Locally refined meshes severely impede the efficiency of explicit Runge-Kutta (RK) methods for the simulation of time-dependent wave phenomena. By taking smaller time-steps precisely where the smallest elements are located, local time-stepping (LTS) methods overcome the bottleneck caused by the stringent stability constraint of but a few small elements in the mesh. Starting from classical or lo...

In this paper, we give an overview of a realtime reservation-based operating system called Nano-RK used primarily in wireless sensor networks.

In appropriate units, the Brown-Ravenhall Hamiltonian for a system of 1 electron relativistic molecules with K fixed nuclei having charge and position Zk, Rk, k = 1, 2, . . . ,K, is of the form B1,K = Λ+ ( D0 + αVc ) Λ+, where Λ+ is the projection onto the positive spectral subspace of the free Dirac operator D0 and Vc = − ∑K k=1 αZk |x−Rk| + ∑K k<l, k,l=1 αZkZl |Rk−Rl| , with α Sommerfeld’s fi...

In this note, we consider the following rational difference equation: xn+1 = f (xn−r1 , . . . , xn−rk )g(xn−m1 , . . . , xn−ml )+ 1 f (xn−r1 , . . . , xn−rk )+ g(xn−m1 , . . . , xn−ml ) , n= 0,1, . . . , where f ∈ C((0,+∞)k, (0,+∞)) and g ∈ C((0,+∞)l, (0,+∞)) with k, l ∈ {1,2, . . .}, 0 r1 < · · ·< rk and 0 m1 < · · ·<ml , and the initial values are positive real numbers. We give sufficient con...

The proposed method is an ((r1, ... , rk) , n)-threshold sharing system: n shares are created by the sharing system to replace the index file of a given quantized image. Security is achieved through the fact that interceptors cannot view the image if they intercept less than r1 shares. Fault-tolerance is also obtained because the VQ version of the image can be fully recovered using any rk share...

This is a dissertation in the field of Mathematics: Logic: Computability Theory: Algorithmic Randomness (Mathematics Subject Classification 03D80, 68Q30). Its focus is relative randomness as measured by rK-reducibility, a refinement of Turing reducibility defined as follows. An infinite binary sequence A is rK-reducible to an infinite binary sequence B, written A ≤rK B, if ∃d ∀n . K(A n|B n) < ...

We obtain linearized oscillation theorems for the equation with distributed delays ẋ(t)+ m ∑ k=1 rk(t) ∫ t −∞ fk(x(s)) ds Rk(t, s) = 0. (1) The results are applied to logistic, Lasota–Wazewska and Nicholson’s blowflies equations with a distributed delay. In addition, the “Mean Value Theorem” is proved which claims that a solution of (1) also satisfies the linear equation with a variable concent...

A landmark result from rational approximation theory states that x1∕p on [0,1] can be approximated by a type-(n,n) function with root-exponential accuracy. Motivated the recursive optimality property of Zolotarev functions (for square root and sign functions), we investigate approximating composite form rk(x,rk−1(x,rk−2(⋯(x,r1(x,1))))). While this class ceases to contain minimax (best) approxim...

Abstract We show that the effective diffusivity matrix D(V n) for the heat operator ∂t − (1/2 − ∇V n∇) in a periodic potential V n = n k=0 Uk(x/Rk) obtained as a superposition of Hölder-continuous periodic potentials Uk (of period Td := R d/Zd , d ∈ N∗, Uk(0) = 0) decays exponentially fast with the number of scales when the scale ratios Rk+1/Rk are bounded above and below. From this we deduce t...

Let Mn be the semigroup of n× n complex matrices under the usual multiplication, and let S be different subgroups or semigroups in Mn including the (special) unitary group, (special) general linear group, the semigroups of matrices with bounded ranks. Suppose Λk(A) is the rank-k numerical range and rk(A) is the rank-k numerical radius of A ∈ Mn. Multiplicative maps φ : S → Mn satisfying rk(φ(A)...