Formalization of Ring Theory in PVS

This paper presents a PVS development of relevant results of the theory of rings. The PVS theory includes complete proofs of the three classical isomorphism theorems for rings, and characterizations of principal, prime and maximal ideals. Algebraic concepts and properties are specified and formalized as generally as possible allowing in this manner their application to other algebraic structures. The development provides the required elements to formalize important algebraic theorems. In particular, the paper presents the formalization of the general algebraic-theoretical version of the Chinese remainder theorem (CRT) for the theory of rings, as given in abstract algebra textbooks, proved as a consequence of the first isomorphism theorem. Also, the PVS theory includes a formalization of the number-theoretical version of CRT for the structure of integers, which is the version of CRT found in formalizations. CRT for integers is obtained as a consequence of the general version of CRT for the theory of rings.

     

Extracellular Vesicles in CNS Developmental Disorders

The central nervous system (CNS) is the most complex structure in the body, consisting of multiple cell types with distinct morphology and function. Development of the neuronal circuit and its function rely on a continuous crosstalk between neurons and non-neural cells. It has been widely accepted that extracellular vesicles (EVs), mainly exosomes, are effective entities responsible for intercellular CNS communication. They contain membrane and cytoplasmic proteins, lipids, non-coding RNAs, microRNAs and mRNAs. Their cargo modulates gene and protein expression in recipient cells. Several lines of evidence indicate that EVs play a role in modifying signal transduction with subsequent physiological changes in neurogenesis, gliogenesis, synaptogenesis and network circuit formation and activity, as well as synaptic pruning and myelination. Several studies demonstrate that neural and non-neural EVs play an important role in physiological and pathological neurodevelopment. The present review discusses the role of EVs in various neurodevelopmental disorders and the prospects of using EVs as disease biomarkers and therapeutics.     

Advanced “Confident Judgments” Method when Choosing Multicriteria Solutions in a Multipurpose Approach

Journal of Computer and Systems Sciences International - The article considers the problem of making multicriteria decisions in which the decision maker (DM) has the opportunity to indicate the...     

Matrix Transformation in Boron Containing High-Temperature Co–Re–Cr Alloys

An addition of boron largely increases the ductility in polycrystalline high-temperature Co–Re alloys. Therefore, the effect of boron on the alloy structural characteristics is of high importance for the stability of the matrix at operational temperatures. Volume fractions of ε (hexagonal close-packed—hcp), γ (face-centered cubic—fcc) and σ (Cr₂Re₃ type) phases were measured at ambient and high temperatures (up to 1500 °C) for a boron-containing Co–17Re–23Cr alloy using neutron diffraction. The matrix phase undergoes an allotropic transformation from ε to γ structure at high temperatures, similar to pure cobalt and to the previously investigated, more complex Co–17Re–23Cr–1.2Ta–2.6C alloy. It was determined in this study that the transformation temperature depends on the boron content (0–1000 wt. ppm). Nevertheless, the transformation temperature did not change monotonically with the increase in the boron content but reached a minimum at approximately 200 ppm of boron. A probable reason is the interplay between the amount of boron in the matrix and the amount of σ phase, which binds hcp-stabilizing elements (Cr and Re). Moreover, borides were identified in alloys with high boron content.     

Influence of Mg concentration on structural,morphological and optical properties of nanoceria

Nano crystalline pure and Mg doped ceriaparticles were synthesized by simple chemical co-precipitation method using cerium nitrate hexahydrate as a source material and magnesium nitrate as doping precursor at room temperature. The effect of doping were investigated by X-ray diffraction pattern(XRD), FT-Raman,fourier transform infrared spectroscopy(FTIR), Ultraviolet spectroscopy(UV), photoluminescence spectroscopy(PL), field emission scanning electron microscope(FESEM) and high resolution transmission electron microscopy with energy dispersive spectroscopy (HRTEM &EDS). The X-ray diffraction pattern and FT-Raman studies showed that the prepared samples were nano particulates with cubic fluorite structure. The XRD pattern analysis showed that the size of the particles ranged from 13 to 20?nm, however 4?wt% Mg doping results in reduction of particle size compared with other doping concentrations. The effects of Mg concentration on various structural parameters of the prepared samples were also determined. The slight blue shift observed upon doping in UV–Vis absorption region around 330–360nmrecorded for reduction in particle size. The FTIR unveils the presence of Metal oxygen bonds below 700?cm^?1in the prepared samples. All samples showed a broad emission band at 430?nm with linearly increasing intensity with respect to dopant concentrations. The Spherical morphology with weak agglomeration was identified through FESEM and HRTEM analysis. The elemental analysis of Ce, O and Mg were confirmed through EDS analysis.     

Tuning of ferrimagnetic nature and hyperfine interaction of Ni2+ doped cobalt ferrite nanoparticles for power transformer applications

Ferrites may contain single domain particles which gets converted into super-paramagnetic state near critical size. To explore the existence of these characteristic feature of ferrites, we have performed magnetization(M-H loop) and Mössbauer spectroscopic studies of Ni²⁺ substitution effect in Co_1-xNi_xFe₂O₄ (where x?=?0, 0.25, 0.5, 0.75 and 1) nanoparticles were fabricated by solution combustion route using mixture of carbamide and glucose as fuels for the first time. As prepared samples exhibit spinel cubic structure with lattice parameters which decreases linearly with increase in Ni²⁺ concentration. The M-H loops reveals that saturation magnetization(M_s), coercive field(H_c) remanence magnetization(M_r) and magnetron number(η_B) decreases significantly with increasing Ni²⁺ substitution. The variation of saturation magnetization has been explained on the basis of Neel's molecular field theory. The coercive field(H_c) is found strongly dependent on the concentration of Ni²⁺ and decrease of coercivity suggests that the particles have single domain and exhibits superparamagnetic behavior. The Mössbauer spectroscopy shows two ferrimagnetically relaxed Zeeman sextets distribution at room temperature. The dependence of Mössbauer parameters such as isomer shift, quadru pole splitting, line width and hyperfine magnetic field on Ni²⁺ concentration have been discussed. Hence our results suggest that synthesized materials are potential candidate for power transformer application.