Rapidly changing dynamics of globalization and increasing market competition are causing the companies all around the world confronting several new challenges and opportunities. To be competitive and successful apart from relative importance of physical resources, companies must adapt modern strategies and policies regarding market flexibility and development. The purpose of this study is to empirically investigate the relationship between intellectual capital and firm value. Furthermore, the moderating role of managerial ownership has been evaluated with the help of regression analysis. The sample included the panel data taken from non-financial firms listed on Pakistan stock exchange (PSX) covering the period 2010-2015. A sample of 79 firms out of 384 firms have been selected with the help of systematic sampling technique. VAIC (Value Added Intellectual Coefficient) model has been used for the calculation of intellectual capital. Tobin's Q has been taken as a measure of firm value. Managerial ownership has been tested as moderator. Based on data analysis, it is concluded that the relationship between intellectual capital and firm value is positively significant. It is also concluded that managerial ownership moderates the relationship between intellectual capital and firm value negatively.

According to the fact that the low convergence level on the complete elliptic integral of the first kind for the modulus which having values approach to one. In this paper we propose novelty of the complete elliptic integral consists of the new infinite series. We apply the scheme of iteration by substituting the common modulus with own modulus function into the new infinite series. We obtained so many new exact formulas of the complete elliptic integral derived from this method correspond to the number of iteration order. On the other hand, it has been also obtained a lot of new modulus functions rather than common used previously. The calculation results show that the number of significant figures of the new infinite series of the complete elliptic integral of the first kind is increased more and more. It means more fastly convergent would be obtained comparison values with the previous infinite series.

The prevalence of differential equations as a mathematical technique has refined the fields of control theory and constrained optimization due to the newfound ability to accurately model chaotic, unbalanced systems. However, in recent research, systems are increasingly more nonlinear and difficult to model using Differential Equations only. Thus, a newer technique is to use policy iteration and Reinforcement Learning, techniques that center around an action and reward sequence for a controller. Reinforcement Learning (RL) can be applied to control theory problems since a system can robustly apply RL in a dynamic environment such as the cartpole system (an inverted pendulum). This solution successfully avoids use of PID or other dynamics optimization systems, in favor of a more robust, reward-based control mechanism. This paper applies RL and Q-Learning to the classic cartpole problem, while also discussing the mathematical background and differential equations which are used to model the aforementioned system.

We introduce the Symplectic Structure of Information Geometry based on Souriau’s Lie Group Thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using Geometric (Planck) Temperature of Souriau model and Symplectic cocycle notion, the Fisher metric is identified as a Souriau Geometric Heat Capacity. Souriau model is based on affine representation of Lie Group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie Group Thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant-Kirillov-Souriau) 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of Information Geometry for the action of an affine Group for exponentiel families, and provide some illustrations of use cases for multivariate Gaussian densities. Information Geometry is presented in the context of seminal work of Fréchet and his Clairaut-Legendre equation. Souriau model of Statistical Physics is validated as compatible with Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

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

In the paper we show that the general relativity in recent Einstein-Palatini formulation is equivalent to a gauge field. We begin with a bit of information of the Einstein-Palatini formulation and derive Einstein field equations from it. In the next section, we consider general relativity with a positive cosmological constant in terms of the corrected curvature. We show that in terms of the corrected curvature general relativity takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature.

This paper presents the application of optimal control problem in modeling of stirred tank heater temperature control. The analysis of the open loop system shows that the system is not efficient without a controller. Linear Quadratic Gaussian (LQG) and Linear Quadratic Integral (LQI) controllers are used to increase the performance of the system. Comparison of the closed loop system with the proposed controllers have been done with Matlab/Simulink Toolbox and a promising results have been analyzed.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

An active power dispatch method for a microgrid (MG) with multi-type loads, renewable energy sources (RESs) and distributed energy storage devices (DESDs) is the focus of this paper. The MG operates in a grid-connected model, and distributed power sources contribute to the service for load demands. The outputs of multiple DESDs are controlled to optimize the active power dispatch. Our goal with optimization is to reduce the economic cost under time-of-use (TOU) price, and to adjust the excessively high or low load rate of distributed transformers (DTs) caused by the peak-valley demand and load uncertainties. To simulate a practical environment, the stochastic characteristics of multi-type loads are formulated. The transition matrix of system state is provided. Then, a finite-horizon Markov decision process (FHMDP) model is established to describe the dispatch optimization problem. A learning-based technique is adopted to search the optimal joint control policy of multiple DESDs. Finally, simulation experiments are performed to validate the effectiveness of the proposed method, and the fuzzification analysis of the method is presented.

