Structure and Properties of Electrodeposited Composite Metal–Nanodisperse Inorganic Compound Coatings

By using the electrodeposition method, composite Sn-inorganic coatings have been obtained. As the inorganic compounds, ultrafine PbMo₆S₈, NbC_xN_y, Ti_xN_y, and Ti_0.63Nb_0.34C_0.38N_0.58 powders were utilized. The Sn–PbMo₆S₈ coatings containing 28-88 wt.% PbMo₆S₈ were superconductive. The highly electroconductive Sn–NbC_xN_y coatings containing 1-88 wt.% of the disperse phase and the Sn–Ti_xN_y coatings with 42-70 wt.% Ti_xN_y were structurally stable at a low temperature (–50°C), solderable, and corrosion resistant on copper. The formation of the structure of the coatings is determined by the electrolyte composition, the cathode current density during the electrolysis, and the codeposition of the disperse phase. By electrodeposition of the chromium carbonitride Cr₃C_1.6N_0.4, in the presence of H₄P₂O₇ in an CrO₃-based electrolyte, mat composite Cr–Cr₃C_1.6N_0.4 coatings with 6.8 wt.% Cr₃C_1.6N_0.4 were obtained, which had a finely uneaven surface structure. Such surfaces are needed in the cases where lubricants are used.     

Nonlocal Symmetries of Integrable Linearly Degenerate Equations: A Comparative Study

We continue the study of Lax integrable equations. We consider four three-dimensional equations: (1) the rdDym equation u_ty = u_xu_xy ? u_yu_xx, (2) the Pavlov equation u_yy = u_tx + u_yu_xx ? u_xu_xy, (3) the universal hierarchy equation u_yy = u_tu_xy ? u_yu_tx, and (4) the modified Veronese web equation u_ty = u_tu_xy ? u_yu_tx. For each equation, expanding the known Lax pairs in formal series in the spectral parameter, we construct two differential coverings and completely describe the nonlocal symmetry algebras associated with these coverings. For all four pairs of coverings, the obtained Lie algebras of symmetries manifest similar (but not identical) structures; they are (semi)direct sums of the Witt algebra, the algebra of vector fields on the line, and loop algebras, all of which contain a component of finite grading. We also discuss actions of recursion operators on shadows of nonlocal symmetries.     

Remarks on a stability problem

The paper considers a system of three differential equations of the following form:x ₁=a₁₁x₁+₂(x₂)+₃(x₃),x ₂=a₂₁x₁+a₂₂x₂+a₂₃x₃,x ₃=a₃₁x₁+a₃₂x₂+a₃₃x₃.It is established that the given system can have periodic solutions if the generalized Routh-Hurwitz conditions hold.Translated from Matematicheskie Zametki, Vol. 10, No. 5, pp. 533–536, November, 1971.     

On the respective terms of the derived and the polycentral series of a free lie algabra and an ideal

Let F be a free Lie algebra of rank> 1 and S be an ideal of F. Denote by F_m and F_{n l},…,n_k the terms of the lower central and the polycentral series of F. The aim of this paper is to provide a sufficient condition for the quotient algebra F_{n l},…,n_k/S_{n l},…,n_k to be infinitely generated. The case F_m/S_m was studied in [6] for free groups and in [ 2 ] for free Lie algebras. In this paper the following main theorem is proved : If F = F2 = S, k > 1 and n_i > 1 for i=l,…, k, then F_{n l}…,n_k/S_{n l} is infinitely generated.     

Distribution of lattice points on surfaces of second order

Let f₁(x₁,..., xl₁) and f₂(y₁,...,yl₂) be positive definite primitive quadratic forms in l₁ and l₂ variables, respectively. We obtain new results in the well-known problem on the number of lattice points on the cone f₁(x₁,...,xl₁)=f₂(y₁,...,yl₂), in the domain f₁(x₁,...,xl₁)≦N for N»∞. Our technical tool is the Rankin-Selberg convolution. In several special cases the results can be sharpened by other methods. In addition, new facts concerning the uniform distribution of lattice points on ellipsoids in l variables, l odd, l≧5 are obtained.     

Some New Optimal Ternary Linear Codes

Let d₃(n,k) be the maximum possible minimum Hamming distance of a ternary [ n,k,d;3]-code for given values of n and k. It is proved that d₃(44,6)=27, d₃(76,6)=48,d₃(94,6)=60 , d₃(124,6)=81,d₃(130,6)=84 , d₃(134,6)=87,d₃(138,6)=90 , d₃(148,6)=96,d₃(152,6)=99 , d₃(156,6)=102,d₃(164,6)=108 , d₃(170,6)=111,d₃(179,6)=117 , d₃(188,6)=123,d₃(206,6)=135 , d₃(211,6)=138,d₃(224,6)=147 , d₃(228,6)=150,d₃(236,6)=156 , d₃(31,7)=17 and d₃(33,7)=18 . These results are obtained by a descent method for designing good linear codes.     

