scholarly journals Special Lattice of Rough Algebras

2011 ◽  
Vol 02 (12) ◽  
pp. 1522-1524 ◽  
Author(s):  
Yonghong Liu
Keyword(s):  
Special Lattice

Tem Investigation of Microstructures in Low-Hysteresis Ti50Ni50-xPdxAlloys with Special Lattice Parameters

ICOMAT ◽  
2013 ◽  
pp. 145-152
Author(s):  
Remi Delville ◽  
Dominique Schryvers ◽  
Zhiyong Zhang ◽  
Shaktivel Kasinathan ◽  
Richard D. James
Keyword(s):  
Lattice Parameters ◽  
Special Lattice

scholarly journals Entropy Inequalities for Lattices

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 784 ◽  
Author(s):  
Peter Harremoës
Keyword(s):  
Group Theory ◽  
Conditional Independence ◽  
Lattice Theory ◽  
Boolean Lattice ◽  
Functional Dependencies ◽  
Modular Lattices ◽  
Special Lattice ◽  
Entropy Inequalities ◽  
Lattice Of Subgroups

We study entropy inequalities for variables that are related by functional dependencies. Although the powerset on four variables is the smallest Boolean lattice with non-Shannon inequalities, there exist lattices with many more variables where the Shannon inequalities are sufficient. We search for conditions that exclude the existence of non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group. In order to formulate and prove the results, one has to bridge lattice theory, group theory, the theory of functional dependences and the theory of conditional independence. It is demonstrated that the Shannon inequalities are sufficient for planar modular lattices. The proof applies a gluing technique that uses that if the Shannon inequalities are sufficient for the pieces, then they are also sufficient for the whole lattice. It is conjectured that the Shannon inequalities are sufficient if and only if the lattice does not contain a special lattice as a sub-semilattice.

INCOMPARABILITY GRAPH OF THE SPECIAL LATTICE $L^{2^{2}}_n$

2020 ◽  
Vol 9 (11) ◽  
pp. 9781-9786
Author(s):  
A. Dabhole
Keyword(s):  
Dominating Set ◽  
Independent Set ◽  
Research Paper ◽  
Expansion Formula ◽  
Special Lattice

In the present research paper, we have studied the incomparability graph of the lattice $L^{2^{2}}_n$. In said graphs, we found a dominating set and the order of a graph. We have expressed the cardinality of neighbourhood of an atom making use of an expansion formula. We have also found the largest independent set of the mentioned graph.

scholarly journals ON THE HERMITICITY OF q-DIFFERENTIAL OPERATORS AND FORMS ON THE QUANTUM EUCLIDEAN SPACES $\mathbb{R}_q^N$

2006 ◽  
Vol 18 (01) ◽  
pp. 79-117 ◽  
Author(s):  
GAETANO FIORE
Keyword(s):  
Hilbert Spaces ◽  
Differential Operators ◽  
Pseudodifferential Operators ◽  
Special Functions ◽  
Radial Coordinate ◽  
Complicated Structure ◽  
Similarity Transformations ◽  
Special Lattice ◽  
Free Parameters ◽  
Scalar Products

We show that the complicated ⋆-structure characterizing for positive q the Uqso(N)-covariant differential calculus on the noncommutative manifold [Formula: see text] boils down to similarity transformations involving the ribbon element of a central extension of Uqso(N) and its formal square root ṽ. Subspaces of the spaces of functions and of p-forms on [Formula: see text] are made into Hilbert spaces by introducing non-conventional "weights" in the integrals defining the corresponding scalar products, namely suitable positive-definite q-pseudodifferential operators ṽ′±1 realizing the action of ṽ±1; this serves to make the partial q-derivatives anti-hermitean and the exterior coderivative equal to the hermitean conjugate of the exterior derivative, as usual. There is a residual freedom in the choice of the weight m(r) along the "radial coordinate" r. Unless we choose a constant m, then the square-integrables functions/forms must fulfill an additional condition, namely, their analytic continuations to the complex r plane can have poles only on the sites of some special lattice. Among the functions naturally selected by this condition there are q-special functions with "quantized" free parameters.

On an integrable two-dimensional special lattice with self-consistent sources

2006 ◽  
Vol 58 (2) ◽  
pp. 195-205 ◽  
Author(s):  
Gegenhasi ◽  
Hon-Wah Tam ◽  
Hong-Yan Wang
Keyword(s):  
Two Dimensional ◽  
Self Consistent ◽  
Special Lattice

scholarly journals Zur spontanen Magnetisierung dünner ferromagnetischer Schichten

1964 ◽  
Vol 19 (13) ◽  
pp. 1580-1591
Author(s):  
Rainer J. Jelitto
Keyword(s):  
Thin Films ◽  
Digital Computer ◽  
Heisenberg Model ◽  
Spontaneous Magnetization ◽  
Preceding Paper ◽  
Cubic Lattice ◽  
Compact Material ◽  
Ferromagnetic Films ◽  
Special Lattice ◽  
The One

In a preceding paper (I) the spectra of the one-spinwave-eigenstates of an ideal HEISENBERG-model for thin ferromagnetic films were derived for a special type of surface-orientations.Now these results are applied to the cubic lattice types. First a theory is given for the calculation of certain coefficients by which the general equations of (I) are related to the special lattice types and surface orientations. It is shown that some of the most important orientations of the cubic lattice types belong to the case treated in (I).For these orientations the dependence of the spontaneous magnetization on temperature and thickness of the film is calculated from the spinwave spectra. The formula obtained for this function was evaluated on a digital computer. The results, some of which are plotted, are discussed and compared with experimental dates.In all cases the deviations from the magnetization of the compact material are found to be small, down to very thin films.

scholarly journals MRA-Wavelet subspace architecture for logic, probability, and symbolic sequence processing

2014 ◽  
Author(s):  
Daniel J. Greenhoe
Keyword(s):  
Boolean Lattice ◽  
Symbolic Sequence ◽  
Sequence Processing ◽  
Linear Subspaces ◽  
Genomic Signal Processing ◽  
Set Inclusion ◽  
Symbolic Sequences ◽  
Special Lattice ◽  
Boolean Lattices ◽  
Selection Of

The linear subspaces of a multiresolution analysis (MRA) and the linear subspaces of the wavelet analysis induced by the MRA, together with the set inclusion relation, form a very special lattice of subspaces which herein is called a "primorial lattice". This paper introduces an operator R that extracts a set of 2^{N-1} element Boolean lattices from a 2^N element Boolean lattice. Used recursively, a sequence of Boolean lattices with decreasing order is generated---a structure that is similar to an MRA. A second operator, which is a special case of a "difference operator", is introduced that operates on consecutive Boolean lattices L_2^n and L_2^{n-1} to produce a sequence of orthocomplemented lattices. These two sequences, together with the subset ordering relation, form a primorial lattice P. A logic or probability constructed on a Boolean lattice L_2^N likewise induces a primorial lattice P. Such a logic or probability can then be rendered at N different "resolutions" by selecting any one of the N Boolean lattices in P and at N different "frequencies" by selecting any of the N different orthocomplemented lattices in P. Furthermore, P can be used for symbolic sequence analysis by projecting sequences of symbols onto the sublattices in P using one of three lattice projectors introduced. P can be used for symbolic sequence processing by judicious rejection and selection of projected sequences. Examples of symbolic sequences include sequences of logic values, sequences of probabilistic events, and genomic sequences (as used in "genomic signal processing").

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