Related papers: On the susceptibility function of piecewise expand…
In this note we study the monotonicity of the function $x\mapsto \psi(1 +bx)^a/\psi(1 + ax)^b$. We also give the several inequalities involving the psi function, whic is the logarithmic derivative of the gamma function.
Let $X$ be a compact strictly pseudoconvex embeddable Cauchy-Riemann manifold and let $T_P$ be the Toeplitz operator on $X$ associated with a first-order pseudodifferential operator $P$. In our previous work we established the asymptotic…
Spurred by theoretical predictions from Spohn and coworkers [Phys. Rev. E {\bf 69}, 035102(R) (2004)], we rederived and extended their result heuristically as well as investigated the scaling properties of the associated Langevin equation…
With recent advances in scanning probe microscopy (SPM), it is now routine to determine the atomic structure of surfaces and molecules while quantifying the local tip-sample interaction potentials. Such quantitative experiments are based on…
This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis,…
We consider a piecewise analytic real expanding map $f: [0,1]\to [0,1]$ of degree $d$ which preserves orientation, and a real analytic positive potential $g: [0,1] \to \mathbb{R}$. We assume the map and the potential have a complex analytic…
Let $f:X\to X$ be a continuous map on a compact metric space with finite topological entropy. Further, we assume that the entropy map $\mu\mapsto h_\mu(f)$ is upper semi-continuous. It is well-known that this implies the continuity of the…
We discuss the computation of the topological susceptibility using the method of spectral projectors and dynamical twisted mass fermions. We present our analysis concerning the O(a)-improvement of the topological susceptibility and we show…
We investigate a particular aspect of the asymptotic expansion of the Wright function ${}_1\Psi_1(z)$ for large $|z|$. The form of the exponentially small expansion associated with this function on certain rays in the $z$-plane (known as…
Given a connected finite graph $G$, an integer-valued function $f$ on $V(G)$ is called $M$-Lipschitz if the value of $f$ changes by at most $M$ along the edges of $G$. In 2013, Peled, Samotij, and Yehudayoff showed that random $M$-Lipschitz…
We study the torus partition function of the SL(2,R)/U(1) SUSY gauged WZW model coupled to N=2 U(1) current. Starting from the path-integral formulation of the theory, we introduce an infra-red regularization which preserves good modular…
We analyze the amplitude fluctuations in a diluted 3D classical XY model near the magnetic phase transition, motivated by the unusual localization properties of the amplitude (Higgs) mode recently found at the disordered superfluid-Mott…
Let $G$ be a locally compact group and $\mu$ a probability measure on $G,$ which is not assumed to be absolutely continuous with respect to Haar measure. Given a unitary representation $(\pi, \cal H)$ of $G,$ we study spectral properties of…
The point spread function (PSF) of a translation invariant imaging system is its impulse response, which cannot always be measured directly. This is the case in high energy X-ray radiography, and it must be estimated from images of…
We consider spline estimates which preserve prescribed piecewise convex properties of the unknown function. A robust version of the penalized likelihood is given and shown to correspond to a variable halfwidth kernel smoother where the…
The near-threshold expansion of the $\pi \pi$ amplitude is developed using the crossing-covariant independent variables. The independent threshold parameters entering the real part of the amplitude in an explicitly Lorentz-invariant way are…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
We study the problem of an appropriate choice of derivatives associated with discrete Fourier-Bessel expansions. We introduce a new so-called essential measure Fourier-Bessel setting, where the relevant derivative is simply the ordinary…
New congruences are found for Andrews' smallest parts partition function spt(n). The generating function for spt(n) is related to the holomorphic part alpha(24z) of a certain weak Maass form M(z) of weight 3/2. We show that a normalized…
For a piecewise linear version of the periodic map with anomalous diffusion, the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions…