共查询到20条相似文献,搜索用时 172 毫秒
1.
T. H. Mark 《manuscripta mathematica》1974,11(3):211-220
Let (X, ) be a complex space and \(\mathfrak{F}\) a coherent -module. In analogy to the reduction red one can define a reduction \(\mathfrak{F}\) red= \(\mathfrak{F}\) / \(\mathfrak{F}\) ′, where \(\mathfrak{F}\) ′ ? \(\mathfrak{F}\) is the subsheaf of “nilvalent” elements of \(\mathfrak{F}\) . (Even if X is reduced, we may have \(\mathfrak{F}\) ′ ≠ 0.) We prove that \(\mathfrak{F}\) ′ is coherent. Therefore we can construct the sheaf \(\mathfrak{F}\) (2)=( \(\mathfrak{F}\) ′)′ of nilvalent elements with respect to \(\mathfrak{F}\) ′. Iterating this process, we get a sequence ( \(\mathfrak{F}\) (n))n∈N of subsheaves of \(\mathfrak{F}\) . We show that on every compact subset of X the sheaves \(\mathfrak{F}\) (n) vanish for n sufficiently large (Satz 2). 相似文献
2.
Prof. T. Thrivikraman 《Monatshefte für Mathematik》1975,79(2):151-155
In this paper, we obtain analogues, in the situation of \(\mathfrak{E}\) -extensions, of Magill's theorem on lattices of compactifications. We define an epireflective subcategory of the categoryT 2 of all Hausdorff spaces to be admissive (respectively finitely admissive) if for any \(\mathfrak{E}\) -regular spaceX, every Hausdorff quotient of \(\beta _\mathfrak{E} X\) which is Urysohn on \(\beta _\mathfrak{E} X - X\) (respectively which is finitary on \(\beta _\mathfrak{E} X - X\) ) and which is identity onX, has \(\mathfrak{E}\) . We notice that there are many proper epireflective subcategories ofT 2 containing all compact spaces and which are admissive; there are many such which are not admissive but finitely admissive. We prove that when \(\mathfrak{E}\) is a finitely admissive epireflective subcategory ofT 2, then the lattices of finitary \(\mathfrak{E}\) -extensions of two spacesX andY are isomorphic if and only if \(\beta _\mathfrak{E} X - X\) and \(\beta _\mathfrak{E} Y - Y\) are homeomorphic. Further if \(\mathfrak{E}\) is admissive, then the lattices of Urysohn \(\mathfrak{E}\) -extensions ofX andY are isomorphic if and only if \(\beta _\mathfrak{E} X - X\) and \(\beta _\mathfrak{E} Y - Y\) are homeomorphic. 相似文献
3.
Andrea Sorbi 《Archive for Mathematical Logic》1990,30(1):29-48
Let \(\mathfrak{M}\) be the Medvedev lattice: this paper investigates some filters and ideals (most of them already introduced by Dyment, [4]) of \(\mathfrak{M}\) . If \(\mathfrak{G}\) is any of the filters or ideals considered, the questions concerning \(\mathfrak{G}\) which we try to answer are: (1) is \(\mathfrak{G}\) prime? What is the cardinality of \({\mathfrak{M} \mathord{\left/ {\vphantom {\mathfrak{M} \mathfrak{G}}} \right. \kern-0em} \mathfrak{G}}\) ? Occasionally, we point out some general facts on theT-degrees or the partial degrees, by which these questions can be answered. 相似文献
4.
Prof. Dr. Wilfried Nöbauer 《Monatshefte für Mathematik》1975,79(4):317-323
Let \(\mathfrak{B}\) be a variety of rings,R a ring of \(\mathfrak{B}\) andx an indeterminate. The free compositionR(x, \(\mathfrak{B}\) ) ofR and the free algebra of \(\mathfrak{B}\) generated byx, is called the \(\mathfrak{B}\) -polynomial ring inx the variety of rings, rings with identity, commutative rings or commutative rings with identity resp. We prove some results about relations between the polynomial ringsR(x, \(\mathfrak{B}\) ), whereR is fixed and \(\mathfrak{B}\) runs over these varieties. Moreover we construct normal form systems for certain polynomial ringsR(x, \(\mathfrak{B}\) ). 相似文献
5.
