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 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.

The Polyurethane (PU) mixture is a high−performance engineering material with different dynamic properties compared to a hot−mixed asphalt mixture (HMA). This paper analyzed whether the Kramers−Kronig (K−K) relation and thermo−rheological simple properties were applicable to the PU mixture. Based on the result discussion, the PU mixture exhibited thermo−rheological simple properties within the test conditions. The time−temperature superposition principle (TTSP) was applicable for the PU mixture to construct the dynamic modulus master curve using the standard logistic Sigmoidal (SLS) model, the generalized logistic sigmoidal (GLS) model, and the Havriliak−Negami (HN) model. The Hilbert integral transformed SLS and GLS models for the phase angle can accurately fit the measured phase angle data with newly fitted shift factors and predict the phase angle within the viscoelastic range. The Core−Core and black space diagrams both displayed single continuous smooth curves, which can be utilized to characterize the viscoelastic property of the PU mixture. The K−K relation is applicable for the PU mixture to obtain the phase angle master curve model, storage modulus, and loss modulus from the complex modulus test results. The phase angle of the PU mixture cannot be derived from the dynamic modulus data and currently needs to be derived from the laboratory measurement.

In the full load operating range, wind turbines typically use pitch control to maintain rotor speed and output power at their rated values to guarantee the whole system’s safety. Blade pitch actuators are subject to physical limitations and safety requirements, which imposes strict constraints on pitch angle’s amplitude and rate of change. These constraints will bring windup problem to the integral part of the pitch controller. It leads to deterioration of the pitch control system’s performance or even the instability problem, especially for large-scale turbines operating in extreme uncertain wind conditions or suffering from cyber attacks. This paper designs an anti-windup robust pitch angle control strategy to deal with pitch rate constraint issue to enhance the security of control system. First, to facilitate controller design, a filtered tracking error technique is employed to transform the nonaffine form into an affine one. Subsequently, a feedback robust controller based on UDE is developed to handle the model’s uncertainty and external disturbances. To address the issue of integral saturation in the pitch system and guarantee its safety, an elliptical bounded constraint is integrated into the designed UDE strategy. This bounded UDE controller can improve the stability of power generation quality, reduces the mechanical loads on components and enhance the whole system’s safety. Finally, the effectiveness of the proposed scheme is verified on the Wind Turbine Blockset platform in Matlab/Simulink. It can achieve better performance than the traditional method.

We study the tight focusing properties of generic bright and dark HyOPS beams in the presence of primary coma. The role of the polarization singularity index and handedness of the polarization of the HyOPS beams on the focused structure has been discussed. Results have been presented for the total intensity, component intensities, and component phase distributions for left-, and right-handed bright and dark star and lemon types singularities. The presence of primary coma distorted the focal plane intensity distributions for both positive and negative index generic C-points. Coma is known to disturb the circular symmetry of the focal plane intensity distribution. Similarly in tight focusing polarization is known to disturb the symmetry. Therefore, a beam with structured and inhomogeneous polarization distribution tightly focused under the influence of coma is a fit case to study. It is found that the presence of primary coma aberration in the focusing system produces a positional shift of the high-intensity peaks and a reduction of the intensity on one side of the center. As the strength of the primary coma increases, the focal plane intensity distributions shift more and more toward the right from the initial position. Unlike the scalar vortex case, in the case of HyOPS beams, the focal plane intensity distribution undergoes rotation, as the helicity of the HyOPS beams is inverted, in addition to shifting. All the component phase distributions are found to be embedded with phase vortices of charge ±1.

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.

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

In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann-Liouville fractional integral. Then the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied for derivation of its properties. In particular, we characterize its domain, null-space, and projector operator, establish the interrelations between its different realisations, and present a generalized fractional Taylor formula involving the generic fractional derivative. Then we consider the fractional relaxation equation containing the generic fractional derivative, derive a closed form formula for its unique solution, and study its complete monotonicity.

