A classical problem in the literature seeks minimal number of proper subgroups whose union is a given finite group. different question, with applications to error-correcting codes and graph colorings, involves covering vector spaces over fields by (minimally many) subspaces. In this note we cover $R$-modules submodules for commutative rings $R$, thereby subsuming recovering both cases above. Sp...

Abstract It is proved that for every positive integer n , the number of non-Tukey-equivalent directed sets cardinality $\leq \aleph _n$ at least $c_{n+2}$ $(n+2)$ -Catalan number. Moreover, class $\mathcal D_{\aleph _n}$ contains an isomorphic copy poset Dyck -paths. Furthermore, we give a complete description whether two successive elements in contain another set between or not.

We designed, implemented and assessed ALEPH, a pure example-based machine translation system. It strictly does not make any use of variables, templates or training, does not have any explicit transfer component, and does not require any preprocessing of the aligned examples. It relies on a specific operation: the resolution of analogical equations, that neutralizes translation divergences in an...

A brief introduction to the א project, a TEX extension providing most of Ω and ε-TEX features.

Several recent results of the ALEPH Collaboration covering different aspects of baryon production on the Z resonance are presented. In particular production rates of hyperons, the full kinematical reconstruction of the Λb, observation of Ξb in its semileptonic decay, and the measurements of the polarization of Λ and Λb baryons are discussed. Talk given at the HADRONS 96 conference 9.6. – 16.6. ...

introduction: nowadays , use of library software is a basic need for libraries and information centers. user interface is a part of computerized systems which is interacting to the user and it is an important factor in information searching process. this study aimed to compare librarian's satisfaction rate from library software interface in isfahan libraries in 2010. methods: this was a descrip...

This paper describes a preliminary study aimed at using the ILP system ALEPH to interactively assist human experts in learning rules to better understand the behaviour of cyberattacks. We develop an ILP formalism for representing network log data obtained from a sandbox computer that was deliberately infected with the CryptoWall-4 malware (a state-of-the-art ransomware attack known to be causin...

For a regular cardinal $\kappa$, a formula of the modal $\mu$-calculus is $\kappa$-continuous in a variable x if, on every model, its interpretation as a unary function of x is monotone and preserves unions of $\kappa$-directed sets. We define the fragment C $\aleph 1 (x) of the modal $\mu$-calculus and prove that all the formulas in this fragment are $\aleph 1-continuous. For each formula $\ph...