In this paper, we study the two following minimization problems: S0(q, φ) = inf u∈H2 0 (Ω),‖u+φ‖q=1 ∫ Ω | u|2 and Sθ (q, φ) = inf u∈H2 θ (Ω),‖u+φ‖q=1 ∫ Ω | u|2. We prove that for a class of maps φ, we have Sθ (q, φ) < S0(q, φ) and for another class, we have Sθ (q, φ) = S0(q, φ). c © 2005 Elsevier Ltd. All rights reserved.

Today power consumption is considered to be one of the important issues. Therefore, its reduction plays a considerable role in developing systems. Previous studies have shown that approximately 50% of total power consumption is used in cache memories. There is a direct relationship between power consumption and replacement quantity made in cache. The less the number of replacements is, the less...

The concept of gyrogroups, with a weaker algebraic structure without associative law, was introduced under the background c -ball relativistically admissible velocities Einstein velocity addition. A topological gyrogroup is just endowed compatible topology such that multiplication jointly continuous and inverse continuous. This generalizes groups. In this paper, we are going to establish for lo...

A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.

an r-module m is called strongly noncosingular if it has no nonzero rad-small (cosingular) homomorphic image in the sense of harada. it is proven that (1) an r-module m is strongly noncosingular if and only if m is coatomic and noncosingular; (2) a right perfect ring r is artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

Denef and Loeser defined a map from the Grothendieck ring of sets definable in pseudo-finite fields to the Grothendieck ring of Chow motives, thus enabling to apply any cohomological invariant to these sets. We generalize this to perfect, pseudo algebraically closed fields with pro-cyclic Galois group. In addition, we define some maps between different Grothendieck rings of definable sets which...

2 Elliptic Curves and Maps Between Them 2 2.1 The Group Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Weierstrass Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Maps Between Elliptic Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Dual Isogenies . . . . . . . . . . . . . . ....