Related papers: Rayleigh's Stretched String
We give an exponential lower bound for Berge-Ramsey problems.
In this paper we consider the field of local times of a discrete-time Markov chain on a general state space, and obtain uniform (in time) upper bounds on the total variation distance between this field and the one of a sequence of $n$…
We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq…
In this work nonlinear pseudo-differential equations with the infinite number of derivatives are studied. These equations form a new class of equations which initially appeared in p-adic string theory. These equations are of much interest…
In this paper we determine the stretch factor of the $L_1$-Delaunay and $L_\infty$-Delaunay triangulations, and we show that this stretch is $\sqrt{4+2\sqrt{2}} \approx 2.61$. Between any two points $x,y$ of such triangulations, we…
Explicit estimates for the Riemann zeta-function on the $1$-line are derived using various methods, in particular van der Corput lemmas of high order and a theorem of Borel and Carath\'{e}odory.
Assuming the Riemann hypothesis, we obtain upper and lower bounds for moments of the Riemann zeta-function averaged over the extreme values between its zeros on the critical line. Our bounds are very nearly the same order of magnitude. The…
We prove a Weyl upper bound on the number of scattering resonances in strips for manifolds with Euclidean infinite ends. In contrast with previous results, we do not make any strong structural assumptions on the geodesic flow on the trapped…
In this paper, we provide explicit upper and lower bounds for the argument of the Riemann zeta-function and its antiderivatives in the critical strip under the assumption of the Riemann hypothesis. This extends the previously known bounds…
It is shown that the string equation can be obtain from field equations. Such work is performed to scalar field. The equation obtained in nonrelativistic limit describes the nonlinear string. Such string has the effective elasticity…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants…
We obtain almost sure bounds for the weighted sum $\sum_{n \leq t} \frac{f(n)}{\sqrt{n}}$, where $f(n)$ is a Steinhaus random multiplicative function. Specifically, we obtain the bounds predicted by exponentiating the law of the iterated…
In this paper, we investigate the existence and characterizations of the Fr\'echet derivatives of the solution to time-harmonic elastic scattering problems with respect to the boundary of the obstacle. Our analysis is based on a technique -…
New types of symmetry for the Rayleigh equation are found. For small Atwood number, an analytic solution is obtained for a smoothly varying density profile. It is shown that a transition layer with a finite width can undergo some kind of…
In this paper, we study estimates for eigenvalues of the clamped plate problem. A sharp upper bound for eigenvalues is given and the lower bound for eigenvalues in [10] is improved.
Assuming the Riemann Hypothesis, we provide effective upper and lower estimates for $\left|\zeta(s)\right|$ right to the critical line. As an application we make explicit Titchmarsh's conditional bound for the Mertens function and…
An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure…
The linear system of differential equations for determination of transmission and reflection amplytudes of scattered electron in the field of one dimensional arbitrary potential is obtained. It is shown that in general the scattering…
We derive sharp bounds for the accuracy of approximate eigenvectors (Ritz vectors) obtained by the Rayleigh-Ritz process for symmetric eigenvalue problems. Using information that is available or easy to estimate, our bounds improve the…