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1.
Jerzy Płonka 《Algebra Universalis》1981,13(1):82-88
Let \(\mathfrak{X}\) =〈X;R〉 be a relational system.X is a non-empty set andR is a collection of subsets ofX α, α an ordinal. The system of equivalence relations onX having the substitution property with respect to members ofR form a complete latticeC( \(\mathfrak{X}\) ) containing the identity but not necessarilyX×X. It is shown that for any relational system (X;R) there is a groupoid definable onX whose congruence lattice isC( \(\mathfrak{X}\) )U{X×X} . Theorem 2 and Corollary 2 contain some interesting combinatorial pecularities associated with oriented complete graphs and simple groupoids. 相似文献
2.
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.
3.
Svetoslav Ivanov Nenov 《Annali dell'Universita di Ferrara》1996,42(1):121-125
The existence and the uniqueness (with respect to a filtration-equivalence) of a vector flowX on ? n ,n≥3, such that:
- X has not any stationary points on ? n ;
- all orbits ofX are bounded;
- there exists a filtration forX are proved in the present note.
4.
R. H. Redfield 《manuscripta mathematica》1986,56(3):247-268
Let T be an ordered ring without divisors of zero, and letA be the set of archimedean subgroups of T generated by a Banaschewski functionτ. LetXΠΔ R be the power series ring of the real numbers ? over the totally ordered semigroup Δ of archimedean classes of T, and letχ be the usual Banaschewski function onXΠΔ R. The following are equivalent:
- τ satisfies the additional condition; for convex subgroups P,Q of T, where
- There exists a one-to-one homomorphism Γ:T→XΠΔ R of ordered rings such that for every convex subgroup Q ofXΠΔ R, there exists a convex subgroup P of T such that \(\Gamma (P) \subseteq Q\) and \(\Gamma (\tau (P)) \subseteq \chi (Q)\) .
5.
A classification theorem is given of smooth threefolds of ?5 covered by a family of dimension at least three of plane integral curves of degreed≧2. It is shown that for such a threefoldX there are two possibilities:
- X is any threefold contained in a hyperquadric;
- d≦3 andX is either the Bordiga or the Palatini scroll.
6.
If the total degree d has no prime divisors less than(n+3)/2,then we prove that the homotopy type of complex odd dimensional smooth weighted complete intersection Xn(d;w) is determined by the dimension n,the total degree d,the Euler characteristic and the Kervaire invariant,provided that the weights w =(ω0,...,ωn+r) is pairwise relatively prime. 相似文献
7.
Yuri Bilu 《Israel Journal of Mathematics》1995,90(1-3):235-252
LetK be an algebraic number field,S?S \t8 a finite set of valuations andC a non-singular algebraic curve overK. Letx∈K(C) be non-constant. A pointP∈C(K) isS-integral if it is not a pole ofx and |x(P)| v >1 impliesv∈S. It is proved that allS-integral points can be effectively determined if the pair (C, x) satisfies certain conditions. In particular, this is the case if
- x:C→P 1 is a Galois covering andg(C)≥1;
- the integral closure of $\bar Q$ [x] in $\bar Q$ (C) has at least two units multiplicatively independent mod $\bar Q$ *.
8.
Michiro Kondo 《Mathematica Slovaca》2014,64(5):1093-1104
We define states on bounded commutative residuated lattices and consider their property. We show that, for a bounded commutative residuated lattice X,
- If s is a state, then X/ker(s) is an MV-algebra.
- If s is a state-morphism, then X/ker(s) is a linearly ordered locally finite MV-algebra.
- s is a state-morphism on X.
- ker(s) is a maximal filter of X.
- s is extremal on X.
9.
