共查询到20条相似文献,搜索用时 24 毫秒
1.
《Indagationes Mathematicae》2021,32(4):847-860
Here, we study some measures that can be represented by infinite Riesz products of 1-periodic functions and are related to the doubling map. We show that these measures are purely singular continuous with respect to Lebesgue measure and that their distribution functions satisfy super-polynomial asymptotics near the origin, thus providing a family of extremal examples of singular measures, including the Thue–Morse measure. 相似文献
2.
N. A. Kuklin 《Proceedings of the Steklov Institute of Mathematics》2015,288(1):99-111
We consider an extremal problem for continuous functions that are nonpositive on a closed interval and can be represented by series in Legendre polynomials with nonnegative coefficients. This problem arises from the Delsarte method of finding an upper bound for the kissing number in the three-dimensional Euclidean space. We prove that the problem has a unique solution, which is a polynomial of degree 27. This polynomial is a linear combination of Legendre polynomials of degrees 0, 1, 2, 3, 4, 5, 8, 9, 10, 20, and 27 with positive coefficients; it has simple root 1/2 and five double roots in (?1, 1/2). We also consider the dual extremal problem for nonnegative measures on [?1, 1/2] and, in particular, prove that an extremal measure is unique. 相似文献
3.
Ronald C. King 《Journal of Combinatorial Theory, Series A》2009,116(2):314-333
The hive model is used to show that the saturation of any essential Horn inequality leads to the factorisation of Littlewood-Richardson coefficients. The proof is based on the use of combinatorial objects known as puzzles. These are shown not only to account for the origin of Horn inequalities, but also to determine the constraints on hives that lead to factorisation. Defining a primitive Littlewood-Richardson coefficient to be one for which all essential Horn inequalities are strict, it is shown that every Littlewood-Richardson coefficient can be expressed as a product of primitive coefficients. Precisely the same result is shown to apply to the polynomials defined by stretched Littlewood-Richardson coefficients. 相似文献
4.
MeiRong Zhang 《中国科学 数学(英文版)》2010,53(10):2573-2588
In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely continuous. By taking Neumann eigenvalues of measure differential equations as an example, we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth functionals. These results can give another explanation for extremal eigenvalues of Sturm-Liouville operators with integrable potentials. 相似文献
5.
Motivated by the work of D. Y. Kleinbock, E. Lindenstrauss, G. A. Margulis, and B. Weiss [8, 9], we explore the Diophantine properties of probability measures invariant under the Gauss map. Specifically, we prove that every such measure which has finite Lyapunov exponent is extremal, i.e., gives zero measure to the set of very well approximable numbers. We show, on the other hand, that there exist examples where the Lyapunov exponent is infinite and the invariant measure is not extremal. Finally, we construct a family of Ahlfors regular measures and prove a Khinchine-type theorem for these measures. The series whose convergence or divergence is used to determine whether or not µ-almost every point is ψ-approximable is different from the series used for Lebesgue measure, so this theorem answers in the negative a question posed by Kleinbock, Lindenstrauss, and Weiss [8]. 相似文献
6.
利用围道估计的方法,刻划在相变点处的平移不变随机串测度,证明了:对二维以上情况,当口充分大时,在临界点处,平移不变随机串测度有且只有两个极点,也即任一平移不变随机串测度都是这两个极点的凸组合. 相似文献
7.
Dominique Simpelaere 《Acta Appl Math》1999,57(2):133-164
In measure theory, one is interested in local behaviours, for example in local dimensions, local entropies or local Lyapunov exponents. It has been relevant to study dynamical systems where one can develop further the study of multifractal and multi-multifractal, particularly when there exist strange attractors or repellers. Multifractal and multi-multifractal refer to a notion of size, which emphasizes the local variations of different values coming from the theory of dynamical systems and generated by the dimension theory of invariant measures. This paper gives some part of the literature in this field. Many results are already known, but the large deviations approach allows us to reprove these results and to obtain quite easily results concerning extremal points and extremal measures. 相似文献
8.
