and Applied Analysis 3 2. Existence and Uniqueness In this section, the existence and uniqueness of the minimizer for the model 1.4 are proved. Some basic notations and properties concerning with the BV 2 space can be seen in 8, 13 . Motivated by 5 , we have the following existence and uniqueness result for the optimization problem 1.4 . Theorem 2.1. Assume Ω is an open, bounded Lipschitz domai...

A S is isometri-cally isomorphic to the second dual of F S. For unbounded selfadjoint operators S the paper establishes the full analogy with the bounded case: A S is isometrically isomorphic to the second dual of F S. The paper also classiies the algebras A S and F S up to isometrical *-isomorphism and obtains some partial results about bounded but not necessarily isometrical

We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope of ring theory. The formalization of this kind of variables and its properties will help us to have a better idea of some algebraic structures and the way th...

The Dynamical Systems Method (DSM) is justified for solving operator equations F (u) = f , where F is a nonlinear operator in a Hilbert space H. It is assumed that F is a global homeomorphism of H onto H, that F ∈ C loc, that is, it has a continuous with respect to u Fréchet derivative F ′(u), that the operator [F ′(u)]−1 exists for all u ∈ H and is bounded, ||[F ′(u)]−1|| ≤ m(u), where m(u) > ...

1 Proofs Lemma 1. If B (j) is the sequence of iterates produced by Algorithm 1, then f B (j+1) ≥ f B (j) holds for any integer j ≥ 0, and both f (B (j)) and B (j) converge. Proof. Since the B-subproblem in Eq. (5) of the main paper is to maximize a continuous function over a compact (i.e., closed and bounded) set, its optimal objective function value f * is finite. As B (j) is feasible for each...

Bounded rewriting for linear term rewriting systems has been defined in (I. Durand, G. Sénizergues, M. Sylvestre. Termination of linear bounded term rewriting systems. Proceedings of the 21st International Conference on Rewriting Techniques and Applications) as a restriction of the usual notion of rewriting. We extend here this notion to the whole class of left-linear term rewriting systems, an...

We examine the behavior of positive bounded, localized solutions of semilinear parabolic equations ut = ∆u + f(u) on RN . Here f ∈ C1, f(0) = 0, and a localized solution refers to a solution u(x, t) which decays to 0 as x → ∞ uniformly with respect to t > 0. In all previously known examples, bounded, localized solutions are convergent or at least quasiconvergent in the sense that all their limi...

In this paper we consider the existence and uniqueness of bounded solutions of periodic evolution equations of the form u = A(t)u + ǫH(t, u) + f(t), where A(t) is an in general unbounded operator depending 1-periodically on t, H is periodic in t with the same period as A, ǫ is small, and f is a bounded and continuous function that is not necessarily uniformly continuous. We propose a new approa...

We study cubic forms on F2 using the Hurwitz-Radon theory of square identities. As an application, we obtain the following elementary statement. Given a family F of subsets of an n-set such that the cardinality of the symmetric di↵erence of any two elements F,F 0 2 F is not a multiple of 4, the maximal size of F is bounded by 2n, unless n ⌘ 3 mod 4 when it is bounded by 2n + 2. We also apply th...

In this paper we provide necesssary and sufficient conditions for the existence of at least one Ψ-bounded solution on R for the system X ′ = A(t)X +XB(t) +F (t), where F (t) is a Lebesgue Ψ-integrable matrix valued function on R. Further, we prove a result relating to the asymptotic behavior of the Ψ-bounded solutions of this system.