This article deals with a new concept of nonlocal proportional segmental boundary conditions with respect to initial and terminal sections of the given domain. Equipped with these conditions, we investigate the existence and uniqueness of solutions for a Caputo-type fractional differential equation with the nonlinearity depending upon the unknown function together with its lower order fractional derivative. We apply the standard tools of the fixed point theory to accomplish the desired results. Our study is useful in the given configuration as it helps to comprehend the fractional boundary value problems in the sense of proportional boundary conditions.
The present paper examines the following Diophantine equation: T-n = F-k & centerdot; F-l & centerdot; F-m where T-n is the n-th Tribonacci number and likewise F-k is the k-th Fibonacci number and so on as variables. As an application of the Baker's method, we show that the equation has only one solution apart from the trivial one, namely (n, k, l, m) = (12, 4, 6, 8). This paper can be considered as a continuation work of the paper by Luca et al, 2023.
This article explores the behavior of Sagbi-Gr & ouml;bner bases for modules over polynomial subalgebras under the process of homogenization and dehomogenization. We prove that the Sagbi-Gr & ouml;bner basis for submodules over subalgebras behaves well in these processes, as the property of being a Sagbi-Gr & ouml;bner basis is preserved under homogenization and dehomogenization.
In this paper, we examine the local well-posedness of the initial value problem for the HirotaSatsuma system within Gevrey spaces. This system, which consists of a coupled nonlinear dispersive partial differential equation, models the interactions between long and short waves and is known for its integrable structure. We demonstrate that the problem is locally well-posed in the Gevrey spaces G(eta,delta,k)(& Ropf;) & times; G(eta,delta,k+1) (& Ropf;) for k > - 1/8 ,delta > 0, and eta >= 1. This finding improves upon existing well-posedness results in Sobolev spaces H-k(& Ropf;) & times; Hk+1(& Ropf;). Our approach involves a meticulous analysis of linear and bilinear estimates within Gevrey classes. By utilizing Fourier analytical techniques and reformulating the system into an integral equation through Duhamels principle, we establish the necessary bounds for applying a fixed-point argument. This process yields results regarding existence, uniqueness, and continuous dependence on initial data. Furthermore, we show that the solution demonstrates Gevrey-3 eta regularity in time, capturing the smoothing properties of the system. These results deepen our understanding of analytic-type regularity in nonlinear dispersive systems.
There are 22 types of doubly semi-equivelar maps, with curvature 0, on the plane which provide infinitely many doubly semi-equivelar maps of respective types on the torus. In this article, we show that every such doubly semi-equivelar map on the torus contains a Hamiltonian cycle. As a consequence, we establish the Nash-Williams conjecture for the graphs associated with these doubly semi-equivelar maps by showing that these graphs are either 3-connected or 4-connected.
Considering the interesting results obtained recently by studying Rabotnov function, in this paper using the normalized Rabotnov function and the concept of subordination related with the Lucas Balancing polynomial, we defined two new subclasses of the bi-starlike and biconvex function of complex order in the open unit disc and obtained bounds of the initial Taylor-Maclaurin coefficients for functions in these classes. Furthermore, we have determined the Fekete-Szego & uml; inequalities for function in the above mentioned classes. Several related corollaries are also presented.
This paper presents a quaternion-based framework for constructing rotation-minimizing motions in Euclidean 3-space, formulated via quaternion operator. By introducing a novel quaternion operator, we derive angular velocity representations directly from the quaternion derivative and its conjugate, enabling smooth and minimal-rotation motion. The proposed approach generates rotation-minimizing motions whose trajectories are aligned with the orbits of a given spatial curve, and it offers a convenient mechanism to compute the corresponding quaternion representation when the orbit and a spatial position are specified. The effectiveness of the method is demonstrated through numerical experiments involving the spherical indicatricestangent, normal, and binormal-of space curves. Additionally, we provide a geometric characterization of quaternionic helical curves with respect to the tangential image T, highlighting the theoretical and practical implications of the proposed model in motion design and spatial kinematics.
In this paper it is introduced a new generalized pseudo-operation with one parameter of the following form: x circle plus(epsilon) y = h(-1)(h(x) + epsilon h(y)), where h is an n vector-valued continuous function, defined on a subset H of R-n and possessing an inverse function h(-1), epsilon is an arbitrary but fixed positive real number. Five kinds of cones are introduced, which are used to establish the constraint qualifications. The generalized Karush-Kuhn-Tucker necessary optimality conditions are developed for a class of generalized (h, phi)(epsilon)-differentiable single-objective programming problems and then for multiobjective programming problems, by using this generalized pseudo-operations, an extension of Avriel-Ben-Tal algebraic operations. The results obtained in this paper generalize and extend previous results obtained in this field. At the same time, in the final chapter, a cryptographic application using Ben-Tal type operators is presented.
This paper develops a unified framework connecting lattice theory and suborbital graphs, with particular focus on Farey graph. By equipping the Farey graph with lattice structures, we reveal new combinatorial and algebraic properties. Essential element graphs, Hasse diagrams, and integer sequences for vertices and edges are systematically explored. This study distinguishes itself from previous studies by expanding proofs, consolidating definitions, and providing illustrative examples. Our results demonstrate how a lattice perspective can enrich theoretical and applied research in number theory, geometry, and network science.
