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## Applications

### Interior Point Methods for Linear Optimization (2005-01-01): 247-258 , January 01, 2005

## A Criterion for Conditional Instability by the First Approximation for Solutions of Differential Systems

### Differential Equations (2005-12-01) 41: 1677-1686 , December 01, 2005

## Modified Alternating $$\vec{k}$$ –generators

### Designs, Codes and Cryptography (2005-05-01) 35: 159-174 , May 01, 2005

This paper deals with a class $$\mathcal{MAG}_{\vec{k}}$$ of pseudorandom bit generators – modified alternating $$\vec{k}$$ –generators. This class is constructed similarly to the class $$\mathcal{ASG}_{\vec{k}}$$ of alternating step generators. Three subclasses of $$\mathcal{MAG}_{\vec{k}}$$ are distinguished, namely linear, mixed and nonlinear generators. The main attention is devoted to the subclass $$\mathcal{MAG}_{\vec{k}}^{max}$$ of linear and mixed generators generating periodic sequences with maximal period lengths. A necessary and sufficient condition for all sequences generated by the linear generators of $$\mathcal{MAG}_{\vec{k}}$$ to be with maximal period lengths is formulated. Such sequences have good statistical properties, such as distribution of zeroes and ones, and large linear complexity. Two methods of cryptanalysis of the proposed generators are given. Finally, three new classes of modified alternating $$\vec{k}$$ –generators, designed especially to be more secure, are presented.

## Kähler–Ricci solitons on compact complex manifolds with C1(M) > 0

### Geometric & Functional Analysis GAFA (2005-06-01) 15: 697-719 , June 01, 2005

### Abstract.

In this paper, we discuss the relation between the existence of Kähler–Ricci solitons and a certain functional associated to some complex Monge–Ampère equation on compact complex manifolds with positive first Chern class. In particular, we obtain a strong inequality of Moser–Trudinger type on a compact complex manifold admitting a Kähler–Ricci soliton.

## Challenges in Surface-Surface Intersections

### Computational Methods for Algebraic Spline Surfaces (2005-01-01): 11-26 , January 01, 2005

Tangential and singular situations are still challenges in a system for surface-surface intersections. This paper presents several real world examples of hard intersection problems, and proposes methods on how to deal with them. In particular, solutions which use the possibility of representing a parametric surface as an algebraic surface through the use of approximate implicitization, are in focus. This allows us to transform an intersection between two parametric surfaces to the problem of finding zeroes of a function of two parameters.

## On Normal Subgroups of Coxeter Groups Generated by Standard Parabolic Subgroups

### Geometriae Dedicata (2005-10-01) 115: 65-78 , October 01, 2005

We discuss one construction of nonstandard subgroups in the category of Coxeter groups. Two formulae for the growth series of such a subgroups are given.

As an application we construct a flag simple convex polytope, whose f-polynomial has non-real roots.

## Functional Fluids and Functionalized Nanotubes

### Microflows and Nanoflows (2005-01-01) 29: 471-505 , January 01, 2005

## A routing algorithm in WDM mesh networks with grooming capacities

### Wuhan University Journal of Natural Sciences (2005-09-01) 10: 873-876 , September 01, 2005

Most of the work in traffic grooming has been in the area of providing efficient network designs in Wavelength division multiplexing (WDM). The objective of these traffic rooming algorithms is to reduce the cost of overall networks. In this paper, a routing algorithm based on transiently chaotic neural network is proposed to solve the problem in WDM logical topology. The objectives of the routing algorithm are accomodating all traffic requirements and using less network resource. The simulation shows that the proposed algorithm is efficient in the routing selection, meanwhile the algorithm can use less network resource.

## Weighted Variational Inequalities

### Journal of Optimization Theory and Applications (2005-11-01) 127: 263-283 , November 01, 2005

In this paper, we introduce weighted variational inequalities over product of sets and system of weighted variational inequalities. It is noted that the weighted variational inequality problem over product of sets and the problem of system of weighted variational inequalities are equivalent. We give a relationship between system of weighted variational inequalities and systems of vector variational inequalities. We define several kinds of weighted monotonicities and establish several existence results for the solution of the above-mentioned problems under these weighted monotonicities. We introduce also the weighted generalized variational inequalities over product of sets, that is, weighted variational inequalities for multivalued maps and systems of weighted generalized variational inequalities. Extensions of weighted monotonicities for multivalued maps are also considered. The existence of a solution of weighted generalized variational inequalities over product of sets is also studied. The existence results for a solution of weighted generalized variational inequality problem give also the existence of solutions of systems of generalized vector variational inequalities.