We investigate the influence of a self-propelling, out-of-equilibrium active particle on generalized elastic systems, including flexible and semiflexible polymers, fluid membranes, and fluctuating interfaces, while accounting for long-ranged hydrodynamic effects. We derive the fractional Langevin equation governing the dynamics of the active particle, as well as that of any other passive particle (or probe) bound to the elastic system. Our study explores the diffusional behavior emerging for both the active particle and a distant probe.

The fractional advection-dispersion equation FADE plays an important role, especially in explaining the process of solute-transport in natural porous media with different degrees of heterogeneity. However, studies of the flow and transport of contaminants in the underground environment are based on the knowledge of many functional parameters of the subsoil. The delay factor caused by nonlinear absorption is one of these parameters inheriting significant ambiguities in its estimation in heterogeneous media. In the study, a fractional advection-dispersion FADE model was developed by the implicit Euler method, based on a Grunwald and Caputo-Liousville approximation to explicitly evaluate and simulate the transport mechanism of contaminants in media with unsaturated porous materials subjected to a nonlinear sorption model. Better solute mass retention was observed for fractional advection-dispersion FADE model. Moreover, the absorption parameter of the retardation coefficient has a better impact on the motion of the solute in a saturated porous medium. In other words, it has a significant effect on the dispersion of pollutants in aquifers. This study highlights the need to characterize the aquifer to predict solute transport in porous media.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudrayshov method for the exact analytical solution. The modified Kudrayshov method converts the nonlinear partial differential equation to algebraic equations, as a result of various steps, which on solving the so obtained equation systems yields the analytical solution. By this way various exact solutions including complex structures are found and drawn their behaviour in complex plane by Maple to compare the uniqueness of solutions.

In our latest studies with the help of the self-similar Ansatz we derived new type of 1 solutions for the regular diffusion equation which are much more complex than the well-known 2 Gaussian and error functions. These solutions contain additional Kummer’s M and Kummer’s U 3 functions with quadratic argument. In the present treaties we perform an analogous analysis for the 4 regular diffusion equation which has a complex diffusion coefficient. Formally, it is equivalent to 5 the free Schrödinger equation however it is far from being trivial how the solutions can be given 6 quantum mechanical interpretation. We investigate both the one dimensional Cartesian and the 7 spherical symmetric equations. We find solutions which fulfill the L2 integrability criteria therefore 8 might have quantum mechanical relevance in the future.

Unidirectional flow of a fluid with pressure-dependent viscosity through a porous structure is considered when the viscosity-pressure relationship is an exponential function of a pressure power function in order to investigate effects of the viscosity-pressure relation on the flow characteristics. The flow is governed by the generalized Brinkman’s equation with constant permeability, and a model flow domain of flow down an inclined porous channel is chosen for the sake of studying flow behaviour. Although the current work considers flow in a constant permeability porous structure, it does represent a first step in studying the more general, flow through a variable permeability porous channel. The arising governing equations are solved numerically using MATLAB and the flow is simulated to illustrate the effects of fluid properties as well as flow and medium parameters on the velocity profiles and shear stress.

The authors intend to establish new oscillation criteria for a class of generalized third order functional difference equation of the form \begin{equation}{\label{eq01}} \Delta_{\ell}\left(a_2(n)\left[\Delta_{\ell}\left(a_1(n)\left[\Delta_{\ell}z(n)\right]^{\beta_1}\right)\right]^{\beta_2}\right)+q(n)f(x(g(n)))=0, ~~n\geq n_0, \end{equation} where $z(n)=x(n)+p(n)x(\tau(n))$. We also present sufficient conditions for the solutions to converges to zero. Suitable examples are presented to validate our main results.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

In wireless sensor networks (WSNs), each sensor node can estimate the global parameter from the local data in distributed manner. This paper proposed a robust diffusion estimation algorithm based on minimum error entropy criterion with self-adjusting step-size, which are referred to as diffusion MEE-SAS (DMEE-SAS) algorithm. The DMEE-SAS algorithm has fast speed of convergence and is robust against non-Gaussian noise in the measurements. The detailed performance analysis of the DMEE-SAS algorithm is performed. By combining the DMEE-SAS with diffusion minimum error entropy (DMEE) algorithms, an Improving DMEE-SAS algorithm is proposed, in non-stationary environment where tracking is very important. The Improving DMEE-SAS algorithm can avoid insensitivity of the DMEE-SAS algorithm due to the small effective step-size near the optimal estimator, and obtain a fast convergence speed. Numerical simulations are given to verify the effectiveness and advantages of these proposed algorithms.

In this paper, we prove some random fixed point theorems for generalized random $\alpha-\psi-$contractive mappings in a Polish space and, as some applications, we show the existence of random solutions of second order random differential equation.

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

Drowsiness is a main factor for various costly defects, even fatal accidents in areas such as construction, transportation, industry and medicine, due to the lack of monitoring vigilance in the mentioned areas. The implementation of a drowsiness detection system can greatly help to reduce the defects and accident rates by alerting individuals when they enter a drowsy state. This research proposes an Electroencephalography (EEG) based approach for detecting drowsiness. EEG signals are passed through a preprocessing chain composed of artifact removal and segmentation to ensure accurate detection followed by different feature extraction methods to extract the different features related to drowsiness. This work explores the use of various machine learning algorithms such as Support Vector Machine (SVM) the K Nearest Neighbor (KNN) the Naive Bayes (NB) the Decision Tree (DT) and the Multilayer Perceptron (MLP) to analyze EEG signals sourced from the DROZY database, carefully labeled into two distinct states of alertness (awake, and drowsy). Segmentation into 10-second intervals ensures precise detection, while a relevant feature selection layer enhances accuracy and generalizability. The proposed approach achieves high accuracy rates of 99.84% and 96.4% for intra (subject by subject) and inter (cross-subject) modes, respectively. SVM emerges as the most effective model for drowsiness detection in the intra mode, while MLP demonstrates superior accuracy in the inter mode. This research offers a promising avenue for implementing proactive drowsiness detection systems to enhance occupational safety across various industries.

In this paper we study a class of impulsive delayed neural networks with parameter uncertainties and reaction-diffusion terms. Using the properties of M-matrices and some inequality techniques, some sufficient conditions are derived to guarantee the global exponential stability of the given system. The results obtained are presented by simple algebraic inequalities, which are certainly more concise than previous methods. Finally, the validity and usefulness of our results are illustrated by arithmetic examples.

