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1.
Stefan Neuwirth 《Journal d'Analyse Mathématique》2008,104(1):371-396
Let Γ be a set of three integers and let
be the space of 2π-periodic functions with spectrum in Γ endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T ∈
and prove that x is unique unless |T| has an axis of symmetry. This enables us to compute the exposed and the extreme points of the unit ball of
, to describe how the maximum modulus of T varies with respect to the arguments of its Fourier coefficients and to compute the norm of unimodular relative Fourier multipliers
on
. We obtain in particular the Sidon constant of Γ. 相似文献
2.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(1):243-252
The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of
a group is subdirectly irreducible. For an MV-algebra
we denote by
, A and
the idempotent modification, the underlying set or the underlying lattice of
, respectively. In the present paper we prove that if
is semisimple and
is a chain, then
is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras. 相似文献
3.
I. S. Kats 《Mathematical Notes》2007,81(3-4):302-307
We establish that the problem of constructing a strictly increasing singular function is equivalent to the problem of constructing subsets and of a closed interval [a; b] ? ? such that (1) ∩ = ø; (2) ∪ = [a; b]; (3) the Lebesgue measures of the intersections of and with an arbitrary interval J ? [a; b] are positive. 相似文献
4.
E. Steingrímsson 《Discrete and Computational Geometry》1994,12(1):465-479
The 2-weak vertex-packing polytope of a loopless graphG withd vertices is the subset of the unitd-cube satisfyingx
i
+x
j
≤1 for every edge (i,j) ofG. The dilation by 2 of this polytope is a polytope
with integral vertices. We triangulate
with lattice simplices of minimal volume and label the maximal simplices with elements of the hyperoctahedral groupB
d
. This labeling gives rise to a shelling of the triangulation
of
, where theh-vector of
(and the Ehrharth
*-vector of
can be computed as a descent statistic on a subset ofB
d
defined in terms ofG. A recursive way of computing theh-vector of
is also given, and a recursive formula for the volume of
.
This work was partially supported by grants from the Icelandic Council of Science and the Royal Swedish Academy of Sciences,
respectively. 相似文献
5.
Anders Björn 《Czechoslovak Mathematical Journal》2006,56(1):179-227
We develop a theory of removable singularities for the weighted Bergman space
, where μ is a Radon measure on ℂ. The set A is weakly removable for
, and strongly removable for
.
The general theory developed is in many ways similar to the theory of removable singularities for Hardy H
p
spaces, BMO and locally Lipschitz spaces of analytic functions, including the existence of counterexamples to many plausible
properties, e.g. the union of two compact removable singularities needs not be removable.
In the case when weak and strong removability are the same for all sets, in particular if μ is absolutely continuous with respect to the Lebesgue measure m, we are able to say more than in the general case. In this case we obtain a Dolzhenko type result saying that a countable
union of compact removable singularities is removable.
When dμ = wdm and w is a Muckenhoupt A
p
weight, 1 < p < ∞, the removable singularities are characterized as the null sets of the weighted Sobolev space capacity with respect to
the dual exponent p′ = p/(p − 1) and the dual weight w′ = w
1/(1 − p). 相似文献
6.
V. A. Solonnikov 《Journal of Mathematical Sciences》2006,135(6):3522-3528
This note is a correction of the proof of Theorem 1.2 in the paper “On a linear problem connected with equilibrium figures
of a uniformly rotating viscous liquid” published in J. Math. Sci. 132 (2006), no. 4, 502–521. The correction concerns the auxiliary problem (3.7)
. where λ ∈ C is a spectral parameter, u(x) = (u1, u2, u3), x ∈
, is a complex-valued vector field, and ρ = ρ(x), x ∈
. Bibliography: 4 titles.
__________
Translated from Problemy Matematicheskogo Analiza, No. 32, 2006, pp. 77–83. 相似文献
7.
A. M. Bikchentaev 《Proceedings of the Steklov Institute of Mathematics》2006,255(1):35-48
Suppose that ? is a von Neumann algebra of operators on a Hilbert space $\mathcal{H}$ and τ is a faithful normal semifinite trace on ?. The set of all τ-measurable operators with the topology t τ of convergence in measure is a topological *-algebra. The topologies of τ-local and weakly τ-local convergence in measure are obtained by localizing t τ and are denoted by t τ1 and t wτ1, respectively. The set with any of these topologies is a topological vector space. The continuity of certain operations and the closedness of certain classes of operators in with respect to the topologies t τ1 and t wτ1 are proved. S.M. Nikol’skii’s theorem (1943) is extended from the algebra $\mathcal{B}(\mathcal{H})$ to semifinite von Neumann algebras. The following theorem is proved: For a von Neumann algebra ? with a faithful normal semifinite trace τ, the following conditions are equivalent: (i) the algebra ? is finite; (ii) t wτ1 = t τ1; (iii) the multiplication is jointly t τ1-continuous from to ; (iv) the multiplication is jointly t τ1-continuous from to ; (v) the involution is t τ1-continuous from to . 相似文献
8.
