Enclosings of λ-fold 4-cycle systems

In this paper we solve the problem of enclosing a λ-fold 4-cycle system of order v into a (λ + m)-fold 4-cycle system of order v + u for all m > 0 and u ≥ 1. An ingredient is constructed that is of interest on its own right, namely the problem of finding equitable partial 4-cycle systems of λ K _v . This supplementary solution builds on a result of Raines and Staniszlo.     

On the Cauchy problem for systems —Parabolic systems—

The author proposes the definition of thep-parabolic system, which is stable under the similar transformations, using thep-determinant of the matrix of differential operators. The relation between thep-parabolic systems andH ^∞ well-posedness is considered. To the memory of Lamberto Cattabriga     

On the peirce decompositions for freudenthal—kantor triple systems

It is the object of this paper to investigate the Peirce decomposition for Freudenthal-Kantor triple systems, by making use of the concept of anti-derivation of the triple systems.     

General Purpose Heuristics for Integer Programming—Part II

In spite of the many special purpose heuristics for specific classes of integer programming (IP) problems, there are few developments that focus on general purpose integer programming heuristics. This stems partly from the perception that general purpose methods are likely to be less effective than specialized procedures for specific problems, and partly from the perception that there is no unifying theoretical basis for creating general purpose heuristics. Still, there is a general acknowledgment that methods which are not limited to solving IP problems on a class by class basis, but which apply to a broader range of problems, have significant value. We provide a theoretical framework and associated explicit proposals for generating general purpose IP heuristics. Our development, makes use of cutting plane derivations that also give a natural basis for marrying heuristics with exact branch and cut methods for integer programming problems.     

Weakly elliptic systems with obstacle constraints Part II — An N × N model problem

Existence, uniqueness (even stability), and regularity are established for a special system of variational inequalities of obstacle type. The system is only considered to be elliptic in the weakest possible sense. The system includes a version of the biharmonic and polyharmonic obstacle problems. The main aspect of this problem and the approach here is its reduction via algebraic invarients to special canonical forms. One might view this work as the beginnings of a “group analysis” of variational inequalities. This paper is dedicated to the memory of Guido Stampacchia (1922–1978).     

Uniqueness for weak flow of H—systems with dirichlet boundary conditons

It is proved that the weak flow of H—system with a Dirichlet boundary condition is unique and regular up to the time of energy concentration. Moreover, if the global weak solution satisfies certain energy inequality, then it is unique for all the time and is regular with the exception of finitely many points     

Several splittings for non-Hermitian linear systems

For large sparse non-Hermitian positive definite system of linear equations,we present several variants of the Hermitian and skew-Hermitian splitting(HSS)about the coefficient matrix and establish correspondingly several HSS-based iterative schemes.Theoretical analyses show that these methods are convergent unconditionally to the exact solution of the referred system of linear equations,and they may show advantages on problems that the HSS method is ineffiective.     

Σ-bounded algebraic systems and universal functions. II

Ershov algebras, Boolean algebras, and abelian p-groups are Σ-bounded systems, and there exist universal Σ-functions in hereditarily finite admissible sets over them.     

Effective stability for generalized Hamiltonian systems

An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems, dimensions of action variables and angle variables might be distinct.     

Liénard systems for quadratic systems with invariant algebraic curves

We study the character of the friction function f(x) and the restoring force g(x) in the Liénard system to which a quadratic system with an invariant second-order algebraic curve (an ellipse that is a limit cycle, a hyperbola defining two separatrix cycles, or a parabola) or fourth-order algebraic curve with an oval being a limit cycle can be reduced. Invariant curves are constructed for quadratic systems in a five-parameter canonical family, which can readily be reduced to Liénard systems.     

Interaction of intelligent and autonomous systems – part II: realization of cognitive technical systems

In this study, the application of a meta-modelling technique to structure complex environments is demonstrated with two examples. A special situation-operator model developed to model the human-machine-interaction is applied to automated supervision within the HMI context and to realize flexible and situated interaction of autonomous systems. A concept to automated monitoring of human operators is introduced to illustrate the structuring of complex environments as the first example. In the second example, this modelling technique is applied to a mobile robot to autonomously build and update a mental model of the interaction with the environment as an example of a cognitive technical system.     

Kinetical systems—local analysis

The paper gives the answer to the question of the number and qualitative character of stationary points of an autonomous detailed balanced kinetical system.     

Standing waves with large frequency for 4-superlinear Schrödinger–Poisson systems

Annali di Matematica Pura ed Applicata (1923 -) - We consider standing waves with frequency $$omega $$ for 4-superlinear Schrödinger–Poisson system. For large $$omega $$ , the problem...     

Linear energy-preserving integrators for Poisson systems

For Hamiltonian systems with non-canonical structure matrix a new class of numerical integrators is proposed. The methods exactly preserve energy, are invariant with respect to linear transformations, and have arbitrarily high order. Those of optimal order also preserve quadratic Casimir functions. The discussion of the order is based on an interpretation as partitioned Runge–Kutta method with infinitely many stages.     

Resolvent estimates for Douglis–Nirenberg systems

We study mixed order parameter-elliptic boundary value problems with boundary conditions of a certain structure. For such operators, we prove resolvent estimates in L ^p based Sobolev spaces of suitable order and the analyticity of the semigroup. Finally, we present an application of this theory to studies of the particle transport in a semi-conductor.     

Quillen’s stratification for fusion systems

The purpose of this note is to provide a reference for the fact that the proof of Quillen’s stratification for finite group cohomology carries over to fusion system. As in the case of Quillen’s stratification for block varieties, the proof is similar to the usual proof for group cohomology except for the use of fusion stable bisets, whose existence is due to Broto et al.     

Logical soft systems modelling for information source analysis—The case of Hongkong Telecom

The paper describes the use of logico-linguistic modelling, a logically enhanced version of Soft System Methodology, to identify the information needed to support decisions made in a marketing department of a Hong Kong telecommunications company. This case indicates that logical complexity need not be a barrier to stakeholder comprehension. However, cross-cultural difficulties were encountered when using the basic SSM method.