It has been empirically observed that the upper tail of the firm size distribution follows either the Pareto distribution or the Zipf distribution, with both patterns being explained by Gibrat’s law (Gabaix, 1999). This article analyzed firm revenue data from China, spanning from 2005 to 2013, to examine the whole range of the firm size distribution. Our empirical analysis revealed that firm revenue data over these years is well fitted by a three-parameter generalized Pareto distribution, with the fitted parameters indicating a dichotomy: The size distribution of large-sized firms, namely the upper tail, is asymptotically characterized by a Pareto distribution or a Zipf distribution, whereas the size distribution of smaller and medium-sized firms is approximated by an exponential distribution. This finding suggests that Gibrat’s law should be extended to account for the emergence of a generalized Pareto distribution.

The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically the problem is reduced to the calculation of the "energy" of the ground state in Schrödinger equation with a complicated potential. A general method to obtain the bottom-part spectrum of such equations based on the approximation of the potential by square wells is proposed and applied. Possible generalization of the approach to other types of nonlinear diffusion equations is discussed.

We introduce a new generalized inverse which is a natural generalization of (pseudo) right core inverse in a Banach *-algebra. We characterize this generalized inverse by using right core and quasi-nilpotent decomposition. We then present its polar-like characterization and investigate related algebraic properties. Finally, the right core-EP inverse is characterized by certain new ways.

In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Pentanacci numbers, and as special cases, we investigate Pentanacci and Pentanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Pentanacci numbers and as special cases, we investigate Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Pentanacci numbers and Gaussian generalized Pentanacci numbers.

J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial reference frames, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic reference frames. There exist some differences between this theory and Einstein's theory of general relativity.

In this paper, we introduce the notion of the generalized $w$-group inverse in a Banach algebra with proper involution. This is a natural generalization of generalized (weak) group inverse in Banach *-algebras. Many elementary properties of such new weighted generalized inverse are presented. We further establish the equivalent relations between generalized weighted group inverse and weighted generalized Drazin inverse. Related properties of generalized (weak) group inverse are extended to the wider cases.

Additive manufacturing processes offer various options to fabricate metal parts, which show numerous ecological and technological advantages compared to formative and subtractive manufacturing methods. Due to quick availability and high accuracy, they are particularly suitable to produce complex prototypes. Metal fused deposition modeling is a relatively new material extrusion additive manufacturing technique based on the widely used fused filament deposition process. This study focuses on the Inconel 625 metal filament from Markforged Inc., it consists of a mixture of metal powder and a binder system, the latter being removed during washing and sintering. In this article, the mechanical properties of printed and sintered Inconel were investigated using tensile testing specimens with three different infill patterns, solid, triangular, and gyroid, printed in flatwise and upright direction. In addition, investigations into the dimensional accuracy of the printed specimens and the sintering shrinkage were carried out. The results showed that neither the dimensional accuracy nor the sintering shrinkage was significantly influenced by the printing orientation. In the context of lightweight engineering, the structures proofed beneficial especially within the elastic region. Generally, triangular infill patterns resulted in higher stiffness, while gyroids led to more ductile specimens. A mass-related evaluation of tensile testing elucidates that with aid of the infill structures weight savings of 40 % resulted in mechanical performance decreased by only 20 % on average.

Dam breaches have catastrophic consequences, causing severe property damage, life loss, and environmental impact. The Kulekhani reservoir rockfill dam break was studied to evaluate the downstream impact. The appropriate breaching parameter of MacDonald and Langridge (1984) regression equations was selected based on the sixteen observed dam failure cases and cross-sectional geometry of the existing dam of Kulekhani. The 2D Diffusion Wave and Full Dynamic Wave Equation were applied for downstream flood assessment, Full Dynamic Wave was able to capture the physical flow phenomena like river bend effects resulting in higher flow velocity at the outer bend, and formation of eddies considering losses. The application of a Full Dynamic Equation was found to be appropriate for rapidly varying unsteady flow considering steep slopes, and sudden changes in channel geometry. Flood mapping of water depth, flow velocity, flood intensity, and arrival time were carried out for flood hazard assessment classified by the American Society of Civil Engineers (ASCE). Flow depth and extension of the flow area were compared to identify the affected area, higher flow depth and larger extension were observed using a Full Dynamic Wave Equation as a result of less flow velocity considering the losses. Almost 17 minutes of the arrival time of peak difference at the Bagmati River confluence was evaluated between the models which plays an important role in decision-making for selection of the flood model. Flood mitigation with river diversion works through a hydraulic measure of Levee was suggested to protect the highly affected households of Ranche, Nagmar, Khanikhet, and Debaltar towns. Most of the household was found to be safe after the construction of the Levee except for eleven houses that lie along the river below flood elevation of 1269.6 m.a.s.l. This signifies the importance of room for the rivers and the human settlement near the river might be life-threatening.

A new generalized definition of Mersenne numbers is proposed of the form (a^n - (a-1)^n), called Global Generalized Mersenne numbers, or simply Generalized Mersenne numbers and noted GM_{a,n} where a is the base and n is the exponent, both being positive integers. The properties are investigated for prime exponents n and several theorems on Mersenne numbers regarding their congruence properties are generalized and demonstrated. In particular, it is found that, for any base a, Generalized Mersenne numbers are in general such that (GM_{a,n} - 1) are even and divisible by n, a and (a-1) for any odd prime exponent n and by (a(a-1)+1) for any prime exponent n > 5. The remaining factor is a function of triangular numbers of (a-1), specific to each prime exponent n. Four theorems on Mersenne numbers are generalized and four new theorems are demonstrated, allowing to show first, that (GM_{a,n} - 1) are divisible by 6, and more precisely GM_{a,n} are congruent to 1(mod 12) or 7(mod 12) depending on the congruence of the base a(mod 4); second, that (GM_{a,n} - 1) are divisible by 10 if n == 1(mod 4) and, if n == 3(mod 4), GM_{a,n} == 1(mod 10), or 7(mod 10) or 9(mod 10) depending on the congruence of the base a(mod 5); third, that all factors c_{i} of GM_{a,n} are of the form (2nf_{i}+1) with f_{i} natural integers such that c_{i} is prime itself or the product of primes of the form (2nj+1) with j natural integer; fourth, that for odd prime exponents n, all GM_{a,n} are periodically congruent to either +/-1\(mod 8) or +/-3(mod 8) depending on the congruence of the base a(mod 8); and fifth, that the factors of a composite GM_{a,n} is of the form (2nf_{i}+1) with f_{i} == u(mod 4) and u being either 0, 1, 2 or 3 depending on the congruence of the exponent n(mod 4) and on the congruence of the base a(mod 8). The potential use of Generalized Mersenne primes in cryptography is shortly addressed.

