In this paper, we find necessary and sufficient conditions for $q$-Sheffer polynomials to be $d$-orthogonal. Moreover, an example is presented and with the help of this example, we rediscover some known $d$-orthogonal polynomial sets.
This paper introduces and explores a novel subclass R-Sigma(h,p) (lambda, gamma) of bi-univalent functions within the open unit disk U. We establish upper bounds for the second, third, and fourth coefficients of functions belonging to this class. Furthermore, we derive estimates for the Fekete-Szego problem in this context. The results, presented in this study extend and enhance several recent works by earlier authors.
Time series data can be analyzed through various techniques to tackle classification or regression tasks. Symbolic Aggregate Approximation (SAX) is one such technique used for time series data reduction that converts the data into a symbolic representation, enabling more efficient storage, retrieval, and analysis by reducing the dimensionality while preserving the essential patterns within the time series. In this paper, we provide a systematic literature review of SAX by examining relevant literature from 2007 to 2025. The review includes 321 articles sourced from the Web of Science (WOS) database. However, the 85 most cited and recently published studies are summarized. Utilizing collaboration network analysis, the study identifies the nations, affiliations, and authors involved in SAX research, as well as their co-authors and commonalities. Additionally, an analysis is conducted to explore the potential relationship between the articles and the United Nations' Sustainable Development Goals. These findings provide insights into the current landscape of SAX research and offer potential avenues for future exploration. By pinpointing research gaps, scholars can use this review to anticipate forthcoming research trajectories.
In the study, the new numerical solutions of fractional Klein-Gordon equations are obtained by utilizing the optimal homotopy analysis method. We determine the residual error function for the selection of arbitrary parameter & hbar;. The serial solutions of fractional Klein-Gordon equations have been obtained satisfactorily by applying this technique. Based on the solutions derived from the requisite equations, it has been demonstrated that this method is applicable to fractional partial differential equations.
This study introduces the Transmuted Half Logistic Garima (THLG) distribution, a novel and flexible model developed for analyzing lifetime data. The THLG distribution extends the Garima distribution by applying the Half Logistic generator to its cumulative distribution function, enhancing its ability to model a wider range of data patterns, including various shapes and hazard rate behaviors. We investigate the statistical properties of the THLG distribution in detail and estimate its parameters using the method of maximum likelihood estimation (MLE). To assess the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Furthermore, the applicability of the THLG distribution is demonstrated through the analysis of three real-world datasets. The findings show that the THLG distribution outperforms several well-known lifetime distributions, highlighting its potential as a robust tool for reliability and survival analysis.
In this study, the solution of the steady magnetohydrodynamic (MHD) equations is considered on various 2D and 3D closed domains (triangle, tetrahedron, pyramid and conic) and channel configurations such as swollen channel, collapsed channel, narrowed channel and wrinkled curved channel which are encountered in many real-life applications. As a numerical procedure both stabilized finite element method (FEM) and coupled dual reciprocity boundary element method (DRBEM) formulation are used. The coupled DRBEM is different from the previous literature on decoupled DRBEM, and it enables the use of different boundary condition types that are proposed for the moderate and high Hartmann number values. The other benefit of coupled DRBEM is that it combines all the coefficients of the unknown variables including the normal derivatives into a single coefficient matrix, therefore in one computation stroke one finds the solution to the problem. The wrinkled curved channel flow may be applied to the analysis of blood flow under the influence of an externally applied magnetic field in the stenosed artery. Some numerical calculations were performed for the different problem parameters and boundary conditions. The comparison of the results for some test problems using the proposed numerical schemes are presented in tables and contour plots.
In this paper, a new generalization of Bernstein operators is defined. The Korovkin type approximation and the statistical approximation of this new operator are studied. Voronovskaja type and quantitative Voronovskaja type approximation theorems are proved. Graphs of the approximation are obtained using the Maple program.
In this paper, we study the balancing and co-balancing problems for the coefficients located along the direction $(1,-1)$ of the Delannoy triangle. Motivated by our search for the solutions of balancing problem, we give a novel identity on the Delannoy triangle.
This paper investigates the resilient multi-period, multi-stage supply chain (SC) network design problem under demand and raw material quality uncertainty within a just-in-time (JIT) distribution setting, based on a real case study. The proposed approach models a four-stage SC comprising suppliers, manufacturers, distributors, and retailers, and develops two-stage stochastic programming and robust optimization models to enhance resilience. Unlike existing studies, this research uniquely integrates JIT distribution with the simultaneous consideration of demand and raw material quality uncertainties, providing practical, data-driven insights for decision-makers. Computational results show that the proposed models produce applicable solutions for real-world implementation. Across all models, high-quality raw materials are preferred 54% in the deterministic model, 55% on average in 30 of 40 stochastic scenarios, and 52% in the robust model, even under worst-case conditions. These findings indicate that prioritizing high-quality raw materials, despite higher purchasing costs, is crucial for maintaining JIT principles and ensuring on-time deliveries. Furthermore, the results highlight that the strategic location of distributors is critical to meeting retailers’ demand at the right time and in the right quantity.
The integrity parameter relates a set of vertices and other disconnected components. For improved connectivity, a vulnerability parameter should address the relation between all vertices. Spanning integrity encourages all the vertices to be connected by means of spanning. In this paper, the vulnerability parameter spanning integrity is introduced, for the signed fuzzy graph (SFG). The parameter is defined and explained with some examples. The spanning integrity is determined for standard SFGs, such as star SFG, complete SFG, bipartite SFG and complete bipartite SFG. Operations on SFGs are discussed. Spanning integrity is calculated for union, join, and Cartesian products of SFG. An algorithm is presented to compute the spanning integrity of SFG. This algorithm is validated by practical application in air networks. It helps to find the best route and to overcome the complicated connection between destinations while implementing a new air project, in a simple manner.
