Higher dimensional Euclidean and hyperbolic matrix spaces

Journal d'Analyse Mathématique -     

Formalism to deal with Reichenbach's special theory of relativity

The objective of this article is to provide a formalism to deal with the special theory of relativity (STR, in short) as riewed by Reichenbach, according to which STR involves an ineradicableconventionality of simultaneity. One of the two postulates of STR asserts that, in empty space, the one-way speed of light relative to inertial frames is constant. Experimental evidence, however, is related to the constancy of the round-trip speed of light and has no bearing on one-way speeds. Following Reichenbach's viewpoint, we relax the second postulate of STR, abandoning the constancy of the one-way speed of light to the more realistic one asserting the constancy of the round-trip speed of light. This, in turn, results in a formalism to deal with Reichenbach's special theory of relativity (RSTR, in short) in which the two one-way speeds of light in empty space, C_±, in the two senses of a round-trip are arbitrarily selected in such a way that their harmonic mean is the measurable round-trip speed of light, c. Experimentally, RSTR and STR are indistinguishable and, hence, represent the same physical theory. It is only the formalism that we use to deal with STR which is extended in RSTR to accommodate the immeasurability of one-way velocities. The usefulness of the proposed formalism to study special relativity is demonstrated.     

Bottonium production at LEP

We investigate the production of Υ(³ S ₁) and η _b (¹ S ₀) with two gluons from Z decay. We find that at LEP luminosities experimental detection will hardly be feasible.     

On the fluctuation theory for the liquid—vapor interface

Using the statistical mechanical formulation of Triezenberg and Zwanzig, we argue that the “intrinsic” or “bare” width of the liquid—vapor interface in the Buff—Lovett—Stillinger capillary model may be identified as the interfacial width described by the “van der Waals-like” theories.     

The length of a (0, 1) matrix

The length of a (0, 1) matrix (a bigraph) is defined and studied.     

Accumulation-layer surface-wave convolver

A new type of coupled silicon?lithium-niobate convolver is reported, in which a known accumulation layer of electrons was produced at the silicon surface. By applying a normal electric field, the electron density was varied, and the convolution signal was a strong function of this surface charge density.     

On the control of certain interacting populations

We study the time optimal control of the system $\text{x}\text{?}{}_1\text{= x}{}_1\text{?}{}_1\text{(x}{}_1\text{, x}{}_2\text{) + u}{}_1\text{(t) g}{}_1\text{(x}{}_1\text{),}\text{x}\text{?}{}_2\text{= x}{}_2\text{?}{}_2\text{(x}{}_1\text{, x}{}_2\text{) + u}{}_2\text{(t)g}{}_2\text{(x}{}_2\text{)}$, where x₁ is the size of the population of one species, x₂ is the population size of the second species, ?₁ and ?₂ are the fractional growth rates of the respective species, g₁ and g₂ are nowhere vanishing functions of class C¹(0, + ∞), and the control u(t) = (u₁(t), u₂(t)) takes on values in a closed rectangle. The functions ?₁ and ?₂ are chosen to represent prey-predator, competitive, and symbiotic interactions.We show, for the various interactions, that a time optimal control, if it exists, must be “bang-bang,” and give sufficient conditions for the controllability, and for the existence, of time optimal controls of the above system.