This paper includes some new investigations and results for post quantum calculus, denoted by (p,q)-calculus. A chain rule for (p,q)-derivative is developed. Also, a new (p,q)-analogue of the exponential function is introduced and some its properties including the addition property for (p,q)-exponential functions are investigated. Several useful results involving (p,q)-binomial coefficients and (p,q)-antiderivative are discovered. At the final part of this paper, (p,q)-analogue of some elementary functions including trigonometric functions and hyperbolic functions are considered and some properties and relations among them are analyzed extensively.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributional sense.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.

Reinforcement learning (RL) is an extensively applied control method for the purpose of designing intelligent control systems to achieve high accuracy as well as better performance. In the present article, the PID controller is considered as the main control strategy for brushless DC (BLDC) motor speed control. For better performance, the fuzzy Q-learning (FQL) method as a reinforcement learning approach is proposed to adjust the PID coefficients. A comparison with the adaptive PID (APID) controller is also performed for the superiority of the proposed method, and the findings demonstrate the reduction of the error of the proposed method and elimination of the overshoot for controlling the motor speed. MATLAB/SIMULINK has been used for modeling, simulation, and control design of the BLDC motor.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations among q-Bernoulli numbers and polynomials, and newly de…ned (q, r, w)-Stirling numbers of the second kind. We also obtain q-Bernstein polynomials as a linear combination of (q, r, w)-Stirling numbers of the second kind and q-Bernoulli polynomials in w.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader–Qi mean.

This paper presents a symmetrical topology for the design of solid-state transformer, made up of power switching converters, to replace conventional bulky transformers. The proposed circuitry not only reduces the overall size but also provides power flow control with the ability to be interfaced with renewable energy resources (RESs) to fulfill the future grid requirements at consumer end. Solid state transformer provides bidirectional power flow with variable voltage and frequency operation and has the ability to maintain unity power factor, and current total harmonic distortion (THD) for any type of load within defined limits of IEEE standard. Solid State Transformer offers much smaller size as compared to that of the conventional iron core transformer. MATLAB/Simulink platform is adopted to test the validity of the proposed circuit for different scenarios by providing the simulation results evaluated at 25 kHz switching frequency.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

In this paper, the design of a low cost portable ventilator with performance analysis have been done to solve the scarcity of respiratory ventilators for COVID-19 patients. The materials used to build the system are: DC motor, rotating disc and pneumatic piston. The system input is the patient heart beat and the output is volume of air to the patient lung with adjusted breathing rate. This ventilator adjusts the breathing rate to the patient depending on his heart beat rate. The performance analysis of this system have been done using Proportional Integral Derivative (PID) and Full State Feedback H2 controllers. Comparison of the system with the proposed controllers have been done using a step change and a random change of the patient heart beat and a promising result have been analyzed successfully.

We consider the problem of coordinating the charging of an entire fleet of electric vehicles (EV), using a model-free approach, i.e. purely data-driven reinforcement learning (RL). The objective of the RL-based control is to optimize charging actions, while fulfilling all EV charging constraints (e.g. timely completion of the charging). In particular, we focus on batch-mode learning and adopt fitted Q-iteration (FQI). A core component in FQI is approximating the Q-function using a regression technique, from which the policy is derived. Recently, a dueling neural networks architecture was proposed and shown to lead to better policy evaluation in the presence of many similar-valued actions, as applied in a computer game context. The main research contributions of the current paper are that (i)we develop a dueling neural networks approach for the setting of joint coordination of an entire EV fleet, and (ii)we evaluate its performance and compare it to an all-knowing benchmark and an FQI approach using EXTRA trees regression technique, a popular approach currently discussed in EV related works. We present a case study where RL agents are trained with an epsilon-greedy approach for different objectives, (a)cost minimization, and (b)maximization of self-consumption of local renewable energy sources. Our results indicate that RL agents achieve significant cost reductions (70--80%) compared to a business-as-usual scenario without smart charging. Comparing the dueling neural networks regression to EXTRA trees indicates that for our case study's EV fleet parameters and training scenario, the EXTRA trees-based agents achieve higher performance in terms of both lower costs (or higher self-consumption) and stronger robustness, i.e. less variation among trained agents. This suggests that adopting dueling neural networks in this EV setting is not particularly beneficial as opposed to the Atari game context from where this idea originated.

In this paper, we introduce a new generalization of the Hermite polynomials via (p, q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, explicit formula, recurrence relation, integral representation. We also de…ne a (p, q)-analogue of the Bernstein polynomials and acquire their some formulas. We then provide some (p, q)-hyperbolic representations of the (p, q)-Bernstein polynomials. In addition, we obtain a correlation between (p, q)-Hermite polynomials and (p, q)-Bernstein polynomials.

