We describe the macroscopic behavior of Gaussian chains confined between impenetrable surfaces and having ends interacting with the surfaces taking into account all multiple reflections from the two surfaces. The statistics of chains with the absorbing boundary conditions

In this paper, an overview of the calculation of synthetic seismograms using the Gaussian beam method is presented accompanied by some representative applications and new extensions of the method. Since caustics are a frequent occurrence in seismic wave propagation, modifications to ray theory are often necessary. In the Gaussian beam method, a summation of paraxial Gaussian beams is used to de...

In an M × N interference network, there are M transmitters and N receivers with each transmitter having independent messages for each of the 2 −1 possible non-empty subsets of the receivers. We consider the 2 × 2 interference network with 6 possible messages, of which the 2 × 2 interference channel and X channel are special cases obtained by using only 2 and 4 messages respectively. Starting fr...

In this paper, we aim to provide a systematic study of the relationship be-tween Chernoff information and topological, as well as algebraic propertiesof the corresponding Gaussian tree graphs for the underlying graphical test-ing problems. We first show the relationship between Chernoff informationand generalized eigenvalues of the associated covariance matrices. It is then<...

We present some simple observations on factors of the qbinomial coefficients, the q-Catalan numbers, and the q-multinomial coefficients. Writing the Gaussian coefficient with numerator n and denominator k in a form such that 2k ≤ n by the symmetry in k, we show that this coefficient has at least k factors. Some divisibility results of Andrews, Brunetti and Del Lungo are also discussed.

An achievable rate for the discrete memoryless relay channel with receiver-transmitter feedback is proposed based on Block-Markov superposition encoding. The achievable rate can also be extended to Gaussian channels. A second achievable rate for the Gaussian relay channel based on a Schalkwijk-Kailath type scheme is presented. For some channels both achievable rates strictly improve upon all pr...

This paper provides a necessary and sufficient condition for the existence of nonautarkic contract in a risk sharing model with two-sided lack of commitment. Verifying the condition takes just one Gaussian elimination of a matrix. Published by Elsevier B.V.

We present improvements to the index-calculus algorithm for the computation of the ideal class group and regulator of a real quadratic field. Our improvements consist of applying the double large prime strategy, an improved structured Gaussian elimination strategy, and the use of Bernstein’s batch smoothness algorithm. We achieve a significant speed-up and are able to compute the ideal class gr...

Higher-dimensional Gaussian weighted integration is of interest in probabilistic simulations. Motivated by the need for variance calculations with functions being at least quadratic, the family of degree 5 formulae is considered. Using an existing formula for the integration over the surface of an n-sphere, an efficient, new formula for Gaussian weighted integration is obtained. Several other f...

We discuss a method of producing computer assisted proofs of almost everywhere strong convergence of the d-dimensional Gauss algorithm. This algorithm is equivalent to Brun's algorithm and to the modi ed Jacobi-Perron algorithm considered by Podsypanin and Schweiger. In this paper we focus on the reduction of the problem to a nite number of calculations. These calculations have been carried out...