Order–disorder transition in nanocrystalline Ni3Al prepared by a chemical route

Ni₃Al alloys of nanometer dimensions in the range 10–38 nm could be synthesized by reaction sintering of sol–gel-derived Ni/SiO₂ nanocomposite and commercially available micrometer-sized aluminum powder. The sintering was carried out at a temperature of 923 K and a pressure of 2.4 MPa. By a suitable choice of sintering conditions a disordered phase of Ni₃Al was stabilized. The disordered phase could be converted to an ordered one by an increase of heat treatment temperature.     

Is there a photon excess or photon deficit in the cosmic events?

Summary Bjorken predicted in the recent past about the large excess emission of photons in high-energy collisions and this was subsequently corroborated by some experimentalists as well. Obviously, this phenomenon is just opposite in nature to pro-centauro events marked by the production of photonless hadrons. In this note we will try to trace the outlines of this confusing and contradictory situation, probe quantitatively into this excess emission of photons (called progammaisation events) and compare them mainly with Bjorken's disoriented-chiral-condensate (DCC) model.     

Electroprotic reactions

Reactions involving the coupled transfer of electrons and protons are called electroprotic reactions. In this article we briefly describe some of our experiences with electroprotic reaction as a tool for executing interesting chemical transformations.     

Pattern formation of zinc nanoparticles in silica film by electrodeposition

Zinc nanoparticles were grown within gel-derived silica films by applying a direct current voltage. Pattern formation of metallic Zn was studied as a function of applied voltage and metal-silica ratio. Average particle size varied from 5.2 to 20.2 nm by changing the applied voltage and silica concentration. It was found that the transition from fractal to dendritic morphology was possible due to crystalline anisotropy. From high-resolution transmission electron microscopy images and X-ray diffraction pattern a possible model is proposed to explain this observation.     

On the Number of Topological Types Occurring in a Parameterized Family of Arrangements

Let be an o-minimal structure over ℝ, a closed definable set, and

Synthesis and thermal behavior of chiral oligomers derived from cholesterol

Synthesis and thermal properties of a series of Schiff base oligomers derived from naturally occurring cholesterol are described. In particular, four of them show smectic A and/or chiral nematic phase/s or an unknown mesophase, while the other is non-mesomorphic. Molecular packing in the SmA phase has been determined by the HRXRD experiment.     

Refined Bounds on the Number of Connected Components of Sign Conditions on a Variety

Let \({\textnormal {R}}\) be a real closed field, \(\mathcal{P},\mathcal{Q} \subset {\textnormal {R}}[X_{1},\ldots,X_{k}]\) finite subsets of polynomials, with the degrees of the polynomials in \(\mathcal{P}\) (resp., \(\mathcal{Q}\)) bounded by d (resp., d ₀). Let \(V \subset {\textnormal {R}}^{k}\) be the real algebraic variety defined by the polynomials in \(\mathcal{Q}\) and suppose that the real dimension of V is bounded by k′. We prove that the number of semi-algebraically connected components of the realizations of all realizable sign conditions of the family \(\mathcal{P}\) on V is bounded by

$\sum_{j=0}^{k'}4^j{s +1\choose j}F_{d,d_0,k,k'}(j),$

where \(s = \operatorname {card}\mathcal{P}\), and

$F_{d,d_0,k,k'}(j)=\binom{k+1}{k-k'+j+1} (2d_0)^{k-k'}d^j \max\{2d_0,d \}^{k'-j}+2(k-j+1).$

In case 2d ₀≤d, the above bound can be written simply as

$\sum_{j = 0}^{k'} {s+1 \choose j}d^{k'} d_0^{k-k'} O(1)^{k}= (sd)^{k'} d_0^{k-k'} O(1)^k$

(in this form the bound was suggested by Matousek 2011). Our result improves in certain cases (when d ₀?d) the best known bound of

$\sum_{1 \leq j \leq k'}\binom{s}{j} 4^{j} d(2d-1)^{k-1}$

on the same number proved in Basu et al. (Proc. Am. Math. Soc. 133(4):965–974, 2005) in the case d=d ₀.

The distinction between the bound d ₀ on the degrees of the polynomials defining the variety V and the bound d on the degrees of the polynomials in \(\mathcal{P}\) that appears in the new bound is motivated by several applications in discrete geometry (Guth and Katz in arXiv:1011.4105v1 [math.CO], 2011; Kaplan et al. in arXiv:1107.1077v1 [math.CO], 2011; Solymosi and Tao in arXiv:1103.2926v2 [math.CO], 2011; Zahl in arXiv:1104.4987v3 [math.CO], 2011).