A finite-dimensional theory of special-affine transforms is developed for position-decorated spectral graphs. A Hermitian graph Laplacian generates a normalized frequency observable, while a normalized diagonal decoration supplies the position observable. Their ordered exponentials define graph Weyl operators, which are coupled to Iwasawa and three-shear graph linear-canonical factors. The resulting transforms are unitary and covariant under decorated graph isomorphisms, including monomial gauge-permutation equivalence for Hermitian directed Laplacians. The commutator generator is proved to be Hilbert–Schmidt orthogonal to the Laplacian commutant, yielding an exact defect formula and a weighted-Laplacian eigenproblem for selecting the position decoration. Quantitative Baker–Campbell–Hausdorff estimates control local Weyl, Egorov, homogeneous, and full special-affine composition errors. For odd-prime cycles, quantized exponentials of centered position and momentum matrices recover the clock-shift system and its exact finite Weil covariance. Frame criteria, canonical Parseval preconditioning, and a reproducible sensor-graph experiment quantify reconstruction accuracy, noise amplification, conditioning trade-offs, and factorization dependence. The theory therefore connects finite operator obstructions with computable graph-transform design.
Delay integral equations provide an effective framework for modelling dynamic systems by incorporating the influence of past states on present behaviour and future evolution. Such equations arise naturally in applications including population dynamics, control theory, and engineering systems with aftereffects. In this paper, we establish the existence of optimal solutions for a system of delay integral equations (DIEs) with a constant delay ρ >0 . To this end, we introduce a new best proximity point (and pair) result in a reflexive Banach space (strictly convex) via a newly proposed condensing operator using the idea of measure of noncompactness. As a consequence, coupled best proximity point results are obtained. Finally, a numerical example is presented to illustrate the applicability and effectiveness of the theoretical results.
We introduce and investigate two new classes of Moore subcategories of the concrete category S[T] associated with an inclusion-preserving endofunctor T:Set⟶Set . We call these kinds of Moore subcategories the nonsingular and the mono Moore (T,Set) -subcategories, respectively. These notions refine the general theory of -Moore subcategories developed in some recent research and arise naturally when addressing specific problems related to the behavior of monomorphisms. For nonsingular Moore (T,Set) -subcategories we prove unique transportability and repleteness. Next, we also exhibit explicit descriptions of subobjects and extremal subobjects in terms of the domains of the monomorphisms arising in suitable (Epi,Mono) -factorizations in S[T] and a version of the Final Coalgebra Theorem for bounded endofunctors preserving extremal monomorphisms. On the other hand, in the case of mono Moore (T,Set) -subcategories we show that these subcategories are automatically nonsingular, that the corresponding faithful functor is a Grothendieck -fibration, that embeddings coincide with extremal monomorphisms, and that an extremal subobject classifier exists.
In this paper, we introduce new inequalities for positive definite matrices using the interpolational paths of the power means. Specifically, for positive definite matrices A, B , given q ≤ 1 ≤ p with q p and 0< ν≤μ < 1 , we prove that ν/μ≤A m_p,ν B - A m_q, ν B/A m_p,μ B - A m_q, μ B≤1 - ν/1 - μ, where A m_p,μ B stands for the interpolational path of the power means. We also introduce the interpolational path for sectorial and accretive matrices, deriving inequalities similar to those in the positive definite case by applying the aforementioned inequality. Additionally, we extend these results to sectorial and accretive matrices. We demonstrate that the proposed interpolational path preserves sectorial properties. These findings contribute to the broader study of matrix means, refining inequalities and improving approximations in matrix analysis. In the final section, we derive nuanced inequalities that describe how the geometric mean distributes over the power mean, clarifying the relationships between these matrix means.
In the present article, our aim is to investigate some geometric characteristics of the Q-tensors on Riemannian manifolds equipped with concurrent-recurrent vector fields (CRVF, in short). At first, we analyze the nature of Q-flat Riemannian manifolds admitting concurrent-recurrent vector fields. We also discuss some differential forms of Q tensors on Riemannian manifolds associated with CRVF. Next we prove that for a Q-symmetric Riemannian manifold admitting CRVF, Ω is a constant function. Also we construct a concrete non-trivial example that proves the existence of CRVF and validate some of our results. Moreover, we explore certain results on Q-flat tensors in the framework of perfect fluid mixed quasi-Einstein spacetimes.
