Related papers: A new construction of wavelet sets
A tuple (s1,t1,s2,t2) of vertices in a simple undirected graph is 2-linked when there are two vertex-disjoint paths respectively from s1 to t1 and s2 to t2. A graph is 2-linked when all such tuples are 2-linked. We give a new and simple…
We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The…
We state and prove a new closure theorem closely related to the classical closure theorems of Poncelet and Steiner. Along the way, we establish a number of theorems concerning conic sections.
We develop a method based on tensor networks to create localized single particle excitations on top of strongly-correlated quantum spin chains. In analogy to the problem of creating localized Wannier modes, this is achieved by optimizing…
Within the framework of Relativistic Schroedinger Theory (an alternative form of quantum mechanics for relativistic many-particle systems) it is shown that a general N-particle system must occur in one of two forms: either as a ``positive''…
We introduce the concept of matching connectivity as a notion of connectivity in graph admitting perfect matchings which heavily relies on the structural properties of those matchings. We generalise a result of Robertson, Seymour and Thomas…
Conditions for the existence of a fixed spectrum \{i.e., the set of fixed modes\} for a multi-channel linear system have been known for a long time. The aim of this paper is to reestablish one of these conditions using a new and transparent…
Balinski (1961) proved that the graph of a $d$-dimensional convex polytope is $d$-connected. We provide a new proof of this result. Our proof provides details on the nature of a separating set with exactly $d$ vertices; some of which appear…
A classical theorem of Wendroff shows that one may reconstructs a sequence of orthogonal polynomials on the real line from two non-constant polynomials of consecutive degrees whose zeros strictly interlace on the real line. In this note we…
The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…
Bohr's principle of complementarity, in the context of a two-slit interference experiment, is understood as the quantitative measures of wave and particle natures following a duality relation ${\mathcal D}^2+{\mathcal V}^2 \le 1$. Here…
A coordinate cone in R^n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is a defnable in an o-minimal structure over the reals, open bounded subset of R^n such that its intersection…
In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept…
The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to…
Based on a symmetry argument we systematically reveal Hartree-Fock broken-symmetry solutions of the one-dimensional two-band extended Peierls-Hubbard model, which covers various materials of interest such as halogen-bridged metal complexes…
This is a survey article on the stable cohomotopy refinement of Seiberg-Witten invariants containing also new results, for example: - Stable cohomotopy groups describe path components of certain mapping spaces. - Relation of stable…
We present a characterization of sets for which Cartwright's theorem holds true. The connection is discussed between these sets and sampling sets for entire functions of exponential type.
A unified theory for the current through a nanoscale region of interacting electrons connected to two leads which can be either ferromagnet or superconductor is presented, yielding Meir-Wingreen-type formulas when applied to specific…
The bipartite entanglement of a pure quantum state is known to be characterized by its Schmidt decomposition. In particular the state is maximally entangled when all the Schmidt coefficients are equal. We point out a convenient method which…
We use the method of interlacing families of polynomials introduced to prove two theorems known to imply a positive solution to the Kadison--Singer problem. The first is Weaver's conjecture $KS_{2}$ \cite{weaver}, which is known to imply…