Search Results (14)

This study investigates the propagation of shear horizontal transverse waves in a functionally graded piezoelectric half-space (FGPHS), where the material properties vary linearly and quadratically. The analysis focuses on deriving and understanding the dispersion characteristics of such waves in in-homogeneous media. The WKB approximation method is employed to obtain the dispersion relation analytically, considering the smooth variation of material properties. To validate and study the wave behavior numerically, two advanced techniques were utilized: the Semi-Analytical Finite Element with Perfectly Matched Layer (SAFE-PML) and the Semi-Analytical Infinite Element (SAIFE) method incorporating a (1/r) decay model to simulate infinite media. The numerical implementation uses the Rayleigh–Ritz method to discretize the wave equation, and Gauss 3-point quadrature is applied for efficient numerical integration. The dispersion curves are plotted to illustrate the wave behavior in the graded piezoelectric medium. The results from SAFE-PML and SAIFE are in excellent agreement, indicating that these techniques effectively model the shear horizontal transverse wave propagation in such structures. This study also demonstrates that combining finite and infinite element approaches provides accurate and reliable simulation of wave phenomena in functionally graded piezoelectric materials, which has applications in sensors, actuators, and non-destructive testing. Full article

This paper extends the previous work by the author on m-null pairs of operators in Hilbert space. If an elementary operator L has elementary symbols A and B that are p-null and q-null, respectively, then L is $(p+q-1)$-null. Here, we prove the converse under strictness conditions, modulo some nonzero multiplicative constant—if L is strictly $(p+q-1)$-null, then a scalar $\lambda \ne 0$ exists such that $\lambda A$ is strictly p-null and ${\lambda }^{-1}B$ is strictly q-null. Our constructive argument relies essentially on algebraic and combinatorial methods. Thus, the result obtained by Gu on m-isometries is recovered without resorting to spectral analysis. For several operator classes that generalize m-isometries and are subsumed by m-null operators, the result is new. Full article

The inverse mixed variational inequality problem comes from classical variational inequality, and it has many applications. In this paper, we propose new algorithms to study the inverse mixed variational inequality problems in Hilbert spaces, and these algorithms are based on the generalized projection operator. Next, we establish convergence theorems under inverse strong monotonicity conditions. In addition, we also provide inertial-type algorithms for the inverse mixed variational inequality problems with conditions that differ from the above convergence theorems. Full article

In the present paper we study a class of Toeplitz operators called concentration operators that are self-adjoint and compact in the linear canonical Dunkl setting. We show that a finite vector space spanned by the first eigenfunctions of such operators is of a maximal phase-space concentration and has the best phase-space concentrated scalogram inside the region of interest. Then, using these eigenfunctions, we can effectively approximate functions that are essentially localized in specific regions, and corresponding error estimates are given. These research results cover in particular the classical and the Hankel settings, and have potential application values in fields such as signal processing and quantum physics, providing a new theoretical basis for relevant research. Full article

This study presents an innovative solution method for ultra-fine group slowing-down equations tailored to stochastic media with double heterogeneity (DH), focusing on advanced nuclear fuels such as fully ceramic microencapsulated (FCM) fuel and Mixed Oxide (MOX) fuel. Addressing the limitations of conventional resonance calculation methods in handling DH effects, the proposed UFGSP method (the ultra-fine group slowing-down method with the Sanchez–Pomraning method) integrates the Sanchez–Pomraning technique with the ultra-fine group transport theory to resolve spatially dependent resonance cross-sections in both matrix and particle phases. The method employs high-fidelity geometric modeling, iterative cross-section homogenization, and flux reconstruction to capture neutron self-shielding effects in stochastically distributed media. Validation across seven FCM fuel cases, four poison particle configurations (BISO/QUADRISO, Bi/Tri-structural Isotropic), and four plutonium spot problems demonstrated exceptional accuracy, with maximum deviations in effective multiplication factor k_eff and resonance cross-sections remaining within ±138 pcm and ±2.4%, respectively. Key innovations include the ability to resolve radial flux distributions within TRISO particles and address resonance interference in MOX fuel matrices. The results confirm that the UFGSP method significantly enhances computational precision for DH problems, offering a robust tool for next-generation reactor design and safety analysis. Full article

In the present paper we define and study a new wavelet transformation associated to the linear canonical Dunkl transform (LCDT), which has been widely used in signal processing and other related fields. Then we define and study a class of pseudo-differential operators known as time-frequency (or localization) operators and we give criteria for its boundedness and Schatten class properties. Full article

