Related papers: Rayleigh's Stretched String
We study the problem of Diophantine approximation on lines in $\mathbb{R}^d$ under certain primality restrictions.
We derive an explicit formula for the evaluation of the classical closed string action for any off-shell string field, and for the calculation of arbitrary off-shell amplitudes. The formulae require a parametrization, in terms of some…
This paper studies the complexity of estimating Renyi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known \emph{a priori}. Extending the results of Acharya et al. (SODA'15) on estimating…
In this paper, we obtain a sharp upper bound for the sum of the first $k$-th eigenvalues for this Dirichlet problem of poly-Laplacian with any order, which is viewed as an extension of the result due to Cheng and Wei (Journal of…
We give an example of a scalar second order differential operator in the plane with double periodic coefficients and describe its modification, which causes an additional spectral band in the essential spectrum. The modified operator is…
In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…
Sufficient conditions for linear electrodynamics with real Dirac field are derived.
We prove a sharpened version of the Strichartz inequality for radial solutions of the Schr\"odinger equation in $\mathbb{R}^2\times \mathbb{R}$. We establish an improved upper bound for functions that nearly extremize the inequality, with a…
We study quasilinear evolutionary partial integro-differential equations of second order which include time fractional $p$-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration…
We investigate the radiation damping experienced by a dielectric spherical particle when it is illuminated by an electromagnetic plane wave within the Rayleigh regime. We derive the equivalent electric dipole of the moving particle and…
We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in particular, the sign of the normal derivative of such…
Sufficient oscillation conditions involving $\limsup $ and $\liminf $ for first-order differential equations with several non-monotone deviating arguments and nonnegative coefficients are obtained. The results are based on the iterative…
We survey the variants of Erd\H{o}s' distinct distances problem and the current best bounds for each of those.
Here we derive some results on so called quantitative Runge approximation in the case of the time-harmonic Maxwell equations. This provides a Runge approximation having more explicit quantitative information. We additionally derive some…
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
An approach to constructing an upper bound for the Riemann-Farey sum is described.
A new set of boundary conditions for string propagators is proposed in this paper. The boundary conditions are parametrized by a complex number $\lambda$. Under these new boundary conditions, the left-moving and right-moving modes are…
The boundary string field theory approach is used to evaluate the one-loop tachyon potential. We first discuss the boundary condition at the two boundaries on annulus diagram and then the exact form of corrected potentials at zero and high…
We study the $c$-approximate near neighbor problem under the continuous Fr\'echet distance: Given a set of $n$ polygonal curves with $m$ vertices, a radius $\delta > 0$, and a parameter $k \leq m$, we want to preprocess the curves into a…
The closed form of the first order non-linear differential equation that is satisfied by the effective range within the variable phase formulation of scattering theory is discussed. It is shown that the conventional method of determining…