For a principal type pseudodifferential operator, we prove that condition (ψ) implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker’s paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from ǫ + 3/2 for any ǫ > 0 (Dencker’s most recent result) to 3/2 ...

In this paper we study a potential problem with a nonlinear boundary condition. Using the Green representation formula for a harmonic function we reformulate the nonlinear boundary value problem as a nonlinear boundary integral equation. We shall give a brief discussion of the solvability of the integral equation. The aim of this paper, however, is to analyse the collocation method for finding ...

Methods are introduced to decide the solvability of transformation problems. Such methods may be applied to save some of the problem solving effort. Supposition for applying the stated methods is that information about the structure of the problem space is available for detecting separated subsets of the situation set. Solvability of transformation problems is decided by means of systems of sep...

This paper investigates a global stabilization problem and a nonlinear H∞ control problem for a class of nonminimum phase nonlinear multivariable systems. To avoid the complicated recursive design procedure, an asymptotic time-scale and eigenstructure assignment method is adopted to construct the control laws for the stabilization problem and the nonlinear H∞ control problem. A sufficient solva...

In this article, the notions of non-abelian tensor and exterior products of two normal crossed submodules of a given crossed module of groups are introduced and some of their basic properties are established. In particular, we investigate some common properties between normal crossed modules and their tensor products, and present some bounds on the nilpotency class and solvability length of the...

Using T50 Monte Carlo simulation, we study the relaxation of graph coloring ~K-COL! and satisfiability ~K-SAT!, two hard problems that have recently been shown to possess a phase transition in solvability as a parameter is varied. A change from exponentially fast to power law relaxation, and a transition to freezing behavior are found. These changes take place for smaller values of the paramete...

It has been shown by Lemke that if a matrix is copositive plus on IR n , then feasibility of the corresponding Linear Complementarity Problem implies solvability. In this article we show, under suitable conditions, that feasibility of a Generalized Linear Complementarity Problem (i.e., deened over a more general closed convex cone in a real Hilbert Space) implies solvability whenever the operat...

Optimization problem for a structural acoustic model with controls governed by unbounded operators on the state space is considered. This type of controls arises naturally in the context of ”smart material technology”. The main result of the paper provides an optimal synthesis and solvability of associated nonstandard Riccati equations. It is shown that in spite of the unboundedness of control ...

can be solved with a ∈ A, b ∈ B, c ∈ C and d ∈ D. Gyarmati and Sárközy [3] generalized the results on the solvability of equation (1.1) to finite fields. They also study the solvability of other (higher degree) algebraic equations with solutions restricted to “large” subsets of Fq, where Fq denote the finite field of q elements. Using exponential sums, Hart and Iosevich [5] studied similar prob...

In this paper we consider medium access scheduling in ad hoc networks as a distributed constraint satisfaction problem (DCSP), and present experimental results on the solvability and complexity of this problem. We show that there are “phase transitions” in solvability and complexity with respect to the transmission power of the wireless nodes. The phase transition curves indicate that there is ...