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

In this paper Brinkman type fluid over an infinite plate between side walls is being investigated. The flow is generated by oscillating shear stress of the bottom plate and the solutions are obtained by using Fourier integral transformation. The obtained results are presented in steady and transient states for both sin and cos shear stresses. The general solutions are reduced to some special cases corresponding, namely to the Brinkman type fluid over an infinite plate and flow of a Newtonian viscous fluid. Graphical illustrations are carried out to have in depth analysis of the involved physical parameters

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

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

In the present paper, we introduce (p, q)-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, explicit formulas and relations for these polynomials and numbers. Moreover, we discover (p, q)-extensions of Carlitz's result [L. Carlitz, Mat. Mag., 32 (1959), 247–260] and Srivastava and Pintér addition theorems in [H. M. Srivastava, A. Pinter, Appl. Math. Lett., 17 (2004), 375–380].

For evaluating probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based upon the Gauss-Laplace law. The latter will be considered here as an element of the newly introduced family of (p,q)-spherical distributions. Based upon a suitably defined non-Euclidean arc-length measure on (p,q)-circles we prove geometric and stochastic representations of these distributions and correspondingly distributed random vectors, respectively. These representations allow dealing with the new probability measures similarly like with elliptically contoured distributions and more general homogeneous star-shaped ones. This is demonstrated at hand of a generalization of the Box-Muller simulation method. En passant, we prove an extension of the sector and circle number functions.

In this paper, a 3 DOF gyrscope position control have been designed and controlled using optimal control theory. An input torque has been given to the first axis and the angular position of the second axis have been analyzed while the third axis are kept free from rotation. The system mathematical model is controllable and observable. Linear Quadratic Integral (LQI) and Linear Quadratic State Feedback Regulator (LQRY) controllers have been used to improve the performance of the system. Comparison of the system with the proposed controllers for tracking a desired step and random angular position have been done using Matlab/Simulink Toolbox and a promising results has been analyzed.

In this paper we establish several Hermite-Hadamard type integral inequalities for hyperbolic p-convex functions. Applications for special means are provided as well.

Increasing the quality factor (Q) of an optical resonator device has been a research focus to be utilized in various applications. Higher Q-factor means light is confined in a longer time which will produce a shaper peak and higher transmission. In this paper, we introduce a novel technique to increase further the Q-factor of a one-dimensional photonic crystal (1D PhC) cavity device by using an end loop-mirror (ELM). The technique utilizes and recycles the light transmission from the conventional 1D PhC cavity design. The design has been proved to work by using the 2.5D FDTD simulation with Lumerical FDTD and MODE softwares. By using the ELM technique, the Q- factor of a 1D PhC design has been shown to have increased up to 79.53 % from the initial Q value without the ELM. This novel design technique can be combined with any high Q-factor and very high Q-factor designs to increase more the Q-factor value of a photonic crystal cavity devices or any other suitable optical resonator devices. The experimental result shows that the device is measurable by adding a Y-branch component to the one-port structure and able to get the high-Q result.

In this paper we introduce the hypo-q-norms on a Cartesian product of inner product spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar Shisha-Mond, Birnacki et al., Grüss type inequalities, Boas-Bellman and Bombieri type inequalities are also given.

In this paper, by using the q-integer, we introduce a new generalization of Fibonacci and Lucas sedenions called q-Fibonacci and q-Lucas sedenions. We present some fundamental properties of these type of sedenions such as Binet formulas, exponential generating fuctions, summation formulas, Catalan's identity, Cassini's identity and d'Ocagne's identity.

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.

Global financial investments in energy production and consumption are significant since all aspects of a country's economic activity, and development require energy resources. In this paper, we assess the investment trends in the global energy sector during, before and after financial crises of 2008 using two data sources: (1) Dealogic database providing cross‐border mergers and acquisitions (M&As), and (2) fDi Intelligence fDi Markets database providing greenfield (GF) foreign direct investments (FDIs). We highlight the changing role of China and compare its M&A and GF FDI activities to those of the United States, Germany, UK, Japan and others during this period. We analyze the investments along each segment of the energy supply chain of these countries to highlight the geographical origin and destination, sectoral distribution, and cross‐border M&As and GF FDI activities. Our paper shows that while energy accounts for nearly 25% of all GF FDI, it only accounts for 4.82% of total M&A FDI activity in the period 1996-2016. China's outbound FDI in the energy sector started its ascent around the time of the global recession and had accelerated in the post-recession phase. In the energy sector, the development of China's outbound cross‐border M&As is similar to USA or UK, located mostly in the developed countries in the west, while their outbound GF investments are spread across many countries around the world. Also, China's outbound energy M&As are concentrated in certain segments (extraction, and electricity generation) while their GF covers all segments of the energy supply chain.