In this article we investigate the analysis of a finite element method for solving H(curl; ??)-elliptic interface problems in general three-dimensional polyhedral domains with smooth interfaces. The continuous problems are discretized by means of the first family of lowest order Nédélec H(curl; ??)-conforming finite elements on a family of tetrahedral meshes which resolve the smooth interface in the sense of sufficient approximation in terms of a parameter ?? that quantifies the mismatch between the smooth interface and the triangulation. Optimal error estimates in the H(curl; ??)-norm are obtained for the first time. The analysis is based on a ??-strip argument, a new extension theorem for H 1(curl; ??)-functions across smooth interfaces, a novel non-standard interface-aware interpolation operator, and a perturbation argument for degrees of freedom for H(curl; ??)-conforming finite elements. Numerical tests are presented to verify the theoretical predictions and confirm the optimal order convergence of the numerical solution. 相似文献
10.
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)),
11.
In this paper, we obtain the following main theorem for a free quadratic bialgebraJ:
- Forp≠0,J is a pointed cosemisimple coalgebra. Forp=0,J is a hyperalgebra.
- Forp≠0 andq≠0,J has antipodeS iffp·q+2=0 andS(x)=x. Forp=0 orq=0,J has antipode andS(x)=×.
- All leftJ *-modules are rational.
12.
Recently, Philippe et al. (C.R. Acad. Sci. Paris. Ser. I 342, 269–274, 2006; Theory Probab. Appl., 2007, to appear) introduced a new class of time-varying fractionally integrated filters A(d)x t =∑ j=0 ∞ a j (t)x t?j , B(d)x t =∑ j=0 ∞ b j (t)x t?j depending on arbitrary given sequence d=(d t ,t∈?) of real numbers, such that A(d)?1=B(?d), B(d)?1=A(?d) and such that when d t ≡d is a constant, A(d)=B(d)=(1?L) d is the usual fractional differencing operator. Philippe et al. studied partial sums limits of (nonstationary) filtered white noise processes X t =B(d)ε t and Y t =A(d)ε t in the case when (1) d is almost periodic having a mean value $\bar{d}\in (0,1/2)$ , or (2) d admits limits d ±=lim? t→±∞ d t ∈(0,1/2) at t=±∞. The present paper extends the above mentioned results of Philippe et al. into two directions. Firstly, we consider the class of time-varying processes with infinite variance, by assuming that ε t ,t∈? are iid rv’s in the domain of attraction of α-stable law (1<α≤2). Secondly, we combine the classes (1) and (2) of sequences d=(d t ,t∈?) into a single class of sequences d=(d t ,t∈?) admitting possibly different Cesaro limits $\bar{d}_{\pm}\in(0,1-(1/\alpha))$ at ±∞. We show that partial sums of X t and Y t converge to some α-stable self-similar processes depending on the asymptotic parameters $\bar{d}_{\pm}$ and having asymptotically stationary or asymptotically vanishing increments. 相似文献
13.
Let X be a topological space upon which a compact connected Lie group G acts. It is well known that the equivariant cohomology H * G (X; Q) is isomorphic to the subalgebra of Weyl group invariants of the equivariant cohomology H * T (X; Q), where T is a maximal torus of G. This relationship breaks down for coefficient rings k other than Q. Instead, we prove that under a mild condition on k the algebra H * G (X; k) is isomorphic to the subalgebra of H * T (X; k) annihilated by the divided difference operators. 相似文献
14.
A code is called distance regular, if for every two codewords x, y and integers i, j the number of codewords z such that d(x, z) = i and d(y, z) = j, with d the Hamming distance, does not depend on the choice of x, y and depends only on d(x, y) and i, j. Using some properties of the discrete Fourier transform we give a new combinatorial proof of the distance regularity of an arbitrary Kerdock code. We also calculate the parameters of the distance regularity of a Kerdock code. 相似文献
15.
J. A. Burns 《Journal of Optimization Theory and Applications》1975,15(4):413-440
The basic problem considered may be described briefly as follows. LetX,Y, andZ be normed linear spaces,T:D(T)→Y,S:D(S)→Z linear operators withD(T) \( \subseteq\) X andD(S) \( \subseteq\) X,Ω \( \subseteq\) X a convex set containing the zero elementθ, andJ a real-valued convex function defined onX×Y such that
- J(x,y)?-0 for (x,y)teX×Y,
- J(θ,θ)=0,
- J(x,y)→+∞, as (∥x∥2+∥y∥2)1/2→+∞.
