Specific-heat study of the triangular-lattice antiferromagnet RbCuCl

We report on the magnetic phase diagram of the distorted triangular-lattice antiferromagnet RbCuCl₃ for a magnetic field applied parallel to the basal plane (). High-resolution measurements of the specific heat and of the magnetocaloric effect have been performed in magnetic fields up to 14 T. The high-field specific-heat data reveal the existence of an intermediate phase between the paramagnetic and the frustrated antiferromagnetic phase. Received 18 October 1999     

Effect of speed fluctuations on a green-light path in a 2d traffic network controlled by signals

When a vehicle moves through a series of green lights, avoiding red signals in a two-dimensional (2d) city traffic network, the vehicle describes a characteristic trajectory (green-light path) and the travel time has a minimal value. The green-light path depends on the cycle time, split, signal-control strategy, and fluctuations of vehicular speed. We clarify the effect of speed fluctuations on a green-light path in a 2d traffic network controlled by signals. Even if an extremely small quantity of speed fluctuation is added, the green-light path changes greatly. It is shown that the root-mean square (RMS) of the deviation from the mean path depends highly on the cycle time. Also, the dependence of the green-light path on the speed-fluctuation strength is shown under a constant value of cycle time.     

Lagrange multipliers and infinite-dimensional equilibrium problems

We prove the existence of the Lagrange multipliers for a constrained optimization problem, being the constraint set given by the convex set which characterizes the most important equilibrium problems. In order to obtain our result, we’ll make use of the new concept of quasi relative interior.     

Rotational spectra of deuterated acetylenes: DCCH, DCCH and DCCH

Rotational spectra of deuterated acetylenes, DCCH, D¹³CCH and DC¹³CH, have been recorded in the millimeter- and submillimeter-wave frequency ranges. In spite of the small dipole moment (0.01001(15) D), ¹³C-containing species have been observed in natural abundance. The present investigation allowed us to provide improved ground state rotational and quartic centrifugal distortion constants for DCCH, D¹³CCH and DC¹³CH. The experimental investigation has also been supported by ab initio calculations.     

On the Balance Equation for Stresses Concentrated on Curves

Conditions of equilibrium of forces are formulated for a force system in a continuous body which consists of a bulk stress and a stress concentrated on a curve. The system of forces is interpreted as a tensor valued measure and the equilibrium of forces is interpreted in a weak sense. The divergence theorem is proved for bulk stress fields with the corresponding singularity. Examples of such stress fields are given.      

Equilibrium conditions and vector variational inequalities: a complex relation

Since a look to the present literature shows that the notion of vector equilibrium is not univocally defined, the relationship between vector equilibrium problems and vector variational inequalities deserves a specific analysis, deeper than in the scalar case. We analyse and compare various definitions and clarify how they depend on the modelling of the problem under consideration. Furthermore, we show that at least one vector variational inequality formulation of the problem is possible, which is equivalent to a Wardrop-type equilibrium condition. The analysis is illustrated through the concrete example of a multiclass and multiobjective supply demand network.      

A dual view of equilibrium problems

The aim of this paper is to introduce and study a dual problem associated to a generalized equilibrium problem (GEP). We show that the solutions of (GEP) and its dual are strictly related to the saddle points of an associated Lagrangian function, and, under some suitable conditions, to the solutions of a family of parametric optimization problems and their dual problems. Our results allow us to show that well-known concepts and results from duality theory of some important particular cases of (GEP) like variational inequalities and optimization problems can be recovered.     

Stability of shallow arches under constant load

Design of large span roof structures requires an analysis of static and dynamic behavior of shallow arches under various loads. In this paper the exact solution is established when the initial shape and the load are given by a linear combination of sinusoidal functions. The load is assumed to be time-independent. Then, the asymptotic stability of the arch is analyzed. For the one-dimensional solutions the arch is shown to have at most three equilibria. The arch motion exhibits a snap-through motion. In the two-dimensional case the location and the stability of equilibria is established under various conditions on the load-free shape, and the load parameters. An interesting phenomenon of a zigzag pattern of the critical pairs is discovered and studied numerically.     

Optical grooming with grooming ratio eight

Grooming uniform all-to-all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The minimum possible drop cost is determined for grooming ratio 8, and this cost is shown to be realized with six exceptions, and 37 possible exceptions, the largest being 105.     

Improved global exponential stability for delay difference equations with impulses

In this paper, by means of constructing an impulsive delay difference inequality, we study the global exponential stability for a class of delay difference equations with impulses. A new criterion ensuring the global exponential stability of the equilibrium point is obtained, which is less restrictive and conservative than that given in the earlier reference. An illustrative example is given to demonstrate the effectiveness and advantage of the obtained result.