Related papers: Equivalence and Separation for Multivariate Matrix…
The Hurwitz form of a projective variety characterizes linear spaces of complementary dimension which meet the variety non-transversally. We extend this notion to varieties in a product of projective spaces. This parallels the multigraded…
Comparing with univariate framelets, the main challenge involved in studying multivariate framelets is that we have to deal with the highly non-trivial problem of factorizing multivariate polynomial matrices. As a consequence, multivariate…
In this paper we investigate peculiarities of phase transition high-symmetry - incommensurate phase in inhomogeneous systems. We obtain the nonlinear dispersion law and then present a renormalization group analysis of phase transitions in…
Dynamic Hubbard models are extensions of the conventional Hubbard model that take into account the fact that atomic orbitals expand upon double occupancy. It is shown here that systems described by dynamic Hubbard models have a tendency to…
The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…
The formation of codimension-one interfaces for multi-well gradient-driven problems is well-known and established in the scalar case, where the equation is often referred to as the Allen-Cahn equation. The proofs rely for a large on a…
A variational model for the interaction between homogenization and phase separation is considered in the regime where the former happens at a finer scale than the latter. The first order $\Gamma-$limit is proven to exhibit a separation of…
Let V be a finite dimensional complex vector space and V^* its dual and let X in P(V) be a smooth projective variety of dimension n and degree d at least two. For a generic n-tuple of hyperplanes H_1,...,H_n in P(V^*)^n, the intersection of…
Matrix Schubert varieties are certain varieties in the affine space of square matrices which are determined by specifying rank conditions on submatrices. We study these varieties for generic matrices, symmetric matrices, and upper…
Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of…
In this article, we provide an infinite family of examples to disprove a recent conjecture due to Ballantine and her collaborators on the injectivity of a class of maps, namely pre_k, defined on integer partitions. These maps arise from…
We study the extended Hubbard model with both on-site (U) and nearest neighbor (V) Coulomb repulsion using the exact diagonalization method within the dynamical mean field theory. For a fixed U (U=2.0), the T-n phase-diagrams are obtained…
We extend the standard semiclassical theory of Excited-State Quantum Phase Transitions (ESQPTs), based on a classification of stationary points in the classical Hamiltonian, to constrained systems. We adopt the method of Lagrange…
We prove existence and regularity for the solutions to a Cahn-Hilliard system describing the phenomenon of phase separation for a material contained in a bounded and regular domain. Since the first equation of the system is perturbed by the…
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…
This paper defines mixed multiplicity systems; the Euler-Poincare characteristic and the mixed multiplicity symbol of $\mathbb{N}^d$-graded modules with respect to a mixed multiplicity system, and proves that the Euler-Poincare…
Diffusion in ternary, multiphase systems was studied theoretically and experimentally in Ni-Cr-Al system at 1200C. The samples were prepared by the multiple method. It has been shown that the method allows obtaining good quality, planar,…
Understanding competing instabilities in systems with correlated fermions remains one of the holy grails of modern condensed matter physics. Among the fermionic lattice models used to this effect, the extended Hubbard model occupies a prime…
This paper discusses Random Matrix Models which exhibit the unusual phenomena of having multiple solutions at the same point in phase space. These matrix models have gaps in their spectrum or density of eigenvalues. The free energy and…
Consideration of a question of E. R. Berlekamp led Carlitz, Roselle, and Scoville to give a combinatorial interpretation of the entries of certain matrices of determinant~1 in terms of lattice paths. Here we generalize this result by…