In this paper, we consider the fractional powers of a linear operator associated with a higher-order abstract Cauchy problem defined by a linear parabolic equation. We also characterize the domain of the fractional powers and discuss the solvability of the fractional equation.
Hybrid nanofluids, with their advanced thermophysical properties and promising role in boosting heat transfer efficiency, have become a key area of focus for many researchers in the current era of technology. Novelty of this paper is mainly involved with heat transmission in variable thickness geometry in the existence of an inclined magnetic field, activation energy, and non-linear thermal radiation. Hybrid nanofluid composites are made by dissolving Al_2 O_3 (Aluminium oxide) and TiO_2 (Titanium oxide) In base fluid, engine oil. The modified governing equations for momentum and temperature, under relevant boundary conditions, are solved numerically using the precise and efficient bvp-4c Method. The Consequences of an inclined magnetic field, non-linear thermal radiation, power index of velocity, and activation energy are analysed thoroughly, and the outcomes are plotted graphically. Based on the results, we can observe that the fluid velocity decreases as a results considering a magnetic field that is inclined. As the power index velocity rises, the velocity profile reveals a decline.
In a historically neglected 1898 axiomatization of three-dimensional projective geometry, Mario Pieri proved that the Hexagon Theorem of Pappus is equivalent to a statement about the harmonic separation of point-pairs on a line. He made no appeal to continuity, but did rely on a weakened version of the Fundamental Theorem of K. G. C. von Staudt. A few months earlier, Pieri had published an axiomatization of n-dimensional projective geometry that was more widely circulated. There he claimed it is possible to demonstrate the equivalence without invoking the Fundamental Theorem. He did not present the proof and no published evidence has been found to support his claim. This paper validates Pieri's assertion with proofs of the hexagon theorem constructed solely from the postulates of incidence and separation of his earlier paper. One proof adopts strategies that Pieri used for his own published proof. The others adapt methods that A. N. Whitehead and H. F. Baker utilized for their proofs. The proofs presented here fulfill, in spirit, Pieri's 1905 promise to send Oswald Veblen a proof of hexagon theorem with no appeal to continuity or von Staudt’s theorem.
Let U be an open subset of a complex Banach space E , let v be a weight on U that separates the points of ℋ_v(U) , and let F be a complex Banach space. We introduce and study the class Π _p^lip_v(U,F) of p -summing weighted holomorphic Lipschitz mappings from U into F . We prove that this class, modulo constant functions, forms an injective Banach ideal of weighted holomorphic mappings. Using the Lipschitz-free space ℱ_v(U) over (U,d_v) , we establish a linearization theorem identifying these mappings with p -summing linear operators from ℱ_v(U) into F . Variants of the Pietsch Domination Theorem, Pietsch Factorization Theorem, and Maurey Extrapolation Theorem are presented. Furthermore, we introduce the space of F -valued ℋ_v -Lipschitz molecules and prove that its dual is isometrically isomorphic to Π _p^lip_v(U,F^*) under a suitable version of the Chevet-Saphar tensor norm.
In this article, we study a partial discrete Dirichlet boundary value problem together with its associated eigenvalue problem. More precisely, in the first part, we identify two eigenvalues λ _1(m) and λ ^*(m) of the associated eigenvalue problem and show that there is no eigenvalue between them. In the second part, we determine intervals of the parameter λ ensuring the existence of solutions, and we investigate the sign of these solutions in relation to λ _1(m) and λ ^*(m) .
In 2020, Carney et al. proved the quaternionic version of the Eneström-Kakeya Theorem. Numerous generalizations of Eneström–Kakeya Theorem are available in the literature [7, 8]. In this paper, we extend some of these generalizations to the quaternionic context and present several extensive results.
