Lower Semimodular Inverse Semigroups, II

The authors’ description of the inverse semigroups S for which the lattice ℒℱ(S) of full inverse subsemigroups is lower semimodular is used to describe those for which (a) the lattice ℒ(S) of all inverse subsemigroups or (b) the lattice �o(S) of convex inverse subsemigroups has that property. In each case, we show that this occurs if and only if the entire lattice is a subdirect product of ℒℱ(S) with ℒ(E S ), or �o(E S ), respectively, where E S is the semilattice of idempotents of S; a simple necessary and sufficient condition is found for each decomposition. For a semilattice E, ℒ(E) is in fact always lower semimodular, and �o(E) is lower semimodular if and only if E is a tree. The conjunction of these results leads to quite a divergence between the ultimate descriptions in the two cases, ℒ(S) and �o(S), with the latter being substantially richer

More on the covariant retarded Green's function for the electromagnetic field in de Sitter spacetime

In a recent paper (Phys. Rev. D78, 084031 (2008), arXiv:0808.0642, Ref. [1]) it was shown in examples that the covariant retarded Green's functions in particular gauges for electromagnetism and linearized gravity can be used to reproduce field configurations correctly in spite of the spacelike nature of past infinity in de Sitter spacetime. In this paper we extend the work of Ref. [1] concerning the electromagnetic field and show that the covariant retarded Green's function with an arbitrary value of the gauge parameter reproduces the electromagnetic field from two opposite charges at antipodal points of de Sitter spacetime.Comment: 4 pages, addendum to PRD 78, 084031 (2008) [arXiv:0808.0642

Biological evaluations of novel 2,3,3-Trisphosphonate in osteoclastic and osteoblastic activities

Bisphosphonates (BPs) are the first line treatment for many bone diseases including hypercalcimia associated with bone malignancies. In this paper, we introduce a new analogue of bisphosphonate called the 2,3,3-Trisphosphonate (2,3,3-TriPP) that was synthesised in a two steps reaction. In vitro investigations using a medically known bisphosphonate (Etidronate) and the 2,3,3-TrisPP were performed with an aim to evaluate biological effect of this novel compound in major bone cells. 2,3,3-TrisPP showed to have potential to supress the bone resorption process, as our data found that this novel compound exhibited cytotoxic effect in osteoclastic cells at a low concentration of 0.172 mg/mL (LC50). A molecular docking computational simulation calculated a high level of binding affinity between the human farnesyl pyrophosphate synthase (hFPPS) and 2,3,3-TrisPP. This calculation suggested 2,3,3TrisPP may have undergone the mevalonate pathway to prevent the prenylation step during biosynthesis and subsequently resulted in the deactivation of osteoclastic cells. Finally, high levels of osteoblast mineralisation potentials were recorded upon treatments with 2,3,3-TrisPP (0.01-0.1 mg/ml), which implied 2,3,3-TrsiPP may also facilitate bone regeneration.Peer reviewe

Designing a hierarchical fuzzy logic controller using the differential evolution approach

In conventional fuzzy logic controllers, the computational complexity increases with the dimensions of the system variables; the number of rules increases exponentially as the number of system variables increases. Hierarchical fuzzy logic controllers ( HFLC) have been introduced to reduce the number of rules to a linear function of system variables. However, the use of hierarchical fuzzy logic controllers raises new issues in the automatic design of controllers, namely the coordination of outputs of sub- controllers at lower levels of the hierarchy. In this paper, a method is described for the automatic design of an HFLC using an evolutionary algorithm called differential evolution ( DE). The aim in this paper is to develop a sufficiently versatile method that can be applied to the design of any HFLC architecture. The feasibility of the method is demonstrated by developing a two- stage HFLC for controlling a cart - pole with four state variables. The merits of the method are automatic generation of the HFLC and simplicity as the number of parameters used for encoding the problem are greatly reduced as compared to conventional methods

On simplifying the automatic design of a fuzzy logic controller

With the availability of a wide range of evolutionary algorithms such as genetic algorithms, evolutionary programming, evolution strategies and differential evolution, every conceivable aspect of the design of a fuzzy logic controller has been optimized and automated. Although there is no doubt that these automated techniques can produce an optimal fuzzy logic controller, the structure of such a controller is often obscure and in many cases these optimizations are simply not needed. We believe that the automatic design of a fuzzy logic controller can be simplified by using a generic rule base such as the Mac Vicar-Whelan rule base and using an evolutionary algorithm to optimize only the membership functions of the fuzzy sets. Furthermore, by restricting the overlapping of fuzzy sets, using triangular membership functions and singletons, and reducing the number of parameters to represent the membership functions, the design can be further simplified. This paper describes this method of simplifying the design and some experiments performed to ascertain its validity

Fe-doping-induced evolution of charge-orbital ordering in a bicritical-state manganite

Impurity effects on the stability of a ferromagnetic metallic state in a bicritical-state manganite, (La0.7Pr0.3)0.65Ca0.35MnO3, on the verge of metal-insulator transition have been investigated by substituting a variety of transition-metal atoms for Mn ones. Among them, Fe doping exhibits the exceptional ability to dramatically decrease the ferromagnetic transition temperature. Systematic studies on the magnetotransport properties and x-ray diffraction for the Fe-doped crystals have revealed that charge-orbital ordering evolves down to low temperatures, which strongly suppresses the ferromagnetic metallic state. The observed glassy magnetic and transport properties as well as diffuse phase transition can be attributed to the phase-separated state where short-range charge-orbital-ordered clusters are embedded in the ferromagnetic metallic matrix. Such a behavior in the Fe-doped manganites form a marked contrast to the Cr-doping effects on charge-orbital-ordered manganites known as impurity-induced collapse of charge-orbital ordering.Comment: 8 pages, 7 figure