相关论文: Decoding Rauzy Induction: An Answer to Bufetov's G…

We consider the phase retrieval problem in which one tries to reconstruct a function from the modulus of its wavelet transform. We study the unicity and stability of the reconstruction. In the case where the wavelets are Cauchy wavelets, we…

Starting from the cycle permutation sigma_(2^k) associated with the (2^k)-periodic orbit of the period doubling cascade we obtain the inverse permutation (sigma_(2^k))^-1. Then we build a matrix permutation related to (sigma_(2^k))^-1,…

An interesting result about the existence of "intermediate" set-valued mappings between pairs of such mappings was obtained by Nepomnyashchii. His construction was for a paracompact domain, and he remarked that his result is similar to…

Multiple conventions have been adopted for denoting Interval Exchange Transformations (IETs). The "non-labeled" convention was the original, while the "labeled" convention has proven convenient when investigating Flat Surfaces as described…

We prove Cauchy's formula for repeated integration on time scales. The obtained relation gives rise to new notions of fractional integration and differentiation on arbitrary nonempty closed sets.

We study the recovery of square-integrable signals from the absolute values of their wavelet transforms, also called wavelet phase retrieval. We present a new uniqueness result for wavelet phase retrieval. To be precise, we show that any…

We present a coherent approach to recurrence and transience, starting from a version of the Riesz decomposition theorem for superharmonic elements. Our approach allows straightforward proofs of some known results, entails new theorems, and…

Various branches of matrix model partition function can be represented as intertwined products of universal elementary constituents: Gaussian partition functions Z_G and Kontsevich tau-functions Z_K. In physical terms, this decomposition is…

The general deterministic recombination equation in continuous time is analysed for various lattices, with special emphasis on the lattice of interval (or ordered) partitions. Based on the recently constructed general solution for the…

In this work, we study a class of random matrices which interpolate between the Wigner matrix model and various types of patterned random matrices such as random Toeplitz, Hankel, and circulant matrices. The interpolation mechanism is…

We extend the notion of intrinsic entropy for endomorphisms of Abelian groups to endomorphisms of modules over an Archimedean non-discrete valuation domain $R$, using the natural non-discrete length function introduced by Northcott and…

We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer…

We prove the nonarchimedean counterpart of a real inequality involving the metric entropy and measure geometric invariants $V_i$, called Vitushkin's variations. Our inequality is based on a new convenient partial preorder on the set of…

The regular representation is related to Zhu's $A(V)$-theory and an induced module from an $A(V)$-module to a $V$-module is defined in terms of the regular representation. As an application, a new proof of Frenkel and Zhu's fusion rule…

Let $x_{1},x_{2},\ldots,x_{n}$ be $n$ numbers, and $y_{1},y_{2},\ldots,y_{n}$ be $n$ further numbers chosen such that all $n^{2}$ pairwise sums $x_{i}+y_{j}$ are nonzero. Consider the $n\times n$-matrix \[ C:=\left(…

We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT) -- a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M…

We decompose a matrix Y into a sum of bilinear terms in a stepwise manner, by considering Y as a mapping from a finite dimensional Banach space into another finite dimensional Banach space. We provide transition formulas, and represent them…

Mutual information is used as a purely geometrical regularization of entanglement entropy applicable to any QFT. A coefficient in the mutual information between concentric circular entangling surfaces gives a precise universal prescription…

We study matrix identities involving multiplication and unary operations such as transposition or Moore-Penrose inversion. We prove that in many cases such identities admit no finite basis.

Symmetrizable matrices are those which are symmetric when multiplied by a diagonal matrix with positive entries. The Cauchy interlace theorem states that the eigenvalues of a real symmetric matrix interlace with those of any principal…