Percolation threshold near the second phase transition in diluted system of Gd2−x(La, Y)xIn

In this paper it is demonstrated that the second phase transition of Gd₂In intermetallic compound gets eliminated by diluting Gd_2−x(LaY)_xIn at a critical composition of x=0.5. The exchange coupling for intra-cluster interactions is estimated in the correlation ranges of 3.3 Å<R_C<3.6 Å (anisotropic source) and for inter-cluster interactions in the ranges of R_C>4 Å where the correlation length is defined as . The sign and strength of the exchange coupling are identified by the eigenvalues λ(k) and are obtained from zeros of the 4×4 matrix of J_ij^RR′ along the three directions of the reciprocal lattice for each dilution (x=0.25, 0.5, 0.75, 1). The transition temperature is calculated using the minimum eigenvalue λ_min (k=0, π) which agrees with the experiment. Magnetic field and temperature dependence of the magnetization and electrical resistivity measurements show that: (i) Elimination of the AFM phase is caused by breaking of some FM short-range exchange couplings, and (ii) Conduction electrons order antiferromagnetically at low temperatures and ferromagnetically at high temperatures.     

An extremal property of Fekete polynomials

The Fekete polynomials are defined as

where is the Legendre symbol. These polynomials arise in a number of contexts in analysis and number theory. For example, after cyclic permutation they provide sequences with smallest known norm out of the polynomials with coefficients.

The main purpose of this paper is to prove the following extremal property that characterizes the Fekete polynomials by their size at roots of unity.

Theorem 0.1. Let with odd and . If

then must be an odd prime and is . Here

This result also gives a partial answer to a problem of Harvey Cohn on character sums.

     

Pair density wave in the pseudogap state of high temperature superconductors

Recent scanning tunneling microscopy experiments of Bi(2)Sr(2)CaCu(2)O(8+delta) have shown evidence of real-space organization of electronic states at low energies in the pseudogap state [Science 303, 1995 (2004)]]. We argue based on symmetry considerations as well as model calculations that the experimentally observed modulations are due to a density wave of d-wave Cooper pairs without global phase coherence. We show that scanning tunneling microscopy measurements can distinguish a pair density wave from more typical electronic modulations such as those due to charge density wave ordering or scattering from an on site periodic potential.     

Statistical modeling of <Emphasis Type="Italic">p</Emphasis>-nitrophenol degradation using a response surface methodology (RSM) over nano zero-valent iron-modified Degussa P25-TiO<Subscript>2</Subscript>/ZnO photocatalyst with persulfate

Zero-valent iron-modified Degussa P25-TiO₂/ZnO nanocomposites (denoted as P25/Fe⁰/ZnO) were designed and prepared via Fe⁰ impregnation of P25-TiO₂/ZnO and then were employed in the visible-light photocatalytic degradation of p-nitrophenol (PNP) in the presence of [K₂S₂O₈]. Central composite design was applied for response surface modeling (RSM) to understand the influence of selected factors (pH, [Fe⁰] wt% and [K₂S₂O₈] concentration) on the degradation of PNP and to determine the interaction between the factors. The maximal PNP degradation efficiency (86.9%) was obtained with P25/1.5 wt% Fe⁰/ZnO at 3 mg/L of [K₂S₂O₈] concentration and pH 7.5. In addition, the RSM showed a satisfactory correlation between the experimental and predicted values of PNP degradation. The P25/Fe⁰/ZnO photocatalyst performance was also examined degrading methyl orange and phenol and high degradation efficiency, 82 and 99%, was achieved, respectively. The structure, morphology, light absorption and photocatalytic properties of as-prepared P25/Fe⁰/ZnO were studied using TEM, BET, XRD, FTIR and DRS.     

Chemical constituents of the essential oil from aerial parts and fruit of Anisosciadium orientale

The essential oils from aerial parts and fruits of Anisosciadium orientale DC. growing wild in Iran were obtained by hydrodistillation and analyzed by GC and GC/MS. Seventy-one compounds were identified in the fruit oil and fifteen in the oil from the aerial parts. The main oil components of the fruits and aerial parts were myristicin (33.5%-33.7%), alpha-terpinolene (22%-25.8%) and limonene (19.5%-19.7%). Some compounds, such as geranyl butyrate and germacrene-D, were only detected in the fruit oil.     

Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces

After a discussion on definability of invariant subdivision rules we discuss rules for sequential data living in Riemannian manifolds and in symmetric spaces, having in mind the space of positive definite matrices as a major example. We show that subdivision rules defined with intrinsic means in Cartan-Hadamard manifolds converge for all input data, which is a much stronger result than those usually available for manifold subdivision rules. We also show weaker convergence results which are true in general but apply only to dense enough input data. Finally we discuss C ¹ and C ² smoothness of limit curves.     

Reaction of Isatoic Anhydride,Amine, and N,N′-Dialkyl Carbodiimides Under Solvent-Free Conditions: New and Efficient Synthesis of 3-Alkyl-2-(alkylamino)quinazolin-4(3H)-ones

Heating a mixture of isatoic anhydride, amines, and N,N′-dialkyl carbodiimides under solvent-free conditions provided novel 3-alkyl-2-(alkylamino)quinazolin-4(3H)-one derivatives for the first time. The products were obtained in moderate to good yields without formation of any by-products.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

Localization of Gravity in Brane World with Arbitrary Extra Dimensions

We study the induced 4-dimensional linearized Einstein field equations in an m-dimensional bulk space by means of a confining potential. We used the confining potential in this model to localized gravitons on the brane. It is shown that in this approach the mass of graviton is quantized. The cosmological constant problem is also addressed within the context of this approach. We show that the difference between the values of the cosmological constant in particle physics and cosmology stems from our measurements in two different scales, small and large.