In the present study, a mathematical model of non-steady partial differential equation from the process of oxygen mass transport in the human pulmonary circulation is proposed. Mathematical modelling of this kind of problems lead to a non-steady partial differential equation and for its numerical simulation, we have used finite differences. The aim of the process is the exact numerical analysis of the study, wherein consistency, stability and convergence is proposed. The necessity of doing the process is that, we would like to increase the order of numerical solution to a higher order scheme. An increment in the order of numerical solution makes the numerical simulation more accurate, also makes the numerical simulation being more complicated. In addition, the process of numerical analysis of the study in this order of solution needs more research work.

By introducing environmental mediator, for avoiding randomness in selecting indicators and subjectivity in deciding interaction path coefficients to reveal interaction mechanism among forest industry, ecology and environmental capacity, structural Pressure–State–Impact–Response (PSIR) and quantitative Structural Equation Modeling (SEM) are utilized with data on thirty–one provinces of China. We can find that: (i) forest industry has a negative influence on ecology, whereas ecology has a positive influence on industry; (ii) the destructive influence that industry has on ecology is much greater than the positive effect ecology has on industry; and (iii) environmental capacity plays a partial mediating role between industry and ecology. According to these results we can conclude that: (i) forest industry and ecology are not in a symbiotic relationship and have not reached a level of ecological security; (ii) the interaction between industry and ecology is in a period of transition from antagonistic to beneficial; and (iii) industry dominates ecology. However, we prospect the following advice: (i) methods of forest industry should be changed; (ii) new modes of industrial integration and circular economy should be developed; and (iii) the ability of the environment to sustain itself should be enhanced. The level of forest ecological security to discuss the symbiotic mechanism of industry and ecology will propose to be measured in future.

Motivated by empirical observations, we propose a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution (Gabaix, 2009), we find that the income distribution is described by a generalized Pareto-type distribution (GPD) with three parameters. We observe that there is a parameter /elta in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically show that, for typical market-economy countries, /elta is close to 0 significantly, such that the income distribution is characterized by a two-class pattern in which the bottom 90% of the population is approximated by an exponential distribution and the richest 1%~3% is approximated by an asymptotic power law. However, we empirically find that, for China both in planned economy period and in early stages of market reformation (from 1978 to 1990), /elta is significantly deviated from 0, such that the bottom of the population no longer conforms to an exponential distribution.

In this paper, we introduce and investigate a new family of sequences called the generalized Fibospinomials (or the generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we handle with $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomial spinors. After a short history on spinors and quaternions, we present Binet's formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some identities of generalized Fibonacci polynomial spinors, $(r,s)$-Fibonacci polynomial spinors and $(r,s)$-Lucas polynomial spinors. Moreover, we give some special identities such as Catalan's and Cassini's identities and we present matrices related with these polynomials.

In this work, an innovative numerical approach for polylinear approximation (polylinearization) of non-self-intersecting compact sensor characteristics (transfer functions) specified either pointwise or analytically is introduced. The goal is to optimally partition the sensor characteristic, i.e. to select the vertices of the approximating polyline (approximant) along with their positions on, the sensor characteristics so that the distance (i.e. the separation) between the approximant and the characteristic is rendered below a certain problem-specific tolerance. To achieve this goal, two alternative non-linear optimization problems are solved, whose essential difference is in the adopted quantitative measure of the separation between the transfer function and the approximant. In the first problem, which relates to absolutely integrable sensor characteristics (their energy is not necessarily finite, but they can be represented in terms of convergent Fourier series), the polylinearization is constructed by numerical minimization of the L^1--metric (a distance-based separation measure), concerning the number of polyline vertices and their locations. In the second problem which covers the quadratically integrable sensor characteristics (whose energy is finite, but they do not necessarily admit a representation in terms of convergent Fourier series), the polylinearization is constructed by minimizing numerically the L^2-metric (area-, or energy-based separation measure) for the same set of optimization variables –the locations, and the number of polyline vertices.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

Transformation formula under the action of a general linear fractional transformation for generalized Dedekind eta-function has been a subject of intensive study, Rademacher, Dieter, Meyer et al. However, the (Hecke) modular relation structure has not been recognized until the work of Goldstein-de la Torre, and streamlining the classical proofs in the modular relation will reveal the meaning hidden in those works. Our main aim is to elucidate the works of these researchers in the context of modular relations.

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

The stability properties of the Hill equation are discussed, and especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu equation for a trapped ion are characterized by using the Floquet theory and Hill's Method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters $a$ and $q$ that are real. Characteristic curves are introduced naturally by the Sturm-Liouville problem for the well known even and odd Mathieu equations $ce_m(z,q)$ and $se_m(z,q)$. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for axial and radial motion. In case of a Paul trap the stable solution corresponds to a superposition of harmonic motions. The problem of evaluating the maximum amplitudes of stable oscillations for the ideal conditions (taken into consideration) is also approached. Anharmonic corrections are discussed within the frame of the perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter. The results apply to 2D and 3D ion traps used for different applications in quantum engineering, among which optical clocks, quantum logic and quantum metrology, but not restricted only to these.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

In the sphere of urban renewal in historic districts, preserving and innovatively reinterpreting traditional architectural styles remains a primary research focus. However, the modernization and adaptive reuse of traditional buildings often necessitate changes in their functionality. To cater to the demands of tourism in historic districts, many traditional residential buildings require conversion to commercial use, resulting in a mismatch between their external form and internal function. This study explores an automated approach to transform traditional residences into commercially viable designs, offering an efficient and scalable solution for the modernization of historic architecture. We developed a methodology based on diffusion models, focusing on a dataset of nighttime shopfront facades. By training a Low-Rank adaptation (LoRA) model and integrating the ControlNet model, we enhanced the accuracy and stability of generated images. The methodology’s performance was validated through qualitative and quantitative assessments, optimizing batch size, repetition, and learning rate configurations. These evaluations confirmed the method’s effectiveness. Our findings significantly advance the modern commercial style transformation of historical architectural facades, providing a novel solution that maintains aesthetic and functional integrity, thereby fostering breakthroughs in traditional de-sign thinking and exploring new possibilities for the preservation and commercial adaptation of historical buildings.

The generation and maintenance of membrane potential is a fundamental part of Membrane Pump Theory. One of the key points of this hypothesis is based on a natural or facilitated molecular diffusion through several types of ion channels and pumps like the Na/K ATPase. Chemistry, physics and especially electrochemistry, however, bring strong contradictions to this theoretical assumption. By respecting the principles of chemistry and electrostatics, it becomes obvious that this theoretical hypothesis cannot work. The ionic diffusion that would be at the origin of this potential cannot take place. Indeed, the topology and the forces involved definitively exclude the current model, which must absolutely be revised according to the current state of our knowledge and allow an advance in the understanding of the phenomena and open new research perspectives.