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.

Motivated by Kurt's work [Filomat 30 (4) 921-927, 2016], we first consider a class of a new generating function for (p, q)-analog of Apostol type polynomials of order a including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order a. By making use of their generating function, we derive some useful identities. We also introduce (p, q)-analog of Stirling numbers of second kind of order v by which we construct a relation including aforementioned polynomials.

The aim of this article is to establish a new class of unified integrals associated with the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function.Some integrals involving trigonometric,generalized Bessel function and Struve functions are also indicated as special cases of our main results.further, with the help of our main results and their special cases, we obtain two reduction formulas for the Wright hypergeometric function.

In this paper, we develop the theory of the multiple q-analogue of the Heine’s binomial formula, chain rule and Leibnitz’s rule. We also derive many useful definitions and results involving multiple q-antiderivative and multiple q-Jackson’s integral. Finally, we list here multiple q-analogue of some elementary functions including trigonometric functions and hyperbolic functions. This may be a good consideration in developing the multiple q-calculus in combinatorics, number theory and other fields of mathematics.

In this paper we obtain some inequalities of Hermite-Hadamard type for composite convex functions. Applications for AG, AH-h-convex functions, GA, GG, GH-h-convex functions and HA, HG, HH-h-convex function are given.

In this paper we obtain some inequalities of Hermite-Hadamard type for composite convex functions. Applications for AG, AH-convex functions, GA, GG, GH-convex functions and HA, HG, HH-convex function are given. Applications for p, r-convex and LogExp functions are presented as well.

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.

The main goal of the present paper is to construct some families of the Carlitz’s q-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and investigate their some explicit properties and identities arising from the bosonic q-Volkenborn integral on ℤ_p. We then define the modified degenerate Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz’s q-Bernoulli polynomials with weight (α, β), the modified degenerate Carlitz’s q-Bernoulli polynomials with weight (α, β), the Stirling numbers of the first kind and second kind.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η- convex function. Moreover, our results include several new and known results as special cases.

This contribution considers an improved control scheme for three-phase two-stage grid-tied photovoltaic (PV) power system based on integral sliding mode control (ISMC) theory. The proposed control scheme consists of maximum power point tracking (MPPT), DC-Link voltage regulation and grid currents synchronization. A modified voltage-oriented maximum power point tracking (VO-MPPT) method based on ISMC theory is proposed for design of an enhanced MPPT under irradiation changes. Moreover, a novel DC-Link voltage control based on ISMC theory is proposed in order to achieve good regulation of DC-Link voltage over its reference. To inject the generated PV power into the grid with high quality, a voltage oriented control based on space vector modulation (SVM) and ISMC (VOC-ISMC-SVM) has been developed to control the grid currents synchronization. Numerical simulations are performed in Matlab/SimulinkTM environment in order to evaluate the proposed control strategy. In comparison with conventional control scheme, the developed control strategy provides an accurate MPP tracking with less power oscillation as well as a fast and an accurate DC-Link regulation under climatic conditions variations. Moreover, the transfer of the extracted power into the grid is achieved with high quality.

This article aims to identify the generating function of modi…ed Apostol type q-Bernoulli polynomials. With the aid of this generating function, some properties of modi…ed Apostol type q-Bernoulli polynomials are given. It is shown that aforementioned polynomials are q-Appell. Hence, we make use of these polynomials to have applications on q-Umbral calculus. From those applications, we derive some theorems in order to get Apostol type modi…ed q-Bernoulli polynomials as a linear combination of some known polynomials which we stated in the paper.

New q-series in the spirit of Jacobi have been found in a publication rst published in 1884 written in Russian and translated into English in 1928. This work was found by chance and appears to be almost totally unknown. From these entirely new q-series, fresh lattice sums have been discovered and are presented here.

In this paper, we revisit the q-states clock model for small systems. We present results for the thermodynamics of the q-states clock model from $q=2$ to $q=20$ for small square lattices $L \times L$, with L ranging from $L=3$ to $L=64$ with free-boundary conditions. Energy, specific heat, entropy and magnetization are measured. We found that the Berezinskii-Kosterlitz-Thouless (BKT)-like transition appears for $q>5$ regardless of lattice size, while the transition at $q=5$ is lost for $L<10$; for $q\leq 4$ the BKT transition is never present. We report the phase diagram in terms of $q$ showing the transition from the ferromagnetic (FM) to the paramagnetic (PM) phases at a critical temperature T$_1$ for small systems which turns into a transition from the FM to the BKT phase for larger systems, while a second phase transition between the BKT and the PM phases occurs at T$_2$. We also show that the magnetic phases are well characterized by the two dimensional (2D) distribution of the magnetization values. We make use of this opportunity to do an information theory analysis of the time series obtained from the Monte Carlo simulations. In particular, we calculate the phenomenological mutability and diversity functions. Diversity characterizes the phase transitions, but the phases are less detectable as $q$ increases. Free boundary conditions are used to better mimic the reality of small systems (far from any thermodynamic limit). The role of size is discussed.

