Abstract We prove Conjecture 4.16 of the paper [ 2] Elagin and Lunts; namely, that a smooth projective curve genus at least $1$ over field has diagonal dimension $2$.

Let φ be a w-continuous homomorphism from a dual Banach algebra to C. The notion of φ-Connes amenability is studied and some characterizations is given. A type of diagonal for dual Banach algebras is dened. It is proved that the existence of such a diagonal is equivalent to φ-Connes amenability. It is also shown that φ-Connes amenability is equivalent to so-called φ-splitting of a certain short...

In this paper, we present a new energy-efficient directed diffusion protocol by using a proposed diagonal-based hexagonal-mesh scheme for a wireless sensor network. The wireless sensor network is more reasonable to carefully build a fixed-topological wireless network environment than the conventional MANET due to the low mobility. Therefore, all sensor nodes are arranged into a fixed-topologica...

We propose an algorithm of coupling design for a long-term anticipating synchronization of chaos and demonstrate its efficacy for typical chaotic systems: namely, the Rössler system, the double-scroll Chua circuit, and the Lorenz system. The maximum prediction time attained with our algorithm is several times larger than with the diagonal coupling usually used in the literature.

It is shown that there are three vacuum and one electrovacuum solutions of diagonal plane waves with M = 0 and constant Maxwell scalars. Namely, these are the single wave, Stoyanov, Babala and Bell-Szekeres solutions. A comparison is made with the planar solutions of Taub.

Abstract: A stability analysis is carried out for certain classes of switched linear systems with tridiagonal structure, under arbitrary switching signal. This analysis is made using diagonal common quadratic Lyapunov functions. Namely, necessary and sufficient conditions for the existence of such Lyapunov functions are proposed for second order switched systems and for third order switched sys...

A recent note induced me to resume the classic problem (Po) and its natural generalization: (P0) To construct a square, the sides of which go through four given points. (P) To construct a quadrilateral Q(XYZT) similar to a given quadrilateral q with its sides XY, YZ, • • • , respectively passing through four given points K, L, M, N. The solution of (P0) is classic: we immediately get a locus fo...

we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modied to drive numerov type nite dierence method. the method yield the tri- diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. stability and error estimation of the...