Dichotomies for C0(X) and C b (X) spaces

Jachymski showed that the set $$\left\{ {(x,y) \in {{\rm{c}}_0} \times {{\rm{c}}_0}:\left( {\sum\limits_{i = 1}^n {\alpha (i)x(i)y(i)} } \right)_{n = 1}^\infty {\rm{ is bounded}}} \right\}$$ is either a meager subset of c ₀ × c ₀ or is equal to c ₀ × c ₀. In the paper we generalize this result by considering more general spaces than c ₀, namely C ₀(X), the space of all continuous functions which vanish at infinity, and C _b (X), the space of all continuous bounded functions. Moreover, we replace the meagerness by σ-porosity.     

The Non—standard Characteristics of Functional Spaces K（X） and C0（X）

ＬｅｔＵｂｅａｓｔａｎｄａｒｄｕｎｉｖｅｒｓｅａｎｄＵｂｅａｎｅｎｌａｒｇｅｄｎｏｎｓｔａｎｄａｒｄｕｎｉｖｅｒｓｅｗｉｔｈｒｅｓｐｅｃｔｔｏＵ．ＸｉｓａｔｏｐｏｌｏｇｉｃａｌｓｐａｃｅｗｈｉｃｈｉｎｃｌｕｄｅｄｉｎｔｈｅｉｎｄｉｖｉｄｕａｌｓｅｔｏｆＵ，ｔｈａｔｉｓ，ＸＸ．Ｄｅｆｉｎｉｔｉｏｎ１　Ｆｏｒｅａｃｈｘ∈Ｘ，ｗｅｄｅｆｉｎｅｍ（ｘ）＝∩｛Ｖ：Ｖ∈Ｉｘ｝ａｎｄｃａｌｌｍ（ｘ）ｔｈｅｍｏｎａｄｏｆｘ（Ｉｘｉｓｔｈｅｏｐｅｎｎｅｉｇｈｂｏｒｈｏｏｄｏｆｘ）．Ｗｅｗｒｉｔｅｙ≈ｘｆｏ…     

Peripheral spectrum of positive quasi-compact operators onC 0(X)

LetX be a locally compact space, andT, a quasi-compact positive operator onC ₀(X), with positive spectral radius,r. Then the peripheral spectrum ofT is a finite set of poles containingr, and the residue of the resolvent ofT at each peripheral pole is of finite rank. Using the concept of closed absorbing set, we develop an iterative process that gives the order,p, ofr, some special bases of the algebraic eigenspaces ker(T-r) ^p and ker(T ^*-r) ^p , and finally the dimension of the algebraic eigenspace associated to each peripheral pole.     

Weierstrass Points on X0(pM) and Supersingular j-Invariants

Weierstrass points are special points on a Riemann surface thatcarry a lot of information. Ogg studied such points on X₀(pM)(for M such that X₀(M) has genus zero and p prime with p M),and he proved that if Q is a Q-rational Weierstrass point onX₀(pM), then its reduction modulo p is supersingular. The papershows that, for square-free M on the list, all supersingularj-invariants are obtained in this way. Furthermore, for mostcases where M is prime, the explicit correspondence betweenWeierstrass points and supersingular j-invariants in characteristicp is described. Along the way, a useful formula of Rohrlichfor computing a certain Wronskian of modular forms modulo pis generalized.     

On primitive elements of algebraic function fields and models of $$X_0(N)$$ X 0 ( N )

The Ramanujan Journal - This paper is a continuation of our previous works where we study maps from $$X_0(N)$$ , $$Nge 1$$ , into $${mathbb {P}}^2$$ constructed via modular forms of the same...     

