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Let $\sigma_a^{(N)}(n)=\sum_{d^{N}|n}d^a$. An explicit transformation is obtained for the generalized Lambert series $\sum_{n=1}^{\infty}\sigma_{a}^{(N)}(n)e^{-ny}$ for Re$(a)>-1$ using the recently established Vorono\"i summation formula…

Nonlinear, relativistic longitudinal waves with sub-luminal phase velocity $v_p$ are the basis of plasma-based electron accelerators. For such application, key properties of the wave are the maximum or ``wave breaking'' amplitude and the…

Let $F$ be a nonarchimedean local field with odd residual characteristic and let $G$ be the $F$-points of a connected reductive group defined over $F$. Let $\theta$ be an $F$-involution of $G$. Let $H$ be the subgroup of $\theta$-fixed…

Nonlinear light-matter interaction, as the core of ultrafast optics, bulk photovoltaics, nonlinear optical sensing and imaging, and efficient generation of entangled photons, has been traditionally studied by first-principles theoretical…

We give an atomic decomposition of closed forms on R n , the coefficients of which belong to some Hardy space of Musielak-Orlicz type. These spaces are natural generalizations of weighted Hardy-Orlicz spaces, when the Orlicz function…

We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-zeta function about any point in the complex plane.

We present an efficient way to calculate the effect of soft QCD radiation at one loop, which is needed for predictions at next-to-next-to-leading logarithmic accuracy. We use rapidity coordinates and isolate the divergences in the…

The resonant generation of relativistic plasma waves and plasma wave guiding by two co-propagating laser pulses has been studied. By proper timing between guiding and driver pulses, a resonant interaction occurs, which generates a…

Translation Matrix Formalism has been used to find an exact analytic solution for linear light propagation in a finite one-dimensional (1D) periodic stratified structure. This modal approach allows to derive a closed formula for the…

We start from the QED Lagrangian to describe a charged many-particle system coupled to the radiation field. A covariant density matrix approach to kinetic theory of QED plasmas, subjected to a strong external electro-magnetic field has…

Let $R=\bigoplus_{n\ges0}R_n$ be a graded commutative ring generated over a field $K=R_0$ by homogeneous elements $x_1,\dots,x_e$ of positive degrees $d_1,\dots,d_e$. The Hilbert-Serre Theorem shows that for each finite graded $R$--module…

Chevalier et al. (Science, 15 November 2019, p. 856-860) report mathematical formulas and a table predicting the threshold and the output power of terahertz molecular lasers based on various molecules. We show that these formulas are not…

Let Gamma be a Q-polynomial distance-regular graph with vertex set X, diameter D geq 3 and adjacency matrix A. Fix x in X and let A*=A*(x) be the corresponding dual adjacency matrix. Recall that the Terwilliger algebra T=T(x) is the…

Direct and resolved photon interactions are shown to be intimately related through the factorization mechanism. It is argued that in theoretically consistent analysis of jet production in $\gamma$p and ep collisions the LO resolved $\gamma$…

A closed formula multiallelic Walsh (or Hadamard) transform is introduced. Basic results are derived, and a statistical interpretation of some of the resulting linear forms is discussed.

The atmospheric-pressure hybrid plasma in the Ar:H2:CH4 mixture, maintained by microwave radiation (2.47 GHz) and CO2 laser radiation (10.6 {\mu}m) in the chamber of an experimental plasma-chemical reactor designed to study the synthesis of…

The Lambert W function was introduced by Euler in 1779, but was not well-known until it was implemented in Maple, and the seminal paper of Corless, Gonnet, Hare, Jeffrey and Khuth was published in 1996. In this note we describe a simple…

Expanding laser plasmas, produced by high energy laser radiation, possess both high thermal and magnetic field energy density. Characterization of such plasma is challenging but needed for understanding of its physical behaviour. Among all…

We present several closed-form expressions of useful mass distributions. These include the potentials and accelerations of circular rings and arcs, the potentials of uniform density rings and arcs at arbitrary eccentricities, and the…

Backward terahertz radiation can be produced by a high-intensity laser normally incident upon an underdense plasma. It is found that terahertz radiation is generated by electrons refluxing along the bubble shell. These shell electrons have…