A new framework in quantum chemistry has been proposed recently ("An approach to first principles electronic structure calculation by symbolic-numeric computation'' by A. Kikuchi). It is based on the modern technique of computational algebraic geometry, viz. the symbolic computation of polynomial systems. Although this framework belongs to molecular orbital theory, it fully adopts the symbolic method. The analytic integrals in the secular equations are approximated by the polynomials. The indeterminate variables of polynomials represent the wave-functions and other parameters for the optimization, such as atomic positions and contraction coefficients of atomic orbitals. Then the symbolic computation digests and decomposes the polynomials into a tame form of the set of equations, to which numerical computations are easily applied. The key technique is Grröbner basis theory, by which one can investigate the electronic structure by unraveling the entangled relations of the involved variables. In this article, at first, we demonstrate the featured result of this new theory. Next, we expound the mathematical basics concerning computational algebraic geometry, which are necessitated in our study. We will see how highly abstract ideas of polynomial algebra would be applied to the solution of the definite problems in quantum mechanics. We solve simple problems in "quantum chemistry in algebraic variety'' by means of algebraic approach. Finally, we review several topics related to polynomial computation, whereby we shall have an outlook for the future direction of the research.

Integral atmospheric dispersion models are used widely for flammable hazard and its risk analysis. There is a widespread belief that flammable distances from these models are conservative when flammable ranges are calculated using the 0.5 lower flammability limits (LFL) concentration threshold. This is erroneous. This paper traces through the development of these models and the research that led to the Birch Guidance. It shows that the 0.5 LFL is a necessary factor to transform the results of dispersion models designed for environmental assessment to applications to flammable hazard assessment in quiescent conditions. Current applications do not take account of turbulence due to wind, large and small obstructions, etc. A set of simple guidance is given in the paper to manage flammable hazards based on results from atmospheric dispersion models, including topics for future research.

In this paper we present experimental results concerning Acoustic Emission (AE) recorded during cyclic compression tests on two different kinds of brittle building materials, namely concrete and basalt. The AE inter-event times were investigated through a non-extensive statistical mechanics analysis which shows that their decumulative probability distributions follow q-exponential laws. The entropic index q and the relaxation parameter q  1=Tq, obtained by fitting the experimental data, exhibit systematic changes during the various stages of the failure process, namely (q; Tq) linearly align. The Tq = 0 point corresponds to the macroscopic breakdown of the material. The slope, including its sign, of the linear alignment appears to depend on the chemical and mechanical properties of the sample. These results provide an insight on the warning signs of the incipient failure of building materials and could therefore be used in monitoring the health of existing structures such as buildings and bridges.

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

In this paper, we introduce a new class of $(p,q)$-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for $(p,q)$-Fubini polynomials associated with $(p,q)$-Bernoulli polynomials, $(p,q)$-Euler polynomials and $(p,q)$-Genocchi polynomials and $(p,q)$-Stirling numbers of the second kind.

Any quantization maps linearly functions on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with symmetry group of the phase space. Covariant means that the quantization map intertwines classical (geometric operation) and quantum (unitary transformations) symmetries. Integral means that we use all ressources of integral calculus, in order to implement the method when we apply it to singular functions, or distributions, for which the integral calculus is an essential ingredient. In this paper we emphasize the deep connection between Fourier transform and covariant integral quantization when the Weyl-Heisenberg and affine groups are involved. We show with our generalisations of the Wigner-Weyl transform that many properties of the Weyl integral quantization, commonly viewed as optimal, are actually shared by a large family of integral quantizations.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

Despite all efforts, the treatment of breast cancer (BC) cannot be considered to be a success story. The advances in surgery, chemotherapy and radiotherapy have not been sufficient. Indeed, the accumulated experience clearly indicates that new perspectives and non-main stream approaches are needed to better characterize the etiopathogenesis and treatment of this disease. This contibution deals with how the new pH-centric anticancer paradigm plays a fundamental role in reaching a more integral understanding of the etiology, etiopathogenesis and treatment of this multifactorial disease. For the first time the armamentarium available for the treatment of the different types and phases of BC is approached here from a Unitarian perspective based upon the hydrogen ion dynamics of cancer. The wide-ranged pH-related molecular, biochemical and metabolic model is able to embrace most the fields and subfields of breast cancer pathology. This single and integrated approach allows to advance a unidirectional program to treatment. Further efforts in this line are likely to first improve the therapeutics of each subtype of this tumor, then every phase of the disease and finally every individual patient.

