In this paper we present numerical methods for the nonlinear Schrödinger equations (NLS) in the semiclassical regimes: iε uεt = − ε 2 ∆u + V (x)u + f(|u|)u, x ∈ R, with nonzero far-field conditions. A time-splitting cosine-spectral (TS-Cosine) method is presented when the nonzero far-field conditions are or can be reduced to homogeneous Neumann conditions, a time-splitting Chebyshev-spectral (T...

We analyze rare kaon decays in models in which the dominant new effect is an enhanced s̄dZ vertex Zds. We point out that in spite of large theoretical uncertainties the CP-violating ratio ε /ε provides at present the strongest constraint on ImZds. Assuming 1.5 · 10−3 ≤ ε/ε ≤ 3 · 10−3 and Standard Model values for the CKM parameters we obtain the bounds BR(KL → π0νν̄) ≤ 3.9 · 10−10 and BR(KL → πee...

We present two uniformly and optimally accurate numerical methods for discretizing the Zakharov system (ZS) with a dimensionless parameter 0 < ε ≤ 1, which is inversely proportional to the acoustic speed. In the subsonic limit regime, i.e. 0 < ε ≪ 1, the solution of ZS propagates waves with O(ε)and O(1)-wavelength in time and space, respectively, and/or rapid outgoing initial layers with speed ...

A new smoothing method for solving ε -support vector regression (ε-SVR), tolerating a small error in fitting a given data sets nonlinearly is proposed in this study. Which is a smooth unconstrained optimization reformulation of the traditional linear programming associated with a ε-insensitive support vector regression. We term this redeveloped problem as ε-smooth support vector regression (ε-S...

Hilbert’s 1928 article, to which this piece is an appendix, was presented in July 1927 to the Hamburg Mathematical Seminar. Hilbert had first introduced his program for the foundations of mathematics in the same venue in a series of talks in 1921 (Hilbert, 1922). In the 1927 talk, he presented a mature version of his program, including technical details of the axiomatization of mathematics base...

One of the main critical steps that should be taken during natural disasters is the assignment and distribution of resources among affected people. In such situations, this can save many lives. Determining the demands for critical items (i.e., the number of injured people) is very important. Accordingly, a number of casualties and injured people have to be known during a disaster. Obtaining an ...

This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization. Existing results show that if NP 6⊆ coNP/poly, no efficient preprocessing algorithm can reduce n-variable instances of cnf-sat with d literals per clause, to equiv...