Effect of Mg and C contents in MgCNi3, and structure and superconductivity of MgCNi3-x -Co x

The effect of Mg and C contents on T_C in MgCN₃, and structure and superconductivity of MgCNi_3-x Co _x were studied. It is found that the excess of Mg and C in initial material mixture is favorable to improvement inT _c and helps to obtain single-phase samples. For preparing MgCNi₃ superconductor, the optimum composition of starting materials is MgC_1.45Ni₃ with excess of Mg (20 wt.%) of the stoichiometric composition. In gCNi_3-x Co _x system, a continuous solid solution is formed, lattice parameter decreases slightly andT _c decreases obviously with increasingx. A suppression of superconductivity is observed due to the substitution of Co (Mn) for Ni. The suppression effect is smaller for the substitution of Co than that of Mn     

Some group actions on K(x 1 , x 2 , x 3 )

LetK be any field which may not be algebraically closed,K(x ₁ ,x ₂ ,x ₃ ) be the rational function field of three variables overK, and σ:K(x ₁ ,x ₂ ,x ₃ ) → K(x ₁ ,x ₂ ,x ₃ ) be aK-automorphism defined by wherea _i ,b _i ,c _i ,d _i ∈K anda _i d _i −b _i c _i ≠0. Let ,f _i (T)=T ² −(a _i +d _i )T+(a _i d _i −b _i c _i )∈K[T] be the “characteristic polynomial” of σ _i . Theorem:Assume that charK≠2.Then the fixed field K(x ₁ ,x ₂ ,x ₃ ) ^<σ> is not rational (=purely transcendental) over K if and only if (i) for each 1≤i≤3, f _i (T) is irreducible; (ii) the Galois group of f ₁ (T)f ₂ (T)f ₃ (T) over K is of order 8; and (iii) for each 1≤i≤3,ord (σ _[itn] )is an even integer.     

Liquid structure of undercooled Cu70Ni30 alloy

Experiments of X-ray diffraction for liquid Cu₇₀Ni₃₀ alloy above and below its liquidus (l 230°C) have been carried out. By the analysis of experimental results, it is discovered that difference between structures of liquid and undercooled Cu₇₀Ni₃₀ alloy is their cluster sizes. The correlation radius of cluster is 1.125 nm and the atom number of cluster is 403 at l 250—l 400°C, and they are 1.3 nm and 704 respectively at the undercooled liquid state (1 200°C). The structure of liquid Cu₇₀Ni₃₀ alloy is fcc short order and its solid structure, fcc, is kept from liquid fcc short order.     

Structure and crystallization of bulk amorphous Pd41Ni10Cu28P21 alloy

Bulk amorphous Pd₄₁,Ni₁₀Cu₂₈P₂₁, alloy has been prepared by water quenching method. The system shows excellent glass forming ability (GFA) with a high value of reduced glass transition temperatureT _rg 0.714. Structural analyses indicate that the Pd₄₁,Ni₁₀Cu₂₈,P₂₁, alloy has a dense packing structure closer to “frozen liquid” than that of amorphous Pd₄₀Ni₄₀,P₂₀, alloy. Experiments on crystallization reveal that several crystalline phases simultaneously precipitate in the early part of crystallization. Below 710 K, a metastable phase forms, and subsequently disappears at elevated temperatures. In addition, the influence of partial substitute of Cu for Ni on GFA has been discussed with regard to thermodynamics and kinetics     

The kernel of the Rost invariant, Serre''s Conjecture II and the Hasse principle for quasi-split groups 3,6 D 4 , E 6 , E 7

