共查询到20条相似文献,搜索用时 15 毫秒
1.
Let $\mathcal{K}$ be the family of graphs on ω1 without cliques or independent subsets of sizew 1. We prove that
- it is consistent with CH that everyGε $\mathcal{K}$ has 2ω many pairwise non-isomorphic subgraphs,
- the following proposition holds in L: (*)there is a Gε $\mathcal{K}$ such that for each partition (A, B) of ω1 either G?G[A] orG?G[B],
- the failure of (*) is consistent with ZFC.
2.
Mendel David 《Israel Journal of Mathematics》1971,9(1):34-42
LetH be a separable infinite-dimensional Hilbert space and letC be a normal operator andG a compact operator onH. It is proved that the following four conditions are equivalent.
- C +G is a commutatorAB-BA with self-adjointA.
- There exists an infinite orthonormal sequencee j inH such that |Σ j n =1 (Ce j, ej)| is bounded.
- C is not of the formC 1 ⊕C 2 whereC 1 has finite dimensional domain andC 2 satisfies inf {|(C 2 x, x)|: ‖x‖=1}>0.
- 0 is in the convex hull of the set of limit points of spC.
3.
Z. I. Szabó 《Periodica Mathematica Hungarica》1979,10(4):293-299
Auf einer differenzierbaren Mannigfaltigkeit betrachtet man eine Familie {(U α,α G)} lokaler nichtlinearer Zusammenhänge mit den folgenden Eigenschaften:
- Der nichtlineare Zusammenhangα G ist auf der offenene MengeU α des Tangentenbündels definiert, ferner bedecken die DefinitionsbereichenU α das ganze Tangentenbündel.
- Die Zusammenhangsobjektα G j i (x, y) des Zusammenhangsα G ist iny positiv homogen von erster Ordnung, die Objekten \(_\alpha G_j^i \mathop = \limits^{def} \frac{{\partial _x G_k^i }}{{\partial y^j }}\) sind inj bzw.k symmetrisch, ferner besitzt je zwei Zusammenhang (U α,α G) bzw. (U β,β G) auf der MengenU α∩U β einen gleichen KrümmungstensorK jk i .
4.
The Dual Group of a Dense Subgroup 总被引:1,自引:1,他引:0
W. W. Comfort S. U. Raczkowski F. Javier Trigos-Arrieta 《Czechoslovak Mathematical Journal》2004,54(2):509-533
Throughout this abstract, G is a topological Abelian group and $\hat G$ is the space of continuous homomorphisms from G into the circle group ${\mathbb{T}}$ in the compact-open topology. A dense subgroup D of G is said to determine G if the (necessarily continuous) surjective isomorphism $\hat G \to \hat D$ given by $h \mapsto h\left| D \right.$ is a homeomorphism, and G is determined if each dense subgroup of G determines G. The principal result in this area, obtained independently by L. Außenhofer and M. J. Chasco, is the following: Every metrizable group is determined. The authors offer several related results, including these. 1. There are (many) nonmetrizable, noncompact, determined groups. 2. If the dense subgroup D i determines G i with G i compact, then $ \oplus _i D_i $ determines Πi G i. In particular, if each G i is compact then $ \oplus _i G_i $ determines Πi G i. 3. Let G be a locally bounded group and let G + denote G with its Bohr topology. Then G is determined if and only if G + is determined. 4. Let non $\left( {\mathcal{N}} \right)$ be the least cardinal κ such that some $X \subseteq {\mathbb{T}}$ of cardinality κ has positive outer measure. No compact G with $w\left( G \right) \geqslant non\left( {\mathcal{N}} \right)$ is determined; thus if $\left( {\mathcal{N}} \right) = {\mathfrak{N}}_1 $ (in particular if CH holds), an infinite compact group G is determined if and only if w(G) = ω. Question. Is there in ZFC a cardinal κ such that a compact group G is determined if and only if w(G) < κ? Is $\kappa = non\left( {\mathcal{N}} \right)?\kappa = {\mathfrak{N}}_1 ?$ 相似文献
5.
