相关论文: Annular and circular rigid inclusions planted into…
We introduce a new class of two(multi)-matrix models of positive Hermitean matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more commonly used in similar models. The…
We study the Dirac equation in 3+1 dimensions with a general combination of scalar, vector and tensor interactions with arbitrary strengths, all of them described by central Coulomb potentials acting on a particular plane of motion. For the…
Nowadays integration of mass matrix components in the element domain is performed using various numerical integration schemes, each one possess different level of accuracy, alters in number of integration (Gauss) points and requires…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
The vector-matrix Riemann boundary value problem for the unit disk with piecewise constant matrix is constructively solved by a method of functional equations. By functional equations we mean iterative functional equations with shifts…
We introduce the strong recursive skeletonization factorization (RS-S), a new approximate matrix factorization based on recursive skeletonization for solving discretizations of linear integral equations associated with elliptic partial…
The radial (penny-shaped) model of hydraulic fracture is considered. The tangential traction on the fracture walls is incorporated, including an updated evaluation of the energy release rate (fracture criterion), system asymptotics and the…
We compute angular phase-space integrals with three and four denominators analytically, working within dimensional regularisation via the Mellin-Barnes (MB) representation. The approach converts multifold MB integrals into real parametric…
In the past few years, the slice-rank lemma of Tao has been applied successfully to many problems in extremal combinatorics. In this paper, first, we define a new notion of triangular tensors which generalizes that of triangular matrices…
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…
An alternative formula for the partition function of the Goulden-Harer-Jackson matrix model is derived, in which the Penner and the orthogonal Penner partition functions are special cases of this formula. Then the free energy that computes…
In this paper we present a treatment of hypersingular integrals and integral equations. It is shown the equivalence of different definitions of hypersingular integrals. Then we construct explicit analytical solution to a characteristic…
We study the fractional Schr\"odinger equations in $\mathbb R^{1+d}, d \geq 3$ of order ${d}/({d-1}) < \al < 2$. Under the angular regularity assumption we prove linear and nonlinear profile decompositions which extend the previous results…
Mechanical modelling of poroelastic media under finite strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical two-scale analysis is only…
Motivated by the paraxial narrow-angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schr\"odinger-type equation posed on…
A finite element framework is presented for the analysis of crack-tip phenomena in an elastic material containing a single edge crack under compressive loading. The mechanical response of the material is modeled by a nonlinear constitutive…
Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties…
We propose that the symbol alphabet for classes of planar, dual-conformal-invariant Feynman integrals can be obtained as truncated cluster algebras purely from their kinematics, which correspond to boundaries of (compactifications of)…
It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…
Finite element plate and shell formulations are ubiquitous in structural analysis for modeling all kinds of slender structures, both for static and dynamic analyses. The latter are particularly challenging as the high order nature of the…