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.

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.

In this study, a mixed rule of degree of precision nine has been developed and implemented in the field of electrical sciences to obtain the instantaneous current in the RLC- circuit for particular value .The linearity has been performed with the Volterra’s integral equation of second kind with particular kernel . Then the definite integral has been evaluated through the mixed quadrature to obtain the numerical result which is very effective. A polynomial has been used to evaluate Volterra’s integral equation in the place of unknown functions. The accuracy of the proposed method has been tested taking different electromotive force in the circuit and absolute error has been estimated.

High efficacy LED lamps combined with adaptive lighting control and greenhouse integrated photovoltaics (PV) could enable the concept of year-round cultivation and become a feasible option even in the harsh climate of the Nordic countries. Meteorological satellite data of this region was analyzed in a parametric study to evaluate the potential of these technologies. The generated maps showed monthly average temperatures fluctuating from -20°C to 20°C throughout the year. The natural photoperiod and light intensity also changed drastically, resulting in monthly average daily light integral (DLI) levels ranging from 45-50 mol·m-2·d-1 in summer and contrasting with 0-5 mol·m-2·d-1 during winter. To compensate, growth room cultivation independent from outdoor conditions could be used in winter. Depending on the efficacy of the lamps, the electricity required for sole-source lighting at 300 µmol·m-2·s-1 for 16 hours would be between 1.4 and 2.4 kWh·m-2·d-1. Greenhouses with supplementary lighting could help start the cultivation earlier in spring and extend it further into autumn. The energy required for lighting highly depends on several factors such as the natural light transmittance, the light threshold settings and the lighting control protocol, resulting in electric demands between 0.6 and 2.4 kWh·m-2·d-1. Integrating PV on the roof or wall structures of the greenhouse could offset some of this electricity, with specific energy yields ranging from 400 to 1120 kWh·kWp-2·yr-1 depending on the region and system design.

The prim objective of commenced article is to determine q-sumudu transforms of a product of unified family of q-polynomials with basic (or q-) analogue of fox’s H-function and q-analog of I-functions. Specialized cases of the leading outcome are further evaluated as q-sumudu transform of general class of q-polynomials and q-sumudu transforms of the basic analogues of Fox’s H-function and I-functions.

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

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are offered to detail such systems. Method: ASA and PATHINT/PATHTREE have been effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Applications are described for COVID-19. Results: Results of detailed calculations have led to new results and insights not previously obtained. Conclusion: These 3 applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.

This paper deals with the study of the existence and non existence of solutions of a three parameter's family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the $\alpha$-Riemann-Liouville fractional derivative, with $\alpha \in (1,2]$. In order to deduce the existence and non existence results, we first study the linear equation, by deducing the main properties of the related Green's functions. We obtain the optimal set of parameters where the Green's function has constant sign. After that, by means of the index theory, the nonlinear boundary value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained results.

In this paper, we consider the zero distributions of q-shift monomi-als and difference polynomials of meromorphic functions with zero order, that extends the classical Hayman results on the zeros of differential poly-nomials to q-shift difference polynomials. We also investigate problem of q-shift difference polynomials that share a common value.

Methods of path integrals are used to develop multi-factor probabilities of bid-ask variables for use in high-frequency trading (HFT). Adaptive Simulated Annealing (ASA) is used to fit the nonlinear forms so developed to a day of BitMEX tick data. Maxima algebraic code is used to develop the path integral codes into C codes, and sampling code is used for the fitting process. After these fits, the resultant C code is very fast and useful for forecasting upcoming ask, bid, midprice, etc., when narrow and wide windows of incoming data are used. A bonus is the availability of canonical momenta indicators (CMI) useful to forecast direction and strengths of these variables.

Our aim in this paper is to establish some new Hermite-Hadamard- Mercer type integral inequalities by utilizing the fractional proportional-integral operators.For this purpose, Hermite-Hadamard-Mercer inequalities for di¤er- antiable mappings whose derivatives in absolute value are convex.

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.

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.

In this paper, we study the p-adic integral representation on Z_p of q-Bernoulli numbers arising from two variable q-Bernstein polynomials and investigate some properties for the q-Bernoulli numbers. In addition, we give some new identities of q-Bernoulli numbers.

Some refinements and reverses of the Fejer's inequality for convex functions are given.

