On five-dimensional unified field theory and projective relativity

The choice between the Kaluza-Klein and the Jordan-Thiry forms of five-dimensional unified field theory has been considered by McInnes. Here a reply is made to criticisms by McInnes of a previous paper. In addition, the implications of projective relativity are considered.     

An adaptive control scheme for a continuous plant under Known output delay, unmodelled dynamics, and input saturation

This paper deals with robustness of adaptive control of continuoussystems subject to known output delay, input saturation, unmodelledlinear dynamics, and bounded disturbances. A simple gradient-typealgorithm with a relative deadzone is used. The relative deadzoneis built with an estimated contribution of the unmodelled dynamicsto the system output. The basic tool used for stability androbustness analysis is Gronwall's lemma.     

A Hyland-Bernstein approach to the digital control of Pritchard-Salamon systems

In this paper we consider the fixed finite-order digital linear-quadraticcontrol of Pritchard-Salamon infinite-dimensional systems withunbounded input and output operators under gaussian disturbances.A set of necessary conditions is given in terms of the solvabilityof a discrete-time Hyland-Bernstein system of equations (twomodified Riccati equations and two modified Lyapunov equationscoupled by an projection operator).     

Invariants de Maslov équivariants

We construct two cohomological invariants associated to pairs of Lagrangian sub-bundles of a symplectic bundle on a compact manifold upon which a compact Lie group is acting. The first invariant, which we call the classical equivariant Maslov H-invariant, provides an obstruction to Lagrangian transversality and lives in the Borel cohomology. The second invariant, which we call the equivariant Maslov U-invariant, generalises the author's results in K-Theory 13 (1998), 347–361 to the equivariant context and provides a necessary and sufficient condition for equivariant Lagrangian transversality, up to homotopic stability, and lives in the U-theory (intermediate between the real complex K-theories). As an application, we show that two Lagrangian sub-bundles of a symplectic bundle on a homogeneous space are always stably transverse.     

Complementary aspects of gravitation and electromagnetism

A convention with regard to geometry, accepting nonholonomic aether motion and coordinate-dependent units, is always valid as an alternative to Einstein's convention. Choosing flat spacetime, Newtonian gravitation is extended, step by step, until equations closely analogous to those of Einstein's theory are obtained. The first step, demanded by considerations of inertia, is the introduction of a vector potential. Treating the electromagnetic and gravitational fields as real and imaginary components of a complex field (gravitational mass being treated as imaginary charge), the Maxwell stress-momentum-energy tensor for the complex field is then used as the source for both fields. The spherically symmetric solution of these unified field equations describes the electron. Third, effects arising from motion of aether fluid with respect to the artificial reference systems of flat spacetime are included. On the grounds that attraction between likes and repulsion between likes are, a priori, equally possible, it is suggested that gravitational and electromagnetic phenomena should enjoy equal status. This can be achieved on the scale of an infinite cosmos by introducing a hierarchy of isolated systems, each of which is a universe when viewed internally and an elementary particle when viewed externally. A universe (defined by the Hubble radius), an electron, and a neutrino are three consecutive isolated systems of the hierarchy. Implied is the existence of antiuniverses where gravitational mass has opposite sign and antimatter predominates. Remarkable relationships between physical constants emerge.     

Spontaneous breakdown and finiteness of supersymmetric theories in two dimensions

Using a single scalar superfield we construct the two dimensional version of the four dimensional Wess-Zumino model and examine its renormalization properties. In the context of this model and in the tree approximation we find that supersymmetry can be spontaneously broken with the appearance of a massless fermion. This solution is then shown to be dynamically unstable at the one-loop level. Finally we use supersymmetry to construct two dimensional theories for which all IPI vertices are finite.     

The synthesis of some derivatives of 4,5,6,6a,7,12-hexahydroisoquinolino [8,l -ab]carbazole

As part of a general project on the chemistry of alkaloid analogues, the synthesis of derivatives 5 , of 4,5,6,6a,7,12-hexahydroisoquinolino[8,l-ab]carbazole, which can be considered as ring D indole analogues of the aporphine skeleton, was investigated. Compounds of this type are of interest on two grounds. Firstly it is conceivable some may occur naturally; and secondly, they may display unusual pharmacological properties, since the side-chain configuration of the tryptophan residue is intermediate between that present in lysergic acid diethylamide and the yohimbine-reserpine type alkaloids.     

宽波段多步激发K_2-系统产生的钾原子高位态辐射

本文首次报道以690.0～715.0nm宽波段范围内任何波长的脉冲染料激光激发K_2—K系统,由高位钾分子与钾原子碰撞以及分子-原子的混合激发等过程而产生钾原子404.4,404.7和470.05～590.0nm波段内高位态辐射的实验结果,并对激发机制进行了探讨.     

A note on scheduling problems arising in satellite communications

We present a brief overview of recent results on scheduling in Time Division Multiple Access (TDMA) satellite communications systems which augment those included in a recent survey. These results address problems arising in Satellite Switched TDMA (SS/TDMA) systems and SS/TDMA systems with intersatellite links, as well as generalizations and relatives of these problems. They also have application in other areas, for example, I/O in parallel computers.