相关论文: On extremizing sequences for the adjoint restricti…

We prove that the set of directions of lines intersecting three disjoint balls in $R^3$ in a given order is a strictly convex subset of $S^2$. We then generalize this result to $n$ disjoint balls in $R^d$. As a consequence, we can improve…

We study the relative Frobenius map associated with a map of derived commutative rings over a field of positive characteristic. As part of this, we examine a relative analog of perfectness and construct a relative inverse limit perfection…

We provide a framework for obtaining error bounds for linear conic problems without assuming constraint qualifications or regularity conditions. The key aspects of our approach are the notions of amenable cones and facial residual…

We prove a quantitative estimate on the number of certain singularities in almost minimizing clusters. In particular, we consider the singular points belonging to the lowest stratum of the Federer-Almgren stratification (namely, where each…

We study the computational complexity of constrained nonnegative Gram feasibility. Given a partially specified symmetric matrix together with affine relations among selected entries, the problem asks whether there exists a nonnegative…

We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras A_i\in V, such that some finitely generated subalgebra S \subseteq A is dense in A under the inverse limit of the discrete topologies…

We propose a natural, bivariate, generalization of the nonsingular similarity relations considered by T. Fine. We also provide an enumeration formulae and a generating tree for those relations. The latter allow us to give a new bijection…

We first study Clarke's tangent cones at infinity to unbounded subsets of $\mathbb{R}^n.$ We prove that these cones are closed convex and show a characterization of their interiors. We then study subgradients at infinity for extended real…

We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal…

We find convergent double series expansions for Legendre's third incomplete elliptic integral valid in overlapping subdomains of the unit square. Truncated expansions provide asymptotic approximations in the neighbourhood of the logarithmic…

Convergence of the solutions of nonhomogeneous linear singularly perturbed systems to that of the corresponding reduced singular system on the half-line [0, $\infty $) is considered. To include the situation on a neighborhood of initial…

We produce examples of complex algebraic surfaces with isolated singularities such that these singularities are not metrically conic, i.e. the germs of the surfaces near singular points are not bi-Lipschitz equivalent, with respect to the…

We derive new bounds on achievable precision in the most general adaptive quantum metrological scenarios. The bounds are proven to be asymptotically saturable and equivalent to the known parallel scheme bounds in the limit of large number…

4x4x3 absolutely nonsingular tensors are characterized by their determinant polynomial. Non-quivalence among absolutely nonsingular tensors with respect to a class of linear transformations, which do not chage the tensor rank,is studied. It…

In this paper we characterize surjective isometries on certain classes of non-commutative spaces associated with semi-finite von Neumann algebras: the Lorentz spaces $L^{w,1}$, as well as the spaces $L^1+L^\infty$ and $L^1\cap L^\infty$.…

Strichartz inequalities are a cornerstone of the modern theory of dispersive PDEs, but their extremizers are known explicitly only in a handful of sharp cases. The non-convexity of the underlying functional makes the problem hard, and to…

We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…

In previous work of the authors, we investigated the Born and inverse Born series for a scalar wave equation with linear and nonlinear terms, the nonlinearity being cubic of Kerr type [8]. We reported conditions which guarantee convergence…

A wide range of applications, most notably in comparative genomics, involve the computation of a shortest sorting sequence of operations for a given permutation, where the set of allowed operations is fixed beforehand. Such sequences are…