O. S. Yakimova 《Functional Analysis and Its Applications》2006,40(1):42-51
The index of a finite-dimensional Lie algebra $\mathfrak{g}$ is the minimum of dimensions of the stabilizers $\mathfrak{g}_\alpha $ over all covectors $\alpha \in \mathfrak{g}^ * $ . Let $\mathfrak{g}$ be a reductive Lie algebra over a field $\mathbb{K}$ of characteristic ≠ = 2. Élashvili conjectured that the index of $\mathfrak{g}_\alpha $ is always equal to the index, or, which is the same, the rank of $\mathfrak{g}$ . In this article, Élashvili’s conjecture is proved for classical Lie algebras. Furthermore, it is shown that if $\mathfrak{g} = \mathfrak{g}\mathfrak{l}_n $ or $\mathfrak{g} = \mathfrak{s}\mathfrak{p}_{2n} $ and $e \in \mathfrak{g}$ is a nilpotent element, then the coadjoint action of $\mathfrak{g}_e $ has a generic stabilizer. For $\mathfrak{g}$ , we give examples of nilpotent elements $e \in \mathfrak{g}$ such that the coadjoint action of $\mathfrak{g}_e $ does not have a generic stabilizer. 相似文献
6.
K. A. Reshko 《Mathematical Notes》1974,16(5):1054-1056
In the theory of formations the concept of an \(\mathfrak{X}\) -normal maximal subgroup is widely used, being some formation [1]. In this note the concept of \(\mathfrak{X}\) normality is introduced for arbitrary subgroups. Subgroups that are not \(\mathfrak{X}\) -normal are called \(\mathfrak{X}\) -abnormal. Finite groups that are not generated by S-abnormal n-th maximal subgroups (n=1, 2, 3, 4) are studied, where S is the formation of all supersolvable groups. The general nature of the results of [3–6] is brought out. 相似文献
7.
V. G. Kanovei 《Mathematical Notes》1975,17(6):563-567
Let \(\mathfrak{M}\) be a fixed countable standard transitive model of ZF+V=L. We consider the structure Mod of degrees of constructibility of real numbers x with respect to \(\mathfrak{M}\) such that \(\mathfrak{M}\) (x) is a model. An initial segment Q \( \subseteq \) Mod is called realizable if some extension of \(\mathfrak{M}\) with the same ordinals contains exclusively the degrees of constructibility of real numbers from Q (and is a model of Z FC). We prove the following: if Q is a realizable initial segment, then $$[y \in Q \to y< x]]\& \forall z\exists y[z< x \to y \in Q\& \sim [y< z]]]$$ . 相似文献
8.
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 .
9.
Mario Marchi 《Journal of Geometry》1983,20(1):95-100
An incidence space \((\beta ,\mathfrak{L})\) which is obtained from an affine space \((\beta _a ,\mathfrak{L}_a )\) by omitting a hyperplane is calledstripe space. If \((\beta _a ,\mathfrak{L}_a )\) is desarguesian, then \(\beta \) can be provided with a group operation “ ○ ” such that \((\beta ,\mathfrak{L}, \circ )\) becomes a kinematic space calledstripe group. It will be shown that there are stripe groups \((\beta ,\mathfrak{L}, \circ )\) where the incidence structure \(\mathfrak{L}\) can be replaced by another incidence structure ? such that \((\beta ,\Re , \circ )\) is afibered incidence group which is not kinematic. An application on translation planes concerning the group of affinities is also given. 相似文献
10.
Hans-Joachim Kroll 《Journal of Geometry》1974,5(1):27-38
Let (P, \(\mathfrak{G}\) ,∥?,∥r) be an incidence space with two parallelisms ∥? and ∥r. (P, \(\mathfrak{G}\) ,∥?,∥r) is called double space [5], if for any two intersecting lines A and B and for any two points a ? A, b ? B the ?-parallel to B through a and the r-parallel to A through b intersect. A double space (P, \(\mathfrak{G}\) ,∥ol,∥r) is called h1-slit, if (P, \(\mathfrak{G}\) ) is a slit space [7] with at most one affine plane through every point of P. We show that every h1-slit double space of at least dimension three contains h1-slit double spaces of dimension three. Every h1-slit double space (P, \(\mathfrak{G}\) , ∥?,∥r) with ∥? ≠ ∥r has dimension three. The h1-slit double spaces of dimension three are characterized. 相似文献
11.
V. A. Baranova 《Mathematical Notes》1969,5(6):444-445
Let \(\mathfrak{M}\) be the set of zeros of the polynomial \(P(z) = \sum\nolimits_{k = 0}^m {A_k S_k (z)} \) , where Sk(z) are functions defined in some region B and the coefficients Ak are arbitrary numbers from the ring $$0 \leqslant \tau _k \leqslant |A_k - a_k | \leqslant R_{_k }< \infty $$ . Conditions necessary and sufficient to ensure that z ∈ \(\mathfrak{M}\) are obtained. 相似文献
12.