In this paper we present Lefschetz type fixed point theorems for maps defined on admissible acyclic dominated spaces.
In this paper, we introduce and study the notion of bipolar fuzzy n-fold positive implicative filters within the framework of hoop algebras, and examine their fundamental properties. We also define and investigate bipolar fuzzy n-fold fantastic filters, thereby extending bipolar fuzzy set theory into a multi-valued logical setting. In addition, we explore the relationships between bipolar fuzzy n-fold positive implicative filters and other related classes of bipolar fuzzy filters, including fuzzy n-fold implicative filters and bipolar fuzzy n-fold fantastic filters. This work offers a detailed analysis of the structural characteristics and interrelations among these filters, contributing to the broader development of non-classical algebraic logic and fuzzy systems. Several illustrative examples are provided to support and clarify the theoretical results.
In the present paper, we propose a new notion, namely, the interpolative contractions in the context of the perturbed metric spaces. For these mappings, we give a fixed-point result and provide an example to support the advances brought by the new results. Moreover, we give extend our results and provide a Meir-Keeler type fixed-point result in perturbed metric spaces.
The Mittag-Leffler function plays an important role in Geometric Function Theory, particularly in the study of analytic and meromorphic function classes. Among its various generalizations, the Barnes-Mittag-Leffler function stands out due to its intricate structure and applications in diverse mathematical fields. In this paper, our main focus is to investigate the convolution properties of these functions and establish conditions that ensure specific geometric characteristics. Additionally, we explore membership relations for functions in these classes. The results obtained in this work are novel, and their significance is demonstrated through various illustrative consequences and corollaries, emphasizing their potential impact in function theory and its applications.
The present article addresses the concept of 2-nil primary ideals in commutative rings, expanding the comprehension of ideal categories such as 2-nil, 2-absorbing ideals, and quasi-primary ideals. The study explores the characteristics and connections of 2-nil primary ideals, offering a comprehensive framework for understanding their significance in ring theory. The paper presents examples and arguments that illustrate the relationships between 2-nil primary ideals and other well-known classes of ideals, such as prime, primary, and n-ideals, while highlighting their differences. Furthermore, we investigate how the 2-nil primary ideal behaves under homomorphisms, quotients, localization, products, and idealizations.
In this paper, we show that there does not exist a polynomial D (2 X + 1)-quadruple { a, b, c, d }, such that 0 < a < b < c < d and deg d = deg b .
In this study, Sheffer stroke Nelson algebras (briefly, s-Nelson algebras), (ultra) ideals, quasi-subalgebras, quotient sets, and fuzzy structures on these algebraic structures are introduced. The relationships between s-Nelson and Nelson algebras are analyzed. It is also shown that an s-Nelson algebra is a bounded distributive modular lattice, and the family of all ideals forms a complete distributive modular lattice. A congruence relation on an s-Nelson algebra is determined by an ideal and quotient s-Nelson algebras are constructed by this congruence relation. Finally, it is indicated that a quotient s-Nelson algebra constructed by the ultra ideal is totally ordered and that the cardinality of the quotient is less than or equal to 2.
In the paper, an approach is proposed that allowed to establish new upper estimates for products of inner radii of mutually non-overlapping domains.
In this paper we propose to study a six-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) universe without time. The way we study this timeless universe is the classic one: we highlight future oriented time-like loops and closed chains of future oriented time-like curves. Inside this six-dimensional FLRW universe it is embedded a four-dimensional classical FLRW universe.
The objective of this paper is to investigate the fundamental solution and Green’s function in a semi-infinite orthotropic photothermoelastic diffusion medium that is based on the Moore-Gibson-Thompson heat equation (MGTPWD). First, we transform the governing equations into a two-dimensional format and then make dimensionless to derive the general solution for the MGTPWD model. Based on the general solution, nine new harmonic functions were used to build the fundamental solution and Green’s function for a steady point heat source on the surface and inside of a semi-infinite material in the proposed model. The elementary functions are used to express the components of displacements, stress, temperature distribution, carrier density distribution and chemical potential. The physical field quantities (stress, temperature distribution, carrier density distribution and chemical potential) are computed numerically and presented graphically to depict diffusion impact. A unique case have been deduced and compared with earlier known results. The results acquired can be used to delineate a variety of semiconductor elements during the coupled photo thermoelastic impact and can also be applied in the material and engineering sciences.
In this paper, we introduce the notion of pointwise hemi-slant sub-manifolds of nearly Kaehler manifolds. Further, we study their warped products and prove the necessary and sufficient condition that a point-wise hemi-slant submanifold to be a warped product manifold. Also, we establish a sharp inequality for the pointwise hemi-slant warped product submanifolds of the form M = M⊥ ×f Mθ which is mixed totally geodesic in an arbitrary nearly Kaehler manifold ~M. The equality case is also discussed.