In this paper, we extend the classical Laguerre theorem on the zeros of polar derivatives to the setting of bicomplex polynomials. Due to the presence of zero divisors and the idempotent representation of bicomplex numbers, the usual complex arguments do not carry over directly. We introduce a notion of polar derivative for bicomplex polynomials and establish a bicomplex analogue of Laguerre’s theorem. The proof relies on a key lemma that expresses certain identities in terms of hyperbolic norms and idempotent components. As an application, we obtain a result on the location of zeros of the polar derivative relative to the original polynomial. These results lay the groundwork for further investigations in bicomplex function theory.
This manuscript discusses the existence and uniqueness result for the boundary value problem (BVP) of generalized hybrid fractional sequential integro-differential equations involving the ψ -Caputo derivative. Our existence results rely on tools of nonlinear analysis. More precisely, we apply the measure of noncompact and degree topology, and the uniqueness results are assured with the Banach contraction principle. The stability of solutions is derived with the help of Ulam-Hyers stability. Finally, we give an example to illustrate the validity of the main results.
In this paper, we study an analog of Titchmarsh’s theorem for the Hartley–Bessel transform on the real line. Using the Hartley–Bessel operator Λ _α , the associated generalized translation, and suitable higher-order differences, we obtain integrability and decay estimates for the Hartley–Bessel transform in weighted L^p spaces. More precisely, we prove conditions ensuring that ℋ_α (f) belongs to L^β (ℝ,dμ _α ) , where 1
In this paper, we prove the existence and uniqueness of common fixed point for two self-mappings satisfying the integral type contraction by using the concept of C-class functions in complete b-metric spaces. Additionally, an example and an application are provided to illustrate and support our main results.
This study investigates the influence of non-local memory effects on the nonlinear dynamics of malaria transmission using a fractional-order human mosquito model formulated in the Atangana–Baleanu–Caputo (ABC) sense. The model incorporates a non-singular kernel to capture hereditary characteristics inherent in epidemiological processes, with the fractional order acting as a control parameter governing system dynamics. Analytical results establish positivity, boundedness, and the existence of unique solutions, while stability conditions for disease-free and endemic equilibria are derived. Although the classical threshold structure governed by the basic reproduction number is preserved, the inclusion of memory effects produces significant qualitative changes in transient behavior. Specifically, decreasing the fractional order delays epidemic peaks, reduces infection intensity, and yields smoother convergence toward equilibrium, indicating a memory-induced modulation of nonlinear dynamics. Model parameters are calibrated using malaria incidence data from 2000–2023 , and numerical simulations confirm the robustness of these effects. The findings demonstrate that fractional dynamics fundamentally reshape transient epidemic evolution, providing new insight into memory-driven processes in complex biological systems and nonlinear epidemiological modeling.
Financial systems often exhibit complex, nonlinear behavior influenced by multiple interrelated economic factors. In this paper, a four-dimensional financial model is developed, incorporating the money supply as a new factor alongside interest rate, investment demand, and the price index. The model is initially formulated in integer order and later extended to fractional order to capture the memory effects characteristic of real-world financial processes. A comprehensive dynamic analysis is performed to investigate equilibrium points, stability conditions, and the impact of varying monetary injection efficiency. The effect of fractional order variation on system dynamics is also examined to understand its role in stability and complexity. To address instability, a feedback control strategy is proposed within the fractional framework to regulate the system’s behavior. Numerical simulations are used to validate the theoretical approach and demonstrate the potential utility of the control mechanism in maintaining financial system stability.
In this paper, we study locally conformally flat almost gradient Ricci solitons. By combining the almost Ricci soliton equation with the vanishing of the Weyl conformal curvature tensor, we prove that every complete connected locally conformally flat almost gradient Ricci soliton is locally isometric to a warped product of a type (t_1, t_2)× _ξ𝔇^m-1 of a real interval (t_1, t_2) and a space form 𝔇^m-1 of constant sectional curvature. The proof relies on geometric properties of the potential function, particularly the fact that its gradient is an eigenvector of both the Ricci tensor and the Hessian operator. Our result extends several rigidity and classification theorems for locally conformally flat gradient Ricci solitons to the broader framework of almost Ricci solitons.