LetH be a subgroup of a groupG. A normal subgroupN H ofH is said to be inheritably normal if there is a normal subgroup N G of G such that N H = N G ∩ H. It is proved in the paper that a subgroup $N_{G_i }$ of a factor G i of the n-periodic product Π i∈I n G i with nontrivial factors G i is an inheritably normal subgroup if and only if $N_{G_i }$ contains the subgroup G i n . It is also proved that for odd n ≥ 665 every nontrivial normal subgroup in a given n-periodic product G = Π i∈I n G i contains the subgroup G n . It follows that almost all n-periodic products G = G 1 * n G 2 are Hopfian, i.e., they are not isomorphic to any of their proper quotient groups. This allows one to construct nonsimple and not residually finite Hopfian groups of bounded exponents. 相似文献
6.
7.
WEI DaSheng 《中国科学 数学(英文版)》2013,56(2):227-238
We propose a method to determine the solvability of the diophantine equation x2-Dy2=n for the following two cases:(1) D = pq,where p,q ≡ 1 mod 4 are distinct primes with(q/p)=1 and(p/q)4(q/p)4=-1.(2) D=2p1p2 ··· pm,where pi ≡ 1 mod 8,1≤i≤m are distinct primes and D=r2+s2 with r,s ≡±3 mod 8. 相似文献
8.
Horst Herrlich 《Applied Categorical Structures》1996,4(1):1-14
In the absence of the axiom of choice four versions of compactness (A-, B-, C-, and D-compactness) are investigated. Typical results:
- C-compact spaces form the epireflective hull in Haus of A-compact completely regular spaces.
- Equivalent are:
- the axiom of choice,
- A-compactness = D-compactness,
- B-compactness = D-compactness,
- C-compactness = D-compactness and complete regularity,
- products of spaces with finite topologies are A-compact,
- products of A-compact spaces are A-compact,
- products of D-compact spaces are D-compact,
- powers X k of 2-point discrete spaces are D-compact,
- finite products of D-compact spaces are D-compact,
- finite coproducts of D-compact spaces are D-compact,
- D-compact Hausdorff spaces form an epireflective subcategory of Haus,
- spaces with finite topologies are D-compact.
- Equivalent are:
- the Boolean prime ideal theorem,
- A-compactness = B-compactness,
- A-compactness and complete regularity = C-compactness,
- products of spaces with finite underlying sets are A-compact,
- products of A-compact Hausdorff spaces are A-compact,
- powers X k of 2-point discrete spaces are A-compact,
- A-compact Hausdorff spaces form an epireflective subcategory of Haus.
- Equivalent are:
- either the axiom of choice holds or every ultrafilter is fixed,
- products of B-compact spaces are B-compact.
- Equivalent are:
- Dedekind-finite sets are finite,
- every set carries some D-compact Hausdorff topology,
- every T 1-space has a T 1-D-compactification,
- Alexandroff-compactifications of discrete spaces and D-compact.
9.
If γ(x)=x+iA(x),tan ?1‖A′‖∞<ω<π/2,S ω 0 ={z∈C}| |argz|<ω, or, |arg(-z)|<ω} We have proved that if φ is a holomorphic function in S ω 0 and \(\left| {\varphi (z)} \right| \leqslant \frac{C}{{\left| z \right|}}\) , denotingT f (z)= ∫?(z-ζ)f(ζ)dζ, ?f∈C 0(γ), ?z∈suppf, where Cc(γ) denotes the class of continuous functions with compact supports, then the following two conditions are equivalent:
- T can be extended to be a bounded operator on L2(γ);
- there exists a function ?1 ∈H ∞(S ω 0 ) such that ?′1(z)=?(z)+?(-z), ?z∈S ω 0 ?z∈S w 0 .
10.
Jacques Wolfmann 《Designs, Codes and Cryptography》2000,20(1):73-88
Let R=GR(4,m) be the Galois ring of cardinality 4m and let T be the Teichmüller system of R. For every map λ of T into { -1,+1} and for every permutation Π of T, we define a map φ λ Π of Rinto { -1,+1} as follows: if x∈R and if x=a+2b is the 2-adic representation of x with x∈T and b∈T, then φ λ Π (x)=λ(a)+2Tr(Π(a)b), where Tr is the trace function of R . For i=1 or i=-1, define D i as the set of x in R such thatφ λ Π =i. We prove the following results: 1) D i is a Hadamard difference set of (R,+). 2) If φ is the Gray map of R into ${\mathbb{F}}_2^{2m}$ , then (D i) is a difference set of ${\mathbb{F}}_2^{2m}$ . 3) The set of D i and the set of φ(D i) obtained for all maps λ and Π, both are one-to-one image of the set of binary Maiorana-McFarland difference sets in a simple way. We also prove that special multiplicative subgroups of R are difference sets of kind D i in the additive group of R. Examples are given by means of morphisms and norm in R. 相似文献
11.
