https://mir.kashanu.ac.ir/ Mathematics Interdisciplinary Research en daily 1 Sun, 01 Mar 2026 00:00:00 +0330 Sun, 01 Mar 2026 00:00:00 +0330 https://mir.kashanu.ac.ir/article_115327.html ‎This document introduces the idea of metallic vector fields in the framework of semi-Riemannian manifolds‎. ‎Then‎, ‎we study the geometry of such vector fields on closed and compact manifolds‎. ‎The existence of metallic fields on immersed submanifolds will also be investigated‎. ‎Finally‎, ‎we investigate metallic vector fields on warped product manifolds‎. https://mir.kashanu.ac.ir/article_115328.html ‎Assume that $ \mathcal{A} $ is a unital C*-algebra and $ a\in\mathcal{A} $ is a positive and invertible element‎. ‎Set \[ \mathcal{S}_a (\mathcal{A})=\{ \dfrac{f}{f(a)} \‎, : ‎\‎, ‎f \in \mathcal{S}(\mathcal{A})‎, ‎\‎, ‎f(a)\neq 0\}‎, ‎\] where $ \mathcal{S}(\mathcal{A}) $ is the state space of $ \mathcal{A} $‎. ‎The main aim of this paper is to introduce and study the notions of approximate a-orthogonality and approximate a-Birkhoff-James orthogonality associated to the norm‎: ‎\[ \|x\|_a = \sup_{\varphi \in \mathcal{S}_a(\mathcal{A})} \sqrt{\varphi(x* ax)}\quad (x\in \mathcal{A}),\] in C*-algebra $\mathcal{A}$‎.‎First‎, ‎by providing some examples‎, ‎we show that these approximate orthogonalities are generally incomparable in non-commutative C*-algebras‎. ‎Next‎, ‎we will see that under what conditions‎, ‎these orthogonality relationships are related‎. ‎Also‎, ‎two different characterizations of approximate a-Birkhoff-James orthogonality in terms of the elements of $ \mathcal{S}_a (\mathcal{A}) $ are obtained‎.‎Moreover‎, ‎the strong version of approximate a-Birkhoff-James orthogonality is studied‎. ‎Finally‎, ‎we prove that if approximate a-Birkhoff-James orthogonality and its strong version coincide on $ \mathcal{A} $‎, ‎then $ \mathcal{A} $ is commutative‎. https://mir.kashanu.ac.ir/article_115329.html ‎This paper proposes several new statistical bounds for graph energy derived from the eigenvalues of the adjacency matrix‎. ‎Using inequalities involving the arithmetic‎, ‎geometric‎, ‎and generalized means‎, ‎along with variance and standard deviation‎, ‎we establish both upper and lower bounds for $E(G)$‎. ‎These statistical bounds capture not only mean relationships but also eigenvalue variability‎, ‎offering more flexible and accurate estimates than conventional deterministic inequalities‎. ‎The approach integrates tools from inequality theory and spectral graph theory‎, ‎with applying weighted means and Jensen-type inequalities‎. ‎We also conjecture based on numerical evidence that the energy-to-geometric mean ratio converges to a constant value for large Erd\"{o}s-R\'{e}nyi random graphs‎. ‎A detailed analysis of path graphs demonstrates the effectiveness of the proposed bounds‎, ‎offering improved estimates‎. https://mir.kashanu.ac.ir/article_115339.html ‎Financial systemic risk refers to the transmission of distress among financial institutions‎, ‎posing a significant threat to economic stability‎. ‎Inspired by epidemiological modelling‎, ‎this study develops an extended compartmental framework based on the classical SIRS model to analyse the spread and control of financial systemic risk within a banking network‎. ‎The model introduces six compartments‎: ‎susceptible‎, ‎immune‎, ‎infected‎, ‎curated‎, ‎mitigated‎, ‎and removed to capture the diverse states of banks under systemic stress and regulatory intervention‎. ‎Central bank actions such as curatorship‎, ‎mitigation‎, ‎and temporary protection are explicitly incorporated‎. ‎The model is formulated as a system of ordinary differential equations‎, ‎and analytical techniques are employed to derive the risk reproduction number‎, ‎$R_{sr}$‎, ‎which serves as a threshold parameter governing the system’s long-term behaviour‎. ‎Two equilibrium points are identified‎: ‎the risk-free equilibrium‎, ‎which is locally and globally asymptotically stable when $R_{sr} < 1$‎, ‎and the endemic equilibrium‎, ‎which persists when $R_{sr} > 1$‎. ‎Numerical simulations demonstrate how variations in key parameters such as the rate of curatorship‎, ‎mitigation‎, ‎and protection affect the prevalence of financial contagion‎. ‎While the model does not yield fundamentally new theoretical insights‎, ‎it offers a structured framework for evaluating the impact of regulatory interventions‎. ‎The findings underscore the utility of epidemiological modelling in financial risk analysis and highlight the importance of timely and targeted control measures to prevent cascading failures in the banking sector‎. https://mir.kashanu.ac.ir/article_115341.html ‎This paper introduces a verified interval iterative method for computing the principal $p$th root of a square matrix along with rigorous interval enclosures‎. ‎Leveraging the epsilon inflation technique‎, ‎the proposed algorithm is reformulated as an inclusion method‎, ‎enabling robust control over approximation and rounding errors in finite-precision arithmetic‎. ‎The method exhibits quadratic convergence and does not require an initial enclosure containing the exact root‎, ‎which is a common limitation in existing interval approaches‎. ‎We further demonstrate that the midpoint matrix sequence generated by the iteration is well-behaved and numerically stable‎. ‎Theoretical analysis confirms the convergence of the interval enclosures to the exact matrix root‎, ‎and numerical experiments validate the method’s efficiency for large-scale matrices and high values of $p$‎. ‎As a practical contribution‎, ‎we provide implementable Mathematica code for the proposed algorithm‎, ‎facilitating reproducibility and further exploration‎. https://mir.kashanu.ac.ir/article_115350.html ‎In this work‎, ‎a novel method to finding the numerical solution of distributed-order fractional differential equations (DFDEs) is introduced‎. ‎This method is based on the Genocchi wavelets (GWs)‎, ‎and weighted residual method (collocations method)‎. ‎For this aim‎, ‎an exact mathematical formula that incorporates regularized beta functions is meticulously formulated to ascertain the Riemann-Liouville fractional integral operator (R-LFIO) corresponding to these specific wavelets‎. ‎By employing the aforementioned integral operator and leveraging the capabilities of Gauss-Legendre numerical integration‎, ‎the original problem is adeptly transformed into a comprehensive system of algebraic equations‎, ‎thereby facilitating a more manageable analysis and solution process‎. ‎Also‎, ‎the error analysis is investigated and examples are given to demonstrate the effectiveness and accuracy of the method‎.