Suffcient Condition Research Articles

Balanced C4-Bowtie Decomposition of Complete Multi-Graphs

We show that the necessary and suffcient condition for the existence of a balanced C4-bowtie decomposition of the complete multigraph λKn is λ(n - 1) ≡ 0 (mod 16) and n ≥ 7. Decomposition algorithms are also given.

NS Condition of Admissibility for the Linear Estimator of Normal Mean with Unknown Variance

Suppose Y ∼ N(β, σ2In), where β ∈ Rn and σ2 > 0 are unknown. We study the admissibility of linear estimators of mean vector under a quadratic loss function. A necessary and suffcient condition of the admissible linear estimator is given.

Generalization of Guaranteed Cost Control.

Chang and Peng proposed a disign procedure of state-feedback systems that guarantees a certain level of linear-quadratic cost for all admissible perturbations. This is called guaranteed cost control. But they considered the case when an input matrix has special perturbations and guaranteed the existence of a controller only for a restricted class of sytems. This paper deals with the case when an input matrix has more general perturbations. Firstly, a suffcient condition for robust stabilization is given. Secondly, in contrast to Chang and Peng method, on the basis of a linear upper bound, it is shown that there exists a controller under some reasonable assumptions.

Two-Sided Search and Perfect Segregation with Fixed Search Costs

This paper studies a two-sided search model with the following characteristics: there is a continuum of agents with different types in each population, match utility is nontransferable, and there is a fixed search cost that agents incur in each period. When utility functions are additively separable in types and strictly increasing in the partner's type, there exists a unique matching equilibrium that exhibits perfect segregation as in Smith (1997) and Burdett and Coles (1997); i.e., agents form clusters and mate only within them. The role of additive separability and fixed search costs is discussed and contrasted with the discounted case, and an intuitive explanation for the different results obtained in the literature is provided. Also, a simple suffcient condition on the match utility function and the density of types allow us to characterize the duration of the search for each type of agent.

Some new viability results for semilinear differential inclusions

Let X be a reflexive and separable Banach space, $ A : D(A) \subset X \rightarrow X $ the infinitesimal generator of a C 0-semigroup $ S(t) : X \rightarrow X, t \geq 0 $ , D a locally weakly closed subset in X and $ F : D \rightarrow 2^X $ a nonempty, closed, convex and bounded valued mapping which is weakly-weakly upper semi-continuous. The main result of the paper is:¶Theorem. Under the general assumptions above a necessary and suffcient condition in order that for each $ \xi \in D $ there exists at least one mild solution u of¶¶ $ {du \over dt} (t) \in Au(t) + F(u(t)) $ ¶satisfying $ u(0) = \xi $ is the so called "bounded w-tangency condition" below. $ (Bw {\cal TC}) $ . There exists a locally bounded function $ {\cal M} : D \rightarrow {\bf R}^*_+ $ enjoying the property that for each $ \xi \in D $ there exists $ y \in F(\xi) $ such that for each $ \delta \gt 0 $ and each weak neighborhood V of 0 there exist $ t \in ({\rm 0},\delta ] $ and $ p \in V $ with $ \parallel p \parallel \leq {\cal M}(\xi) $ and satisfying¶¶ $ S(t)\xi + t(y + p) \in D. $

Canonical Form for Descriptor Systems

A new canonical form for descriptor system Ex=Ax+Bu, y=Cx+Du is presented. In this canonical form the structures concerning impulse controllability and impulse observability of the descriptor system are indicated. Therefor the presented canonical form is the natural extension to descriptor system from Kalman's canonical form for state equation.Io this paper the problem of eliminating impulsive modes by output feedback for descriptor system is also considered. By using the canonical form the necessary and suffcient condition is proposed.

An Adaptive Procedure for Multiclass Pattern Classification

Abstract—A more general adaptive procedure for determining linear or piecewise linear discriminant functions for multiclass pattern classification is proposed. The adaptive procedure is a many-pattern or group-pattern adaptation. The training sequence consists of groups of vectors in matrix form instead of single vectors. The convergence proof shows that this procedure terminates in a finite number of adaptions if the solution exists. A necessary and suffcient condition is developed for testing the linear separability of each subset of (d + 1) samples. Furthermore, the proposed procedure can be implemented with the addition of only a little complexity to existing systems. Computer simulations indecate satisfactory results.