https://mir.kashanu.ac.ir/ Mathematics Interdisciplinary Research en daily 1 Tue, 01 Sep 2026 00:00:00 +0330 Tue, 01 Sep 2026 00:00:00 +0330 https://mir.kashanu.ac.ir/article_115556.html ‎Considering the importance of mixed 3-Sasakian manifolds which admit Einstein metrics‎, ‎we introduce generalized mixed 3-$ \psi $-recurrent manifolds on mixed 3-Sasakian structures‎. ‎We prove that a non-flat generalized mixed 3-$\psi$-recurrent manifold is a generalized recurrent manifold with its horizontal vector fields‎. ‎Also‎, ‎we obtain a relation between associated 1-forms $\gamma_{i} $'s‎ and $\theta_{i} $'s for a generalized mixed 3-$ \psi$-recurrent manifold‎. ‎Moreover‎, ‎we give a necessary and sufficient condition for a mixed 3-Sasakian manifold to be a generalized mixed 3-$\psi$-recurrent‎. ‎Next‎, ‎we find the Riemannian curvature representation of a mixed 3-Sasakian manifold when that is a generalized mixed 3-$\psi$-recurrent‎. https://mir.kashanu.ac.ir/article_115592.html ‎This paper presents a novel integration of mimetic gravity and massive bi-gravity theories‎. ‎Despite the success of general relativity (GR)‎, ‎explaining cosmic phenomena requires additional elements like dark matter and dark energy‎. ‎Mimetic gravity extends GR's degrees of freedom while respecting conformal symmetry‎, ‎and bi-gravity introduces an additional metric field for massive gravity‎. We redefine the action for combining these theories and linearize it around a flat spacetime solution‎. ‎Our analysis highlights the dynamical behavior and stability of the combined model‎, ‎offering insights for further theoretical and empirical investigations‎. ‎This work contributes to bridging GR with quantum field theories and exploring new directions in gravitational research‎. https://mir.kashanu.ac.ir/article_115653.html ‎A vertex subset $S \subseteq V(G)$ is defined as a secure dominating set if‎, ‎for any vertex u outside of S‎, ‎there is a neighbor $v \in S$ such that the set $(S \setminus \{v\}) \cup \{u\}$ remains a dominating set for the graph $G$‎. ‎The minimum cardinality of such a set is termed the secure domination number and is denoted by $\gamma_s(G)$‎. ‎In the present study‎, ‎we establish specific bounds for the secure domination number of Kneser graphs K(n‎, ‎k)‎. ‎We further prove that for the condition $n \ge k^2‎ + ‎2k$‎, ‎the value of $\gamma_s(K(n‎, ‎k))$ is precisely k‎ + ‎2‎. https://mir.kashanu.ac.ir/article_115673.html ‎In this paper‎, ‎we propose a novel descent-based hybrid algorithm for solving nonsmooth box-constrained optimization problems‎. ‎The method combines an $\varepsilon$-subdifferential approximation with heuristic local and global line search strategies‎. ‎Theoretical analysis establishes the global convergence‎ ‎of the algorithm‎ ‎under Fritz John optimality conditions‎. ‎To demonstrate the effectiveness of the proposed approach‎, ‎it is applied to several standard grayscale test images for denoising purposes‎, ‎addressing various types of noise‎, ‎including Gaussian and salt-and-pepper noise‎. ‎Moreover‎, ‎extensive experiments and comparative analyses with existing denoising algorithms confirm the superior performance of our method in terms of restoration quality‎, ‎particularly with respect to PSNR and SSIM metrics‎. https://mir.kashanu.ac.ir/article_115674.html ‎We present a simplified formulation of multipliers in commutative Banach algebras by relaxing the classical faithfulness condition in [1, Theorem 3.2]‎. ‎A concise and transparent proof is provided‎. ‎These multipliers have significant applications in engineering‎, ‎particularly in earthquake engineering‎, ‎where frequency-domain analysis plays a central role‎. ‎This study investigates their use in signal theory for seismic wave analysis through the Fourier transform‎. ‎Multipliers are interpreted as frequency-domain operators for filtering and modeling structural responses‎, ‎illustrating their relevance to seismic optimization‎. ‎Numerical simulations support the theoretical results and demonstrate that multiplier-based filtering can effectively modify seismic signal spectra in applied settings‎. https://mir.kashanu.ac.ir/article_115557.html ‎Basic vector differential operators‎, ‎such as gradient‎, ‎divergence‎, ‎Laplacian‎, ‎and curl operators‎, ‎are generalized and developed in elliptical coordinate systems in fractional space‎. ‎The equation of Helmholtz in fractional space in an elliptical coordinate system is modified and solved in this coordinate and space for the investigation of wave propagation in the mentioned configuration‎. The general solutions of the scalar wave equation in fractional space in the elliptical coordinate system are obtained regarding the confluent Heun function‎. ‎In terms of longitudinal electromagnetic field components in elliptical coordinate systems in fractional space‎, ‎transverse electromagnetic field components are obtained‎. ‎The electric and magnetic fields in elliptical coordinates systems in fractional space are developed in terms of‎ ‎vector potentials‎, ‎and so TE and TM modes are investigated‎. ‎For all cases studied‎, ‎when the dimension is assumed to be an integer‎, ‎the classical results are rewritten to validate the results‎. https://mir.kashanu.ac.ir/article_115655.html ‎In this paper‎, ‎an inverse nodal problem (INP) is solved for the Sturm-Liouville (S-L) equation with Dirichlet boundary conditions and discontinuity conditions inside (0,L)‎. ‎First‎, ‎by new Pr\"{u}fer substitutions‎, ‎we obtain the asymptotic estimates of the eigenvalues‎. ‎Then‎, ‎by using the nodal points and nodal lengths‎, ‎we solve the inverse nodal problem and present the potential‎.