Product spaces and semi-separation axioms

In this paper new characterizations of semi-R₀ and semi-R₁ spaces are obtained and used to prove that the product space of semi-R₀, semi-T₁, and semi-T₀ spaces is, respectively, semi-R₀, semi-T₁, and semi-T₀; and that the product space of semi-R₁ space need not be semi-R₁. An example is given where the product space is semi-T₂ and one of the factor spaces is not semi-T₀ or semi-R₀.     

N.M.R. and I.R. studies of 1, 1, 1 trifluoroacetone in proton donor solvents

Interactions of 1, 1, 1 trifluoroacetone with proton donor solvents of the type RH [where R=HO, CH₃S, CH₃CH₂CH₂CH₂S, CH₃O, (CH₃)₂N, (C₂H₅)₂N] have been investigated using NMR and infra-red techniques. Evidence of the formation of addition products of the type CF₃.C(OH)R.CH₃ where OH group is hydrogen-bonded with the fluorine of the CF₃ group has been obtained.     

Regular sequences in Rees and symmetric algebras,II

In continuing [7] we study necessary and sufficient conditions for a system of elements b₁,...,b_s,a₁,...,a_t of a local Noetherian ring A such that the sequence b₁,...,b_s,a₁T,a₁-a₂T,...,a_t–1-a_tT,a_t in the Rees algebra A[a₁ T,...,a_t T], T is an indeterminate, constitutes a regular sequence.     

The minimum increment of f-divergences given total variation distances

Let (P _i , Q _i ), i = 0, 1, be two pairs of probability measures defined on measurable spaces (Ω _i ,F _i ) respectively. Assume that the pair (P₁, Q₁) is more informative than (P₀,Q₀) for testing problems. This amounts to say that If (P₁,Q₁) ≥ If (P₀,Q₀), where If (·, ·) is an arbitrary f-divergence. We find a precise lower bound for the increment of f-divergences I_f(P₁,Q₁) ? I_f(P₀,Q₀) provided that the total variation distances ||Q₁ ? P₁|| and ||Q₀ ? P₀|| are given. This optimization problem can be reduced to the case where P₁ and Q₁ are defined on the space consisting of four points, and P₀ and Q₀ are obtained from P₁ and Q₁ respectively by merging two of these four points. The result includes the well-known lower and upper bounds for I_f(P,Q) given ||Q ? P||.     

非线性算子具误差的隐迭代程序的强收敛性

设K是一致凸Banach空间中的非空闭凸子集,T_i:K→K(i=1,2,…,N)是有限族完全渐近非扩张映象.对任意的x_0∈K,具误差的隐迭代序列{x_n}为:x_n=α_nx_n-1+β_nT_n~kx_n+γ_nu_n,n≥1,其中{α_n},{β_n},{γ_n}■[0,1]满足α_n+β_n+γ_n=1,{u_n}是K中的有界序列.在一定的条件下,该文建立了隐迭代序列{x_n}的强收敛性.得到隐迭代序列{x_n}强收敛于有限族完全渐近非扩张映象公共不动点的充要条件.所得结果改进和推广了Shahzad与Zegeye,Zhou与Chang,Chang,Tan,Lee与Chan等人的相应结果.     

Phonon spectroscopy and transport properties of Y1-x Nd x Sr2Cu2.7Mo0.3O7-δ

The Raman and infrared spectra, resistivity as well as thermoelectric power of Y_1-xNd_xSr₂Cu_2.7Mo_0.3 O₇ δ(.x =0, 0.1. 0.2. 0.5, 0.8 and 1.0) are studied carefully. It was found that the structure characteristics of RSr₂Cu_2.7Mo_0.3O₇ δ cuprates are different from those of RBa₂Cu₃0₇ δ. The variations of the microstructure in Y_1-x Nd_xSr₂Cu_2.7Mo_0.3O₇ δ with Nd-doping affect the carrier distribution. so as a result the superconductivity changes. Furthermore, it is pointed out that the microstructure variations with the large rare earth ionic substitution cause the widely existing rare earth ionic size effect in HTSC. Project supported by the National Natural Science Foundation of China and the National Center for R & D Superconductivity.     

一四元数矩阵方程组的广义(反)反射解

该文给出了四元数矩阵方程组X_1B_1=C_1,X_2B_2=C2,A_1X_1B_3+A_2X_2B_4=C_b可解的充要条件及其通解的表达式,利用此结果建立了四元数矩阵方程组XB_a=C_a,A_bXB_b=C_b有广义(反)反射解的充要条件及其有此种解时通解的表达式.     