Mehdi Shabani Attar 《Archiv der Mathematik》2009,93(5):399-403
Let G be a nonabelian finite p-group. A longstanding conjecture asserts that G admits a noninner automorphism of order p. In this paper, we prove that if G satisfies one of the following conditions
- ${\mathrm{rank}(G'\cap Z(G))\neq \mathrm{rank}(Z(G))}$
- ${\frac{Z_{2}(G)}{Z(G)}}$ is cyclic
- C G (Z(Φ(G))) = Φ(G) and ${\frac{Z_{2}(G)\cap Z(\Phi(G))}{Z(G)} }$ is not elementary abelian of rank rs, where r = d(G) and s = rank (Z(G)),
12.
LetX be ann-element set and letA and? be families of subsets ofX. We say thatA and? are crosst-intersecting if |A ∩ B| ≥ t holds for all A ∈A and for allB ∈ ?. Suppose thatA and ? are crosst-intersecting. This paper first proves a crosst-intersecting version of Harper's Theorem:
- There are two crosst-intersecting Hamming spheresA 0,? 0 with centerX such that |A| ≤ |A 0| and|?| ≤ |? 0| hold.
- Suppose thatt ≥ 2 and that the pair of integers (|A) is maximal with respect to direct product ordering among pairs of crosst-intersecting families. Then,A and? are Hamming spheres with centerX.
- Ifn + t = 2k ? 1 then |A| |?| ≤ max \(\left\{ {\left( {K_k^n + \left( {_{k - 1}^{n - 1} } \right)} \right)^2 ,K_k^n K_{k - 1}^n } \right\}\) holds, whereK l n is defined as \(\left( {_n^n } \right)\left( {_{n - 1}^n } \right) + \cdots + \left( {_l^n } \right).\)
- Ifn + t = 2k then |A| |? ≤ (K k n )2 holds.
13.
Moti Gitik 《Israel Journal of Mathematics》1995,92(1-3):61-112
The strength of precipitousness, presaturatedness and saturatedness of NSκ and NS κ λ is studied. In particular, it is shown that:
- The exact strength of “ $NS_{\mu ^ + }^\lambda $ for a regularμ > max(λ, ?1)” is a (ω,μ)-repeat point.
- The exact strength of “NSκ is presaturated over inaccessible κ” is an up-repeat point.
- “NSκ is saturated over inaccessible κ” implies an inner model with ?αo(α) =α ++.
14.
Let Ks be the canonical bundle on a non singular projective surface S (over an algebraically closed field F, char F=p) and L be a very ample line bundle on S. Suppose (S,L) is not one of the following pairs: (P2,O(e)), e=1,2, a quadric, a scroll, a Del Pezzo surface, a conic bundle. Then
- (Ks?L)2 is spanned at each point by global sections. Let \(\phi :S \to P^N _F \) be the map given by the sections Γ(Ks?L)2, and let φ=s o r its Stein factorization.
- r:S→S′=r(S) is the contraction of a finite number of lines, Ei for i=1,...r, such that Ei·Ei=KS·Ei=?L·Ei=?1.
- If h°(L)≥6 and L·L≥9, then s is an embedding.
15.
Enumerating rooted simple planar maps 总被引:1,自引:0,他引:1
刘彦佩 《应用数学学报(英文版)》1985,2(2):101-111
The main purpose of this paper is to find the number of combinatorially distinct rooted simpleplanar maps,i.e.,maps having no loops and no multi-edges,with the edge number given.We haveobtained the following results.1.The number of rooted boundary loopless planar [m,2]-maps.i.e.,maps in which there areno loops on the boundaries of the outer faces,and the edge number is m,the number of edges on theouter face boundaries is 2,is(?)for m≥1.G_0~N=0.2.The number of rooted loopless planar [m,2]-maps is(?)3.The number of rooted simple planar maps with m edges H_m~s satisfies the following recursiveformula:(?)where H_m~(NL) is the number of rooted loopless planar maps with m edges given in [2].4.In addition,γ(i,m),i≥1,are determined by(?)for m≥i.γ(i,j)=0,when i>j. 相似文献
16.
