In this paper, we have focused to study convex $L$-subgroups of an $L$-ordered group. First, we introduce the concept of a convex $L$-subgroup and a convex $L$-lattice subgroup of an $L$-ordered group and give some examples. Then we find some properties and use them to construct convex $L$-subgroup generated by a subset $S$ of an $L$-ordered group $G$ . Also, we generalize a well known result a...

Cation ordering in solids is important for controlling physical properties and leads to ilmenite (FeTiO3) LiNbO3 type derivatives of the corundum structure, with ferroelectricity resulting from breaking inversion symmetry latter. However, a hypothetical third ABO3 derivative R32 has never been observed. Here we show that Co2InSbO6 recovered high pressure new, ordered-R32 A2BCO6 variant structur...

Empirical studies on the relationship between income and happiness commonly use standard ordered response models, the most well-known representatives being the ordered logit and the ordered probit. However, these models restrict the marginal probability effects by design, and therefore limit the analysis of distributional aspects of a change in income, that is, the study of whether the income e...

The standard denotational semantics of a programming language, being based on Tarski’s Theorem, is often not capable of expressing program properties. Annotated semantic domains and corresponding semantic functions capacitate us to express the properties, but the resulting structures may no longer be partially ordered sets. Instead we obtain quasi ordered sets, which lack the antisymmetry of pa...

Three-dimensional cubic ordered mesoporous carbons with tunable pore sizes have been synthesized by using cubic Ia3d mesoporous KIT-6 silica as the hard template and boric acid as the pore expanding agent. The prepared ordered mesoporous carbons were characterized by powder X-ray diffraction, scanning electron microscopy, transmission electron microscopy, and nitrogen adsorption-desorption anal...

A totally ordered tree is a tree equipped with an additional total order on its nodes. It provides a formal model for data that comes with both a hierarchical and a sequential structure; one example for such data are natural language sentences, where a sequential structure is given by word order, and a hierarchical structure is given by grammatical relations between words. In this paper, we stu...

The low-temperature structure of AC 60 (A=K, Rb) is an ordered array of polymerized C 60 chains, with magnetic properties that suggest a non-metallic ground state. We study the paramagnetic state of this phase using first-principles electronic-structure methods, and examine the magnetic fluctuations around this state using a model Hamiltonian. The electronic and magnetic properties of even this...

Shelah’s pcf theory describes a certain structure which must exist if אω is strong limit and 2ω > אω1 holds. Jech and Shelah proved the surprising result that this structure exists in ZFC. They first give a forcing extension in which the structure exists then argue that by some absoluteness results it must exist anyway. We reformulate the statement to the existence of a certain partially ordere...