In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method based on the weakly singular boundary integral equation, the quadrature techniques, dedicated for the weakly singular and regular integrals, are applied in the method. A new formula for the generation of collocation points is suggested to take the full advantage of the multi-patch technique. The generated collo-cation points are essentially inside the patches without any correction. If the boundary conditions are assumed to be continuous in every patch, no collocation point lies on the discontinuous boundaries, thus simplifying the implementation. The multi-patch WSIGABEM is verified by the simple examples with analytical solutions. The feature of the present multi-patch WSIGABEM is investigated by the comparison with the traditional IGABEM. Furthermore, the combination of the present multi-patch WSIGABEM and the particle swarm optimization algorithm results in a shape optimization method in two-dimensional elastostatics. By changing some specific control points and their weights, the shape optimizations of the fillet corner, the spanner and the arch bridge are verified to be effective.

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.

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.

One of the rapidly developing research areas is the creation of systems. which are commonly referred to as cyberphysical complexes. In such systems, devices and complexes interact with a completely different physical nature. The role of a person in such systems usually consists in the formation of final tasks for “artificial intelligence” and executive mechanisms. The functioning of actuators is controlled by accurate information systems.

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 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 this work, an improved collocation method based on the Bernoulli polynomials is presented to solve the Volterra integral equation (VIE) of the second kind. The main idea of the proposed method is to improve the results of the classic Bernoulli collocation method (BCM) by dividing the interval into some sub-intervals and considering the collocation points on each of them. Here, the zeros of the shifted Chebyshev polynomials (SCPs) are considered as collocation points. Then, BCM is applied step by step from the first sub-interval to the last one. By this process, a system of algebraic equations is attained for each sub-interval that could be easily solved. Convergence of the scheme is analyzed. For the purpose of demonstrating the validity, applicability, and efficiency of the suggested scheme several numerical examples are provided. Numerical results illustrate that the accuracy of the improved Bernoulli collocation method (IBCM) is more than BCM.

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

The purpose of the research is to investigate the unique solvability of a nonlocal boundary value problem for a loaded equation of parabolic-hyperbolic type in a special domain. Methods: Using representations of a general regular solution, the existence and uniqueness of the problem posed is proved. Results: A new method for proving the unique solvability of nonlocal boundary value problems for one loaded equation of mixed type in a special domain has been formed and developed. Conclusions: The obtained results make it possible to solve some problems of genetics, immunology, transonic gas dynamics and thermal physics, which are associated with displacement.

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 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.

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.

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.

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.

The aim of this research is to present both a sensorless control and a torque derating algorithm in the overload region of a permanent magnet motor for e-bike. First the theoretical backgrounds and the field oriented control are presented. Then a sensorless control, based on the back-emf estimation with a second order generalized integral flux observer for permanent magnet motor, has been designed. The second order generalized integral flux observer is an adaptive filter which can eliminate the DC offset and strongly attenuate the harmonics of the estimated rotor flux. The algorithms have been simulated and then validated by means of tests on a permanent magnet motor for e-bike.

This work presents emission line flux and kinematic structure mapping based on IFU data of the planetary nebulae Abell 30 (A30). The IFU has a field of view (FoV) of 16" x 12.3" and was used to partially cover knots J1 and J2, and completely cover knots J3 and J4 of A30. Our emission line flux map shows recombination species C II, C III, He I, O II as well as forbidden line species [O III], [Ne III] and [Ne IV] of high excitation level are all distributed in different parts of the knots. The kinematic structure shows considerable variation in both the velocities and spatial locations of these knots with positive and negative velocity excursions from the systematic value. Forbidden line species [O III], [Ne III] are distributed in both knots J3 and J4 but they are travelling at different speeds in opposite directions. Despite variation in distribution of the species, the velocities of [Ne IV] and [O III] are similar and travelling in the same direction while the other species [Ne III], He I, and O II share similar velocity of 200kms−1 up in the opposite direction. The complexity of distribution and kinematic structure of the knots revealed in this work indicates a strong tendency towards the hypothesis of multiple triggering events in the past history of A30.