For the past few decades, researchers have been intrigued with glassy polymers, which have applications ranging from gas separations to corrosion protection to drug delivery systems. The techniques employed to examine the sorption and diffusion of small molecules in glassy polymers are the subject of this review. Diffusion models in glassy polymers are regulated by Fickian and non-Fickian diffusion, with non-Fickian diffusion being more prevalent. The characteristics of glassy polymers are determined by sorption isotherms, and different models have been proposed in the literature to explain sorption in glassy polymers during the last few years. This review also includes the applications of glassy polymer. Despite having so many applications, current researchers still have difficulty in implementing coating challenges due to issues like as physical ageing, which is briefly discussed in the review.

Modern physics is situated on the fine line between scientific research and an attempt to answer metaphysical questions. Contemporary scholars such as Henry Stapp and Roger Penrose attempt to create an ontological interpretation of Schrödinger's equation in superposition state and its reduction or collapse to classical state. In this short essay I will try to explore how Immanuel Kant's metaphysics and the concept of noumena can be possibly integrated with quantum physics and Schrödinger's equation.

This study focuses on a new class of functions called sub-b-s-preinvex, that is a generalization of sub-b-s-convex and preinvex functions, and discusses some of their properties. A new sub-b-s-preinvex programming is introduced and the sufficient conditions of optimality under this type of function is established.

The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. Dichotomy is modulated by allowing more than one negative eigenvalues, or by abandoning it altogether, yielding generalized operator valued arguments for contextuality. We also discuss a form of state-dependent contextuality by variation of the functional relations of the operators; in particular, by additivity.

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.

We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE) that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutions to the governing equation efficiently.

Combining modern thermodynamics theory branches, including finite time thermodynamics or entropy generation minimization, constructal theory and entransy theory, with metallurgical process engineering, this paper provides a new exploration on generalized thermodynamic optimization theory for iron and steel production processes. The theoretical core is to thermodynamically optimize performances of elemental packages, working procedure modules, functional subsystems, and whole process of iron and steel production processes with real finite-resource and/or finite-size constraints with various irreversibilities toward saving energy, decreasing consumption, reducing emission and increasing yield, and to achieve the comprehensive coordination among the material flow, energy flow and environment of the hierarchical process systems. A series of application cases of the theory are reviewed. It can provide a new angle of view for the iron and steel production processes from thermodynamics, and can also provide some guidelines for other process industries.

A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

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.

Mutations in KRT1 (keratin 1) or KRT10 (keratin 10) underlie a spectrum of diseases known as keratinopathic ichthyoses. Epidermolytic ichthyosis (EI) is caused by heterozygous missense mutations in the genes KRT1 or KRT10, mutations in the gene KRT2 (keratin 2) lead to superficial epidermolytic ichthyosis, and congenital reticular ichthyosiform erythroderma is caused by frameshift mutations in the genes KRT10 or KRT1, which lead to the phenomenon of revertant mosaicism. Epidermolytic ichthyosis is also present in a mosaic pattern known as epidermolytic (acantholytic) nevus, isolated or diffuse. In the latter case, gonadic involvement is possible, leading to a rare pedigree in which a parent with diffuse epidermolytic nevus (linear EI) gives birth to a child affected by EI. We present here an update on the phenotypic presentations of keratinopathic ichthyoses and their molecular mechanisms.

The diffusion coefficient (D) is a key parameter characterizing gas transport in coal seams. Usually, the D is calculated from the desorption curve of particle coal, which cannot accurately reflect the diffusion characteristics under the stress constraint conditions of in-situ coal seams. In this paper, based on Fick's law of counter diffusion, different metamorphic deformed coals of medium and high coal rank are taken as the research object. The change laws of D under different confining pressure, gas pressure, and temperature conditions are tested and analyzed, and the influencing mechanisms on the D are discussed. The results show that the D of different metamorphic deformed coals decreases exponentially with the increase of confining pressure, and increases exponentially with the increase of gas pressure and temperature. There is a limit diffusion coefficient. The influence of confining pressure on the D is essentially determined by the change of effective stress, and the D has a negative effect of effective stress similar to permeability. The effect of gas pressure on the D involves two mechanisms, namely, mechanical and adsorption effects, which are jointly restricted by effective stress and coal particle shrinkage and expansion deformation. The effect of temperature on the D is mainly achieved by changing the root mean square speed and average free path of gas molecules. Under the same temperature and pressure conditions, the D increases first and then decreases with the increase of deformation degree, and the D of fragmented coal is the largest. Under similar deformation conditions, the D of high-rank anthracite is greater than that of medium-rank fat coal. It is considered that porosity is the key factor affecting the change of D in different metamorphic deformed coals.

An interesting anomaly of the diffusion process with an apparently negative diffusion coefficient defined through the mean-square displacement in a one-dimensional quantum molecular chain model is shown. Nevertheless, the system satisfies the H-theorem, so that the second law of thermodynamics is satisfied. The reason why the “diffusion constant” becomes negative is due to the effect of the phase mixing process, which is a characteristic result of the one-dimensionality of the system. We illustrate the situation where this negative “diffusion constant” appears.

In this paper, we investigate the generalized Padovan sequences and we deal with, in detail, four special cases, namely, Padovan, Perrin, Padovan-Perrin and modified Padovan sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

In this paper, we introduce the generalized Tetranacci quaternions and present some properties of these quaternions.

P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For example, a second order polynomial that contains 3 free parameters was presumed based on in-situ SMP data. The polynomial is currently parameterized based on 3 backscatter observations provided by AirMOSS (i.e. one frequency at three polarizations of HH, VV and HV). In this paper, a more realistic, physically-based SMP model containing 3 free parameters is derived based on a solution to Richards’ equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

The study aimed to analyze thoracic and lumbar erector spinae muscle activations during 3D elongation exercises in individuals with adolescent idiopathic scoliosis (AIS). Participants included 24 adolescents, meeting specific criteria such as a Cobb angle between 10° and 20°, and not having undergone surgical or brace treatments. EMG data were collected to evaluate muscle activations. The study found no significant interaction between exercise type and the side of the curve, but a significant main effect of exercise type on muscle activation, irrespective of Cobb angle. Different exercise types significantly affected muscle activity, with the highest activations in the TheraBand exercise, followed by manual and without equipment conditions. This suggests that exercise type significantly impacts muscle engagement in AIS patients, providing valuable insights for targeted exercise program design. The study, however, focused on short-term muscle activation, not long-term Cobb angle progression, pointing to the need for further research in this area.

