Given a Boolean function f on n-variables, we find a reduced set of homogeneous linear equations by solving which one can decide whether there exist annihilators at degree d or not. Using our method the size of the associated matrix becomes νf × ( ∑d

The technique of weighted integral averages, known in the oscillation theory of ordinary differential equations, is extended to the half–linear partial differential equation div(||∇u||p−2∇u) + c(x)|u|p−2u = 0. p > 1 (E) This technique is used to obtain new oscillation criteria for (E) on the unbounded domains.

Let A and B be finite subsets of C such that |B| = C|A|. We show the following variant of the sum product phenomenon: If |AB| < α|A| and α ! log |A|, then |kA+ lB|" |A|k|B|l. This is an application of a result of Evertse, Schlickewei, and Schmidt on linear equations with variables taking values in multiplicative groups of finite rank, in combination with an earlier theorem of Ruzsa about sumset...

By using a Picone type formula in comparison with oscillatory unforced half-linear equations, we derive new oscillation criteria for second order forced super-half-linear impulsive differential equations having fixed moments of impulse actions. In the superlinear case, the effect of a damping term is also considered. c © 2007 Elsevier Ltd. All rights reserved.

The new curve contains all of the information about the original curve’s tangent lines. For example, it crosses the y-axis whenever the original curve has a horizontal tangent line. The straight line y = mx + b, or (x(t), y(t)) = (t,mt + b), has only one tangent line and thus a trivial transformation to a point, (x∗(t), y∗(t)) = (m, b). Some conic sections transform to conic sections. For examp...

In this article, we consider the robustness of a nonuniform (μ, ν) trichotomy in Banach spaces, in the sense that the existence of such a trichotomy for a given linear equation persists under sufficiently small linear perturbations. The continuous dependence with the perturbation of the constants in the notion of trichotomy is studied, and the related robustness of strong (μ, ν) trichotomy is a...

In this paper, we propose new types of solutions (an L-localized solution and an R-localized solution) to interval systems ofmax-separable linear equationsA⊗x = b, whereA = [A, A] and b = [b, b]. We provide some small application examples to emphasize the importance of our proposed solutions. We give necessary and sufficient conditions for checking L-localized and R-localized solvabilities and ...

It is known that the satisfiability problem for equations over free partially commutative monoids is decidable but computationally hard. In this paper we consider the satisfiability problem for equations over free partially commutative monoids under the constraint that the solution is a subset of the alphabet. We prove that this problem is NP-complete for quadratic equations and that its unifor...

and we are going to determine all the possible dynamics of this type of equation. Also, we can say that generically there are two different T-periodic solutions. In this equation we emphasize the following antecedents. First, in 1975, there appeared a paper written by N. G. Lloyd [5] about complex solutions of a real Riccati equation. This study was continued in a 1984 paper by H. S. Hassan [3]...