The study of coherent vortices remains an urgent field of singular optics of vortex beams. In this paper, coherent properties of partially coherent vortex Bessel—Gaussian optical beams propagating through a uniform medium (free space) or a turbulent atmosphere are examined theoretically. The consideration is based on analytical solution of the equation for the transverse second-order mutual coherence function of the field of a partially coherent optical radiation in a turbulent atmosphere. For the partially coherent Bessel—Gaussian beam, the second-order mutual coherence function of the source field is taken as a Gaussian Shell-model. In this approximation, we analyze the behavior of the coherence degree and the integral coherence scale of these beams as a function of the propagation pathlength, propagation conditions, and beam parameters, such as the radius of the Gauss factor of the beam, parameter of the Bessel factor of the beam, topological charge, and correlation width of the source field of partially coherent radiation. In addition, the integral coherence scale of the partially coherent vortex Bessel—Gaussian beam is compared with that of the partially coherent Gaussian beam. It is found that as a partially coherent vortex Bessel—Gaussian beam propagates through a turbulent atmosphere, there appear not two (as might be expected: one due to atmospheric turbulence and another due to partial coherence of the source field), but only one ring dislocation of the coherence degree (due to the simultaneous effect of both these factors on the optical radiation). In addition, it is shown that the dislocation of the coherence degree that affects significantly the beam coherence level is formed only for beams, for which the coherence width of the source field is larger than the diameter of the first Fresnel zone.

Recent research on fractional order control laws has introduced the fractional calculus concept into the field of control engineering. As described herein, we apply fractional order LQR control to a current-controlled attractive-force type magnetic levitation system, which is a strongly nonlinear and unstable system, to investigate its control performance through experimentation. First, to design the controller, a current-controlled attractive-force type magnetic levitation system expressed as an integer-order system is extended to a fractional order system expressed using fractional order derivatives. Then target value tracking control of levitated objects is achieved by adding states, described by the integrals of the deviation between the output and the target value, to the extended system. Next, a fractional order LQR controller is designed for the extended system. For state-feedback control such as fractional order servo LQR control, which requires information of all states, a fractional order state-observer is configured to estimate fractional order states. Simulation results demonstrate that fractional order servo LQR control can achieve equilibrium point stabilization and enable target-value tracking. Finally, to verify the fractional order servo LQR control effectiveness, experiments using the designed fractional order servo LQR control law are done with comparison to conventional integer-order servo LQR control.

We obtain some generalised Minkowski-type integral formulas for compact Riemannian (resp. spacelike) hypersurfaces in Riemannian (resp. Lorentzian) manifolds admitting an arbitrary vector field that we assume to be timelike in the case where the ambient space is Lorentzian. Some of these formulas generalize existing formulas in the case of conformal and Killing vector fields. We apply these integral formulas to obtain interesting results concerning the characterization of such hypersurfaces in some particular cases such as when the ambient space is Einstein admitting an arbitrary (in particular, conformal or Killing) vector field, and when the hypersurface has constant mean curvature.

In this article, the multitouch option, also called the n  touch option (or the “baseball” option when n  3 ) is analyzed and valued in closed form. This is a kind of barrier option that sets a gradual knockout / knock-in mechanism based on the number of times the underlying asset has crossed a predefined barrier in various time intervals before expiry. The higher the number of predefined time intervals during which the barrier has been touched, the lower the value of a knock-out contract at expiry, and conversely for a knock-in one. Multitouch options can be viewed as an extension of step barrier options, preserving the ability of the latter to adjust the exposure to risk over time, while eliminating the notorious danger of “sudden death” that holders of step barrier options are faced with. Unlike occupation time derivatives, the payoff at expiry does not depend on the amount of time spent outside the authorized range, but on the number of passages beyond the authorized range.