从属解析函数族的有限阶哈达玛乘积

设P[A,B]={f(z):f(z)(?)(1+Az)/(1-Bz),A+B≠0,|B|≤1,f(z)在单位开圆盘内解析}.定义函数族H_1,H_2,…,H_n的有限阶哈达玛乘积为H_1*H_2*H_3…*H_n(z)={f_1*f_2*f_3*…f_n(z):f_i∈H_i,i=1,2,…,n,n∈Z~+}.讨论并得到了P(A_1,B_1)*P(A_2,B_2)*P(A_3,B_3)*…*P(A_n,B_n)=P(X,Y)的充分必要条件,主要结果是对先前相应研究内容的直接推广.     

Prime links in some skew-polynomial and skew-laurent rings

Let R be a Noetherian commutative ring and a α₁,…,α_n commuting automorphisms of R. Define T = R[θ₁,…,θ_n;α₁,…,α_n] to be the skew-polynomial ring with θ_ir = α_i(r)θ_i and θ_iθ_j= θ_jθ_i, for all i,j ? (1,…,n) and r ? R, and let S = Rθ₁,θ₁:^-1,…,θ_n:,θ_n;^-1;α₁:,…,α_n] be the corresponding skew-Laurent ring. In this paper we show that S and T satisfy the strong second layer condition and characterize the links between prime ideals in these rings.     

Estimates in the Carleson corona theorem,ideals of the algebra H∞, a problem of S.-Nagy

Let E₁, E₂, be Hilbert spaces, H^∞(E₁,E₂) be the space of functions, bounded and analytic in the disk D, with values in the space of bounded linear operators from E₁ to E₂. Estimates are investigated for a solution of the problem of S.-Nagy of finding a left inverse element for a function F, FεH^∞(E₁,E₂). For dim E₁=1 this problem is a generalization of the corona problem. Let C_n(δ)= sup_¦G¦_∞∶FεH^∞(E₁,E₂),dim E₁=n, ¦F¦_∞?1, ¦F(z)a¦₂?δ¦a¦₂(zεD,aεE₁);Gε H^∞(E₂,E₁) is a function of minimal norm for which . Then where a_n, C_n are constants depending only on n. The behavior of the function C₁ as δ→1 is described. Other results are obtained also.     

Regular sequences in Rees and symmetric algebras I

In this paper we describe necessary and sufficient conditions for a system of elements a₁,...,a_t of a local Noetherian ring A such that the sequence a₁T,a₁–a₂T,...,a_t–1– a_tT, a_tin the Rees algebra A[a₁T,...,a_tT], T is an indeterminate, constitutes a regular sequence.     

On some characterization of probability distributions in Hilbert spaces

Summary The aim of this paper is to prove the following theorem about characterization of probability distributions in Hilbert spaces:Theorem. — Let x₁, x₂, …, x_n be n (n≥3) independent random variables in the Hilbert spaceH, having their characteristic functionals f_k(t) = E[e^i(t,x _k)], (k=1, 2, …, n): let y₁=x₁ + x_n, y₂=x₂ + x_n, …, y_n−1=x_n−1 + x_n. If the characteristic functional f(t₁, t₂, …, t_n−1) of the random variables (y₁, y₂, …, y_n−1) does not vanish, then the joint distribution of (y₁, y₂, …, y_n−1) determines all the distributions of x₁, x₂, …, x_n up to change of location.     

Some notes on Hermite-Fejer type interpolation

Let S_n(f,x) be the Hermite-Fejér type interpolation satisfying S_n(f,x_k)=f(x_k), S′_n(f,x_k)=0, k=1,2,…,n and S_n(f,y_i)=f(y_i), j=1,2,…,m. For m=0, let H_n(f,x)≔S_n(f,x). This paper investigates relationship between S_n(f,x) and H_n(f,x), as well as, the saturation of S_n(f,x).     

Group of units of group algebras

By a right (left resp.) S_2n-polynomial we mean a multilinear polynomial f(X₁,…, X_t) over the ring of integers with noncommuting in-determinates X_isuch that for any prime ring R if f( X₁,…, X _t) is a PI of some nonzero right (left resp.) ideal of R, then R satisfies S_2nthe standard identity of degree 2n. In this paper we prove the theorem:Let R be a prime ring, d a nonzero derivation of R, L a noncommutative Lie ideal of R and f(X₁,…, X_t) a right or left S_2n-polynomial. Suppose that f(d( u₁)ⁿ¹,…,d(u_t)^nt)=0 for all u_iu,_i[d] L, where n₁,…,n_tare fixed positive integers. Then R satisfies S_2n+2. Also, the one-sided version of the theorem is given.