In this paper we study bound state solutions of a class of two-component nonlinear elliptic systems with a large parameter tending to infinity. The large parameter giving strong intercomponent repulsion induces phase separation and forms segregated nodal domains divided by an interface. To obtain the profile of bound state solutions near the interface, we prove the uniform Lipschitz continuity ...

We consider the elliptic equation −∆u = f(u) in the whole R , where f is of bistable type. It is known that there exists a saddleshaped solution in R. This is a solution which changes sign in R and vanishes only on the Simons cone C = {(x, x) ∈ R×R : |x| = |x|}. It is also known that these solutions are unstable in dimensions 2 and 4. In this article we establish that when 2m = 6 every saddle-s...

In the previous two decades, a number of qualitative constraint calculi have been developed, which are used to represent and reason about spatial configurations. A common property of almost all of these calculi is that reasoning in them can be understood as solving a binary constraint satisfaction problem over infinite domains. The main algorithmic method that is used is constraint propagation ...

We demonstrate an automated method for proving temporal logic statements about solutions to ordinary differential equations (ODES), even in the face of an incomplete specification of the ODE. The method combines an implemented, on-the-fly, model checking algorithm for statements in the temporal logic CTL* with the output of the qualitative simulation algorithm QSIM. Based on the QSIM Guaranteed...

We introduce different extensions of LTL where propositional variables are replaced by constraints interpreted in Z. We show different decidability and complexity results for the satisfiability and model checking problems of these logics. The extension of LTL over a wide set of qualitative constraints is shown to be pspace-complete. When introducing some quantitative constraints, we must consid...

introduction: the spatial variability of soil properties and its importance in production is a matter-of-debate. insight about the variability of soil properties as well as the yield of orchards is necessary to achieve higher productivity and better management. orange is one of the most important export products in our country and to sustainable production of this product, it is necessary to id...

where the initial conditions x−5, x−4, x−3, x−2, x−1, x0 are arbitrary positive real numbers and α, β, γ, δ are constants. In addition, we obtain the form of solution of some special cases. Recently, there has been great interest in studying difference equation systems. One of the reasons for this is a necessity for some techniques which can be used in investigating equations arising in mathema...

where aj ∈R are scalars, τ j are iterates of a function τ : T→ T and T is a time scale unbounded above. Under some specific choices of τ , this dynamic equation involves several significant particular cases such as linear autonomous differential equations with several delays or linear autonomous higher-order difference equations. For proportional τ , we formulate an asymptotic result joint for ...

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