Near rings without zero divisors

Near rings without zero divisors, and a dual structure, near codomains, are studied. It is shown that a near ring is a near field if and only if it is an integral near ring, a near codomain, and has a non-zero distributive element. If the additive group (N, +) of a near integral domainN is cohopfian, then (N, +) possesses a fixed point free automorphism which is either torsion free or of prime order. This generalizes a well-known theorem of Ligh for finite near integral domains. A result ofGanesan [1] on the non-zero divisors in a finite ring is generalized to near rings.     

On systems of binomials in the ideal of a toric variety

Let be a toric set in the affine space . Given a set of binomials in the toric ideal of , we give a criterion for deciding the equality rad( ) = . This criterion extends to arbitrary dimension, and to arbitrary fields, an earlier result which concerned only monomial curves over an algebraically closed field of characteristic zero.

     

Invariant measures for algebraic actions, Zariski dense subgroups and Kazhdan's property

Let be any locally compact non-discrete field. We show that finite invariant measures for -algebraic actions are obtained only via actions of compact groups. This extends both Borel's density and fixed point theorems over local fields (for semisimple/solvable groups, resp.). We then prove that for -algebraic actions, finitely additive finite invariant measures are obtained only via actions of amenable groups. This gives a new criterion for Zariski density of subgroups and is shown to have representation theoretic applications. The main one is to Kazhdan's property for algebraic groups, which we investigate and strengthen.

     

Stochastic (white noise) analysis of resonant absorption in laser generated plasma

We suggest to use stochastic differential equations for laser-plasma problems. Using this technique we solve analytically the motion of the electrons at the critical layer and calculate the density profile scaling length (L). For an Nd laser flux of 10¹⁷ W/cm² we estimate L ≈ 0.15 μm, while for a CO₂ laser flux of 10¹⁵ W/cm² we get L ≈ 1.5 μm.     

Kilohertz laser frequency sensing with Brillouin mutually modulated cross-gain modulation

Using mutually modulated cross-gain modulation, Stokes optical frequency changes are converted into modulation phase changes with high sensitivity. In the slow-light transition regime, we demonstrate kilohertz sensitivity to the Stokes optical carrier frequency. The sensitivity is inversely proportional to the modulation frequency of the pump and Stokes beams.     

Practical anodes for Li-ion batteries comprising metallurgical silicon particles and multiwall carbon nanotubes

Journal of Solid State Electrochemistry - Silicon is considered to be a very attractive anode material for next-generation lithium-ion batteries due to its high theoretical capacity...