The article considers an internal boundary value problem of the distribution of an electrostatic field in a lens formed by two identical semi-infinite circular cylinders coaxially located inside an infinite external cylinder. The problem is reduced to solving a system of singular Wiener-Hopf integral equations, which is further solved by the Wiener-Hopf method using factorized Bessel functions. Solutions to the problem for each region inside the infinite outer cylinder are presented as exponentially converging series in terms of eigenfunctions and eigenvalues.

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 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.

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 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.

Monogenity is a classical area of algebraic number theory that is very actively researched even today. This paper is a collection of the results obtained during the last few years in this area. Several of these results were presented at the series of online conferences "Monogenity and power integral bases".

Covariant integral quantization with rotational symmetry SO(3) is established for the quantum motion on this group manifold, or, alternatively, for Gabor signal analysis on this group. We revisit the action of the related (non-unitary) Weyl-Gabor operator on the Hilbert space of square integrable functions on SO(3) and disclose a set of various properties. By selecting weight functions on the corresponding discrete-continuous phase space, one derives related coherent states and Wigner transform.

In this paper we suggest a first ever construction of fractional integral and differential operators based on signed measures including a vector-valued case. The study focuses on constructing the fractional power of the Riemann-Stieltjes integral with a signed measure, using semigroup theory. The main result is a theorem that provides the exact form of a semigroup for the Riemann-Stieltjes integral with a measure having a countable number of extrema. The article provides examples of semigroups based on integral operators with signed measures and discusses the fractional powers of differential operators with partial derivatives.

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 $$ \begin{split} n^{2m+1}+1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{N}}[n],\\ n^{2m+1}-1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{Z}_{>0}}[n],\\ n^{2m+1}&=\sum_{r=0}^{m}A_{m,r}\sum_{k=1}^{n} k^r(n-k)^r\\ &=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1} k^r(n-k)^r. \end{split} $$

Circles, semicircles and its derived circular sectors are ubiquitous both in human creations and in the natural realm. However, mathematically speaking they have always represented a certain level of enigma or even mysticism since ancient times for being such a perfect shape that enclosed the irrational value that we now call π. Such figure was relatively unknown until the seventeenth century; polymaths like Guarini even equated it, after so many centuries, to the Archimedes fraction of 22/7 or sometimes 25/8 which, giving a value 3.125 introduces a considerable degree of error; Eventually, Lambert had to demonstrate, well advanced the eighteenth century that π was actually an irrational number. In recent years, the author has worked with sections of spheres and other curved bodies as related to radiative heat transfer and applied to the finding of form factors pertaining to such special geometries, to the point of defining new postulates. The main theorems so far enunciated refer to the radiative exchange between circles and half disks, but recently the possibility to treat circular sectors has arrived, thanks to the research already conducted in which, by virtue of Cabeza-Lainez first postulate, we are able to know the form factor of any spherical segment over itself, discarding in this way, the former uncertainties that appeared when dealing with the inner side of spherical surfaces. As it is known, to find the exact expression of the configuration factor by integration alone is mostly a tedious task and the results are not readily available as it has been frequently proved. In the said problem of the circular sectors, the author could integrate the first two steps of the basic formulation for radiant exchange. Subsequently, the novelty of the procedure lies in introducing a finite differences approximation for the third and fourth integrals which still remain unsolved, once that we have been able to find the first and second integrals of the form factor. This possibility had not been identified by former research. This sole output provides us with an ample variety of scenarios previously unforeseen. As a consequence, we would be able to analyze with more precision but freely, the spatial transference of radiant heat for figures composed of circular sectors such as spherical sectors like quarters or octaves of spheres. Many architectural, industrial or aircraft modules and objects fall into this category. We already know that spherical shapes cannot be discretized with any accuracy as there are no spherical tiles of the same size, therefore we hope to overcome with our finding a persistent extent of error. In this situation we are able to reduce a considerable amount of hindrances in the progress of thermal radiation science, due to the advances hereby presented. As the new formulations found can be adapted for algorithms, they will be integrated in simulation procedures with significant avail. Our achievement may be considered timely in the effort invested to square the elements of mathematics for radiative transfer. Important sequels are already being derived for radiation in the entrance to tunnels, aircraft design, low-energy building construction and also lighting and HVAC industries to cite just a few.

