Abstract:
Interrupt Timed Automata (ITA) form a subclass of stopwatch automata where reachability and some variants of timed model checking are decidable even in presence of parameters. They are well suited to model and analyze real-time operating systems. Here we extend ITA with polynomial guards and updates, leading to the class of polynomial ITA (PolITA). We prove the decidability of the reachability and model checking of a timed version of CTL by an adaptation of the cylindrical decomposition method for the first-order theory of reals. Compared to previous approaches, our procedure handles parameters and clocks in a unified way. Moreover, we show that PolITA are incomparable with stopwatch automata. Finally additional features are introduced while preserving decidability.

Abstract:
Parameter dependent non-Hermitian quantum systems typically not only possess eigenvalue degeneracies, but also degeneracies of the corresponding eigenfunctions at exceptional points. While the effect of two coalescing eigenfunctions on cyclic parameter variation is well investigated, little attention has hitherto been paid to the effect of more than two coalescing eigenfunctions. Here a characterisation of behaviours of symmetric Hamiltonians with three coalescing eigenfunctions is presented, using perturbation theory for non-Hermitian operators. Two main types of parameter perturbations need to be distinguished, which lead to characteristic eigenvalue and eigenvector patterns under cyclic variation. A physical system is introduced for which both behaviours might be experimentally accessible.

Abstract:
We introduce the class of Interrupt Timed Automata (ITA), a subclass of hybrid automata well suited to the description of timed multi-task systems with interruptions in a single processor environment. While the reachability problem is undecidable for hybrid automata we show that it is decidable for ITA. More precisely we prove that the untimed language of an ITA is regular, by building a finite automaton as a generalized class graph. We then establish that the reachability problem for ITA is in NEXPTIME and in PTIME when the number of clocks is fixed. To prove the first result, we define a subclass ITA- of ITA, and show that (1) any ITA can be reduced to a language-equivalent automaton in ITA- and (2) the reachability problem in this subclass is in NEXPTIME (without any class graph). In the next step, we investigate the verification of real time properties over ITA. We prove that model checking SCL, a fragment of a timed linear time logic, is undecidable. On the other hand, we give model checking procedures for two fragments of timed branching time logic. We also compare the expressive power of classical timed automata and ITA and prove that the corresponding families of accepted languages are incomparable. The result also holds for languages accepted by controlled real-time automata (CRTA), that extend timed automata. We finally combine ITA with CRTA, in a model which encompasses both classes and show that the reachability problem is still decidable. Additionally we show that the languages of ITA are neither closed under complementation nor under intersection.

Abstract:
Interrupt strategy of an operating system can help computer to tackle with urgent orimportant events,and to run programs in a reasonable fashion in order to achieve a satisfactoryperformance.But a sophisticated strategy will cause an amount of system costs.In this paperwe introduce the concept of “layered interrupt priorities”which will care both the system costsand the response capability.This strategy can be applied in timesharing systems,realtimesystems,or multiprocessor systems.At the end of the paper we exploit the advantages of thisstrategy using data acquired by simulation of a real computer system.

Abstract:
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both configurations become identical after a reasonable time. We prove coalescence for two elementary rules and show that there exists infinitely many coalescing CA. We then conduct an experimental study on all elementary CA and show that some rules exhibit a phase transition, which belongs to the universality class of directed percolation.

Abstract:
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to study moment closure generally within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, e.g. $P_N$, diffusion, and diffusion correction closures. In addition, the formalism gives rise to new parabolic systems, the reordered $P_N$ equations, that are similar to the simplified $P_N$ equations. Furthermore, we propose a modification to existing closures. Although simple and with no extra cost, this newly derived crescendo diffusion yields better approximations in numerical tests.

Abstract:
In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are related to those of its sorted counterpart. As this formula relies only on the minimum and maximum functions we use it to define the notion of sorting for lattices. A major difference of sorting in lattices is that it does not guarantee that sequence elements are only rearranged. However, we can show that other fundamental properties that are associated with sorting are preserved.

Abstract:
A kind of heap sorting method based on array sorting was proposed. Some advantages and disadvantages of it were discussed. It was compared with the traditional method of direct application. In the method, the ordered keywords in the array are put into the heap one by one after building an empty heap. This method needs relatively less space and is fit for ordered sequence.

Abstract:
Coalescing compact binaries with neutron star or black hole components provide the most promising sources of gravitational radiation for detection by the LIGO/VIRGO/GEO/TAMA laser interferometers now under construction. This fact has motivated several different theoretical studies of the inspiral and hydrodynamic merging of compact binaries. Analytic analyses of the inspiral waveforms have been performed in the Post-Newtonian approximation. Analytic and numerical treatments of the coalescence waveforms from binary neutron stars have been performed using Newtonian hydrodynamics and the quadrupole radiation approximation. Numerical simulations of coalescing black hole and neutron star binaries are also underway in full general relativity. Recent results from each of these approaches will be described and their virtues and limitations summarized.

Abstract:
We consider a bivariate polynomial that generalizes both the length and reflection length generating functions in a finite Coxeter group. In seeking a combinatorial description of the coefficients, we are led to the study of a new Mahonian statistic, which we call the sorting index. The sorting index of a permutation and its type B and type D analogues have natural combinatorial descriptions which we describe in detail.