On the Extension of PM-Ring

ＯｎｔｈｅＥｘｔｅｎｓｉｏｎｏｆＰＭ－Ｒｉｎｇ朱元森ＯｎｔｈｅＥｘｔｅｎｓｉｏｎｏｆＰＭ－Ｒｉｎｇ￥ＺｈｕＹｕａｎｓｅｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＨｅｂｅｉＴｅａｃｈｅｒｓＵｎｉｖ．，Ｓｈｉｊｉａｘｈｕａｎｇ，０５００１６）Ａｂｓｔｒａｃｔ：Ａｒｉ...     

On the Integral Extension of Lattices

ＯｎｔｈｅＩｎｔｅｇｒａｌＥｘｔｅｎｓｉｏｎｏｆＬａｔｉｃｅｓＨａｎＳｈｉａｎ（韩士安）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＥａｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ，２０００６２）ＡｂｓｔｒａｃｔＩｎｔｈｉｓ...     

Estimation for the Dilatation of the Generalized Beurling-Ahlfors' Extension

51.IntroductionLethbeahomeomorphismontherealaxisR,andsatisfyh(lco)=loo.Wecallaquasisymmetricfunction.lfthereexistsa'constantMsuchthatM-1Sp(x,t)SM,x,teR,(l.2)then(1.2)iscalledtheM-condition-Byvirtueoftheclassicresultofpaper[lj,ifp(x,t)sat-isfiestheM-condition,thenthereexistsaK(M')-quasiconformaIextensiononthel1alfplaneH,whichisthewell-knownBeurling-Ahlfors'extension:ytz)=u(x,y) iv(x,y),whereAfterpaper[lj,manyworkshavebeendoneforestimatingK-Particularly,itshouldbere-markedheretl1atM.Leht…     

An Extension of the Mitrinovi c-Djokovi e Inequality

A certain generalization of the Mitrinovi c-Djokovi c inequality is proved by means of elementary calculus.     

An Extension of the Rényi Formula

In this paper, as a natural extension of the Rényi formula which counts labeled connected unicyclic graphs, we present a formula for the number of labeled(k + 1)-uniform(p, q)-unicycles as follows:U(k+1)p, q={p!/2[(k-1)!]~q·∑qt=2(q~(q-t-1)· sgn(tk- 2))/(q- t)!, p = qk,0, p≠qk,where k, p, q are positive integers.     

Another Extension of the Mitrinovic—Djokovic Inequality

Another generalization of the Mitrinovic-Djokovic inequality is proved by elementarymeans.     

An Extension of the Parallelogram Characterization of Inner Product Spaces

We give in the following a characterization of inner product spaces, of which the well-known parallelogram law and its integral analogue given recently by A.T.Penico and C.V.Stanojevic [1] are special cases.     

Extension of the Set of Complex Hadamard Matrices of Size 8

A complex Hadamard matrix is defined as a matrix H which fulfills two conditions, \(|H_{j,k}|=1\) for all j and k and \(HH^{*}=N \mathbb {I}_N\) where \(\mathbb {I}_N\) is an identity matrix of size N. We explore the set of complex Hadamard matrices \(\mathcal {H}_N\) of size \(N=8\) and present two previously unknown structures: a one-parametric, non-affine family \(T_8^{(1)}\) of complex Hadamard matrices and a single symmetric and isolated matrix \(A_8^{(0)}\).     

A Nonlinear Extension of the Coale–Lopez Theorem

For a sequence (T _n)_nof nonlinear positive operators on a real Banach space, certain monotonicity conditions are specified under which asymptotic equality holds for the inhomogeneous iterates T _n T _n-1 T ₁ T ₀. As a consequence, weak ergodicity or even path stability holds in the norm-topology. Finally, a nonlinear extension of the Coale–Lopez theorem in demography is shown.     