An advanced driver-assistance system (ADAS) is critical to driver-vehicle-interaction systems. Driving behaviour modelling and control significantly improves the global performance of ADAS. A haptic assistive system assists the driver by providing a specific torque on the steering wheel according to the driving-vehicle-road profile to improve the steering control. However, the main problem is designing a compensator dealing with the high-level uncertainties in different driving scenarios with haptic driver assistance, where different personalities and diverse perceptions of drivers are considered. If not properly accounted for, these differences can lead to poor driving performance. This paper focuses on designing a data-driven model-free compensator considering various driving behaviours with a haptic feedback system. A back propagation neural network (BPNN) models driving behaviour based on real driving data (speed, acceleration, vehicle orientation, and current steering angle). Then using the genetic algorithm (GA) and the integral time absolute error (ITEA) criterion to optimize multiple PID compensation parameters for various driving behaviour (such as speeding/braking, lane-keeping and turning), which are then be combined by the fuzzy logic to provide different driving commands. An experiment was conducted with 5 participants in a driving simulator. During the second experiment, seven participants drove in the simulator to evaluate the robustness of the proposed combined GA-PID offline and the Fuzzy-PID controller applied online. The experiment results evaluated the ITAE of lateral displacement and yaw angle, during various driving behaviour. The results validated the proposed method by significantly enhancing the driving performance.

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.

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 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 our previous published papers, considering 3 large atomic gravitational constants assumed to be associated with weak, strong and electromagnetic interactions, we have proposed the existence of a nuclear charge of magnitude, e_n=2.95e and developed a nuclear mass formula associated with strong and weak interactions having 4 simple terms and only one energy coefficient. Two important assumptions are, there exists a weak fermion of rest energy 585 GeV and strong coupling constant is the squared ratio of electromagnetic charge and nuclear charge. The aim of this paper is associated with understanding the mystery of quantum of magnetic flux, Planck’s quantum radiation constant and Reduced Planck’s constant. Proceeding further, quark charges, strong coupling constant, nuclear stability, nuclear binding energy, medium and heavy atomic X-ray levels and celestial magnetic moments can be understood in a unified approach. It may also be noted that, by considering integral nature of elementary particle masses, it seems possible to understand the discreteness of angular momentum. Considering our proposed e_n=2.95e=3e as a characteristic nuclear charge, it seems possible to understand the integral nature of quarks electromagnetic charge. With this idea, neutron, proton and pions decay can be understood very easily. In all the cases, up quark of charge (±2e) seems to play a crucial role with the internal transformation of down quark of charge (±e) and external observable elementary basic elementary particles. It needs further study at fundamental level.

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.

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 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.

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.

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.

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.

We delve into nonrelativistic quantum electrodynamics within a background magnetic field, ensuring gauge invariance via a vector potential. Our exploration extends to the Lagrangian, which incorporates electron self-interactions and electromagnetic field interactions. Through the path integral formalism, we elucidate the effective action, with a specific focus on the photon propagator and screening effects. Examining density and current components reveals Laurent expansions in the hydrodynamic limit. The equations of motion in real space are derived, leading to discussions on phenomena such as Poiseuille-like flow and the Navier-Stokes equation. To ground our theoretical framework at practical contexts, we consider applications such as the fluid dynamics at binary star systems. Depending on the velocity of the expelled fluid, our analysis allows for both nonrelativistic and relativistic treatments, providing a versatile tool for understanding the intricacies of fluid behavior at astrophysical scenarios. Additionally, we recognize that at the presence of a magnetic field, magnetohydrodynamics becomes crucial. While our current focus is at nonrelativistic quantum electrodynamics, the insights gained here contribute to a broader understanding, offering a comprehensive foundation for quantum electrodynamics analysis at diverse physical systems.

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