On searching for solutions of the Diophantine equation

We propose a new search algorithm to solve the equation for a fixed value of . By parametrizing min, this algorithm obtains and (if they exist) by solving a quadratic equation derived from divisors of . By using several efficient number-theoretic sieves, the new algorithm is much faster on average than previous straightforward algorithms. We performed a computer search for 51 values of below 1000 (except ) for which no solution has previously been found. We found eight new integer solutions for and in the range of .

     

Upper bound for the decay rate of the joint queue-length distribution in a two-node Markovian queueing system

This paper studies the geometric decay property of the joint queue-length distribution {p(n ₁,n ₂)} of a two-node Markovian queueing system in the steady state. For arbitrarily given positive integers c ₁,c ₂,d ₁ and d ₂, an upper bound of the decay rate is derived in the sense

Large and Moderate Deviations of Random Upper Semicontinuous Functions

We firstly discuss the topological properties of the space of upper semicontinuous functions, and then we obtain large deviation principles for random upper semicontinuous functions under various topologies. Finally, we prove moderate deviation principles for random sets and random upper semicontinuous functions.     

A prediction problem in

For a nonnegative integrable weight function on the unit circle , we provide an expression for , in terms of the series coefficients of the outer function of , for the weighted distance , where is the normalized Lebesgue measure and ranges over trigonometric polynomials with frequencies in , , . The problem is open for .

     

Wide-band dereverberation method based on multichannel linear prediction using prewhitening filter

Several dereverberation algorithms have been studied. The sampling frequencies used in conventional studies are typically 8–16 kHz because their main purpose is preprocessing for improving the intelligibility of speech communication and articulation for automatic speech recognition. However, in next-generation communication systems, techniques to analyze and reproduce not only semantic information of sound but also more high-definition components such as spatial information and directivity will be increasingly necessary. To decompose these sound field characteristics with high definition, a dereverberation algorithm that is useful at high sampling frequencies is an important technique to process sound that includes high-frequency spectra such as musical sounds. The LInear-predictive Multichannel Equalization (LIME) algorithm is a promising dereverberation method. Using the LIME algorithm, however, a dereverberation signal cannot be solved at high sampling frequencies when the source signal is colored, such as in the case of speech and sound of musical signals. Because the rank of the correlation matrix calculated from such a colored signal is not full, the characteristic polynomial cannot be calculated precisely. To alleviate this problem, we propose preprocessing of all input signals with filters to whiten their spectra so that this algorithm can function for colored signals at high sampling frequencies.     

A Theoretical Study of ãA2 CH2

The potential energy surface and dipole moment surfaces of the ã⁴A₂ electronic state of CH₂⁺ are calculated ab initio using an augmented correlation-consistent polarized valence quadruple-ζ (aug-cc-pVQZ) basis set, with the incorporation of dynamical correlation using the coupled cluster method with single and double excitations and perturbatively connected triple excitations [CCSD(T)]. We use these surfaces in the MORBID program system to calculate rotation and rotation-vibration term values for ã-state CH₂⁺, CD⁺₂, and CHD⁺ and to simulate the rotation and rotation-vibration absorption spectrum of CH₂⁺ in the ã⁴A₂ electronic state. Our work is motivated by studies of CH₂⁺ that use the Coulomb explosion imaging technique and by the goal of predicting spectra that may be obtained from discharge sources. Although the ã state is the lowest-lying excited state above the X?/Ã ground state pair, it turns out to be relatively high-lying, and we determine that T_e(ã)=30447.5 cm⁻¹. The equilibrium bond angle for ã-state CH₂⁺ is only 77.1°; as a result the asymmetric top κ value is close to 0, and the molecule is equally far from the oblate and prolate symmetric top limits in this electronic state.     

Evolutionary construction of geographical networks with nearly optimal robustness and efficient routing properties

Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property, we investigate such a design from the following viewpoints: (1) network evolution according to a spatially heterogeneous population, (2) trimodal low degrees for the tolerant connectivity against both failures and attacks, and (3) decentralized routing within short paths. Furthermore, we point out the weakened tolerance by geographical constraints on local cycles, and propose a practical strategy by adding a small fraction of shortcut links between randomly chosen nodes in order to improve the robustness to a similar level to that of the optimal bimodal networks with a larger degree for the network size N. These properties will be useful for constructing future ad hoc networks in wide-area communications.