Multi-valued totally quasi-ϕ-asymptotically nonexpansive semi-groups and strong convergence theorems in banach spaces

The purpose of this article is first to introduce the concept of multi-valued totally Quasi?-asymptotically nonexpansive semi-groups, which contains many kinds of semi-groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi?-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.     

Combinatorial data analysis: Confirmatory comparisons between sets of matrices

The task of assessing the similarity of pattern between the entries of two square matrices has been discussed extensively over the last decade, as a unifying strategy for approaching a variety of seemingly disparate statistical problems. As typically defined, the comparison depends on a measure of matrix correspondence, usually a normalized cross-product measure of some form, that is evaluated for relative size by the use of a reference distribution constructed through an equally likely permutation hypothesis defined at the level of the objects corresponding to the rows and columns of the two matrices. The extreme generality provided by this very simple framework subsumes a variety of different statistical problems, ranging from the study of spatial autocorrelation for variables observed over a set of geographic locations, to the topics of analysis of variance, the measurement of rank correlation, and confirmation techniques concerned with various conjectures of combinatorial structure that might be posited for an empirically determined measure of relationship between pairs of a given set of objects. The comparison strategies extant always assume that both matrices are fixed, and in those cases where one of the matrices codifies a given theoretical structure to be evaluated according to a second, this assumption can lead to substantial arbitrariness in how matrix similarity might be indexed, and thus, in how the comparison is implemented. As developed in this paper, exactly the same principles appropriate for use in the fixed comparison context can be extended to include matrices constructed through optimally weighted linear combinations of other sets of matrices. This generalization provides one mechanism for developing comparison strategies that allow assessment against very broad classes of matrices, which in turn serve to represent very general conjectures of possible combinatorial structure. This paper reviews some of these extensions in detail, with a particular emphasis on categorical and ordered categorical variables and whether they may reflect an empirically generated measure of object relationship.     

Strong approximations of the Hoeffding,Blum, Kiefer,Rosenblatt multivariate empirical process

Hoeffding (Ann. Math. Statist. 1948) and Blum, Kiefer and Rosenblatt (Ann. Math. Statist. 1961) constructed distribution free tests of independence based on a multivariate empirical process. We establish strong invariance principles for the latter and also for appropriate functionals of it.     

Combination of analytical and microbiological techniques to study the antimicrobial activity of a new active food packaging containing cinnamon or oregano against E. coli and S. aureus

The aim of this work is the optimization and application of a group of analytical and microbiological techniques in the study of the activity of essential oils (EOs) incorporated in a new antimicrobial packaging material and the research in depth of the interaction between the microbial cells and the individual compounds present in the active material. For this purpose the antimicrobial activity of the active packaging containing cinnamon or oregano was evaluated against E. coli and S. aureus. The vapour phase activity and the direct contact between the antimicrobial agents themselves, or once incorporated in the packaging material, and the microbial cells have been studied. The direct contact was studied using a broth dilution method. The vapour phase was evaluated by using a new method which involves the use of a filter disk containing the EOs. Furthermore, the kill time assay was used to determine the exposure time for the maximum efficiency in packaging, and transmission electron microscopy was used to investigate the antimicrobial activity and the possible mechanism of action against E. coli and S. aureus. Finally, the compounds absorbed by cells were identified. The results showed that the techniques used provide relevant information about the antibacterial activity of cinnamon and oregano in direct contact as well as in the vapour phase. The antimicrobial packaging showed a fast efficiency which supports its likely application as a food packaging material. Bacteria treated with EOs exhibit a wide range of significant abnormalities; these include formation of blebs, coagulation of cytoplasmatic constituents, collapse of the cell structure and lack of cytoplasmatic material. Some of these observations are correlated to the ability of some of these substances to disrupt envelop structure, especially the inner membrane. After an extraction from dead cells, cinnamaldehyde was detected by GC-MS in E. coli exposed to the active packaging containing cinnamon.     

Leading and higher twists in proton,neutron and deuteron unpolarized structure functions F<Subscript>2</Subscript>

We summarize the results of a recent global analysis of proton and deuteron F₂ structure function world data performed over a large range of kinematics, including recent measurements done at JLab with the CLAS detector. From these data the lowest moments (n≤10) of the unpolarized structure functions are determined with good statistics and systematics. The Q² evolution of the extracted moments is analyzed in terms of an OPE-based twist expansion, taking into account soft-gluon effects at large x. A clean separation among the leading- and higher-twist terms is achieved. By combining proton and deuteron measurements the lowest moments of the neutron F₂ structure function are determined and its leading-twist term is extracted. Particular attention is paid to nuclear effects in the deuteron, which become increasingly important for the higher moments. Our results for the non-singlet, isovector (p-n) combination of the leading-twist moments are used to test recent lattice simulations. We also determine the lowest few moments of the higher-twist contributions, and find these to be approximately isospin independent, suggesting the possible dominance of ud correlations over uu and dd in the nucleon.