Diffusion bonding is often used on pre-machined parts to generate internal cavities, e.g. for cooling injection molding tools close to the mold cavity. Only then, the workpieces are finished to their final dimensions. In the case of micro-process devices, however, it is essential to precisely control the deformation, as otherwise uncontrollable pressure losses will occur with channel cross-sections in the sub-millimeter range. Post-processing is not possible. The most important process parameters for diffusion bonding are temperature, dwell time and contact pressure, with the bonding temperature and contact pressure acting in opposite directions and showing a strong non-linear dependence on deformation. In addition, the deformation is influenced by a number of other factors such as the absolute size of the cross-section and the aspect ratio of the parts, the dimensions and distribution of the internal cross sections and the overall percentage of the cross-section to be bonded. In micro process engineering, small material cross-sections in the range of the materials microstructure can facilitate additional deformation mechanisms such as grain boundary sliding, which are not relevant at all for larger structures. For parts consisting of multiple layers, tolerances in thickness and roughness of multiple surfaces must be levelled, contributing to the percentaged deformation. This makes it difficult, especially in micro process engineering and in single or small series production, to determine suitable joining parameters in advance, which on the one hand do not cause unforeseen large deformations, but on the other hand reliably produce highly vacuum-tight components. Hence, a definition of a fixed percentaged deformation does not work for all kinds of components. This makes it difficult to specify parameters for surely obtain high-vacuum tight parts. For successful diffusion bonding, atoms must diffuse over the bonding planes, forming a monolithic part in which the original layers are no longer visible. Only then, mechanical properties identical to those of the base material, which has been subjected to identical heat treatment, can be achieved. In this paper, the impacts of different material cross section widths as well as of the aspect ratio on deformation were investigated. By accident, it was found that also accuracy of the temperature measurement may have a serious impact in terms of deformation.

It is shown by numerical modelling that anisotropic diffusion can compensate and even overcome diffusion broadening - the main limiting factor of devices working at atmospheric pressure. The thickness of ion clouds coming out of the ionisation chamber is reduced ~ 1000 times in the ADMA inlet increasing the resolution. This finding has a great potential that enables construction of a device with resolution close to that of currently available desktop ion separation devices – high pressure mass spectrometers, but with much lower cost of manufacture and with smaller dimensions. Comprehensive numerical modelling along with mathematical analysis of physical concepts enables reduction of the footprint and manufacturing costs. Modelling determined that the resolving power (RP) potential of the ADMA is greater than the RP of currently available on the market devices for the airport security market. The ADMA technology enables very fast detection of threats; at least 100 times faster than currently used in Ion Mobility Spectrometers (IMS). This potentially allows an increase in passenger throughput in airports.

A set of programs for the numerical simulation of the diffusion decomposition processes was developed by using simulation methods, kinetic and particle method. The complex has been validated on the model system Ni-Al by the growth of -phase separations. The results on the evolution of the distribution function and other characteristics of the ensemble, which in the zero volume fraction approximation are asymptotically in good agreement with the theory and the experiment, have been obtained. The peculiarity of the created program complex is the possibility of its adaptation to the description of the decomposition of multicomponent multiphase systems. Fig. 6, list of references - 19 titles.

Current physiology attributes the mechanism of membrane potential generation to transmembrane ion transport, but ion adsorption could just as well play this fundamental role. The evidence shows that the ion adsorption mechanism accurately reproduces the experimentally measured membrane potential. The Goldman-Hodgkin-Katz equation (GHK eq.) and the Nernst equation (Nernst eq.) are the typical mathematical formulas representing the membrane potential in current physiology. However, the authors were able to show that the potential formulas by ion adsorption mechanism give identical results to GHK eq. and Nernst. eq. Our experimental and theoretical analyses suggest that there is a special relationship between the membrane potential and the membrane surface charge density, and this unique equation inevitably leads to the establishment of a GHK eq and/or a Nernst eq. The authors found that the unique equation is the foundation of thermodynamics “Boltzmann distribution”. Thus, the GHK eq. and the Nernst eq. are simply the natural consequence of thermodynamics from the view of the ion adsorption mechanism.

This work aims to generate some types of M_(j )–neighborhoods. Relationships among these M_(j )-neighborhoods and some other types of neighborhoods are discussed. Additionally, M_(j )-lower, M_(j )-upper approximations and M_(j )-accuracy in terms of M_(j )-neighborhoods are presented. Their properties, with some examples, are investigated. Finally, We addressed the comparisons among M_(j )approach and other approaches.

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

The effects on Raychaudhuri's equation of an intrinsically discrete or particle nature of spacetime are investigated, through consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. This is done from an effective point of view, meaning through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point; this on top of resulting non vanishing the limiting cross-sectional area itself of the congruence.

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

In this paper, it is introduced the notion of r-fuzzy β-T_i, i = 0, 1, 2 separation axioms related to a fuzzy operator β on the initial set X which is a generalization of previous fuzzy separation axioms. An r-fuzzy α-connectedness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of r-fuzzy connectedness. An r-fuzzy α-compactness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of fuzzy compactness.

In this paper, I investigate Hyers-Ulam-Rassias stabilities of the general quintic functional equation and the general sextic functional equation.

Behavior analysis is a widely used non-invasive tool in the practical production routine, as the animal acts as a biosensor capable of reflecting its degree of adaptation and discomfort to some environmental challenge. Predominantly, conventional statistics use occurrence data for behavioral evaluation and well-being estimation, disregarding the temporal sequence of events. The Generalized Sequential Pattern (GSP) algorithm is a data mining method that identifies recurrent sequences that exceed a user-specified support threshold, whose potential has not yet been investigated for broiler chickens in enriched environments. Enrichment aims to increase environmental complexity with promising effects on animal welfare, stimulating priority behaviors and potentially reducing the deleterious effects of heat stress. The objective was to validate the application of the GSP algorithm to identify temporal correlations between heat stress and the behavior of broiler chickens in enriched environments through proof of concept. Video image collection was carried out automatically for 48 continuous hours, analyzing a continuous period of seven hours, from 12:00 PM to 6:00 PM, during two consecutive days of tests for chickens housed in enriched and non-enriched environments under comfort and stress temperatures. Chickens at comfort temperature showed high motivation to perform the behaviors of Preening (P), Foraging (F), Lying down (Ld), Eating (E), and Walking (W) whose sequences <{Ld,P}>; <{Ld,F}>; <{P,F,P}>; <{Ld,P,F}> and <{E,W,F}> were the only ones observed in both treatments. All other sequential patterns (comfort and stress) were distinct, suggesting that environmental enrichment alters the behavioral pattern of broiler chickens. Heat stress drastically reduced the sequential patterns found at the 20% threshold level in the tested environments. The behavior of lying laterally "Ll" is a strong indicator of heat stress in broilers and was only frequent in the non-enriched environment, which may suggest that environmental enrichment provides the animal with better opportunities to adapt to stress-inducing challenges, such as heat.

