A common generalization for MV-algebras and Łukasiewicz–Moisil algebras

We introduce the notion of n-nuanced MV-algebra by performing a Łukasiewicz–Moisil nuancing construction on top of MV-algebras. These structures extend both MV-algebras and Łukasiewicz–Moisil algebras, thus unifying two important types of structures in the algebra of logic. On a logical level, n-nuanced MV-algebras amalgamate two distinct approaches to many valuedness: that of the infinitely valued Łukasiewicz logic, more related in spirit to the fuzzy approach, and that of Moisil n-nuanced logic, which is more concerned with nuances of truth rather than truth degree. We study n-nuanced MV-algebras mainly from the algebraic and categorical points of view, and also consider some basic model-theoretic aspects. The relationship with a suitable notion of n-nuanced ordered group via an extension of the Γ construction is also analyzed.     

Liquid phase oxidation of p-chlorotoluene to p-chlorobenzaldehyde over cobalt-doped mesoporous titania with a crystalline framework

Cobalt-doped mesoporous titania with a crystalline framework synthesized by surfactant templating method presented highly selective (99%) and reasonable conversion rate (49%) of catalytic oxidation of para-chlorotoluene to para-chlorobenzaldehyde in acetic acid using aqueous hydrogen peroxide as oxidant for the first time. Recycling of the catalyst indicates that the catalyst can be used a number of times without losing its activity to a greater extent. By contrast, cobalt-doped mesoporous titania without a crystalline structure and cobalt doped the commercial titania, Degussa P25 prepared by impregnation method with the similar concentration of cobalt were found inactive. The effects of catalyst concentration, reaction time, reaction temperature, and solvents on the performance of the catalyst were also investigated.     

Synthesis and adsorption properties of gold nanoparticles within pores of surface‐functional porous polymer microspheres

Mesoporous polymer microspheres with gold (Au) nanoparticles inside their pores were prepared considering their surface functionality and porosity. The Au/polymer composite microspheres prepared were characterized by transmission electron microscope (TEM), X‐ray diffraction (XRD), and Brunauer–Emmett–Teller (BET) techniques. The results showed that the adsorption of Au nanoparticles could be increased by imparting the pore structure and surface‐functional groups into the supporting polymer microspheres (in this study, poly (ethylene glycol dimethacrylate‐co‐acrylonitrile) and poly (EGDMA‐co‐AN) system). Above all, from this study, it was established that the porosity of the polymer microspheres is the most important factor that determines the distribution and adsorption amount of face‐centered cubic (fcc) Au nanoparticles in the final products. Our study showed that the continuous adsorption of Au nanoparticles with the aid of the large surface area and surface interaction sites formed more favorably the Au/polymer composite microspheres. The BET measurements of Au/poly(EGDMA‐co‐AN) composite microspheres reveals that the adsorption of Au nanoparticles into the pores kept the pore structure intact and made it more porous. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5627–5635, 2004     

On then-cutset property

For a partially ordered setP and an elementx ofP, a subsetS ofP is called a cutset forx inP if every element ofS is noncomparable tox and every maximal chain ofP meets {x}∪S. We letc(P) denote the smallest integerk such that every elementx ofP has a cutsetS with ‖S‖?k: Ifc(P)?n we say thatP has then-cutset property. Our results bear on the following question: givenP, what is the smallestn such thatP can be embedded in a partially ordered set having then-cutset property? As usual, 2 ⁿ denotes the Boolean lattice of all subsets of ann-element set, andB _n denotes the set of atoms and co-atoms of 2 ⁿ . We establish the following results: (i) a characterization, by means of forbidden configurations, of whichP can be embedded in a partially ordered set having the 1-cutset property; (ii) ifP contains a copy of 2 ⁿ , thenc(P)?2^[n/2]?1; (iii) for everyn>3 there is a partially ordered setP containing 2 ⁿ such thatc(P)<c(2 ⁿ ); (iv) for every positive integern there is a positive integerN such that, ifB _m is contained in a partially ordered set having then-cutset property, thenm?N.     

Mössbauer spectroscopy study of spin structure and its in-field and temperature dynamics in B2 ordered Fe(Al) alloys

The experimental data from Mössbauer spectroscopy and magnetic measurements are presented as functions of the temperature and external magnetic field for a B2-type ordered Fe ₆₆ Al ₃₄ alloy.     

The intertwining lifting theorem for ordered groups

Sz.-Nagy's dilation theorem for a contraction on a Hilbert space has been extended by Mlak to the case of a contraction semigroup whose indices are the positive elements of a totally ordered discrete group. We generalize to this case the intertwining lifting theorem of Sz.-Nagy and Foias. Some previous interpolation results on ordered groups are obtained as consequences.     

Measure of Ordering in Statistical Systems

In this paper, we introduce a phenomenological measure of ordering in statistical systems. Using this characteristic, we construct a formal model of a system evolving according to the law of steepest ascent as the control parameter increases.     

Banach空间中二阶积分-微分方程的初值问题

使用锥理论及单调迭代技术，首先讨论了Banach空间中一阶积分-微分方程初值问题的最小最大解的存在性，并在此基础上讨论了带有一阶微分项的二阶积分-微分方程初值问题的最小最大解的存在性。     

All Subvarieties of ℒpq Have Finite Bases of Identities

We consider the varieties of lattice ordered groups with the identity of commutation of the nth powers of elements. We establish that every such l-variety with n=pq, where p and q are distinct prime numbers, has a finite basis of identities.     

Sulfur Concentration in Nanoporous Alumina Membrane

Nanoporous alumina membrane prepared by anodic oxidation using sulfuric acid electrolyte was subjected to TG-DTA and X-ray Photoelectron Spectroscopy (XPS or ESCA) to further study the distribution of sulfur. In XPS study, Ar⁺ ion bombardment was performed on the sample to etch the surface at a rate of 3 nm min^-1. As a result, sulfur was found to be concentrated within a depth of 3nm from the surface. The S content of the surface was found to be 2.7±0.5 wt%, and that at a depth of ca. 3 nm and ca. 10 nm was found to be as low as about 0.6±0.11 wt% (5.37±1.0 wt%→ 1.26±0.2wt% SO₂). In TG-DTA, the mass loss of 7.3% was in fair agreement with that calculated on XPS results (7.1±1.2%). This revised version was published online in July 2006 with corrections to the Cover Date.