相关论文: Roles of Log-concavity, log-convexity, and growth …
A class of growth functions $u$ is introduced to construct Hida distributions and test functions. The Legendre transform $\ell_{u}$ of $u$ is used to define a sequence $\a(n)=(\ell_{u}(n) n!)^{-1}, n\geq 0$, of positive numbers. From this…
We survey recent work on normal functions, including limits and singularities of admissible normal functions, the Griffiths-Green approach to the Hodge conjecture, algebraicity of the zero-locus of a normal function, Neron models, and…
Let $u$ be a positive continuous function on $[0, \infty)$ satisfying the conditions: (i) $\lim_{r\to\infty} r^{-1/2}\log u(r)=\infty$, (ii) $\inf_{r\geq 0} u(r)=1$, (iii) $\lim_{r\to \infty}\break r^{-1}\log u(r)<\infty$, (iv) the function…
We present a "learning to learn" approach for automatically constructing white-box classification loss functions that are robust to label noise in the training data. We parameterize a flexible family of loss functions using Taylor…
We introduce and study new transformations between two functions satisfying some basic growth properties and generalize the known lower and upper Legendre conjugate (or envelope). We also investigate how these transformations modify…
It is shown that the order and the lower order of growth are equal for all non-trivial solutions of $f^{(k)}+A f=0$ if and only if the coefficient $A$ is analytic in the unit disc and $\log^+ M(r,A)/\log(1-r)$ tends to a finite limit as…
The Wilson Coefficients for all 4-parton operators which arise in matching QCD to Soft-Collinear Effective Theory (SCET) are computed at 1-loop. Any dijet observable calculated in SCET beyond leading order will require these results. The…
Let $\ce^{*}$ be the space of tempered distributions and $\m$ be the standard Gaussian measure on $\ce^{*}$. Being motivated by the distribution theory on infinite dimensional space by Cochran, Kuo and Sengupta (CKS) \cite{cks}, Asai, Kubo…
In this article, we study the growth of solutions of the homogeneous complex linear differential equation \begin{equation*} f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f^{\prime}+ A_{0}(z)f=0, \end{equation*}% where the coefficients…
Using the dynamic renormalization group (DRG) technique, we analyze general nonlinearities in a conservative nonlinear growth equation with non-conserved gaussian white noise. We show that they fall in two classes only: the…
In the spirit of very recent articles by J. Bonet, W. Lusky and J. Taskinen we are studying the so-called solid hulls and cores of spaces of weighted entire functions when the weights are given in terms of associated weight functions coming…
We characterize the inclusion relations between weighted classes of entire functions with rapid decreasing growth and study strong growth comparison relations between given weights. In our considerations first we focus on weights defined in…
We present consistently ordered calculations of the structure functions F_2(x,Q^2) and F_L(x,Q^2), in different expansion schemes. After discussing the standard expansion in powers of alpha_s(Q^2) we consider a leading-order expansion in…
The concept of proximate order is widely used in the theories of entire, meromorphic, subharmonic and plurisubharmonic functions. We give a general interpretation of this concept as a proximate growth function relative to a model growth…
Consider the following stochastic reaction-diffusion equation with logarithmic superlinear coefficient b, driven by space-time white noise W: $$ u_t(t,x) = (1/2)u_{xx}(t,x) + b(u(t,x)) + \sigma(u(t,x))W(dt,dx) $$ for $t > 0$ and $x \in…
For the $1+1$ dimensional nonlinear damped stochastic Klein-Gordon equation driven by space-time white noise, we prove that the second-order increments of the solution can be approximated, after scaling with the diffusion coefficient, by…
The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy. Because of the dual conformal field theory (CFT) formulation in the anti-de Sitter space the conformal dimension…
White noise is a fundamental and fairly well understood stochastic process that conforms the conceptual basis for many other processes, as well as for the modeling of time series. Here we push a fresh perspective toward white noise that,…
Leading (large) logarithms in non-renormalizable theories have been investigated in the recent past. Besides some general considerations, explicit results for the expansion coefficients (in terms of leading logarithms) of partial wave…
We present calculations of the structure functions F_2(x,Q^2) and F_L(x,Q^2), concentrating on small x. After discussing the standard expansion of the structure functions in powers of \alpha_s(Q^2) we consider a leading-order expansion in…