相关论文: Variational Analysis for the Bilateral Minimal Tim…
We calculate the temperature dependence of the weak localization correction in a two dimensional system at arbitrary relation between temperature, $T$ and the elastic mean free time. We describe the crossover in the dephasing time…
A subequation on an open subset $X\subset \mathbb R^n$ is a subset $F$ of the space of $2$-jets on $X$ with certain properties. A smooth function is said to be $F$-subharmonic if all of its $2$-jets lie in $F$, and using the viscosity…
The aim of this work is to extend the recent work of the author on the discrete frequency function to the more delicate continuous frequency function $\mathcal{T}$, and further to investigate its relations to the Hardy-Littlewood maximal…
Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univariate distributional data has advanced rapidly in recent years, multivariate distributions, which…
The paper is devoted to study analogues of the van der Corput lemmas involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study oscillatory integrals…
We introduce a new type of multiple zeta functions, which we call bilateral zeta functions, analogous to the Barnes zeta functions. The bilateral zeta function is a periodic function and shares certain basic properties of Barnes zeta…
We add an analytic trans-exponential function $\varphi$ to $\mathbb{R}_{an,\exp}$. We reduce the o-minimality of $\mathbb{R}_{an,\exp,\varphi}$ to the existence of "many" regular values for some definable systems of functions, which is a…
The analytical formula for the time-resolved dynamical Franz-Keldysh effect (Tr-DFKE) under an elliptically polarized laser in sub-femtosecond time-scale is reported. The Houston function is assumed as the time-dependent wave function of…
We study the moments of the partial transpose of the reduced density matrix of two intervals for the free massless Dirac fermion. By means of a direct calculation based on coherent state path integral, we find an analytic form for these…
In this manuscript, we deal with some particular type of homogeneous first order linear systems with variable coefficients, in which we provide qualitative properties of the solution. When the coefficients of the indeterminate functions are…
Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of important classes of functions in variational analysis. Focusing mainly on the behavior of the…
We use the framework of a type of abstract convexity ($\Phi_{lsc}$-convexity) to investigate properties of lower semicontinuous quadratically minorized functions in Hilbert spaces. A new result, which states that, for every local…
Fr\'echet regression extends the principles of linear regression to accommodate responses valued in generic metric spaces. While this approach has primarily focused on exploring relationships between Euclidean predictors and non-Euclidean…
The Lipschitz differential equation, $\dot x=f(x)$, in spaces $X \in C^n$ and $X \in R^n$ is considered. The minimal period problem is to find the exact lower bound for peri-ods of non-constant solutions, expressed in the Lipschitz constant…
In recent years, samples of time-varying object data such as time-varying networks that are not in a vector space have been increasingly collected. These data can be viewed as elements of a general metric space that lacks local or global…
In this paper, we study the shift on the space of uniformly bounded continuous functions band-limited in a given compact interval with the standard topology of tempered distributions. We give a constructive proof of the existence of minimal…
Fr\'echet mean and variance provide a way of obtaining mean and variance for general metric space valued random variables and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and…
The paper deals with variational approaches to the segmentation of time series into smooth pieces, but allowing for sharp breaks. In discrete time, the corresponding functionals are of Blake-Zisserman type. Their natural counterpart in…
This is the continuation of previous article. For subspaces $M^n(t)$ and $M^{n-m}(t)$ which are invariant manifolds of the differential equation under consideration we build a change of variables which splits this equation into a system of…
The two-parameter Mittag-Leffler function $E_{\alpha, \beta}$ is of fundamental importance in fractional calculus. It appears frequently in the solutions of fractional differential and integral equations. Nonetheless, this vital function is…