In this paper, we first introduce the notions of thick and prime tensor ideals in tensor n-angulated categories and then obtain the Balmer spectrum of such categories. We consider the topological properties of this spectrum. Moreover, we introduce the notion of radical tensor ideals in tensor n-angulated categories and show that they can be parametrized by supports of subcategories. Furthermore, we provide Balmer's classification theorem in terms of Thomason subsets of the spectrum space.
This paper studied the characterization and existence of solutions to complex Hessian equations associated with a given weight. We provided a complete characterization of the Radon measures that could be represented as the complex Hessian measure of an Fm degrees chi (S2)-function, where chi was a decreasing weight function. Our main results provided both global and local characterizations of the range of the complex Hessian operator acting on these classes. Specifically, we demonstrated that the solvability of the equation Hm(cp) = & micro; in the class Fm degrees chi(S2) is equivalent to a certain functional inequality involving the measure & micro; and the weighted energy (m degrees chi. Furthermore, we demonstrate that this global condition could be localized: a solution existed globally if, and only if, for every point in the closure S2 of the domain, a solution existed in some neighborhood of that point.
We establish Lyapunov-type inequalities for Dirichlet boundary value problems driven by the modified discrete Helmholtz operator on finite balls of the integer lattice Z. This yields weighted inequalities for scalar problems and a spectral-radius criterion for coupled systems, as well as sharpness results. As an application, we study a weighted eigenvalue problem and obtain explicit two-sided bounds for the first eigenvalue by combining a Lyapunov-type lower estimate with a variational upper bound. Numerical illustrations are provided for localized weights.
We develop an objective Bayesian framework for estimating the common standardized mean difference in meta-analysis. To construct noninformative priors, we derive both probability matching and reference priors. Our analysis reveals that although general second-order matching prior does not exist, a valid version can be obtained when the sample sizes of the two arms in each study are equal. Among the reference priors evaluated, we find that both one-at-a-time and two-group reference priors satisfy the first-order matching criterion, whereas Jeffreys' prior does not. Simulation studies demonstrate that the proposed matching prior and the one-at-a-time reference prior yield accurate frequentist coverage probabilities, consistently outperforming Jeffreys' prior. Finally, the practical utility of this framework is validated through two real-world meta-analytic applications, underscoring its effectiveness for robust objective Bayesian inference in standardized mean difference models.
In many practical situations, distance measurements are affected by unavoidable inaccuracies due to instrumental limitations and external factors. Although such errors are often small, their accumulation may significantly impact the validity of mathematical models. This motivates the use of perturbed metric spaces as a natural framework to incorporate such imperfections into fixed point theory. In the current study, many theorems are established for three-point mappings contracting the perimeters of triangles under the structure of triple perturbed metric spaces. The findings presented here extend and consolidate numerous known results in fixed point theory by combining three-point contraction techniques with different perturbed metric structures. The use of three distinct perturbed metrics provides a more flexible and generalized contractive framework. Some examples are given showing that these satisfy the proposed conditions, while existing results cannot be applied to these examples, highlighting the wider applicability of the present results. Finally, we derived rigorous existence and uniqueness conditions that guarantee solutions for fractional differential equations and illustrated their relevance in modeling population dynamics, including factors such as memory effects and mortality in rabbit growth. A complementary numerical example further validates the rigorous results and demonstrates the practical applications of the iterative approximation scheme.
