Weak index pairs and the Conley index for discrete multivalued dynamical systems. Part II: properties of the index

Motivation to revisit the Conley index theory for discrete multivalued dynamical systems stems from the needs of broader real applications, in particular in sampled dynamics or in combinatorial dynamics. The new construction of the index in [B. Batko and M. Mrozek, {\em SIAM J. Applied Dynamical Systems}, 15(2016), pp. 1143-1162] based on weak index pairs, under the circumstances of the absence of index pairs caused by relaxing the isolation property, seems to be a promising step towards this direction. The present paper is a direct continuation of [B. Batko and M. Mrozek, {\em SIAM J. Applied Dynamical Systems}, 15(2016), pp. 1143-1162] and concerns properties of the index defined therin, namely Wa\.zewski property, the additivity property, the homotopy (continuation) property and the commutativity property. We also present the construction of weak index pairs in an isolating block

Weak index pairs and the Conley index for discrete multivalued dynamical systems

Motivated by the problem of reconstructing dynamics from samples we revisit the Conley index theory for discrete multivalued dynamical systems. We introduce a new, less restrictive definition of the isolating neighbourhood. It turns out that then the main tool for the construction of the index, i.e. the index pair, is no longer useful. In order to overcome this obstacle we use the concept of weak index pairs

Off-shell effects in heavy particle production

Off-shell propagation of nucleons is neglected in one-body transport models of heavy-ion collisions, but it could be significant in processes that are limited by phase space, such as the threshold production of heavy particles. We estimate the relative magnitude of off-shell production to on-shell production of the N$^*$(1535) resonance in heavy ion collisions. In the region where the on-shell production is dominated by a~two-step mechanism with an intermediate $\Delta$, we find that the contribution of off-shell scattering between projectile and target nucleons is indeed small. Beyond the latter contribution, however, correlations in the initial wave function produce off-shell contributions which can exceed those of the on-shell $\Delta$ mechanism.Comment: 8 pages, 1 uuencoded Postscript figur

Changes to immigration policy in Japan : a chance to secure economic growth?

The aim of the article is to analyse changes in the immigration policy of Japan since 2012. The main reasons for undertaking such research are twofold. Firstly, it is the rapid decline in Japanese population. Secondly, it is a complex plan of economic revitalisation published by the government, in which immigration policy is one of the important components. The assumptions made in the article concern the current changes to immigration laws that constitute a substantial yet insufficient step towards transforming the perception of immigrants. The success of this policy is equally dependent on the change of attitude towards immigrants among Japanese people. Hence, the government should introduce certain initiatives aimed at changing this largely negative approach. With regards to methodology, mixed methods have been applied. From a quantitative perspective, statistics published by the Japanese Immigration Bureau and Ministry of Justice have been implemented. As for qualitative methods, official documents and reports as well as changes to the law have been analysed

Antiproton production in pp,dppp, dp and dddd collisions close to threshold

The production of antiprotons in $pp$ collisions is investigated close to threshold where experimental data about the total cross section are not available. We analyze the latter reaction within the LUND string model for inclusive $\bar{p}$ production and within the framework of a one-boson exchange model for the exclusive reaction $pp \rightarrow ppp\bar{p}$. The application of our new results to the analysis of subthreshold antiproton production in $d + p$ and $d + d$ collisions shows cross sections that are much lower than expected before. Nevertheless, the comparison of experimental $\bar{p}$ differential cross sections from $d +p$ and $d + d$ is expected to provide valuable information about a nonnucleonic component in the deuteron wavefunction.Comment: 10 pages, LaTeX, plus 4 postscript figures, Phys. Lett. B, in pres

The spectral properties of the Falicov-Kimball model in the weak-coupling limit

The $f$ and $d$ electron density of states of the one-dimensional Falicov-Kimball model are studied in the weak-coupling limit by exact diagonalization calculations. The resultant behaviors are used to examine the $d$-electron gap ($\Delta_{d}$), the $f$-electron gap ($\Delta_{f}$), and the $fd$-electron gap ($\Delta_{fd}$) as functions of the $f$-level energy $E_f$ and hybridization $V$. It is shown that the spinless Falicov-Kimball model behaves fully differently for zero and finite hybridization between $f$ and $d$ states. At zero hybridization the energy gaps do not coincide ($\Delta_{d}\neq \Delta_{f} \neq \Delta_{fd}$), and the activation gap $\Delta_{fd}$ vanishes discontinuously at some critical value of the $f$-level energy $E_{fc}$. On the other hand, at finite hybridization all energy gaps coincide and vanish continuously at the insulator-metal transition point $E_f=E_{fc}$. The importance of these results for a description of real materials is discussed.Comment: 10 pages, 7 figures, LaTe

M-Grid: Similarity Searching in Grids

The problem of similarity searching is nowadays attracting a lot of attention, because upcoming applications process complex data and the traditional exact match searching is not sufficient. There are efficient solutions, but they are tailored for the needs of specific data domains. General solutions, based on the metric space abstraction, are extensible, but they are designed to operate on a single computer only. Therefore, their scalability is limited and they cannot adapt to different performance requirements. In this paper, we propose a distributed access structure which is fully dynamic and exploits a Grid infrastructure. We study properties of this structure in numerous experiments. Besides, the performance tuning is analyzed with respect to user-specific requirements which include the maximum response time and the number of queries executed concurrently.The problem of similarity searching is nowadays attracting a lot of attention, because upcoming applications process complex data and the traditional exact match searching is not sufficient. There are efficient solutions, but they are tailored for the needs of specific data domains. General solutions, based on the metric space abstraction, are extensible, but they are designed to operate on a single computer only. Therefore, their scalability is limited and they cannot adapt to different performance requirements. In this paper, we propose a distributed access structure which is fully dynamic and exploits a Grid infrastructure. We study properties of this structure in numerous experiments. Besides, the performance tuning is analyzed with respect to user-specific requirements which include the maximum response time and the number of queries executed concurrently