The main purpose of this paper is to introduce a new class of $q$-Hermite-Fubini numbers and polynomials by combining the $q$-Hermite polynomials and $q$-Fubini polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive $q$-integers. Also, we establish some relationships for $q$-Hermite-Fubini polynomials associated with $q$-Bernoulli polynomials, $q$-Euler polynomials and $q$-Genocchi polynomials and $q$-Stirling numbers of the second kind.

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.

Spatial planning holds a key role in preventing or mitigating the impacts of climate change on both cities and rural areas, taking a forward-thinking and holistic approach to urban and regional development. As such, spatial planning deals with challenges occurring at different scales and across sectors. The international literature points out the need for horizontal and vertical cooperation to tackle climate change impacts. While there is abundant knowledge regarding the challenges related to climate change at different spatial levels, procedural integration into planning frameworks and practice is currently under-researched. This paper presents a novel theoretical framework that integrates various steps towards a holistic, integrative and adaptive climate proofing process. An iterative process was used for conceptual development, based on literature review followed by external feedback meetings and two workshops with the core team of planning experts responsible for exchange across federal states. By specifically addressing the challenges relating to cross-regional and cross-sectoral planning, this novel framework attempts to (i) facilitate a hierarchy of measures, (ii) maximise co-benefits for various adaptation purposes and climate change mitigation and (iii) foster the long-term institutionalisation of integrative processes across sectors, planning areas and policy levels.

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,

This paper presents Chebyshev Type inequalities for the Riemann-Liouville variable-order fractional integral operator using two synchronous functions on the set of real numbers. It is the first result of its kind in the current literature using variable-order Riemann-Liouville fractional integral operator. Some special cases for the result obtained in the paper are discussed.

In this paper we provide amongst others some simple error bounds in approximating the weighted Riemann-Stieltjes integral $\int_{a}^{b}f\left(t\right) g\left(t\right) dv\left(t\right) $ by the use of three points formula \begin{equation*} f\left(b\right) \int_{c}^{b}g\left(s\right) dv\left(s\right) +f\left(a\right) \int_{a}^{d}g\left( s\right) dv\left( s\right) -f\left(x\right) \int_{c}^{d}g\left(t\right) dv\left(t\right) \end{equation*} where $x,$ $c,$ $d\in \left[a,b\right],$ $g,$ $v:\left[a,b\right] \rightarrow \mathbb{C}$ under bounded variation and Lipschitzian assumptions for the function $f$ and such that the involved Riemann-Stieltjes integrals exist.

In this paper, we investigate a new $q$-analogue of the higher order degenerate Changhee polynomials and numbers, which are called the Witt-type formula for the $q$-analogue of degenerate Changhee polynomials of order $r$. We can derive some new interesting identities related to the degenerate $(h,q)$-Changhee polynomials and numbers.

This article discusses the outcomes of a quantitative analysis of the competitiveness of grain and its recycling in the countries-members of the Eurasian Economic Union (EEU) through econometric panel data models. The analysis is based on the data of public authorities’ statistics of the countries-members of the EEU, as well as the United Nations Comtrade Database which is a repository of official international trade statistics. The results of the analysis allow to assess the level of competitiveness of produced agro-food products in the countries-members of the EEU and determine the extent to which various factors affect it. The research conclusions can be used to develop and adjust the agreed with the agro-food policy in the EEU.

In this paper we provide some bounds for the error in approximating the Riemann-Stieltjes integral $\int_{a}^{b}f (t) du (t)$ by the generalized trapezoidal rule \begin{equation*} \left[ u\left( b\right) -u\left( x\right) \right] f\left( b\right) +\left[ u\left( x\right) -u\left( a\right) \right] f\left( a\right) \end{equation*} under various assumptions for the integrand $f$ and the integrator $u$ for which the above integral exists. Applications for continuous functions of selfadjoint operators and unitary operators in Hilbert spaces are provided as well.

This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are offered to detail such systems. Method: ASA and PATHINT/PATHTREE have been effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Applications are described for COVID-19. Results: Results of detailed calculations have led to new results and insights not previously obtained. Conclusion: These 3 applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.

β-Ga2O3 crystal have attracted great attentions in the fields of photonics and photoelectronics because of its ultra wide-band gap and high thermal conductivity. Here, pure β-Ga2O3 crystal was successfully grown by optical floating zone (OFZ) method, and used as saturable absorbers to realize a passively Q-switched all-solid-state 1μm laser for the first time. By placing the as-grown β-Ga2O3 crystal into the resonator of Nd:GYAP solid-state laser, a Q-switched pulses at the center wavelength of 1080.4 nm are generated under a output coupling of 10%. The maximum output power is 191.5 mW while the shortest pulse width is 606.54 ns, and the maximum repetition frequency is 344.06 kHz. The maximum pulse energy and peak power are 0.567 μJ and 0.93 W, respectively. Our experimental results show that β-Ga2O3 crystal has great potential in the development of all-solid-state 1μm pulsed laser.