A monotone structure (
;μ) consists of a structure
and a monotone systemμ over the domain of
.L(Q
n
) is
, enlarged by a newn-ary quantifierQ
n
.
says in (
;μ) that there isU ∈μ such thatϕ[ā] is valid in (
;μ) for allā ∈U
n
. If
is a class of monotone structures,
means thatϕ is valid in all expansions of monotone structures in
. We show for the class
of all ultrafilters that interpolation with respect to
holds forL(Q
n
) exactly in casen=1. Then we prove for a large class of
(e.g. the class of topological groups) thatL(Q
n
) satisfies interpolation with respect to
for alln ≧ 1. Counterexamples indicate that the class of
is sharp in some sense. Finally the results are carried over to certain topological structures and the interior quantifiersI
n
instead ofQ
n
, thereby generalizing results of Makowsky/Ziegler and Sgro, and to a multidimensional type of monotone structures including
uniform spaces. 相似文献
9.
Takaaki Nomura 《Annals of Global Analysis and Geometry》1994,12(1):237-260
We study the set of rankp idempotents in a topologically simple Hilbert Jordan algebra (JH-algebra for short). To produce the differential geometric structure on, we establish Jordan algebraic results concerning the structure of some two-generator subalgebras. We identify geodesics, the Riemannian distance and the sectional curvature of by using the Jordan algebraic structure. 相似文献
10.
K. R. Apt 《Israel Journal of Mathematics》1978,29(2-3):221-238
The connections between inductive definability and models of comprehension are studied. Let
= 〈A, R
l, ...,R
n 〉 be an infinite structure and letI
φ
be a set inductively defined by a formulaφ of the second order language
. We prove that if
is a model of Δ
1
1
-Comprehension relativized toφ, andφ is
-absolute, then for everyη smaller than the height of
(h(
)),I
φ
is in
. If
is aβ-structure which satisfies Σ
1
1
-Comprehension relativized toφ and WF(X), and φ is
-absolute, thenI
φ
is in
and ‖φ| <h (
). These results imply that Barwise-Grilliot theorem is false in the case of uncountable acceptable structures. We also study
the notion of invariant definability over models1 of Δ
1
1
-Comprehension.
This paper is registered as Report ZW 69/76 of the Mathematical Centre. 相似文献
11.
D. Z. Arov 《Journal of Mathematical Sciences》1985,31(1):2645-2659
We consider the class II of operator functions f(z), meromorphic for ¦z¦1, which admit a representation in the form f(z)=f
2
–1
(z)f1(z), where f1(z) is an operatorvalued holomorphic function and f2(z) a scalar-valued bounded holomorphic function, such that the strong limits and coincide a.e. on the unit circle ¦¦=1. We prove that any function of class II can be represented as a block of some J-inner function of class II. We describe all such representations. The results found are applied to the question of realizations of functions of class II as transfer functions of linear systems.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta.im. V. A. Steklova AN SSSR, Vol. 135, pp. 5–30, 1984. 相似文献
12.
P. Koosis 《Journal of Mathematical Sciences》1985,31(1):2687-2693
One says that an entire function f of finite exponential type belongs to the Cartwright class C, if
Let N+(r)(N–(r)) denote the number of zeros of the function f in the disk ¦z¦R, such that Re z0 (Re z<0, respectively). We give a simple derivation of the folfollowing result of importance in the theory of entire functions, from a weak type Kolmogorov inequality.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 76–86, 1984.I am happy to note that this paper was written in connection with the 50th birthday of my friend V. P. Khavin. 相似文献
13.
Let
be a family of two-valued functions defined on ann-element set in which each pair of functions in
satisfy a given intersection condition. For certain intersection conditions we determine the maximal value of
. 相似文献
14.
V. I. Ivanov 《Mathematical Notes》1995,58(6):1269-1275
For any infinitely metrizable compact Abelian groupG; 1pq<,n , the following relations are proved: whereK
pq(G, n, G) is the largest Jackson constant in the approximation of the system of characters by polynomials of ordern, d
pq(G, n, G) is the best Jackson constant,J(L
p(G), Lq(G)) is the Jung constant of the pair of real spaces (L
p(G), Lq(G)), and.Translated fromMatematicheskie Zametki, Vol. 58, No. 6, pp. 828–836, December, 1995.This work was supported by the Russian Foundation for Basic Research under grant No. 95-01-00657. 相似文献
15.
