Letter: Some Remarks on Standing Gravitational Waves

An intuitive definition of standing gravitational waves is proposed. Some main classes of exact vacuum solutions are searched for standing gravitational waves, in most cases with a negative result. Only some Einstein–Rosen waves meet the conditions.     

First order dynamic inclusions on time scales

In this paper, we study existence of solutions of first order dynamic inclusions on time scales with general boundary conditions. Both the ∇-derivative and Δ-derivative cases are considered. Examples are presented to illustrate that the Δ-derivative case needs more restrictive assumptions.     

Production of superfine fibers by the electrospinning method

Weakly conducting fluid flows in an electric field in the presence of phase interfaces are investigated theoretically and experimentally. The object of the investigation is an axisymmetric jet. The analysis is carried out within the framework of electrohydrodynamics (EHD) with allowance for surface charge transfer on mobile interfaces. The jet shape is calculated at large distances from the outflow point. The theoretical and experimental data are compared for Newtonian and polymeric fluids.     

PERIODIC SOLUTIONS OF PLANAR SYSTEM WITH SIX DELAYS

In this paper we obtain some sufficient conditions for the existence of non-constant periodic solutions of the following planar system with six delaysOur approach is based on the continuation theorem of the coincidence degree.     

Analysis of a Multiserver Queue with Setup Times

This paper deals with the analysis of an M/M/c queueing system with setup times. This queueing model captures the major characteristics of phenomena occurring in production when the system consists in a set of machines monitored by a single operator. We carry out an extensive analysis of the system including limiting distribution of the system state, waiting time analysis, busy period and maximum queue length. AMS subject classification: 90B22, 60K25     

EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH ZERO EIGENVALUES＊＊＊

For a class of mixed initial-boundary value problem for general quasilinear hyperbolic sys-tems with zero eigenvalues, the authors establish the local exact controllability with boundary controls acting on one end or on two ends and internai controls acting on a part of equations in the system.     

Cellulose-based fibers from liquid–crystalline solutions. II. Processing and morphology of acetate/butyrate esters

Fibers were spun from isotropic and anisotropic dimethylacetamide solutions of cellulose esters. Take-up speeds of the dry jet/wet spinning process varied. Water served as the coagulant. The mechanical properties of the fibers increased as spinning progressed from the isotropic to the anisotropic state of the solution. A trade-off in solubility and fiber properties was noted as the butyryl acetyl ratio decreased. Whereas high butyryl content enhances both overall solubility and the formation of liquid–crystalline solutions at lower concentration, it results in lower fiber modulus and strength. Morphology of the fibers depended on the coagulation rate which was influenced by the concentration of the sppinning solution. The level of orientation and crystallinity of the fibers increased somewhat when they were spun from liquid-crystalline solutions. © 1993 John Wiley & Sons, Inc.     

On a Quadratic Optimization Problem with Equality Constraints

The constrained optimization problem with a quadratic cost functional and two quadratic equality constraints has been studied by Bar-on and Grasse, with positive-definite matrix in the objective. In this note, we shall relax the matrix in the objective to be positive semidefinite. A necessary and sufficient condition to characterize a local optimal solution to be global is established. Also, a perturbation scheme is proposed to solve this generalized problem.     

Exact Controllability and Asymptotic Analysis for Shallow Shells

The authors consider the exact controllability of the vibrations of a thin shallow shell, of thickness 2εwith controls imposed on the lateral surface and at the top and bottom of the shell. Apart from proving the existence of exact controls, it is shown that the solutions of the three dimensional exact controllability problems converge, as the thickness of the shell goes to zero, to the solution of an exact controllability problem in two dimensions.     

SOLVABILITY OF FORWARD-BACKWARD SDES AND THE NODAL SET OF HAMILTON-JACOBI-BELLMAN EQUATIONS

The solvability of a class of forward-backward stochastic differential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. The authors design a stochastic relaxed control problem, with both drift and difftusion all being controlled, so that the solvability problem is converted to a problem of finding the nodal set of the viscosity solution to a certain Hamilton-Jacobi-Bellman equation. This method overcomes the fatal difficulty encountered in the traditional contraction mapping approach to the existence theorem of such SDEs.