THE OSCILLATION OF A CLASS NONLINEAR MATRIX DIFFERENTIAL EQUATION

1DefinitionandPropertyInthematrixdifferentialequation,weconsider(p(t)y,(t)), Q(t)y(t) F(t,y(t),y'(t))=0(1)P,Q,y,Farearealcontinuousnxn-th--ordermatrixintheinterval[a, co),andP,Q,Fareasymmetricmatrix,andPisapositivedefinitematrix.F(t,:!/(t),y'(t))gfij(t,yl…     

The minimum size instance of a Pallet Loading Problem equivalence class

The Pallet Loading Problem (PLP) maximizes the number of identical rectangular boxes placed within a rectangular pallet. Boxes may be rotated 90° so long as they are packed with edges parallel to the pallet’s edges, i.e., in an orthogonal packing. This paper defines the Minimum Size Instance (MSI) of an equivalence class of PLP, and shows that every class has one and only one MSI. We develop bounds on the dimensions of box and pallet for the MSI of any class. Applying our new bounds on MSI dimensions, we present an algorithm for MSI generation and use it to enumerate all 3,080,730 equivalence classes with an area ratio (pallet area divided by box area) smaller than 101 boxes. Previous work only provides bounds on the ratio of box dimensions and only considers a subset of all classes presented here.     

Labile Metabolites

The importance of ascertaining the possible presence of unstable metabolites at an early stage in the drug development process cannot be underestimated. Failure to detect labile metabolites could lead to costly delays to development. Very often, erratic or difficult to explain analytical or kinetic data provide clues to metabolite degradation, the most commonly encountered reaction being the conversion of a metabolite to parent drug. Examples of unstable glucuronide conjugates, N-oxides, alcohols and phenols abound in the literature. They are not easy to find, however, and have to be ‘mined’ by extensive searching. This report, by no means exhaustive, brings together the major examples according to substance class. Remedial action to avoid metabolite degradation is discussed, as well as a number of specific examples which cannot be categorised under the main substance classes.     

Stability properties of an abstract system with applications to linear thermoelastic plates

This paper deals with an abstract version of the evolution system $$\left\{\begin{array}{ll}u_{tt}-\omega \Delta u_{tt}+\Delta (\Delta u + \theta)=0 \\\theta_t - \Delta \theta -\Delta u_t=0\end{array}\right.$$ with ω ≥  0, ruling the dynamics of linear thermoelastic plates. In particular, we will consider a more general coupling term depending on a real parameter σ. The (exponential and polynomial) decay properties of the related solution semigroup are investigated in dependence of the values of σ.     

Two-mode dipolar bosonic junctions

We consider a two-mode atomic Josephson junction realized with dilute dipolar bosons confined by a double-well. We employ the two-site extended Bose-Hubbard Hamiltonian and characterize the ground-state of this system by the Fisher information, coherence visibility, and entanglement entropy. These quantities are studied as functions of the interaction between bosons in different wells. The emergence of Schrödinger’s cat-like state with a loss of coherence is also commented.     

Graph models for scheduling systems with machine saturation property

Let be a set of n independent tasks and a set of m processors. During each time instant, each processor can be used by a single task at most. A schedule is for each task an allocation of one or more time intervals to one or more processors. A schedule is said to be optimal if it minimizes the maximum completion time. We say a schedule S has the machine saturation property (MS property) if, at any time instant of task execution, all the machines are simultaneously busy. In this paper, we analyze the conditions under which a parallel scheduling system allows a schedule with the MS property. While for some simple models the analytical conditions can be easily stated, a graph model approach is required when conflicts of processor usage are present. For this reason, we define the class of saturated graphs that correspond to scheduling systems with the MS property. We present efficient graph recognition algorithms to verify the MS property directly on some classes of saturated graphs     

Instabilities and vortex-lattice formation in rotating conventional and dipolar dilute-gas Bose-Einstein condensates

A theoretical study of vortex-lattice formation in atomic Bose-Einstein condensates confined by a rotating elliptical trap is presented. For the conventional case of purely s-wave interatomic interactions, this is done through a consideration of both hydrodynamic equations and time-dependent simulations of the Gross-Pitaevskii equation. We discriminate three distinct, experimentally testable regimes of instability: ripple, interbranch, and catastrophic. Additionally, we generalize the classical hydrodynamical approach to include long-range dipolar interactions, showing how the static solutions and their stability in the rotating frame are significantly altered. This enables us to examine the routes towards unstable dynamics, which, in analogy to conventional condensates, may lead to vortex-lattice formation.     

Relativistic particle separation by means of transition radiation utilizing multiwire proportional chambers

Investigations have been made on a transition radiation detection system consisting of a series of radiator-wire proportional chamber sandwiches and its feasibility for particle separation. A method for eliminating the “Landau” tail in the ionization distribution of a charged particle is described.     

Search for single photon direct production in p + p collisions at s=53.2 GeV

From measurements at the ISR of CERN with a lead glass counter matrix we establish an upper limit of 6% (at 95% C.L.) for the ratio of the directly produced photons to the produced π⁰ at 90° and $\text{s}\text{= 53.2}\text{GeV}$ in the $\text{p}{}^1{}_{\mathrm{<mtext>T</mtext>}}$ region 2.3–3.7 GeV/c.