 We prove that for a simple simply connected quasi-split group of type ^3,6 D ₄ ,E ₆ ,E ₇ defined over a perfect field F of characteristic ≠=2,3 the Rost invariant has trivial kernel. In certain cases we give a formula for the Rost invariant. It follows immediately from the result above that if cd F≤2 (resp. vcd F≤2) then Serre's Conjecture II (resp. the Hasse principle) holds for such a group. For a (C ₂ )-field, in particular ℂ(x,y), we prove the stronger result that Serre's Conjecture II holds for all (not necessary quasi-split) exceptional groups of type ^3,6 D ₄ ,E ₆ ,E ₇ . Received: 27 March 2002 / Published online: 28 March 2003 The author gratefully acknowledge the support of TMR ERB FMRX CT-97-0107 and Forschungsinstitut für Mathematik, ETH in Zürich     

关于m-HPK(n1,n2,n3,n4)-残差图

本文研究了3-维超平面完备残差图以及m 重3-维超平面完备残差图. 利用容斥原理以及集合的运算性质等方法, 分别获得了3-维超平面完备残差图和m 重3-维超平面完备残差图的最下阶以及二者的唯一极图, 将文献[1] 中定义的残差图从平面推广到超平面上.     

On the Diophantine System a^2 ＋ b^2 = c^3 and a^x ＋ b^y = c^z for b is an Odd Prime

Let a, b and c be fixed coprime positive integers. In this paper we prove that if a^2 ＋ b^2 = c^3 and b is an odd prime, then the equation a^x ＋ b^y = c^z has only the positive integer solution （x, y, z） = （2,2,3）.     

Some Arithmetic on the Hardy Sums s2（h, κ） and s3（h, κ）

In this work, Rademacher‘s two questions about Dedekind sums are applied to the Hardy sums s2(h,κ) and s3(h,κ). Some relations between these sums are obtained and some inequalities are given.     

Fourier Transforms of Bounded Bilinear Forms on C＊（S1）×C＊（S2） of Foundation ＊-semigroups S1 and S2

The author gives a characterization of the Fourier transforms of bounded bilinear forms on C＊（S1）×C＊（S2） of two foundation semigroups S1 and S2 in terms of Jordan ＊-representations, hemimogeneous random fields, and as well as weakly harmonizable random fields of S1 and S2 into Hilbert spaces.     

The Lower Algebraic K -theory of Γ3

We explicitly compute the lower algebraic K-theory of Γ₃ a discrete subgroup of the group of isometries of hyperbolic 3-space. An erratum to this article is available at .     

The Crossing Number of Cartesian Products of Complete Bipartite Graphs K 2, m with Paths P n

Most results on the crossing number of a graph focus on the special graphs, such as Cartesian products of small graphs with paths P_n, cycles C_n or stars S_n. In this paper, we extend the results to Cartesian products of complete bipartite graphs K_2,m with paths P_n for arbitrary m ≥ 2 and n ≥ 1. Supported by the NSFC (No. 10771062) and the program for New Century Excellent Talents in University.     

Full-potential LMTO study on the electronic structure of heavy-fermion compound LiV2O4

The electronic structure of heavy fermion compound LiV₂O₄ has been calculated using a self-consistent full-potential LMTO method. The results show that the conduction bands in this compound are formed from V 3 d states with a bandwidth of 2.5 eV. The symmetric characteristics of conduction bands are of t_2g in principle. The energy gap between conduction bands and fully occupied oxygen 2p bands is 1.9 eV. The band dispersions near Fermi energy display complicated structures. Furthermore, the N( E_F) and y_cal are 11.1 (states/eV/f.u.) and 26.7 mJ/mol.K₂ determined numerically by LDA calculation, respectively. It is insufficient to clarify the origin of local moment in LiV₂O₄ from plain LDA calculations. In addition to the above LDA calculation, we also found a LSDA solution of LiV₂O₄ that is lower in total energy than that of LDA calculation. Similarly, LSDA + GGA calculation yields almost the identical result as that in LSDA. We conclude that the mechanism responsible for heavy fermion properties in LiV₂O₄ might be somewhat different from the plain Kondo mechanism in conventional 4f and 5f heavy fermion compounds and perhaps the quantum transition might play an adequate role in heavy-ferrnion behaviors in LiV₂O₄.     

