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     

Deductive systems of a cone algebra — II: Isomorphism theorem

We prove that there is an isomorphism φ of the lattice of deductive systems of a cone algebra onto the lattice of convex ℓ-subgroups of a lattice ordered group (determined by the cone algebra) such that for any deductive system A of the cone algebra, A is respectively a prime, normal or polar if and only if φ(A) is a prime convex ℓ-subgroup, ℓ-ideal or polar subgroup of the ℓ-group, thus generalizing and extending the result of Rachůnek that the lattice of ideals of a pseudo MV-algebra is isomorphic to the lattice of convex ℓ-subgroups of a unital lattice ordered group.      

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.     

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     

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).     

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.     

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.     

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...     

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.     

Webb’s conjecture for fusion systems

We give a short and conceptual proof of Webb’s conjecture. Our methods are general enough to prove an analogue of the conjecture for saturated fusion systems. The author was supported by an EPSRC grant EP/D506484/1.     

Clifford’s theorem for coherent systems

Let C be an algebraic curve of genus g ≥ 2. We prove an analogue of Clifford’s theorem for coherent systems on C and some refinements using results of Re and Mercat. Received: 27 July 2007     

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.