16.
A. A. Fora 《Periodica Mathematica Hungarica》1985,16(2):97-113
In this paper, we definen-segmentwise metric spaces and then we prove the following results:
- (i)|Let (X, d) be ann-segmentwise metric space. ThenX n has the fixed point property with respect to uniformly continuous bounded functions if and only if, for any continuous functionF: C *(X) → C*(X) and for anyn-tuple of distinct points x1, x2, ?, xn ∈X, there exists anh ∈C *(X) such that $$F(h)(x_1 ) = h(x_1 ),i = 1,2,...,n;$$ whereC *(X) has either the uniform topology or the subspace product (Tychonoff) topology \((C^ * (X) \subseteq X^X )\) .
- LetX i (i = 1, 2, ?) be countably compact Hausdorff spaces such thatX 1 × ? × Xn has the fixed point property for alln ∈N Then the product spaceX 1 × X2 × ? has the fixed point property. We shall also discuss several problems in the Fixed Point Theory and give examples if necessary. Among these examples, we have:
- There exists a connected metric spaceX which can be decomposed as a disjoint union of a closed setA and an open setB such thatA andB have the fixed point property andX does not have.
- There exists a locally compact metrizable spaceX which has the fixed point property but its one-point compactificationX + does not have the fixed point property.
17.
Strong CP(HCP)-netted spaces are defined and some properties are shown. In particular, the following results are shown.
- A submetrizable space is strong CP(HCP)-netted provided that the space admits a perfect map onto a strong CP(HCP)-netted space.
- The image of a strong CP(HCP)-netted space under a perfect map is strong CP(HCP)-netted space.
- A stratifiable space is strong HCP-netted if the space has a countable closed cover consisting of strong HCP-netted subspaces.
18.
Wei Li 《Israel Journal of Mathematics》2014,201(2):989-1012
In this paper, we study the structure of Turing degrees below 0′ in the theory that is a fragment of Peano arithmetic without Σ1 induction, with special focus on proper d-r.e. degrees and non-r.e. degrees. We prove:
- P ? + BΣ1 + Exp ? There is a proper d-r.e. degree.
- P ? +BΣ1+ Exp ? IΣ1 ? There is a proper d-r.e. degree below 0′.
- P ? + BΣ1 + Exp ? There is a non-r.e. degree below 0′.
19.
Alano Ancona 《Arkiv f?r Matematik》1995,33(1):1-44
Letf:V→R be a function defined on a subsetV ofR n ×R d let?:x→inf{f(x t);t such that(x t)∈V} denote theshadow off and letΦ={(x t)∈V; f(x t)=?(x)} This paper deals with the characterization of some properties of ? in terms of the infinitesimal behavior off near points ζ∈Φ proving in particular a conjecture of J M Trépreau concerning the cased=1 Characterizations of this type are provided for the convexity the subharmonicity or theC 1 1 regularity of ? in the interior ofI={x∈ R n;εR d (x t)∈V} and in theC 1 1 case an expression forD 2? is given To some extent an answer is given to the following question: which convex function ?:I→R I interval ?R (resp which function √:I→R of classC 1 1) is the shadow of aC 2 functionf:I×R→R? 相似文献
20.
Wei-Bin Zeng 《Journal of Theoretical Probability》1995,8(1):1-15
LetX 1,X 2, ...,X n be independent and identically distributed random vectors inR d , and letY=(Y 1,Y 2, ...,Y n )′ be a random coefficient vector inR n , independent ofX j /′ . We characterize the multivariate stable distributions by considering the independence of the random linear statistic $$U = Y_1 X_1 + Y_2 X_2 + \cdot \cdot \cdot + Y_n X_n $$ and the random coefficient vectorY. 相似文献