Quasirecognizability by the Set of Element Orders for Groups 3D4(q) and F4(q), for q Odd

It is proved that if L is one of the simple groups ³D₄(q) or F₄(q), where q is odd, and G is a finite group with the set of element orders as in L, then the derived subgroup of G/F(G) is isomorphic to L and the factor group G/G′ is a cyclic {2, 3}-group. __________ Translated from Algebra i Logika, Vol. 44, No. 5, pp. 517–539, September–October, 2005. Supported by RFBR grant No. 04-01-00463.     

On K1 and K2 of Algebraic Surfaces

In this paper we study higher Chow groups of smooth, projective surfaces over a field k of characteristic zero, using some new Hodge theoretic methods which we develop for this purpose. In particular we investigate the subgroup of CH ^r+1 (X,r) with r = 1,2 consisting of cycles that are supported over a normal crossing divisor Z on X. In this case, the Hodge theory of the complement forms an interesting variation of mixed Hodge structures in any geometric deformation of the situation. Our main result is a structure theorem in the case where X is a very general hypersurface of degree d in projective 3-space for d sufficiently large and Z is a union of very general hypersurface sections of X. In this case we show that the subgroup of CH ^r+1 (X,r) we consider is generated by obvious cycles only arising from rational functions on X with poles along Z. This can be seen as a generalization of the Noether–Lefschetz theorem for r = 0. In the case r = 1 there is a similar generalization by Müller-Stach, but our result is more precise than it, since it is geometric and not only cohomological. The case r = 2 is entirely new and original in this paper. For small d, we construct some explicit examples for r = 1 and 2 where the corresponding higher Chow groups are indecomposable, i.e. not the image of certain products of lower order groups. In an appendix Alberto Collino constructs even more indecomposable examples in CH ³ (X,2) which move in a one-dimensional family on the surface X.Contribution to appendix.     

A Hamilton cycle in the Cayley graph of the 2,p,3 presentation of PSL2(p)

We construct a Hamilton cycle in the Cayley graph of the 2,p,3 presentation of PSL₂(p).     

Infimal convolution and Muckenhoupt A p (.) condition in variable L p spaces

We study the Hardy-Littlewood maximal operator M on . Under the assumptions that the exponent p satisfies and is constant outside some large ball, we prove that if and only if . Received: 2 June 2006 Revised: 28 November 2006     

Laser molecular-beam epitaxy and second-order optical nonlinearity of BaTiO3/SrTiO3 superlattices

A series of c-axis oriented BaTiO₃/SrTiO₃ superlattices with the atomic-scale precision were epitaxially grown on single-crystal SrTiO₃(l00) substrates using laser molecular-beam epitaxy (LMBE). A periodic modulation of the intensity of reflection high-energy electron diffraction (RHEED) in BaTiO₃ and SrTiO₃ layers was observed and attributed to the lattice-misfit-induced periodic variation of the terrace density in film surface. The relationship between the second-order nonlinear optical susceptibilities and the superlattice structure was systematically studied. The experimental and theoretical fitting results indicate that the second-order nonlinear optical susceptibilities of BaTiO₃/SrTiO₃ superlattices were greatly enhanced with the maximum value being more than one order of magnitude larger than that of bulk BaTiO₃ crystal. The mechanism of the enhancement of the second-order optical nonlinearity was discussed by taking into account the stress-induced lattice distortion and polarization enhancement.     

Quasirecognition by the set of element orders of the groups E 6( q ) and 2 E 6( q )

We prove that if L is one of the simple groups E ₆(q) and ² E ₆(q) and G is some finite group with the same spectrum as L, then the commutant of G/F(G) is isomorphic to L and the quotient G/G′ is a cyclic {2,3}-group. Original Russian Text Copyright ? 2007 Kondrat’ev A. S. The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00463) and the RFBR-NSFC (Grant 05-01-39000). __________ Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 6, pp. 1250–1271, November–December, 2007.