singularities. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers was also proved.

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.

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 $X_0(N)$.

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.

unlike the volume, the expression for the surface area of a regular conoid has not yet been obtained by means of direct integration or a differential geometry procedure. As this non-developable form is relatively used in engineering, the difficulty to determine its surface, represents a serious shortcoming for several problems which arise in radiative transfer, lighting and construction, to cite just a few. In order to solve the problem, I conceived the surface as a set of linearly dwindling ellipses which remain parallel to a circular directrix, a typical problem appears when searching the length of such ellipses. I employed a new procedure which, in principle, consists in dividing the surface into infinitesimal elliptic strips to which we have successively applied Ramanujan’s second approximation for the longitude of the ellipse. In this manner, we can obtain the perimeter of any transversal curve pertaining to the said form as a function of the radius of the directrix and the position of the ellipse’s center on the X-axis. Integrating the so-found perimeters of the differential strips for the whole span of the conoid, an unexpected solution emerges through the newly found number psi (ψ) which seems like a refined approximation to the third decimal of Pi but derived from a definite integral equation. As the strips are in truth slanted in the symmetry axis, their width is not uniform and we need to perform some adjustments in order to complete the problem with sufficient precision, but this is discussed separately in the annexes. Relevant implications for mathematical symmetry applied to multifarious architectural and engineering forms can be derived from this finding

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 <0.005). A direct correlation was observed between sensory improvement and thermal discrimination (Spearman coefficient 0.9, p-value <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.

One third of a person’s life is spent on sleep, therefore the quality and habit of sleep affects health. A single case study indicated that perspiration could serve as a prognostic marker. Diagnosing nocturnal perspiration is common clinical practice, since this serves as a major symptom in many pathologies. Till this day no specific evidence-based approach for diagnosing nocturnal perspiration exists. By introducing the Q-strip, a device which quantitatively measures nocturnal perspiration, this could be acquired. The Q-strip could serve a purpose in diagnosing nocturnal perspiration more efficient without being intrusive. In addition to its health sensing potentials, the Q-strip makes it possible to visualise perspiration patterns. This introduces the possibility to examine the quality of sleep. Future research is recommended to investigate this.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

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.

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.

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Z_p of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

The classical propositional calculus (zero-order logic, classical propositional logic), is the most fundamental two-valued logical system. In this paper we present a proof of inconsistency of the classical propositional calculus. Then, we get right away the conclusion that the metatheory of the classical propositional calculus is inconsistent.

This paper describes a proposed fractional filter-based multi-scale underwater and hazy image enhancement algorithm. The proposed system combines a modified global contrast operator with fractional order-based multi-scale filters used to generate several images, which are fused based on entropy and standard deviation. The multi-scale-global enhancement technique enables fully adaptive and controlled colour correction and contrast enhancement without over exposure of highlights when processing hazy and underwater images. This in addition to illumination/reflectance estimation coupled with global and local contrast enhancement. The proposed algorithm is also compared with the most recent available state-of-the-art multi-scale fusion de-hazing algorithm. Experimental comparisons indicate that the proposed approach yields better edge and contrast enhancement results without halo effect, colour degradation and is faster and more adaptive than all other algorithms from the literature.

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.

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.

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.

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

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

In this paper, we introduce the (ρ,q)-analogue of the p-adic factorial function. By utilizing some properties of (ρ,q)-numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic (ρ,q)-gamma function by means of the mentioned factorial function. We investigate several properties and relationships belonging to the foregoing gamma function, some of which are given for the case p = 2. We also derive more representations of the p-adic (ρ,q)-gamma function in general case. Moreover, we consider the p-adic (ρ,q)-Euler constant derived from the derivation of p-adic (ρ,q)-gamma function at x = 1. Furthermore, we provide a limit representation of aforementioned Euler constant based on (ρ,q)-numbers. Finally, we consider (ρ,q)-extension of the p-adic beta function via the p-adic (ρ,q)-gamma function and we then investigate various formulas and identities.

In this paper, we investigate several relations for p-adic gamma function by means of their Mahler expansion and fermionic p-adic q-integral on ℤ_{p}. We also derive two fermionic p-adic q-integrals of p-adic gamma function in terms of q-Boole polynomials and numbers. Moreover, we discover fermionic p-adic q-integral of the derivative of p-adic gamma function. We acquire a representation for the p-adic Euler constant by means of the q-Boole polynomials. We finally develop a novel, explicit and interesting representation for the p-adic Euler constant including Stirling numbers of the first kind.

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on ℤ_{p} of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

In the present paper, the (p,q)-Hermite based Apostol type Frobenius-Euler polynomials and numbers are firstly considered and then diverse basic identities and properties for the mentioned polynomials and numbers, including addition theorems, difference equations, integral representations, derivative properties, recurrence relations. Moreover, we provide summation formulas and relations associated with the Stirling numbers of the second kind.

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

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.

In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.

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.

Mereotopology is a concept rooted in analytical philosophy. The phase-field concept is based on mathematical physics and finds applications in materials engineering. The two concepts seem to be disjoint at a first glance. While mereotopology qualitatively describes static relations between things like x isConnected y (topology) or x isPartOf y (mereology) by first order logic and Boolean algebra, the phase-field concept describes the geometric shape of things and its dynamic evolution by drawing on a scalar field. The geometric shape of any thing is defined by its boundaries to one or more neighboring things. The notion and description of boundaries thus provides a bridge between mereotopology and the phase-field concept. The present article aims to relate phase-field expressions describing boundaries and especially triple junctions to their Boolean counterparts in mereotopology and contact algebra. An introductory overview on mereotopology is followed by an introduction to the phase-field concept already indicating first relations to mereo- topology. Mereotopological axioms and definitions are then discussed in detail from a phase-field perspective. A dedicated section introduces and discusses further notions of the isConnected relation emerging from the phase-field perspective like isSpatiallyConnected, isTemporallyConnected, isPhysicallyConnected, isPathConnected and wasConnected. Such relations introduce dynamics and thus physics into mereotopology as transitions from isDisconnected to isPartOf can be described.

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

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

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