An adequate representation of the water infiltration process in the soil allows improving the efficiency in application and the uniformity in surface irrigation. The Green and Ampt model has shown a good representation of the process, and researchers from the United States Department of Agriculture (USDA) determined the values of their parameters for soils of that country, which are shown in tables or through functional relationships and this information is used as reference in several parts of the world, although there is no certainty that they are representative of the soils in Mexico. In this study, the parameters of the Green & Ampt equation were determined and evaluated in some soils of agricultural importance in Mexico. The parameters were obtained in four ways: one of them applied a methodology adapted from Brooks and Corey to quantify the wetting front capillary pressure head and used an permeameter under constant hydraulic head to determine the saturated hydraulic conductivity, and the other three consisted in taking them from three studies reported by the USDA. The values of the parameters suggested in Mexico drastically underestimated the results with relative errors (RE) in a range of -49.0 to -94.0% and the most representative were those obtained with the methodology proposed in this research with RE of -15.0 to 6.0%.

Defining integrals over volume element in curved spacetime together with the mass and energy densities within that region of spacetime is apparently equivalent to the given energy and mass of that body or particle. With this in mind equations involving energies and mass can be rewritten in terms of their densities and the integral over the volume element. The idea find its place in the Hamiltonian formulations, and can be carried over into quantum mechanical frameworks systematically accounting for the effect of spacetime volume structures and gravity on dynamics of quantum systems. This article briefly explores this concept and runs through various frameworks and equations relevant to this idea, particularly the schrodinger-Newton equation and discusses the cosmological constant as a vacuum energy density.

In this paper, we introduce a way of representing a given mapping as the sum of odd and even mappings. Then, by using this representation, we investigate the stability of various forms for the general nonic functional equation.

Electrically charged particles such as Electrons and Protons carry electric, E, and magnetic, B, fields. In addition to these fields, Quantum Mechanics (QM) endows these particles with an `arcane and spooky' field --- the wavefunction. This wavefunction of QM is not only assumed to be separate but distinct from the electromagnetic field. We herein upend this view by demonstrating otherwise. That is, we demonstrate that the four components of the Dirac wavefunction, can be shown to not only be an intimate, but, a direct function of the electromagnetic field carried by the particle in question. Insofar as unity, depth in our understanding and insight into both Dirac and Maxwell's equations as major pillars of Modern Physics, we believe that this work may very well inch us one-step-closer to the truth.

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum spacetime. It is based in the Minimum Group Representation Principle (MGRP). Within this framework new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space-times. Our main results here are: {\bf(i)} We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, as the spectral scalar and tensor indices, $n_S$ an $n_T$, and the tensor to scalar ratio $r$. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. {\bf(ii)} The pure entangled states in the minimum group (metaplectic) $Mp(n)$ representation for quantum de Sitter space-time and black holes are found. {\bf(iii)} For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp(n)$ group is found: This is a {\it new non-diagonal} coherent state representation complementary to the known Sudarshan diagonal one. {\bf(iv)} Mean value generators of $Mp(2)$ are related to the adiabatic invariant and topological charge of the spacetime (matrix element of the transition $-\infty < t < \infty$). {\bf(v)} The basic {\it even} and {\it odd} $n$-sectors of the Hilbert space are intrinsic to the quantum spacetime and its discrete levels (in particular continuum for $n \rightarrow \infty$), they do not require any extrinsic generation process as the standard Schrodinger cat states, and are {\it entangled}. {\bf(vi)} The gravity or cosmological domains in one side and another of the Planck scale are {\it entangled}. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity reqion and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space-time are entangled. {\bf(vii)} The general classical-quantum gravity duality is associated to the Metaplectic $Mp(n)$ group symmetry which provides the complete full covering of the phase space and of the quantum space-time mapped from it.

Background: Periodontitis is a disease that leads to serious functional and aesthetic dysfunctions resulting in impairment of life quality; it exists in different forms and its etiology is related with multiple component causes. Angiogenesis, together with inflammatory infiltrate, are two key processes in the evolution of inflammatory processes involving gingival tissues. The aim of this study was to evaluate their alterations in relation to some important periodontal diseases-associated factors (i.e. smoke, sex, age, plaque, pus, probing pocket depth) in patients with diagnosis of Generalized Aggressive Periodontitis (GAP). Methods: Eighteen subjects with GAP were enrolled for this study. Percentage of inflammatory cells and vascular area were measured and evaluated in relation with each periodontal diseases-associated factor. Results: The results showed a significant decrease of the percentage of vascular area in association with almost all the periodontal diseases-related factors (smoke, age, PPD, plaque) and not significant differences in the percentage of inflammatory cells. Conclusions: Data suggest that, even if these factors are often commonly related to worsening of periodontal status, they did not affect inflammatory and vascular pattern, as we can assume. For the future, additional studies, aimed to evaluated each singular factor in a wider sample size, should be planned.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

An algorithm for the treatment of images affected by both blurring and salt&pepper noise is proposed with a cost only proportional to the number of pixels. The methodology uses a discretization scheme for the Laplace operator multiplied by a suitable nonlinear term depending on the gradient. Even if this approach resembles a diffusion type algorithm, only one step of the procedure is applied, leading to significant time savings. The procedure is successfully tested on some standard black&white natural images.

Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase shift diffusion equation (EPSDE) method and an observing the signal intensity at the origin method. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function type PFG signal attenuation. The methods here provide a clear view of spin evolution under field gradient, and their results will help the analysis of PFG anomalous diffusion.

We introduce a new generalized inverse (i.e., generalized EP element) which is a natural generalization of EP and *-DMP elements in a Banach *-algebra. We present polar-like characterizations of generalized EP elements. The necessary and sufficient conditions under which the sum of two generalized EP elements is a generalized EP element are investigated. Finally, the generalized core-EP orders for generalized EP elements are characterized.

One open question remains regarding the theory of the generalized variational principle, that is, why the stress-strain relation still be derived from the generalized variational principle while the Lagrangian multiplier method is applied in vain? This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics. As long as the functional has one of the combination $A(\epsilon_{ij})-\sigma_{ij}\epsilon_{ij}$ or $B(\sigma_{ij})-\sigma_{ij}\epsilon_{ij}$, its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method. It is proved herein that the Hu-Washizu functional $\Pi_{HW}[u_i,\epsilon_{ij},\sigma_{ij}]$ and Hu-Washizu variational principle comprise a real three-field functional.

