We say that a C*-algebra A has the ‘sublattice property’ if the set P(A) of all projections in A is a sublattice of the projection lattice of its enveloping von Neumann algebra A∗∗. It is shown that this property is equivalent to the requirement that all pairs of projections have strictly positive ‘angle’. We discuss this property in relation to some results obtained by C. Akemann and by A. Laz...

We present a solution to the problem of finding the complete sublattice of a given concept lattice generated by given set of elements. We construct the closed subrelation of the incidence relation of the corresponding formal context whose concept lattice is equal to the desired complete sublattice. The construction does not require the presence of the original concept lattice. We introduce an e...

Neutron diffraction study of nanostructured magnetite was performed at room temperature. The actual grain-size was determined from evaluation of X-ray diffraction profiles by the modified Williamson-Hall plot. The atomic structure parameters and the sublattice magnetic moments were determined using the Rietveld refinement of the neutron diffraction spectra. The sublattice magnetization at the o...

The covering relation in the lattice of subuniverses of a finite distributive lattice is characterized in terms of how new elements in a covering sublattice fit with the sublattice covered. In general, although the lattice of subuniverses of a finite distributive lattice will not be modular, nevertheless we are able to show that certain instances of Dedekind’s Transposition Principle still hold...

A probability function P on an algebra of events is assumed. Some of the events are scientific refutations in the sense that the assumption of their occurrence leads to a contradiction. It is shown that the scientific refutations form a a boolean sublattice in terms of the subset ordering. In general, the restriction of P to the sublattice is not a probability function on the sublattice. It doe...

Abstract. We investigate the influence of impurities and vacancies in the formation of magnetic moment in CaB6 using full potential ab initio band structure calculations. CaB6 is found to be a band insulator with a band gap of about 0.2 eV. The calculated results indicate that carbon and oxygen substitution in boron sublattice, usually expected as impurity in low purity borons, do not play sign...

The t-concept lattice is introduced as a set of triples associated to graded tabular information interpreted in a non-commutative fuzzy logic. Following the general techniques of formal concept analysis, and based on the works by Georgescu and Popescu, given a non-commutative conjunctor it is possible to provide generalizations of the mappings for the intension and the extension in two differen...

The Number Field Sieve and its numerous variants is the best algorithm to compute discrete logarithms in medium large characteristic finite fields. When extension degree n composite p of size, Tower variant (TNFS) asymptotically most efficient one. Our work deals with last main step, namely individual logarithm that computes a smooth decomposition given target T field thanks two distinct phases...