We study a random permutation of lattice box in which each is given Boltzmann weight with energy equal to the total Euclidean displacement. Our main result establishes band structure model as box-size N tends infinity and inverse temperature $$\beta $$ zero; particular, we show that mean displacement order $$\min \{1/\beta , N\}$$ . In one dimension our results are more precise, specifying lead...

In the present investigation, inspired by work on Yamaguchi type class of analytic functions satisfyingthe criteria $\mathfrak{Re}\{\frac{f (z)}{z}\} > 0, $ in openunit disk $\Delta=\{z \in \mathbb{C}\colon |z|<1\}$ and making use S\v{a}l\v{a}gean-difference operator, which is a special Dunkl operator with constant $\vartheta$ $\Delta$ , wedesignate definite new classes $\mathcal{R}_{\lam...

Based on the results obtained in [Hucht, J. Phys. A: Math. Theor. 50, 065201 (2017)], we show that partition function of anisotropic square lattice Ising model $L \times M$ rectangle, with open boundary conditions both directions, is given by determinant a $M/2 M/2$ Hankel matrix, equivalently can be written as Pfaffian skew-symmetric $M Toeplitz matrix. The $M-1$ independent matrix elements ma...

A Hankel operator $\mathbf{H}_\varphi$ on the Hardy space $H^2$ of unit circle with analytic symbol $\varphi$ has minimal norm if $\|\mathbf{H}_\varphi\|=\|\varphi \|_2$ and maximal $\|\mathbf{H}_\varphi\| = \|\varphi\|_\infty$. The both only $|\varphi|$ is constant almost everywhere or, equivalently, a multiple an inner function. We show that norm-attaining norm, then norm. If continuous but n...

Let $\mathcal{S}^{\ast}_{L}(\lambda)$ be the class of functions $f$, analytic in unit disc $\Delta=\{z:|z|<1\}$, with normalization $f(0)=f'(0)-1=0$, which satisfy condition\begin{equation*}\frac{zf'(z)}{f(z)}\prec \left(1+z\right)^{\lambda},\end{equation*}where $\prec$ is subordination relation. The a subfamily known strongly starlike order $\lambda$. In this paper,the relations between and...

The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bou...

The bulk scaling limit of eigenvalue distribution on the complex plane ${\mathbb{C}}$ Ginibre random matrices provides a determinantal point process (DPP). This is typical example disordered hyperuniform system characterized by an anomalous suppression large-scale density fluctuations. As extensions DPP, we consider family DPPs defined $D$-dimensional spaces ${\mathbb{C}}$, $D \in {\mathbb{N}}$...

An intriguing correspondence between ingredients in geometric function theory related to the famous Bieberbach conjecture (de Branges' theorem) and non-perturbative crossing symmetric representation of 2-2 scattering amplitudes identical scalars is pointed out. Using dispersion relation unitarity, we are able derive several inequalities, analogous those which arise discussions conjecture. We ne...

We study convergence and asymptotic zero distribution of sequences of rational functions with xed location of poles that approximate an analytic function in a multiply connected domain Although the study of zero distributions of polynomials has a long history analogous results for truncations of Laurent series have been obtained only recently by A Edrei We obtain extensions of Edrei s results f...