A New Inequality for Weakly （K1, K2）-Quasiregular Mappings

We obtain a new inequality for weakly （K1,K2）-quasiregular mappings by using the McShane extension method. This inequality can be used to derive the self-improving regularity of （K1, K2）-Quasiregular Mappings.     

Musielak—Orlicz空间L^p（x）（Ω）的若干凸性

本文研究了一类特殊的Musielak-Orlicz空间Lp(x)(Ω)赋予Luxemburg范数时的严格凸性,局部一致凸性,弱局部一致凸性,中点局部一致凸性与一致凸性.利用Banach空间几何学中刻画凸性的一般方法,并结合一般Musielak-Orlicz空间凸性的判别准则,获得了用p(x)刻画空间Lp(x)(Ω)赋予Luxemburg范数时,上述几种凸性的充分必要条件.     

1^∞型极限源于重要极限lim（x→0（1＋x）^1/x，又胜于重要极限

举例说明1^∞型极限比重要极限lim（x→0（1＋x）^1/x更重要.     

EXISTENCE OF THREE SOLUTIONS TO A CLASS OF QUASILINEAR ELLIPTIC SYSTEMS INVOLVING THE（p1（x）, · · ·, pn（x））-LAPLACIAN

In this paper, we investigate a class of Dirichlet quasilinear elliptic systems involving the(p1(x), ···, pn(x))-Laplacian. Based on the general three critical points theorem of B. Ricceri, we prove the existence of at least three weak solutions to the system.     

A note about the cyclotomic polynomial Фpq（x） and some related results

Abstract. The expression of cyclotomic polynomial Фpq （x） is concerned for a long time. A simple and explicit expression of Фpq （x） in Z[x] has been showed. The form of the factors of Фpq （x） over F2 and the upper, lower bounds of their Hamming weight are provided.     

四元空间形式中具有常数K(a)hler角的浸入曲面

对四元K(a)hler流形中的浸入曲面引入了K(a)hler角的概念,同时讨论K(a)hler角是常数的情形.主要结果是:若x:M→N(c)是具有常数Q-截面曲率c的实四维四元空间形式N(c)中具有常数K(a)hler角θ(sinθ≠0)的等距浸入曲面,则必有c=0.     

在空间W_0~(1，x)L~(P(x))(Q)及其共轭空间中的若干收敛性定理

本文证明了在空间W_0~(1,x)L~(p(x))(Q)及其共轭空间中三个收敛性定理.在附加较弱条件的情况下,给出了几乎处处收敛蕴含弱收敛,弱收敛蕴含强收敛.     

H^1（K）空间的J—型与B—型定理

K是局部域,带有非阿基米德模|·|,O是K的整子环,P是O的唯一极大理想,如所周知,O/PGF(q),q=p~c,p为一素数,c∈N。记P~k{x∈K:|x|≤q~(-k)},dx表K~+上Harr测度。对f∈L_(loc)(K),记f(·,K)=f*R(·,K),R(·,K)是Poisson核,K∈Z。空间H~1(K)≡H~1定义如下:     

(x)方程解的关于参数依赖性

本文作者研究拟凸域上的(x)-方程解关于参数的解析依赖性.     

逼近非扩张非自映像不动点（英文）

设E是一致凸Banach空间,K是E中非空闭凸集且是一个非扩张收缩核,T：K→E是具非空不动点集F（T）：={x∈K：Tx=x}的非扩张映像.设{α_n},{β_n},{γ_n},{α′_n},{β′_n},{γ′_n}是[0,1]中实数列满足α_n＋β_n＋γ_n=α′_n＋γ′_n＋γ′_n=1,对任意初值x_1∈K,定义{x_n}如下（ⅰ）如果对偶空间E＊具有Kadec-Klee性质,那么{x_n}弱收敛于T的某不动点x＊∈F（T）;（ⅱ）若T满足（A）条件,那么{x_n}强收敛于T的某不动点x＊∈F（T）.     

On the Elliptic Equation △u ＋ K（x）e^2u -0 with K（x） Positive Somewhere

This paper considers the existence problem of an elliptic equation.which is equivalent to the prescribing conformal Gaussian curvature problem on R2.An existence result is pried.In particular,K(x)is allowed to be unbounded above.     

Regularity for weakly (K 1, K 2(x))-quasiregular mappings of several n-dimensional variables

The definition for weakly (K ₁,K ₂(x))-quasiregular mappings of several n-dimensional variables is given. A regularity property is obtained by using the stability result of Hodge decomposition, some analytical tools of Sobolev spaces, and differential geometry, which can be regarded as a generalization of the results due to T. Iwaniec and Hongya Gao.     

Automorphisms of the semigroup End(K[x 1 , . . . , x n ])

We describe the group G = AutEnd(K[x ₁ , . . . , x _n ]), where K is an arbitrary field. A similar result is obtained also for the automorphism group of the category $ \mathcal{C}{\mathcal{A}^{\circ }} $ of finitely generated free commutative-associative algebras of the variety commutative algebras. This solves two problems posed by B. Plotkin ( [4, Problems 12 and 15]).     

Fields with vanishing K2. Torsion in H1(X,K2) and Ch2(x)

This paper describes fields F of nonzero characteristic with the property that for all finite extensions E/F K₂E=0. We consider a somewhat wider class of fields which includes finite and separably closed fields. For smooth projective varieties X over such a field we show that the groups H¹(X, K₂){} and H²(X_et, (2)), NH³(X_et, (2)) and Ch²(X){} are isomorphic. These results are applied to describe the groups SK₁ of a smooth affine curve over such a field.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 116, pp. 108–118, 1982.     

Ueber die Transcendente FunctionQ(x)=Д(x)−P(x)

Ohne Zusammenfassung     

On the equationx″+f(x)h(x′)x′+g(x)=e(t)

Summary We consider the equation x″+f(x)h(x′)x′+g(x)=e(t) in which f, g, and h are continuous, e is sectionally continuous and absolutely integrable, h(u)>0, xg(x)>0 if x ≠ 0, and f(x)≥0. Necessary and sufficient conditions are given for boundedness of all solutions and their derivatives. When f(0)>(0) we give necessary and sufficient conditions for all solutions and their derivatives to converge to zero. Entrata in Redazione il 14 giugno 1969.     

C1 Solutions of the Iterative Equation G(x, f(x), ..., fn(x)) =F(x)

In this paper we consider the iterative equation G(x,f(x),...,f n(x)) = F(x) on R,and give the existence of C 1 solutions near the fixed point of F,which generalize some results on the leading coefficient problem from the form of the polynomial-like iterative equations to the general form.     

The functional differential equation x′(t) = x(x(t))

A classification of the solutions of the functional differential equation x′(t) = x(x(t)) is given and it is proved that every solution either vanishes identically or is strictly monotonie. For monotonically increasing solutions existence and uniqueness of the solution x are proved with the condition x(t₀) = x₀ where (t₀, x₀) is any given pair of reals in some specified subset of $\text{R}$². Every monotonically increasing solution is thus obtained. It is analytic and depends analytically on t₀ and x₀. Only for t₀ = x₀ = 1 is the question of analyticity still open.