In this work, we establish some new Hermite-Hadamard type inequalities for convex functions via conformable fractional integral. Moreover, we show that through the conformable fractional integral we can find some new Hermite-Hadamard type inequalities for convex functions via the classical integrals.

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

The statistics of grain displacements probability distribution function (pdf) during the shear of a granular medium displays an unusual dependence with the shear increment upscaling as recently evinced [Phys. Rev. Lett. 115 238301 2015]. Basically, the pdf of grain displacements has clear nonextensive ($q$-Gaussian) features at small scales but approaches to Gaussian characteristics at large shear window scales -- the granulence effect. Here, we extend this analysis studying a larger system (more grains considered in the experimental setup) which exhibits a severe shear band fault during the macroscopic straining. We calculate the pdf of grain displacements and the dependency of the $q$-statistics with the shear increment. This analysis have shown a singular behavior of $q$ at large scales, displaying a non-monotonic dependence with the shear increment. By means of an independent image analysis, we demonstrate that this singular non-monotonicity could be associated with the emergence of a shear band within the confined system. We show that the exact point where the $q$-value inverts its tendency coincides with the emergence of a giant percolation cluster along the system, caused by the shear band. We believe that this original approach using Statistical Mechanics tools to identify shear bands can be a very useful piece to solve the complex puzzle of the rheology of dense granular systems.

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.

In this paper, we investigate a new $q$-analogue of the higher order degenerate Changhee polynomials and numbers, which are called the Witt-type formula for the $q$-analogue of degenerate Changhee polynomials of order $r$. We can derive some new interesting identities related to the degenerate $(h,q)$-Changhee polynomials and numbers.

In this article, a new class of $q$-Hermite based unified Apostol type polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating methods. We also introduce $q$-analog of Stirling numbers of second kind of order $\nu$ by which we construct a relation including aforementioned polynomials.

In this article, we introduce a relatively new concept of multi-valued (θ;R)-contractions and utilize the same to prove some xed point results for a new class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type.

Background: Since circa 1980, a model of neocortical interactions, Statistical Mechanics of Neocortical Interactions (SMNI) has been successful in calculating many experimental phenomena, including fits to electroencephalographic (EEG) data in attention tasks, using an importance-sampling code Adaptive Simulated Annealing (ASA). The SMNI model is developed in the context of classical path-integrals, which affords intuitive insights as well as direct numerical benefits, e.g., using the effective Action as a a cost/objective function for parameter fits to data. Objective: Previous authors have fit affective EEG data to neural-network models. This project seeks to use models based on physics and biology to fit this same data. Previous work showed improvements in fits to EEG for attention states; this project extends these methods to affective states. Method: Path integrals are used in both classical and quantum contexts. Classical path integrals are used to define a cost/objective function to fit data, and quantum path integrals are used to derive a closed-form analytic expression for Ca-ion waves in the presence of a magnetic vector potential which is generated by highly synchronous neuronal firings which give rise to EEG. ASA is used to fit EEG data. Results: The mathematical-physics and computer parts of the study are successful, in that cost/objective functions used to fit EEG data using these models are consistent with previous work published by other authors. However, since the SMNI model includes these quantum effects, this is another reason to continue examining these issues. The results here are consistent, not better, than previous work using neural-network models, albeit only one parameter was used here, instead of multiple filters and kernels used previously on such data. Conclusion: Although these quantum effects are highly speculative, explicit calculations have shown them to be consistent with experimental data, at least to date. The current supercomputer project extends this model to affective/emotion data. Results from several authors using neural-network approaches at individual electrode sites show some predictive capabilities; the results given here are consistent with these other results. However, since the SMNI model includes these quantum effects, this is another reason to continue examining these issues.

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.

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.

In this paper, we study the third order semilocal convergence of the Newton-like method for finding the approximate solution of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis under ω-continuity condition, which is weaker than the Lipschitz and Hölder continuity conditions. Second, we apply our approach to solve Fredholm integral equations, where the first derivative of involved operator not necessarily satisfy the Hölder and Lipschitz continuity conditions. Finally, we also prove that the R-order of the method is 2p + 1 for any p $\in$ (0,1].

In this paper, we have established some new bounds of Fejér type Hermite-Hadamard inequality for k−fractional integrals involving r−times differentiable preinvex functions. It is noteworthy that in the past there was no weighted version of left and right sides of the Hermite-Hadamard inequality for k-fractional integrals for generalized convex functions available in literature.