Let
i(L), i(L*) denote the successive minima of a latticeL and its reciprocal latticeL
*, and let [b1,..., b
n
] be a basis ofL that is reduced in the sense of Korkin and Zolotarev. We prove that and, where and
j denotes Hermite's constant. As a consequence the inequalities are obtained forn7. Given a basisB of a latticeL in
m
of rankn andx
m
, we define polynomial time computable quantities(B) and(x,B) that are lower bounds for 1(L) and(x,L), where(x,L) is the Euclidean distance fromx to the closest vector inL. If in additionB is reciprocal to a Korkin-Zolotarev basis ofL
*, then 1(L)
n
*
(B) and.The research of the second author was supported by NSF contract DMS 87-06176. The research of the third author was performed at the University of California, Berkeley, with support from NSF grant 21823, and at AT&T Bell Laboratories. 相似文献
16.
Claudio Bernardi 《Annali dell'Universita di Ferrara》1973,18(1):1-14
Riassunto In questo lavoro si cercano condizioni perchè una classe di algebre simili filtrali sia essa stessa filtrale. Si trova che
se
è una famiglia finita di algebre simili e filtrali, che siano indipendenti (cfr.A. L. Foster [2]), allora anche
è filtrale. Introdotto poi il concetto disemi-indipendenza, si arriva a un risultato analogo per le algebre semifiltrali e a una condizione sufficiente per la semifiltralità di un'algebra
finita. Infine si osserva che i risultati trovati possono essere estesi alle classi ideali.
Summary This paper refers to the concept offiltrale class of similar algebras, which has been introduced byR. Magari in [6]. First I observe that a class of similarfiltrale algebras is not generallyfiltrale, not even if is a finite family of finite algebras. However I find that if is a finite family of similarfiltrale algebras, which are also independent (using this term in the sense ofA. L. Foster [2]), then also isfiltrale. Then introducing the notion of independent varieties, one arrives at a generalization of the above mentioned result. Given then a family of similar algebras , we say that these aresemi-indipendenti if for everyJ⊂I there exists an algebraic functionf J defined in II i so thatf J(x, y)=z wherez i=xi ifi∈J andz i=yi ifi∉J for every . I prove that if is a finite family ofsemifiltrali andsemi-indipendenti algebras, then also issemifiltrale. I also find that a finite algebra, which is simple andsemi-indipendente of itself (in the sense that there exists in a binary algebraic functionf withf(x, y)=<x 0,y 1>) issemifiltrale. Then I give the notion ofsemi-indipendente variety, which leads to some further results. Finally I observe that all these results can be extended to ideal classes of similar algebras.相似文献
17.
This paper introduces the concept of ‘symmetric centres’ of braided monoidal categories. LetH be a Hopf algebra with bijective antipode over a fieldk. We address the symmetric centre of the Yetter-Drinfel’d module category:
and show that a left Yetter-Drinfel’d moduleM belongs to the symmetric centre of
and only ifM is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give
a sufficient and necessary condition for the braid of,
Hℳ to induce the braid of
, or equivalently, the braid of
, whereA is a quantum commutativeH-module algebra 相似文献
18.
Satoru Fujishige 《Mathematical Programming》1984,29(2):125-141
The present paper shows that for any submodular functionf on a crossing family
with
, if the polyhedron
is nonempty, then there exist a unique distributive lattice
with
and a unique submodular function
with
such thatB(f) coincides with the base polyhedron
associated with the submodular system
. Here, iff is integer-valued, thenf
1 is also integer-valued.
Based on this fact, we also show the relationship between the independent-flow problem considered by the author and the minimum
cost flow problem considered by J. Edmonds and R. Giles. 相似文献
19.
We study the complex reflection groups G(r, p, n). By considering these groups as subgroups of the wreath products
, and by using Clifford theory, we define combinatorial parameters and descent representations of G(r, p, n), previously known for classical Weyl groups. One of these parameters is the flag major index, which also has an important
role in the decomposition of these representations into irreducibles. A Carlitz type identity relating the combinatorial parameters
with the degrees of the group, is presented. 相似文献
20.
O. Naselli 《Journal of Optimization Theory and Applications》1996,91(1):81-90
In this paper, we present a class of functions:f:X such that inf
xX
f(x)=
, whereX is a nonempty, finitely compact and convex set in a vector space andB
x
={xX: y aff(X){x:[x, y]X={x}. Our main tool is a recent minimax theorem by Ricceri (Ref. 1). 相似文献