E. A. Fernandez-Culma 《Transformation Groups》2012,17(3):639-656
The problem of classifying Einstein solvmanifolds, or equivalently, Ricci soliton nilmanifolds, is known to be equivalent to a question on the variety $ {\mathfrak{N}_n}\left( \mathbb{C} \right) $ of n-dimensional complex nilpotent Lie algebra laws. Namely, one has to determine which GL n (?)-orbits in $ {\mathfrak{N}_n}\left( \mathbb{C} \right) $ have a critical point of the squared norm of the moment map. In this paper, we give a classification result of such distinguished orbits for n?=?7. The set $ {{{{\mathfrak{N}_n}\left( \mathbb{C} \right)}} \left/ {{{\text{G}}{{\text{L}}_7}\left( \mathbb{C} \right)}} \right.} $ is formed by 148 nilpotent Lie algebras and 6 one-parameter families of pairwise non-isomorphic nilpotent Lie algebras. We have applied to each Lie algebra one of three main techniques to decide whether it has a distinguished orbit or not. 相似文献
13.
Kay Sörensen 《Journal of Geometry》1988,31(1-2):159-171
For pseudoaffine spaces (P, \(\mathfrak{G}\) ) of order 3 the following questions are answered: 1) Let τ be a “translation” of (P, \(\mathfrak{G}\) ) which fixes all lines parallel to a given line A. Are lines X,Y ∥ A parallel? 2) Are there pseudoaffine euclidean spaces which are not affine? 3) How are pseudoaffine spaces characterized which are derivated from groups of exponent 3? 相似文献
14.
Dr. Ya§ar Ataman 《Monatshefte für Mathematik》1975,79(4):265-272
In this paper we study the Fourier transform of unbounded measures on a locally compact groupG. After a short introductory section containing background material, especially results established byL. Argabright andJ. Gil De Lamadrid we turn to the main subjects of the paper: first we characterize \(\Re \left( G \right), \mathfrak{J}\left( G \right)\) andB(G) cones in \(\mathfrak{W}\left( G \right)\) . After that we establish the subspace \(\mathfrak{W}_\Delta \left( G \right)\) of \(\mathfrak{W}\left( G \right)\) which contains \(\mathfrak{W}_p \left( G \right)\) , the linear span of all positive definite measures. 相似文献
15.
M. Laczkovich 《Analysis Mathematica》1977,3(3):199-206
qVЕРхНИИ пРЕДЕл пОслЕД ОВАтЕльНОстИ МНОжЕс тВA n ОпРЕДЕльЕтсь сООтНО шЕНИЕМ \(\mathop {\lim sup}\limits_{n \to \infty } A_n = \mathop \cap \limits_{k = 1}^\infty \mathop \cup \limits_{n = k}^\infty A_n . B\) стАтьЕ РАссМАтРИВА Етсь слЕДУУЩИИ ВОпРО с: ЧтО МОжНО скАжАть О ВЕРхНИх пРЕДЕлАх \(\mathop {\lim sup}\limits_{k \to \infty } A_{n_k }\) , еслИ ИжВЕстНО, ЧтО пРЕсЕЧЕНИь \(\mathop \cap \limits_{k = 1}^\infty A_{n_k }\) «МАлы» Дль кАж-ДОИ пОДпОслЕДОВАтЕльНОстИ \((A_{n_k } )\) ? ДОкАжыВАЕтсь, Ч тО
- ЕслИ \(\mathop \cap \limits_{k = 1}^\infty A_{n_k }\) — кОНЕЧНОЕ МНО жЕстВО Дль кАжДОИ пОДпОслЕДОВАтЕльНОстИ \((A_{n_k } )\) , тО НАИДЕтсь тАкАь пОДпО слЕДОВАтЕльНОсть, Дл ь кОтОРОИ МНОжЕстВО \(\mathop {\lim sup}\limits_{k \to \infty } A_{n_k }\) сЧЕтНО;
- ЕслИ \(2^{\aleph _0 } = \aleph _1\) , тО сУЩЕстВУЕ т тАкАь пОслЕДОВАтЕл ьНОсть (An), ЧтО \(\mathop \cap \limits_{k = 1}^\infty A_{n_k }\) — сЧЕтНОЕ МНОжЕстВО Дль лУБОИ п ОДпОслЕДОВАтЕльНОстИ \((A_{n_k } )\) , НО \(\mathop {\lim sup}\limits_{k \to \infty } A_{n_k }\) ИМЕЕт МОЩ-НОсть кОНтИНУУМА;
- ЕслИA n — БОРЕлЕ ВскИЕ МНОжЕстВА В НЕкОтОРО М пОлНОМ сЕпАРАБЕльНО М МЕтРИЧЕскОМ пРОстРАНстВЕ, И \(\mathop \cap \limits_{k = 1}^\infty A_{n_k }\) — сЧЕт НОЕ МНОжЕстВО Дль кАж ДОИ пОДпОслЕДОВАтЕльНОстИ \((A_{n_k } )\) , тО сУЩЕстВУЕт тАкАь п ОДпОслЕДОВАтЕльНОсть, ЧтО \(\mathop {\lim sup}\limits_{k \to \infty } A_{n_k }\) — сЧЕтНОЕ МНОжЕстВО. кРОМЕ тОгО, ДОкАжАНО, Ч тО В слУЧАьх А) И В) В пОслЕДОВАтЕльНОстИ (A n ) сУЩЕстВУЕт схОДьЩА ьсь пОДпОслЕДОВАтЕльНО сть.
