Crystal chemistry peculiarities of Cs2Te4O12

The Raman and IR-absorption spectra of the Cs₂Te₄O₁₂ lattice are first recorded and interpreted. Extraordinary features observed in the structure and Raman spectra of Cs₂Te₄O₁₂ are analyzed by using ab initio and lattice-dynamical model calculations. This compound is specified as a caesium-tellurium tellurate Cs₂Te^IV(Te^VIO₄)₃ in which Te^IV atoms transfer their 5p electrons to [Te^VIO₄]₃⁶⁻ tellurate anions, thus fulfilling (jointly with Cs atoms) the role of cations. The Te^VI-O-Te^VI bridge vibration Raman intensity is found abnormally weak, which is reproduced by model treatment including the Cs⁺ ion polarizability properties in consideration.     

The number of extreme points of tropical polyhedra

The celebrated upper bound theorem of McMullen determines the maximal number of extreme points of a polyhedron in terms of its dimension and the number of constraints which define it, showing that the maximum is attained by the polar of the cyclic polytope. We show that the same bound is valid in the tropical setting, up to a trivial modification. Then, we study the tropical analogues of the polars of a family of cyclic polytopes equipped with a sign pattern. We construct bijections between the extreme points of these polars and lattice paths depending on the sign pattern, from which we deduce explicit bounds for the number of extreme points, showing in particular that the upper bound is asymptotically tight as the dimension tends to infinity, keeping the number of constraints fixed. When transposed to the classical case, the previous constructions yield some lattice path generalizations of Gale's evenness criterion.     

Weak sense of direction labelings and graph embeddings

An edge-labeling λ for a directed graph G has a weak sense of direction (WSD) if there is a function f that satisfies the condition that for any node u and for any two label sequences α and α^′ generated by non-trivial walks on G starting at u, f(α)=f(α^′) if and only if the two walks end at the same node. The function f is referred to as a coding function of λ. The weak sense of direction number of G, WSD(G), is the smallest integer k so that G has a WSD-labeling that uses k labels. It is known that WSD(G)≥Δ⁺(G), where Δ⁺(G) is the maximum outdegree of G.Let us say that a function τ:V(G)→V(H) is an embedding from G onto H if τ demonstrates that G is isomorphic to a subgraph of H. We show that there are deep connections between WSD-labelings and graph embeddings. First, we prove that when f_H is the coding function that naturally accompanies a Cayley graph H and G has a node that can reach every other node in the graph, then G has a WSD-labeling that has f_H as a coding function if and only if G can be embedded onto H. Additionally, we show that the problem “Given G, does G have a WSD-labeling that uses a particular coding function f?” is NP-complete even when G and f are fairly simple.Second, when D is a distributive lattice, H(D) is its Hasse diagram and G(D) is its cover graph, then WSD(H(D))=Δ⁺(H(D))=d^∗, where d^∗ is the smallest integer d so that H(D) can be embedded onto the d-dimensional mesh. Along the way, we also prove that the isometric dimension of G(D) is its diameter, and the lattice dimension of G(D) is Δ⁺(H(D)). Our WSD-labelings are poset-based, making use of Birkhoff’s characterization of distributive lattices and Dilworth’s theorem for posets.     

S-fuzzy Version of Stone's Theorem for Distributive Lattices

In this paper,we initiate a study of S-fuzzy ideal(filter) of a lattice where S stands for a meet semilattice.A S-fuzzy prime ideal(filter) of a lattice is defined and it is proved that a S-fuzzy ideal(filter) of a lattice is S-fuzzy prime ideal(filter) if and only if any non-empty α-cut of it is a prime ideal(filter).Stone's theorem for a distributive lattice is extended by considering S-fuzzy ideals(filters).     

Fuzzy Ideals and Fuzzy Distributive Lattices

Our main objective is to study properties of a fuzzy ideals(fuzzy dual ideals).A study of special types of fuzzy ideals(fuzzy dual ideals) is also furnished.Some properties of a fuzzy ideals(fuzzy dual ideals) are furnished.Properties of a fuzzy lattice homomorphism are discussed.Fuzzy ideal lattice of a fuzzy lattice is defined and discussed.Some results in fuzzy distributive lattice are proved.     

HC-偏序集的若干性质

基于超连续格的内蕴式刻画,引入HC-偏序集的概念,讨论了HC-偏序集的一些性质.类似地,作为超代数格的推广,引入了HA-偏序集并讨论其相关性质.     

关于G-代数的一些注记

引进了基于一般剩余格的G-代数-G(RL)-代数的概念,并且分别给出了G-滤子和(全序)G(RL)-代数的一系列特征刻画,同时还证明了任何正则的G(RL)-代数必为Boolean代数,本文所得结果分别是已有结果的一般化.     

Intrinsic polyatomic defects in Sc2(WO4)3

The intrinsic formation of polyatomic defects in Sc₂(WO₄)₃-type structures is studied by Mott Littleton calculations and Molecular Dynamics simulations. Defects involving the WO₄²⁻ tetrahedron are found to be energetically favorable when compared to isolated W and O defects. WO₄²⁻ Frenkel and (2Sc³⁺, 3WO₄²⁻) Schottky defects exhibit formation energies of 1.23 eV and 1.97 eV, respectively and therefore may occur as intrinsic defects in Sc₂(WO₄)₃ at elevated temperatures. WO₄²⁻ vacancy and interstitial migration processes have been simulated by classical Molecular Dynamics simulations. The interstitial defect exhibits a nearly 10 times higher mobility (with a migration energy of 0.68 eV), than the vacancy mechanism (with a slightly higher migration energy of 0.74 eV) and thus should dominate the overall ionic conduction. Still both models reproduce the experimental activation energy (0.67 eV) nearly within experimental uncertainty.     

Effect of grain size on the magnetic properties of superparamagnetic Ni0.5Zn0.5Fe2O4 nanoparticles by co-precipitation process

Ni_0.5Zn_0.5Fe₂O₄ (NZFO) spinel-type nanoparticles were directly fabricated by the chemical co-precipitation process using metal nitrate and acetate as precursors since nitrogen and carbon would be taken away in the forms of oxynitride and oxycarbide, respectively, after the precursors were annealed and then investigated in detail by employing X-ray diffraction (XRD), magnetic measurement and Raman spectroscopy. XRD analysis indicates that the as-prepared nanocrystals are all of a pure cubic spinel structure with their sizes ranging from 20.8 to 53.3 nm, as well as peaks of some samples shifting to lower angles due to lattice expansion. Calculations from the derived XRD data indicate that the activation energy is 30.83 kJ/mol. The magnetic measurements show that these samples are superparamagnetic. The saturation magnetization increases with annealing temperature, which may be explained by super-exchange interactions of Fe ions occurring at A- and B-sites. The variation of coercivity with particle size is interpreted on the basis of domain structure and crystal anisotropy. Furthermore, these nanoparticles exhibit a redshift phenomenon at lower temperatures seen in the Raman spectra, which could be related to ionic substitution.