The method of potential envelopes is used to analyse the bound-state spectrum of the Schrödinger Hamiltonian H = −∆− v/(r+ b) , where v and b are positive. We established simple formulas yielding upper and lower energy bounds for all the energy eigenvalues. PACS 31.15.Gy, 31.15.Pf, 03.65.Ge. Spectral bounds for the cutoff Coulomb potential page 2

J. K. Aggarwal (S62-M9653M’74-F’76) was born in Amritsar, India. He received the B.S. degree in mathematics and physics from the University of Bombay, Bombay, India, in 1956, the B. Eng. degree from the University of Liverpool, Liverpool, England, in 1960, and the MS. and Ph.D. degrees from the University of Illinois, Urbana, IL, in the years 1961 and 1964, respectively. He joined the Universit...

We consider the problem of proving the existence of an L2-cutoff for families of ergodic Markov processes started from given initial distributions and associated with reversible (more, generally, normal) Markov semigroups. This includes classical examples such as families of finite reversible Markov chains and Brownian motion on compact Riemannian manifolds. We give conditions that are equivale...

K.-I. Ishikawa, Y. Iwasaki, Yu Nakayama, and T. Yoshie Graduate School of Science, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japan Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan California Institute of Technology, Pasadena, California 91125, USA (Received 21 January 2013; published 30 April 2013) We give a new perspective on the dyn...

We consider the class of finite-state programs executed by an unbounded number of replicated threads communicating via shared variables. The thread-state reachability problem for this class is essential in software verification using predicate abstraction. While this problem is decidable via Petri net coverability analysis, techniques solely based on coverability suffer from the problem’s expon...

Given a continuous time Markov Chain {q(x, y)} on a finite set S, the associated noisy voter model is the continuous time Markov chain on {0,1}S , which evolves in the following way: (1) for each two sites x and y in S, the state at site x changes to the value of the state at site y at rate q(x, y); (2) each site rerandomizes its state at rate 1. We show that if there is a uniform bound on the ...

We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together.

The optical response of axially uniform nonlinear photonic bandgap fibers is studied theoretically. We observe gap-soliton-like generation and associated bistability, similar to what is typically found in periodically modulated nonlinear structures. This response stems from the nature of the guided-mode dispersion relations, which involve a frequency cutoff at zero wave vector. In such systems,...

We construct a family of trees on which a lazy simple random walk exhibits total variation cutoff. The main idea behind the construction is that hitting times of large sets should be concentrated around their means. For this sequence of trees we compute the mixing time, the relaxation time and the cutoff window.

background: increasing evidence suggests an association between ele­vated serum aminotransferase levels and metabolic disorders (metabolic syndrome, hyperlipemia and diabetes mellitus). however, the significance of relatively low levels of aminotransferases in relation to metabolic disorders has not been fully investigated in the general population. we inves­tigated the association between seru...