In this paper, we investigate the gradient Schouten soliton structure on the tangent bundle TM of a Riemannian manifold endowed with the Sasaki metric (S)g. The study is carried out with respect to an adapted frame. We derive necessary and sufficient conditions for the quadruples (TM, (S)g, (V)f, lambda) and (TM, (S)g, (C)f, lambda) to define gradient Schouten solitons.
In this study, we consider the Klein–Gordon s-wave equation defined on the half line under impulsive condition and construct the corresponding differential operator. We then introduce the transfer matrices associated with the impulsive Klein–Gordon s-wave operator on the half line and employ them to analyze the scattering function and its analytic structure through an alternative operator-theoretic method. This approach enables a new characterization of the scattering behavior and establishes connections between the analytic properties of the transfer matrices and the spectral features of the operator. In the final part of the study, we construct the resolvent operator and examine its analytic structure.
The present study concerns the investigation of Kenmotsu manifolds endowed with $\eta$-Ricci-Bourguignon solitons. In particular, we aim to establish certain properties of $\eta$-Ricci-Bourguignon solitons on submanifolds isometrically immersed into a Kenmotsu manifold when its potential vector field is the tangential component of the $\varphi(\mathcal{R}ic)$-vector field. Finally, we prove that an $\eta$-Ricci-Bourguignon soliton on a hypersurface whose potential vector field is the tangential component of the $\varphi(\mathcal{R}ic)$-vector field is both a generalized and a pseudo-generalized quasi-Einstein manifold.
Let $\Phi_1, \Phi_2$ be Young functions. In this paper, we examine the inclusion relations among the Orlicz amalgam spaces $W(L^{\Phi_1} (\mathbb{R}^n), L^{\Phi_2} (\mathbb{R}^n))$, where the Orlicz spaces $L^{\Phi_1}(\mathbb{R}^n)$ and $L^{\Phi_2}(\mathbb{R}^n)$ are called the local and global components, respectively. Besides Lebesgue type Wiener amalgam spaces, our study is a generalization of the results that have been obtained for the Orlicz spaces and Lebesgue spaces.
In this paper, we first reconsider Sabban frame of curves on $2-$sphere $S^{2}$ in $\mathbb{R}^{3}$ with the help of the properties of quaternion algebra and then, we define two different types of quaternionic Sabban frame of the curves on $3$-sphere $S^{3}$ in $\mathbb{R}^{4}$. Also, we support the theory in the paper with some examples.
Let $\mathcal{P}_{\mu}$ represent the class of analytic functions $\wp(z)$ defined in the open unit disc $\varDelta=\{z: |z|<1 \}$ with $\wp(0)=1$ and $$ \left| \frac{\wp(z)-1}{\wp(z)+1} \right| < \mu. $$ In this paper, we introduce two new subclasses $\mathcal{L}_{u,v}(\alpha,\beta,\mu)$ and $\mathcal{L}^\lambda_{u,v}(\alpha,\beta,\mu)$ of the class of close-to-star functions that satisfy the conditions: $$ \left( \alpha \frac{(\mathscr{L}_{u,v} f(z))'}{g'(z)}+\beta \frac{\mathscr{L}_{u,v} f(z)}{g(z)} \right) \in\mathcal{P}_{\mu} $$ and $$ \left(\alpha \frac{((\mathscr{L}_{u,v} f(z))')^{\lambda}}{(g'(z))^{\lambda}}+\beta \frac{(\mathscr{L}_{u,v} f(z))^{\lambda}}{(g(z))^{\lambda}} \right) \in\mathcal{P}_{\mu}, $$ respectively. Functions $f$ in the new classes are normalized analytic functions defined in the unit disc $\varDelta$ such that $g$ is starlike and $\mathscr{L}_{u,v}$ is the Carlson-Shaffer operator. Some reported results for $f\in\mathcal{L}_{u,v}(\alpha,\beta,\mu)$ include the integral representation formula, some coefficient estimates, Fekete-Szegö estimates for real and complex parameters, and some inclusion properties. All the results are sharp. Again, some early coefficient estimates for functions $f\in\mathcal{L}^\lambda_{u,v}(\alpha,\beta,\mu)$ are investigated. Furthermore, a number of remarks to show the relationship between the new classes and some existing classes are clearly discussed.
. In this paper, we study the cooling of an infinitely long heated cylinder with an arbitrary initial temperature profile, modeled by the one-dimensional heat conduction equation in cylindrical coordinates. Extending the work of Chandel and Gupta, who used the multivariable H-function, we apply the multivariable Aleph-function, Srivastava-Daoust function, and multivariable polynomials to derive new integral and series solutions. The temperature distribution is expressed using Bessel functions and multivariable expansions, allowing for generalization, limiting cases, and asymptotic analysis. These results contribute to the analytical modeling of heat conduction and may be useful in thermal analysis and mathematical physics.
. Algebraic graph theory is a rapidly growing research area in which several graphs based on algebraic structures are introduced and investigated. The algebraic intersection graphs, called the n-inordinate invariant intersection graphs, and the n-inordinate invariant non-intersection graphs, have been constructed on the symmetric group and various properties of these graphs are studied, in the literature. In this article, we analyse the structure of these graphs by examining different types of geodetic sets in them.
Let Phi 1, Phi 2 be Young functions. In this paper, we examine the inclusion relations among the Orlicz amalgam spaces W (L Phi 1 (Rn), L Phi 2 (Rn)), where the Orlicz spaces L Phi 1 (Rn) and L Phi 2 (Rn) are called the local and global components, respectively. Besides Lebesgue type Wiener amalgam spaces, our study is a generalization of the results that have been obtained for the Orlicz spaces and Lebesgue spaces.