Extension of a Theorem of Carleson-Duren

1. Introduction A theorem of Carleson,as generalized by Duren characterizes those positive measure μ on the unit disc U={z∈C:|z|<1} for which the H~p norm domiates the L~q(μ) norm of elements of H~p. Later on, Hasting proved an analogous results with H~p replaced by A~p, the Bergman space of fuctions f     

An Extension of Bernstein Polynomials on the Semi–Axis

The paper deals with the approximation of functions f on (0,+), where f can be singular at the origin, by means of Bernstein-type sequences. Error estimates in weighted uniform spaces with some converse results are given.Research was supported in part by grant INDAM-GNIM Progetto Equazioni Integrali e Problemi di Algebra Lineare Connessi.     

Free C-Algebras and the Problem of Uniquenes of Extension in Non-commutative Hahn-Banach Theorem

ＦｒｅＣ＊┐ＡｌｇｅｂｒａｓａｎｄｔｈｅＰｒｏｂｌｅｍｏｆＵｎｉｑｕｅｎｅｓｏｆＥｘｔｅｎｓｉｏｎｉｎＮｏｎ┐ｃｏｍｍｕｔａｔｉｖｅＨａｈｎ┐ＢａｎａｃｈＴｈｅｏｒｅｍ＊）ＺｈａｎｇＬｕｎｃｈｕａｎ（张伦传）ａｎｄＭａＪｉｐｕ（马吉溥）（Ｄｅｐａｒｔ...     

Further Extension on a Theorem of the Value Distribution of f＇f^n

By using small function method, the following result is obtained. If f(z) is transcendental meromorphic and that Ψ(z) is non-zero meromorphic and that T(r, Ψ) =S(r, f), then (n 1)T(r,f)≤(-N)(r,1/f'fn-Ψ) 2(-N)(r,1/f) (-N)(r,f) S(r,f).     

An Extension of the Weak Law of Large Numbers for Exchangeable Sequences

We prove an extension of the Kolmogorov-Feller weak law of large numbers for exchangeable sequences, by relaxing the finite mean condition therein.     

Extension of isometries on the unit sphere of l~p (Γ) space

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 p ∞,p≠2) onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto E,so,we give an affirmative answer to the corresponding Tingley's problem.     

Further Extension on a Theorem of the Value Distribution of f′f~n

By using small function method,the following result is obtained.If f(z) is transcendental meromorphic and thatΨ(z) is non-zero meromorphic and that T(r,Ψ)= S(r,f),then (n 1)T(r,f)≤■(r,(1/f′f~n-Ψ)) 2■(r,(1/f)) ■(r,f) S(r,f).     

A Correction on the Paper of ＜A Extension of the Mitrinovit－Djokovie Inequality＞

ＡＣｏｒｒｅｃｔｉｏｎｏｎｔｈｅＰａｐｅｒｏｆ＜ＡＥｘｔｅｎｓｉｏｎｏｆｔｈｅＭｉｔｒｉｎｏｖｉｔ－ＤｊｏｋｏｖｉｅＩｎｅｑｕａｌｉｔｙ＞冯慈璜ＡＣｏｒｒｅｃｔｉｏｎｏｎｔｈｅＰａｐｅｒｏｆ＜ＡＥｘｔｅｎｓｉｏｎｏｆｔｈｅＭｉｔｒｉｎｏｖｉｔ－Ｄｊｏ...     

On the Existence of p-Bases and -Adic p-Bases of a Semi-Local Ring Extension

Let R ^p  ? R′ ? R be a tower of Noetherian semi-local rings of prime characteristic p. When R has locally p-bases over R′ which consist of countably infinite elements, we show the existence of a countably infinite subset {? _i } _i?? of R such that {? _i } _i?? is p-independent over R′, R′[? _i ] _i?? is Noetherian, and R = R′[? _i ] _i?? + ? ^{′ l} R for all l ? ?, where ?′ is the Jacobson radical of R′. Moreover, we consider the existence of p-bases in the case of a tower of semi-local affine k-algebras.