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We study the Horn problem in the context of algebraic codes on a smooth projective curve defined over a finite field, reducing the problem to the representation theory of the special linear group $SL(2,F_q)$. We characterize the…
In this paper, we study extremal problems for coefficient functionals associated with a distinguished subclass of holomorphic semigroup generators, denoted by $\mathcal{A}_{\beta}$ ($0 \le \beta \le 1$), defined on the unit disk…
In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…
Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on…
This paper investigates the projectivization of real vector bundles over small covers. We first give a necessary and sufficient condition for such a projectivization to be a small cover. Then associated with moment-angle manifolds, we…
In real analysis, the Lojasiewicz inequalities, revitalized by Leon Simon in his pioneering work on singularities of energy minimizing maps, have proven to be monumental in differential geometry, geometric measure theory, and variational…
We prove the global-time existence of weak solutions to the supercooled Stefan problem. Our result holds in general space dimensions and with a general class of initial data. In addition, our solution is maximal in the sense of a certain…
We give sharp bounds on the vanishing of the cohomology of a tensor product of vector bundles on the n-dimensional projective space in terms of the vanishing of the cohomology of the factors. For this purpose we introduce regularity indices…
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
In this paper we study the regularized analytic torsion of finite volume hyperbolic manifolds. We consider sequences of coverings $X_i$ of a fixed hyperbolic orbifold $X_0$. Our main result is that for certain sequences of coverings and…
Border's theorem gives an intuitive linear characterization of the feasible interim allocation rules of a Bayesian single-item environment, and it has several applications in economic and algorithmic mechanism design. All known…
Let T be the unit circle in the complex plane C. This paper proves the existence of analytic structure in a compact subset K of T X C^n, where K has so-called "lineally convex" or "hypoconvex" fibers over T. It also addresses a related…
We study the complex-analytic geometry of semi-positive holomorphic line bundles on compact K\"ahler manifolds. In one of our main results, for a $\mathbb{Q}$-effective line bundle satisfying a natural torsion-type assumption, we show the…
A fundamental theorem of linear programming states that a feasible linear program is solvable if and only if its objective function is copositive with respect to the recession cone of its feasible set. This paper demonstrates that this…
Let $E$ be a vector bundle on a smooth complex projective variety $X$. We study the family of sections $s_t\in H^0(E\otimes L_t)$ where $L_t\in Pic^0(X)$ is a family of topologically trivial line bundle and $L_0=\mathcal O_X,$ that is, we…
Parallel to the study of finite dimensional Banach spaces, there is a growing interest in the corresponding local theory of operator spaces. We define a family of Hilbertian operator spaces H_n^k,0< k < n+1, generalizing the row and column…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
We deal with linear programming problems involving absolute values in their formulations, so that they are no more expressible as standard linear programs. The presence of absolute values causes the problems to be nonconvex and nonsmooth,…
The Einstein field equations, or generalizations thereof, are difficult to solve analytically. On the other hand, numerical solutions of the same equations have become increasingly common, in particular concerning compact objects. Whereas…
The paper deals with Henselian valued field with analytic structure. Actually, we are focused on separated analytic structures, but the results remain valid for strictly convergent analytic ones as well. A classical example of the latter is…