Dual representations of hulls for functions satisfying f (0) = inf f (X\{0}) *

Let Xbe a setW set of extended-real valued functions on Xand 0 an element of Xsuch that w(0) = 0 for all win W. We give a general theory of dual representations, without any extra parameters, of various hulls for extended-real valued functions on X satisfying f(0)= inf f(X\{0})We use the unifying framework of quasi-convex functions with respect to families of subsets of Xand a condition generalizing the bipolar theorem. Our results contain, as particular cases, some recent results of Thach (1991, 1993) and Rubinov and Glover (1996) on W-pseudo-affine and W-quasi-coaffine hulls.We also give some

results in the converse direction. These yield, in particular, that the bipolar theorem is equivalent to a certain property of the lower semi-continuous quasi-convex hulls of functions on locally convex spaces     

高次矩阵方程f（X）=0的一种解法

关于m次矩阵方程Xm+a1Xm-1+…+am-1X+amEn=0,其中En是n阶单位矩阵,a1,a2,…,am∈R,X∈Cn×n,本文利用矩阵的化零多项式,最小多项式的相关结论以及Jordan标准形分解,讨论了该方程的所有可能解.     

Points de petite hauteur sur les courbes modulaires X0(N)

Let N be a square free integer, prime to 6. Let φ the imbeding of X ₀(N) in its Jacobian relative to the point ∞. We show that the set is finite and that is infinite. This explicit form of the Bogomolov conjecture is obtained by an estimation of the self-intersection of the dualizing sheaf, in the sense of Arakelov theory, of modular curves. This result is obtained by estimating several quantities attached to the Arakelov metric on X ₀(N), starting with Petersson's trace formula Oblatum 1-I-1997 & 30-IV-1997     

On polarized 3-folds (X, L) withg(L)=q(X)+1 andh 0(L)≥4

Let (X, L) be a polarized 3-fold over the complex number field. In [Fk3], we proved thatg(L)≥q(X) ifh ⁰(L)≥2 and moreover we classified (X, L) withh ⁰(L)≥3 andg(L)=q(X), whereg(L) is the sectional genus of (X, L) andq(X)=dimH ¹(O _X ) the irregularity ofX. In this paper we will classify polarized 3-folds (X, L) withh ⁰(L)≥4 andg(L)=q(X)+1 by the method of [Fk3].     

Linear Independence of Hecke Operators in the Homology of X0(N)

In Merel's recent proof [7] of the uniform boundedness conjecturefor the torsion of elliptic curves over number fields, a keystep is to show that for sufficiently large primes N, the Heckeoperators T₁, T₂, ..., T_D are linearly independent in theiractions on the cycle e from 0 to i in H₁(X₀(N) (C), Q). In particular,he shows independence when max(D⁸, 400D⁴) < N/(log N)⁴. Inthis paper we use analytic techniques to show that one can chooseD considerably larger than this, provided that N is large.     

Strong barrelledness properties inl 0 ∞ (X A) and bounded finite additive measures

Supported in part by DGICYT, projects 0050 and 0114     

Präsentation der Einheitengruppe der quadratischen FormF(X)=−X 0 2 +X 1 2 +...+X 18 2

Ohne ZusammenfassungZusammenfassung einer Diplomarbeit, die unter der Betreuung von Prof. Dr. Jens Mennicke in Bielefeld geschrieben wurde.     

Full Crossed Products by Coactions, C0(X)-Algebras and C*-Bundles

Let be a coaction of a locally compact group G on a C*-algebraA. We show that if I is a -invariant ideal in A, then for full crossed products, as Landstadet al. have done for spatial crossed products by coactions.We prove that for suitable coactions, the crossed products ofC₀(X)-algebras are again C₀(X)-algebras, and the crossed productsof continuous C*-bundles by a locally compact group are againcontinuous C*-bundles. 1991 Mathematics Subject Classification46L55.     

An algorithm of MCMC method for solving F(X) =0

An algorithm of continuous stage-space MCMC method for solving algebra equation f(x)=0 is given. It is available for the case that the sign of f(x) changes frequently or the derivative f′(x) does not exist in the neighborhood of the root, while the Newton method is hard to work. Let n be the number of random variables created by computer in our algorithm. Then after m=O(n) transactions from the initial value x ₀,x* can be got such that |f(x*)|<e ^−cm |f(x ₀)| by choosing suitable positive constant c. An illustration is also given with the discussion of convergence by adjusting the parameters in the algorithm. Supported by the National Natural Science Foundation of China (70171008).