16.
Dr. Bernhard Roider 《Monatshefte für Mathematik》1975,79(4):325-332
In Schwartz' terminology, a real or complex valued functionf, defined and infinitely differentiable on ? n , belongs to \(\mathfrak{O}_M \) iff, as well as any of its derivatives, is at most of polynomial growth. The topology of \(\mathfrak{O}_M \) is defined by the seminorms sup{∣?(x)D p f(x)∣;x∈? n }, where ? belongs to \(\mathfrak{S}\) andD p is any derivative. It is well-known that \(\mathfrak{O}_M \) is non-metrisable. For any μ: ? n →?, let \(\mathfrak{B}_\mu \) be the space of all infinitely differentiable functionsf satisfying, for eachp, sup{∣(1+∣x∣2)?μ(p) D p f(x)∣;x∈? n }<∞, with the obvious topology. These spaces, which are of very little use elsewhere in the theory of distributions, can be conveniently applied to characterise the metrisable linear subspaces of \(\mathfrak{O}_M \) : A linear subspace of \(\mathfrak{O}_M \) is metrisable if and only if it is, algebraically and topologically, a subspace of some \(\mathfrak{B}_\mu \) . 相似文献
17.
18.
А. X. гЕРМАН 《Analysis Mathematica》1980,6(2):121-135
LetD be a simply connected domain, the boundary of which is a closed Jordan curveγ; \(\mathfrak{M} = \left\{ {z_{k, n} } \right\}\) , 0≦k≦n; n=1, 2, 3, ..., a matrix of interpolation knots, \(\mathfrak{M} \subset \Gamma ; A_c \left( {\bar D} \right)\) the space of the functions that are analytic inD and continuous on \(\bar D; \left\{ {L_n \left( {\mathfrak{M}; f, z} \right)} \right\}\) the sequence of the Lagrange interpolation polynomials. We say that a matrix \(\mathfrak{M}\) satisfies condition (B m ), \(\mathfrak{M}\) ∈(B m ), if for some positive integerm there exist a setB m containingm points and a sequencen p p=1 ∞ of integers such that the series \(\mathop \Sigma \limits_{p = 1}^\infty \frac{1}{{n_p }}\) diverges and for all pairsn i ,n j ∈{n p } p=1 ∞ the set \(\left( {\bigcap\limits_{k = 0}^{n_i } {z_{k, n_i } } } \right)\bigcap {\left( {\bigcup\limits_{k = 0}^{n_j } {z_{k, n_j } } } \right)} \) is contained inB m . The main result reads as follows. {Let D=z: ¦z¦ \(\Gamma = \partial \bar D\) and let the matrix \(\mathfrak{M} \subset \Gamma \) satisfy condition (Bm). Then there exists a function \(f \in A_c \left( {\bar D} \right)\) such that the relation $$\mathop {\lim \sup }\limits_{n \to \infty } \left| {L_n \left( {\mathfrak{M}, f, z} \right)} \right| = \infty $$ holds almost everywhere on γ. 相似文献
19.
A scalar functionf is called opertor differentiable if its extension via spectral theory to the self-adjoint members of \(\mathfrak{B}\) (H) is differentiable. The study of differentiation and perturbation of such operator functions leads to the theory of mappings defined by the double operator integral $$x \mapsto \smallint \smallint \frac{{f(\lambda ) - f(\mu )}}{{\lambda - \mu }}F(d\mu )xE(d\lambda ).$$ We give a new condition under which this mapping is bounded on \(\mathfrak{B}\) (H). We also present a means of extendingf to a function on all of \(\mathfrak{B}\) (H) and determine corresponding perturbation and differentiation formulas. A connection with the “joint Peirce decomposition” from the theory ofJB *-triples is found. As an application we broaden the class of functions known to preserve the domain of the generator of a strongly continuous one-parameter group of*-automorphisms of aC *-algebra. 相似文献
20.