In this study, using the neutrosophic soft definitions, we define some new concept such as the neutrosophic soft lattice, neutrosophic soft sublattice, complete neutrosophic soft lattice, modular neutrosophic soft lattice, distributive neutrosophic soft lattice, neutrosophic soft chain then we study the relationship and observe some common properties.

In this work we prove that the set of congruences on an nd-groupoid under suitable conditions is a complete lattice which is a sublattice of the lattice of equivalence relations on the nd-groupoid. The study of these conditions allowed to construct a counterexample to the statement that the set of (fuzzy) congruences on a hypergroupoid is a complete lattice.

The O’Nan-Scott theorem weakly classifies the maximal subgroups of the symmetric group S, providing some information about the lattice Λ of subgroups of S. We wish to obtain more information about Λ. We proceed by determining the intersection H of suitable pairs of maximal subgroups of S and the sublattice of overgroups of H in S.

We discuss the possible structures for and mutual relationships between a finite distributive lattice L, a maximal sublattice M of L and the corresponding ‘remainder’ R = L\M with the aid of Birkhoff duality, and contrast the results with the analogous situations for a general finite lattice L. @ 1999 Elsevier Science B.V. All rights reserved

Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.

Nikulin has classified all finite abelian groups acting symplectically on a K3 surface and he has shown that the induced action on the K3 lattice U⊕E8(−1) depends only on the group but not on the K3 surface. For all the groups in the list of Nikulin we compute the invariant sublattice and its orthogonal complement by using some special elliptic K3 surfaces.

The effect of uniaxial strain on the optical transition energies of single-walled carbon nanotubes with known chiral indices was measured by Rayleigh scattering spectroscopy. Existing theory accurately predicts the trends in the measured strain-induced shifts, but overestimates their magnitude. Modification of the analysis to account for internal sublattice relaxation results in quantitative ag...

Soft set theory was introduced by Molodtsov in 1999 as a general mathematical tool for dealing with problems that contain uncertainty. In this paper, we define concept of fuzzy soft lattice, fuzzy soft sublattice, complete fuzzy soft lattice, modular fuzzy soft lattice, distributive fuzzy soft lattice, fuzzy soft chain and study their basic properties.

This paper studies the terahertz optical properties of nonlinear potassium titanyl phosphate crystals with different conductivities in the spectral range of 0.2 to 2.6 THz. The observed properties are characterized by several absorption lines lying along different optical axes which represent the relevant potassium sublattice phonon modes. The peculiarities of these absorption lines are attribu...

The applications of lanthanide-doped upconversion nanocrystals in biological imaging, photonics, photovoltaics and therapeutics have fuelled a growing demand for rational control over the emission profiles of the nanocrystals. A common strategy for tuning upconversion luminescence is to control the doping concentration of lanthanide ions. However, the phenomenon of concentration quenching of th...