In this paper, we introduce the generalized dual hyperbolic Fibonacci numbers. As special cases, we deal with dual hyperbolic Fibonacci and dual hyperbolic Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesàro's, Melham's identities and present matrices related with these sequences.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

Maxwell equation for the electric field has been solved for any medium by suggesting the wavenumber and angular frequency be complex quantities. This accounts for the field decay by interaction with the medium.This expression for the time and special decay of the electric field in a medium is used to construct a new wave function sensitive to the medium physical properties. This new wave function, unlike the conventional one, differentiates between a beam of particles in a vacuum and that enters a medium which is an attenuated due to the scattering effect.Another expression for time decaying electric field was obtained using Newton’s laws for frictional medium. This expression shows that the electric field diminishes due to friction.Fortunately, this time decaying part of the electric field is typical to that derived from Maxwell’s equations. Finally, a new Schrodinger equation sensitive to the medium properties was derived. This equation, fortunately, describes some scattering processes for Protein scattering, scattering of x-rays, opto-acoustic phonons, and Raman scattering for some materials successfully .

: Oscillation synchronization through diffusion-based communication of active materials can lead to emergence of diverse patterns and collective behaviors. A detailed general description of the formation process of synchronization or resynchronization dynamics is a challenging task. We employ a photosensitive Belousov-Zhabotinsky reaction-diffusion model (within a gel media) to investigate the recovery process of oscillation synchronization between a pair of gel patches. The recovery time for oscillation resynchronization can be modulated by patch-distance, species of signaling molecules, intensity and duration of illumination. Analysis reveals that the “switch effect” of the gel-distance and the “promotion effect” from illumination on the oscillation resynchronization originate from the competition between processes of photo-promotion of oscillation, diffusion of signaling molecules (HBrO2 and Br-) and disproportionation of HBrO2. These results will benefit studies on bio-inspired active materials and soft motors.

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models, by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam’s opinion diffusion model (see, e.g. , ). For a given selection of the coefficients in our model, this proposal yields the original Galam’s model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided.

Dynamics of human populations can be affected by various socio-economic factors through their influence on the natality and mortality rates, and on the migration intensity and directions. In this work we study an economic-demographic model which takes into account the dependence of the wealth production rate on the available resources. In the case of nonlocal consumption of resources the homogeneous in space wealth-population distribution is replaced by a periodic in space distribution for which the total wealth increases. For the global consumption of resources, if the wealth redistribution is small enough, then the homogeneous distribution is replaced by a heterogeneous one with a single wealth accumulation center. Thus, economic and demographic characteristics of nonlocal and global economies can be quite different in comparison with the local economy.

Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.

Almost all modern inorganic light-emitting diode (LED) designs are based on double heterojunctions (DHJs) whose structure and current injection principle have remained essentially unchanged for decades. Although highly efficient devices based on the DHJ design have been developed and commercialized for energy-efficient general lighting, the conventional DHJ design requires burying the active region (AR) inside a pn-junction. This has hindered the development of emitters utilizing nanostructured ARs located close to device surfaces such as nanowires or surface quantum wells. Modern DHJ III-N LEDs also exhibit resistive losses which arise from the DHJ device geometry. The recently introduced diffusion-driven charge transport (DDCT) emitter design offers a novel way to transport charge carriers to unconventionally placed ARs. In a DDCT device, the AR is located apart from the pn-junction and the charge carriers are injected into the AR by bipolar diffusion. This device design allows the integration of surface ARs to semiconductor LEDs and offers a promising method to reduce resistive losses in high power devices. In this work, we present a review of the recent progress in gallium nitride (GaN) based DDCT devices, and an outlook of potential DDCT has for opto- and microelectronics.

Proposed in 1889 by Svante Arrhenius, the Arrhenius equation is an important result in physical chemistry which aims to find the relationship between temperature and reaction rates. It is also an essential equation for analytic chemistry which helps to determine the energy barrier for a given reaction. In this article, we will go through a detailed derivation of the exponential factor in the Arrhenius Equation based on the Boltzmann distribution of particle energy probability. Then, we will attempt to model the pre-exponential factor in accordance with the principles of collision theory for bi-molecular reaction with gaseous reactants. Understanding the basic principles of chemical reaction provides valuable tools to analyze complex reaction mechanisms in the perspective of optimizing existing industrial processes.

It is shown that the 5D geodetic equations and 5D Ricci identities give us a way to create a new viewpoint on some problems of Modern Physics, Astrophysics, and Cosmology. Specifically, the application of the 5D geodetic equations in (4+1) and (3+1+1) splintered forms obtained with the help of the monad and dyad methods made it possible to introduce a new, effective generalized concept of the rest mass of the elementary particle. The latter leads one to novel connections between the General Relativity and quantum field theories, as well as all of that, including the (4+1) splitting of the 5D Ricci identities, brings about a better understanding of the magnetic monopole problem and the vital difference in the origins of the Maxwell equations and gives rise to surprising connections between them. The obtained results also provide new insight into the mechanism of the 4D Universe’s expansion and its following acceleration.

We study the generalized χ and η cross helicities for non-ideal non-barotropic magnetohydrodynamics (MHD). χ and η, the additional label translation symmetry group, have been used to generalize the cross helicity in ideal flows. Both new helicities are additional topological invariants of ideal MHD. To study there behaviour in non-ideal MHD, we derive the time derivative of both helicities using the non-ideal MHD equations taking viscosity, finite resistivity and heat conduction into account. Physical variables are divided into ideal and non-ideal quantities separately during the mathematical analysis for simplification. The analytical results indicate that χ and η cross helicities are not strict constant of motion in the non-ideal MHD and show the rate of dissipation which is compared to the dissipation of other topological constants of motion.

In the paper, the authors find two explicit formulas and recover a recursive formula for the generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the restricted hexagonal numbers respectively.

A harmful impact of climate change and global warming has concerned various sectors of the international community. Numerous energy policies aiming at climate change mitigation have been implemented on a national and global scale. Renewable Energy Technologies (RET) play a critical role in enhancing sustainable solutions that significantly limit greenhouse gases (GHG) emissions. Such innovative technologies can facilitate energy transition through providing e.g. energy security, sustainable development, or effective usage of indigenous resources. However, the commercialization of RET becomes extremely challenging. The barriers can be of a different nature, although in this study the focus has been put on socio-economic and regulatory issues. In fact, there is ample evidence that energy policies play a central role in supporting renewables adoption. It is also claimed that RET require the whole ecosystem to support their successful diffusion. In this study, we explore multifarious barriers for a widespread RET diffusion in two European Union countries: Finland and Poland, indicating the most common barriers existing in the literature as well as analyzing major bottlenecks in the viewpoint of renewable energy companies’ executives. We also present statistics of the most commonly used RET in these countries in order to express the diffusion issues more appropriately. The outcomes of this study provide useful insight for the researchers in the energy transition field as well as practical managerial and regulatory implications aimed at overcoming these challenges.

