We review the development and extensions of the classical total least squares method and describe algorithms for its generalization to weighted and structured approximation problems. In the generic case, the classical total least squares problem has a unique solution, which is given in analytic form in terms of the singular value decomposition of the data matrix. The weighted and structured tot...

Abstract In a decision-making process, one finds that there are alternatives which can be categorized into several groups, based on his or her perspectives, and/or on expected outcome, such as whether his or her choice brings about gains or losses, or that such a choice is right or wrong. Besides, there are many cases with a dilemma where it is hard to select the best choice through transitive ...

This study considers the solution of a class of linear systems related with the fractional Poisson equation FPE −∇2 φ g x, y with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linea...

1) We identify new parameter branches for the ultra-local boundary Poisson bracket in d spatial dimension with a (d− 1)-dimensional spatial boundary. There exist 2 r-dimensional parameter branches for each d-box, r-row Young tableau. The already known branch (hepth/9912017) corresponds to a vertical 1-column, d-box Young tableau. 2) We consider a local distribution product among the so-called b...

We establish a reflection principle for three lattice walkers and use this principle to reduce the enumeration of the configurations of three vicious walkers to that of configurations of two vicious walkers. In the combinatorial treatment of two vicious walkers, we make connections to two-chain watermelons and to the classical ballot problem. Precisely, the reflection principle leads to a bijec...

in this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. the homotopy analysis method (ham) is used for solving this equation. several examples are given to reconfirm the efficiency of these algorithms. the results of applying this procedure...

The paper presents Leviathan, an LTL satisfiability checking tool based on a novel one-pass, treelike tableau system, which is way simpler than existing solutions. Despite the simplicity of the algorithm, the tool has performance comparable in speed and memory consumption with other tools on a number of standard benchmark sets, and, in various cases, it outperforms the other tableau-based tools.

We propose so called clausal tableau systems for the common modal logics K4, KD4 and S4. Basing on these systems, we give more eecient decision procedures than those hitherto known for the considered logics. In particular space requirements for our logics are reduced from the previously established bound O(n 2 : log n) to O(n: log n).

The Kostka numbers Kλμ are important in several areas of mathematics, including symmetric function theory, representation theory, combinatorics and invariant theory. The q-Kostka polynomials Kλμ(q) are the q-analogues of the Kostka numbers. They generalize and extend the mathematical meaning of the Kostka numbers. Lascoux and Schützenberger proved one can attach a non-negative integer statistic...

We study the crystal base B(∞) associated with the negative part of the quantum group for finite simple Lie algebras of types E6 and E7. We present an explicit description of B(∞) as the image of a Kashiwara embedding that is in natural correspondence with the tableau description of B(∞).