S. V. Belyutin 《Theoretical and Mathematical Physics》1997,110(2):190-198
It is shown that the multiwave nonlinear Schrödinger equation describing the evolution of several quasimonochromatic waves having the same group velocities is not exactly integrable (in the sense that no infinite sequence of local conservation laws and symmetries exists). The exact integrability for systems of the form w t i =αiw xx i +a klm i wkwlwm is investigated, where αi are different from zero. 相似文献
17.
We consider the weighted space W 1 (2) (?,q) of Sobolev type $$W_1^{(2)} (\mathbb{R},q) = \left\{ {y \in A_{loc}^{(1)} (\mathbb{R}):\left\| {y''} \right\|_{L_1 (\mathbb{R})} + \left\| {qy} \right\|_{L_1 (\mathbb{R})} < \infty } \right\} $$ and the equation $$ - y''(x) + q(x)y(x) = f(x),x \in \mathbb{R} $$ Here f ε L 1(?) and 0 ? q ∈ L 1 loc (?). We prove the following:
- The problems of embedding W 1 (2) (?q) ? L 1(?) and of correct solvability of (1) in L 1(?) are equivalent
- an embedding W 1 (2) (?,q) ? L 1(?) exists if and only if $$\exists a > 0:\mathop {\inf }\limits_{x \in R} \int_{x - a}^{x + a} {q(t)dt > 0} $$
18.
LetG be a lattice inR n and letS 1 ,S 2 , ... be the family of unit spheres whose centres are the lattice-points ofG. This set is called ak-fold lattice packing (k-fold lattice covering) if each point ofR n lies in at most (at least)k of the open (closed) spheresS i . Letd k n be the density of the closestk-fold lattice packing and letD k n be the density of the thinnestk-fold lattice covering ofR n . In the present paper we are considering the following problem: For which valuesn≧2 andk≧2 are the inequalitiesd k n >kd 1 n ,D k n 1 n valid?Theorem 1:For all pairs (n, k), n≧3, k≧2, with the exception of (3, k), (4, k), k=3, 5, 7, 9, 11 and (5, 3) we prove d k n >kd 1 n .Theorem 2:For each k≧3 is D k 2 1 2 . The proofs make use of the works ofBlundon, Danzer, Few andHeppes. 相似文献
19.
Rolf Trautner 《Analysis Mathematica》1988,14(2):111-122
Рассматриваются слу чайная величина \(\mathfrak{X} = (X_n (\omega ))\) , удовлетворяющая усл овиюE(X n 4 )≦M, и соответствующ ий случайный степенн ой ряд \(f_x (z;\omega ) = \mathop \sum \limits_{n = 0}^\infty a_n X_n (\omega )z^n\) . Устанавливаются тео ремы непродолжимост и почти наверное:
- дляf x при условиях с лабой мультипликати вности на \(\mathfrak{X}\) ,
- для \(f_{\tilde x}\) , где \(\mathop \mathfrak{X}\limits^ \sim = (\mathop X\limits^ \sim _n )\) есть подп оследовательность в \(\mathfrak{X}\) ,
- для по крайней мере од ного из рядовf x′ илиf x″ , где \(\mathfrak{X}'\) и \(\mathfrak{X}''\) — некоторые п ерестановки \(\mathfrak{X}\) , выбираемые универс ально, т. е. независимо от коэффициентовa n .
20.
Johan Philip 《Mathematical Programming》1972,2(1):207-229
We consider a convex setB inR n described as the intersection of halfspacesa i T x ≦b i (i ∈ I) and a set of linear objective functionsf j =c j T x (j ∈ J). The index setsI andJ are allowed to be infinite in one of the algorithms. We give the definition of theefficient points ofB (also called functionally efficient or Pareto optimal points) and present the mathematical theory which is needed in the algorithms. In the last section of the paper, we present algorithms that solve the following problems:
- To decide if a given point inB is efficient.
- To find an efficient point inB.
- To decide if a given efficient point is the only one that exists, and if not, find other ones.
- The solutions of the above problems do not depend on the absolute magnitudes of thec j. They only describe the relative importance of the different activitiesx i. Therefore we also consider $$\begin{gathered} \max G^T x \hfill \\ x efficient \hfill \\ \end{gathered} $$ for some vectorG.