In the present work, a Cauchy (initial) problem for a fractional linear system with distributed delays and Caputo-type derivatives of incommensurate order is considered. As the main result, a new straightforward approach to study the considered initial problem via an equivalent Volterra–Stieltjes integral system is introduced. This approach is based on the existence and uniqueness of a global fundamental matrix for the corresponding homogeneous system, which allows us to prove that the corresponding resolvent system possesses a unique measure resolvent kernel. As a consequence, an integral representation of the solutions of the studied system is obtained. Then, using the obtained results, relations between the stability of the zero solution of the homogeneous system and different kinds of boundedness of its other solutions are established. Full article

We study a Dirichlet $\mu$-parametric differential problem driven by a variable competing exponent operator, given by the sum of a negative p-Laplace differential operator and a positive q-Laplace differential operator, with a multivalued reaction term in the sense of a Clarke subdifferential. The parameter $\mu \in \mathbb{R}$ makes it possible to distinguish between the cases of an elliptic principal operator $(\mu \le 0$) and a non-elliptic principal operator ($\mu >0$). We focus on the well-posedness of the problem in variable exponent Sobolev spaces, starting with energy functional analysis. Using a Galerkin approach with a priori estimate and embedding results, we show that the functional associated with the problem is coercive; hence, we prove the existence of generalized and weak solutions. Full article

In this paper, a new and general form of truncated-exponential-based general-Appell polynomials is introduced using the two-variable general-Appell polynomials. For this new polynomial family, we present an explicit representation, recurrence relation, shift operators, differential equation, determinant representation, and some other properties. Finally, two special cases of this family, truncated-exponential-based Hermite-type and truncated-exponential-based Laguerre–Frobenius Euler polynomials, are introduced and their corresponding properties are obtained. Full article

In this paper, we consider a problem of decreasing the summation order in the Abel-Lidskii sense. The problem has a significant prehistory since 1962 created by such mathematicians as Lidskii V.B., Katsnelson V.E., Matsaev V.I., Agranovich M.S. As a main result, we will show that the summation order can be decreased from the values more than a convergence exponent, in accordance with the Lidskii V.B. results, to an arbitrary small positive number. Additionally, we construct a qualitative theory of summation in the Abel-Lidkii sense and produce a number of fundamental propositions that may represent the interest themselves. Full article

Locally solid convergence structures provide a unifying framework for both topological and non-topological convergences in vector lattice theory. In this paper, we explore various extensions and applications of locally solid convergence structures. We characterize unbounded locally solid convergences in different spaces, establish connections with bornological convergences, and investigate their applications in functional analysis. Additionally, we generalize these structures to non-Archimedean vector lattices and compare them with traditional topological frameworks. Finally, we develop applications in fixed point theory and operator spaces. Our results contribute to a deeper understanding of the interplay between different types of convergence structures in mathematical analysis. Full article

In this manuscript, we define the $(E,F)$-invex set, $(E,F)$-invex functions, and $(E,F)$-preinvex functions on Euclidean space, i.e., simply vector space. We extend these concepts on the Riemannian manifold. We also detail the fundamental properties of $(E,F)$-preinvex functions and provide some examples that illustrate the concepts well. We have established a relation between $(E,F)$-invex and $(E,F)$-preinvex functions on Riemannian manifolds. We introduce the conditions $\mathcal{A}$ and define the $(E,F)$-proximal sub-gradient. $(E,F)$-preinvex functions are also used to demonstrate their applicability in optimization problems. In the last, we establish the points of extrema of a non-smooth $(E,F)$-preinvex functions on $(E,F)$-invex subset of the Riemannian manifolds by using the $(E,F)$-proximal sub-gradient. Full article

Motivated by Botelho and Jamison’s seminal 2010 study on elementary operators that are m-isometries, in this paper, we introduce the concept of m-null pairs of operators and establish some structural properties and characterizations of the class of elementary operators whose symbols are m-null (so-called m-null elementary operators). It is shown that if the symbols of an elementary operator L are, in turn, a p-null elementary operator and a q-null elementary operator, then L is a $(p+q-1)$-null elementary operator. Some extant results on elementary m-isometries can be recovered from this renewed perspective, often providing added value. Full article

In this paper, a completely smooth lower-order penalty method for solving a second-order cone mixed complementarity problem (SOCMCP) is studied. Four distinct types of smoothing functions are taken into account. According to this method, SOCMCP is approximated by asymptotically completely smooth lower-order penalty equations (CSLOPEs), which includes penalty and smoothing parameters. Under mild assumptions, the main results show that as the penalty parameter approaches positive infinity and the smooth parameter monotonically decreases to zero, the solution sequence of asymptotic CSLOPEs converges exponentially to the solution of SOCMCP. An algorithm based on this approach is developed, and numerical experiments demonstrate its feasibility. The performance profile of four specific smooth functions is given. The final results show that the numerical performance of CSLOPEs is better than that of a smooth-like lower-order penalty method. Full article