A number of experiments suggest that the elementary particles are non-local entities. A dissipative self-organization, that treats particles as open systems may provide a better understanding of the underlying phenomena than conservative models. The proposed toy model is such an attempt. We found that self-gravitation (although accompanied by self-diffusion) may not only be compatible with the quantum phenomena but is perhaps the major reason for the existence of quantum fields. According to the proposed model, fields/particles (resemble those of the Standard Model) emerge from a dynamic self-organized medium (which we associate with vacuum dust) from competition between self-gravitation and self-diffusion. These forces produce turbulence in the form of vortices (which we call vacuum cells) that serve as the building blocks for fields and particles. Field/particle features and symmetries are based on their internal (intracellular) dynamics and vortex synchronization (intercellular dynamics). This model allows for rough estimations of relative field coupling strengths, the quantity of charges and flavors, the probabilities of quark transmutations, the dimensionality and the topologies of phase spaces, and other Standard Model parameters that came not from the theory but rather determined by experiment.

Recently quantum cosmology in tomographic representation was considered. as an important tool to analyze the quantum states of the early universe in relation with the subsequent classical evolution. Given a wave function the correspondent tomogram is defined proportional to the square modulus of its fractional Fourier transform. The classical limit obtained by taking the limit ℏ→0 can be compared with the classical tomogram obtained from the classical hamiltonian formalism. In this paper we show that a set of tomograms can be derived as exact solutions of a third order equation when a de Sitter quantum universe is considered. We finally discuss the limits of this approach to quantum cosmology because the extension to equations with arbitrary potentials can become extremely complicated for potentials given by algebraic polynomials of degree greater than two and therefore also for potentials expressible by arbitrary functions.

Let $n \geq 2$ be a fixed integer and $\mathcal{A}$ be a $C^*$-algebra. A permuting $ n $-linear map $ \mathcal{G} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ is known to be symmetric generalized $n$-derivation if there exists a symmetric $n$-derivation $ \mathfrak{D} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ such that $ \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i} x_{i}^{\prime}, \ldots, x_{n}\right)= \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i}, \ldots, x_{n}\right) x_{i}^{\prime}+x_{i} \mathfrak{D} (x_{1}, x_{2},\ldots, x_{i}^{\prime}, \ldots, x_{n})$ holds for all $x_{i}, x_{i}^{\prime} \in \mathcal{A} $. In this paper, we investigate the structure of $C^*$-algebras involving generalized linear $n$-derivations. Moreover, we describe the forms of traces of linear $n$-derivations satisfying certain functional identity.

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

Let {ξ1, ξ2. . . .} be a sequence of independent possibly differently distributed random variables defined on a probability space (Ω, F, P) with distribution functions {F_ξ1., F_ξ2 , . . .}. Let η be a counting random variable independent of sequence {ξ1, ξ2. . . .}. In this paper, we find conditions under which distribution function of randomly stopped sum Sη = ξ1 + ξ2 + . . . + ξη belongs to the class of generalized subexponential distributions.

In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of the generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss generating function approach using which we derive different entropy measures. Finally, using the newly introduced entropy measures, we establish some relationships between entropy and extropy measures.

In theory and applications, it is often inevitable to work with projectors onto convex sets, where a linear transform is involved. In this article, a novel projector is presented, which generalizes previous results in that it admits a broader family of linear transforms, but on the other hand it is limited to box-type convex sets in the transformed domain. The new projector has an explicit formula and it can be interpreted within the framework of proximal optimization. The benefit of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.

Polymer electrolyte was used as a medium for testing the performance of microband electrodes under conditions of linear diffusion. Cyclic voltammetry and chronoamperometry experiments were performed in such viscous medium, where diffusion rates are much slower than in fluid solutions. Confirmation of the existence of such conditions from the log i vs. log v or log i vs. log t relationships in the current equation always yielded values lower than the expected value of 0.5. This could indicate impure linear diffusion profile, i. e. some contribution from radial diffusion (edge effect). However, performing these tests in monomeric solvents of similar viscosities, such as glycerol or propylene glycol, gave the desired value of 0.5. These results lead to the conclusion that current equations which are based on Fick’s laws may not be applicable for polymer electrolytes, where various obstruction to diffusion make it a more complicated process than in monomeric solvents.

The presence of phase diffusion can lead to the loss of the advantages of quantum measurements. Squeezing is considered to be an effective method to reduce the detrimental effect of phase diffusion on the measurement. The Mach-Zehnder (MZ) interferometer has been exploited as a generic tool for precise phase measurement. Describing the reduction in quantum advantage caused by phase diffusion in an MZ interferometer that can be mitigated by squeezing is not easy to handle analytically, because the input state will change from a pure state to a mixed state after experiencing the diffusion noise in the MZ interferometer. We introduce a truncated MZ interferometer that can achieve the same potential phase sensitivity as the conventional MZ interferometer. This scheme can theoretically explain how phase diffusion reduces phase estimation and why squeezing counteracts in the presence of phase diffusion. Using the Gaussian property of the input state and the characteristic of Gaussian operation in the squeezing, the two orthogonal field quantities of the quantum state are squeezed and anti-squeezed to different degrees, and the analytic results are obtained. The truncated MZ interferometer is simpler to build and operate than the conventional MZ interferometer, and also mitigates the phase diffusion noise by the squeezing operation, thus making it useful for applications in precision metrology.

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. \ref{GROWTH2}. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with $p$-branches leaving each vertex. Such trees are endowed with algebraic structure, the $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling {\it dynamics on energy landscapes.} To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider {\it linearly increasing barriers.} This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

The present work is concerned with the study of the generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of Langevin equation depend critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation. By further demanding time reversibility of the drift the Langevin equation can also describe equivalent quantum-mechanical systems in a path-wise manner. The resulting statistical description obeys the Fokker-Plank equation of the probability density of the differential system, which can be readily estimated from Monte Carlo simulations of the random paths. Based on the Fokker-Plank formalism a new derivation of the transient probability densities is presented. Finally, stochastic simulations are compared to the theoretical results.

We still do not have satisfactory answers about the inflationary and accelerating expansions of the universe, the missing mass problem, and the origins of the four fundamental forces and the quantum phenomena. Here, we introduce a new model of matter and space and a postulate on a constant of motion, and then show that an equation of motion derived from the constant of motion could provide new understandings of the above problems. For example, we show that there is a natural inflation scenario and that the co-moving distance to the closest accelerating supernova is clearly given as $c/(\sqrt{3} H)$ ($\sim$8.1 billion ly). In addition, we show that, in a system including a proton and an electron, the equation of motion has eight acceleration terms, some of which are suspected to be responsible for the four fundamental forces and the galaxy rotation anomaly. From further discussion, we conjecture that in order to understand the gravitational and strong interactions and the quantum phenomena, it is necessary to consider the expansion of the universe. The lensing mass distribution is explained, based on another postulate on a method of representing superposition.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.