Related papers: Pre-threshold fractional susceptibility function: …

Let $\mathfrak g$ be an infinite-dimensional Lie algebra, and $G$ be the algebraic completion of a $\mathfrak g$-module. Using the geometric model of Schottky uniformization of Riemann sphere to obtain a higher genus Riemann surface, we…

In a private communication, K. Ono conjectured that any mock theta function of weight 1/2 or 3/2 can be congruent modulo a prime $p$ to a weakly holomorphic modular form for just a few values of $p$. In this paper we describe when such a…

Statistical manifolds, the parameter spaces of smooth families of probability density functions, are the central objects of study in information geometry. While the elementary differential geometry of Riemannian statistical manifolds is…

This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n. This notion was reviewed in great detail in a paper in J.…

We consider a class of numerical approximations to the Caputo fractional derivative. Our assumptions permit the use of nonuniform time steps, such as is appropriate for accurately resolving the behavior of a solution whose derivatives are…

This paper develops a unified framework for observables in n-plectic geometry, extending the L_infty-algebra of Hamiltonian (n-1)-forms to Hamiltonian forms of all degrees via a degree-shifting Grassmann variable u that encodes submanifold…

We establish an omega theorem for logarithmic derivative of the Riemann zeta function near the 1-line by resonance method. We show that the inequality $\left| \zeta^{\prime}\left(\sigma_A+it\right)/\zeta\left(\sigma_A+it\right) \right|…

We construct a family $I_{n_{\eps}}(f)_{t}$ of continuous stochastic processes that converges in the sense of finite dimensional distributions to a multiple Wiener-It\^o integral $I_{n}^{H}(f1^{\otimes n}_{[0,t]})$ with respect to the…

We perform simulations to evaluate a recent experimental technique for using in-line holographic microscopy and an effective-sphere model to measure the population-averaged fractal dimension $D_f$ of an ensemble of colloidal fractal…

We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three…

The magnetic susceptibility of the quarter-filled one-dimensional extended Hubbard model is calculated using the density-matrix renormalization group technique. It is found that in the charge gap regime of the model ($U> 4t $ and $V > 2t$),…

We consider inertial manifolds and their approximation for a class of partial differential equations with a nonlocal Laplacian operator $-(-\Delta)^{\frac{\alpha}{2}}$, with $0<\alpha<2$. The nonlocal or fractional Laplacian operator…

We consider the family of all meromorphic functions $f$ of the form $$ f(z)=\frac{1}{z}+b_0+b_1z+b_2z^2+\cdots $$ analytic and locally univalent in the puncture disk $\mathbb{D}_0:=\{z\in\mathbb{C}:\,0<|z|<1\}$. Our first objective in this…

The average R(t) of a smooth function with respect to the SRB measure of a smooth one-parameter family f_t of piecewise expanding interval maps is not always Lipschitz. We prove that if f_t is tangent to the topological class of f_0, then…

We give a list of $113$ holomorphic eta-quotients of integral weight ($66$ of which are primitive) and provide a uniform closed formula for their Fourier coefficients $c(l)$ where $l\equiv1\bmod{m}$ with some fixed $m\mid24$. The proof…

The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p>0$. We introduce a category of cochain complexes equipped with an endomorphism $F$ of underlying…

We prove one-level density results for L-functions attached to primitive forms of level q, averaged over square-free q, conditional on the Generalized Riemann Hypothesis (GRH). We treat the even and odd orthogonal families separately and…

Motivated by recent work on strict deformation quantization of the unit disk and the Riemann sphere, we study the Fr\'echet space structure of the set of holomorphic functions on the complement $\Omega:=\{(z,w)\in \hat{\mathbb{C}}^2\, :\,…

We consider a family of analytic and normalized functions that are related to the domains $\mathbb{H}(s)$, with a right branch of a hyperbolas $H(s)$ as a boundary. The hyperbola $H(s)$ is given by the relation $\frac{1}{\rho}=\left(…

The two-parametric Mittag-Leffler function (MLF), $E_{\alpha,\beta}$, is fundamental to the study and simulation of fractional differential and integral equations. However, these functions are computationally expensive and their numerical…