相关论文: Some Connections Between (Sub)Critical Branching M…

Certain subclasses of $B_1(K)$, the Baire-1 functions on a compact metric space $K$, are defined and characterized. Some applications to Banach spaces are given.

We establish a relation between Hahn spin-echo of a spin-$\frac 1 2 $ particle and quantum phase transition in a spin-chain, which couples to the particle. The Hahn echo is calculated and discussed at zero as well as at finite temperatures.…

The critical behavior of $d$-dimensional systems with $n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial Lifshitz point where a wave-vector instability occurs in an $m$-dimensional subspace ${\mathbb R}^m$ ($m{>}1$). Field…

Let $0 \leq \alpha<n$, $M_{\alpha}$ be the fractional maximal operator, $M^{\sharp}$ be the sharp maximal operator and $b$ be the locally integrable function. Denote by $[b, M_{\alpha}]$ and $[b, M^{\sharp}]$ be the commutators of the…

We have studied some properties of the special Gram points of the Riemann zeta function which lie on contour lines ${\bf Im}(\zeta ( s )) = 0$ which do not contain zeroes of $\zeta ( s )$. We find that certain functions of these points,…

Structure and properties of families of critical points for classes of functions $W(z,\bar{z})$ obeying the elliptic Euler-Poisson-Darboux equation $E(1/2,1/2)$ are studied. General variational and differential equations governing the…

Given a Banach space $E$ consisting of functions, we ask whether there exists a reproducing kernel Hilbert space $H$ with bounded kernel such that $E\subset H$. More generally, we consider the question, whether for a given Banach space…

The quantization in quadratic order of the Hitchin functional, which defines by critical points a Calabi-Yau structure on a six-dimensional manifold, is performed. The conjectured relation between the topological B-model and the Hitchin…

Binary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid…

Learning from non-independent and non-identically distributed data poses a persistent challenge in statistical learning. In this study, we introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert…

Interacting physical systems in the neighborhood of criticality (and massive continuum field theories) can often be characterized by just two physical scales: a (macroscopic) correlation length and a (microscopic) interaction range, related…

An extension of the method and results of A. Schwarz for evaluating the partition function of a quadratic functional is presented. This enables the partition functions to be evaluated for a wide class of quadratic functionals of interest in…

In this paper we defined some function spaces on time scale which are Banach spaces respect to supremum norm. We study integral transformations which are carry to some important properties between mentioned above function spaces.

Let $ E $ be a space of holomorphic functions on the unit ball $ B_X $ of a Banach space $ X.$ In this work, we introduce a Banach structure associated to $ E $ on the linear space $ WE(Y) $ containing $ Y$-valued holomorphic functions on $…

Characteristic functions contain complete information about all the moments of a classical distribution and the same holds for the Fourier transform of the Wigner function: a quantum characteristic function, or the chord function. However,…

Using notions from the geometry of Banach spaces we introduce square functions $\gamma(\Omega,X)$ for functions with values in an arbitrary Banach space $X$. We show that they have very convenient function space properties comparable to the…

The Brjuno and Wilton functions bear a striking resemblance, despite their very different origins; while the Brjuno function $B(x)$ is a fundamental tool in one-dimensional holomorphic dynamics, the Wilton function $W(x)$ stems from the…

A function in a class $\mathcal{F}(X)$ is said to be subdifferentially determined in $\mathcal{F}(X)$ if it is equal up to an additive constant to any function in $\mathcal{F}(X)$ with the same subdifferential. A function is said to be…

We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function…

Most engineering models contain several parameters, and the map from input parameters to model output can be viewed as a multivariate function. An active subspace is a low-dimensional subspace of the space of inputs that explains the…