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The estimation of the spectral measure is challenging in practice and virtually impossible in high dimensions. This motivates the problem studied in this work, which is to find universal lower and upper bounds of the extreme Value-at-Risk under practically estimable constraints. That is, we study the infimum and supremum of the extreme Value-at-Risk functional, over the infinite dimensional space of all possible spectral measures that meet a finite set of constraints. We focus on extremal coefficient constraints, which are popular and easy to interpret in practice. Our contributions are twofold. First, we show that optimization problems over an infinite dimensional space of spectral measures are in fact dual problems to linear semi-infinite programs (LSIPs) – linear optimization problems in Euclidean space with an uncountable set of linear constraints. This allows us to prove that the optimal solutions are in fact attained by discrete spectral measures supported on finitely many atoms. Second, in the case of balanced portfolia, we establish further structural results for the lower bounds as well as closed form solutions for both the lower- and upper-bounds of extreme Value-at-Risk in the special case of a single extremal coefficient constraint. The solutions unveil important connections to the Tawn–Molchanov max-stable models. The results are illustrated with two applications: a real data example and closed-form formulae in a market plus sectors framework. 相似文献
9.
The extremal coefficients are the natural dependence measures for multivariate extreme value distributions. For an m-variate distribution 2m distinct extremal coefficients of different orders exist; they are closely linked and therefore a complete set of 2m coefficients cannot take any arbitrary values. We give a full characterization of all the sets of extremal coefficients. To this end, we introduce a simple class of extreme value distributions that allows for a 1-1 mapping to the complete sets of extremal coefficients. We construct bounds that higher order extremal coefficients need to satisfy to be consistent with lower order extremal coefficients. These bounds are useful as lower order extremal coefficients are the most easily inferred from data. 相似文献
10.
It is shown that both the ham sandwich theoremand Richard Rado's theorem on general measure (see [6]), whichis known to be a measure theoretic equivalent of E. Helly'stheorem on convex sets, belong to the same family of resultsabout geometric, extremal properties of measures which are definedon Borel sets in Rn. 相似文献
11.
Kevin Purbhoo 《Journal of Algebraic Combinatorics》2008,28(4):461-480
We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows
they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is that we obtain
bijective proofs of commutativity and associativity for the ring structures defined either of these objects. In particular,
we obtain a new, easy proof of the Littlewood-Richardson rule. Finally we discuss how our operation is related to other known
constructions, particularly jeu de taquin. 相似文献
12.
The multivariate extremal index function is a direction specific extension of the well-known univariate extremal index. Since
statistical inference on this function is difficult it is desirable to have a broad characterization of its attributes. We
extend the set of common properties of the multivariate extremal index function and derive sharp bounds for the entire function
given only marginal dependence. Our results correspond to certain restrictions on the two dependence functions defining the
multivariate extremal index, which are opposed to Smith and Weissman’s (1996) conjecture on arbitrary dependence functions. We show further how another popular dependence measure, the extremal coefficient,
is closely related to the multivariate extremal index. Thus, given the value of the former it turns out that the above bounds
may be improved substantially. Conversely, we specify improved bounds for the extremal coefficient itself that capitalize
on marginal dependence, thereby approximating two views of dependence that have frequently been treated separately. Our results
are completed with example processes.
相似文献
13.
Leonardo Constantin Mihalcea 《Advances in Mathematics》2006,203(1):1-33
We study the T-equivariant quantum cohomology of the Grassmannian. We prove the vanishing of a certain class of equivariant quantum Littlewood-Richardson coefficients, which implies an equivariant quantum Pieri rule. As in the equivariant case, this implies an algorithm to compute the equivariant quantum Littlewood-Richardson coefficients. 相似文献
14.
Ulrich Oppel 《manuscripta mathematica》1973,10(4):359-377
Let ((Xi, Ki, i) iI) be a family of normed measure spaces. We study the extremal points of the convex set F of normed measures on the product of ((Xi, Ki): iI) with the marginal measures i. We give a construction principle for extremal points. If i is the Lebesgue measure on [0, 1] and I is countable, we prove by using this principle that the set of extremal points of F is weakly dense in F. Finally we give a necessary and some sufficient conditions for extremal points in the case that I={1,2} and i is the Lebesgue measure on [0,1] for i=1,2. 相似文献
15.
Muhammed Ali Alan 《Potential Analysis》2013,38(2):457-470
We analyze the supports of weighted equilibrium measures in ? n . We give explicit examples of families of compact sets which arise as the support of a weighted equilibrium measure for some admissible weight w. These examples also give new constructions of plurisubharmonic functions in the Lelong class. We also include a list of open problems on the support of extremal measures which are related to solutions of Monge–Ampère equations. 相似文献
16.
Olaf Mordhorst 《Israel Journal of Mathematics》2017,219(2):529-548
We prove a conjecture of B. Grünbaum stating that the set of affine invariant points of a convex body equals the set of points invariant under all affine linear symmetries of the convex body. As a consequence we give a short proof of the fact that the affine space of affine linear points is infinite dimensional. In particular, we show that the set of affine invariant points with no dual is of the second category. We investigate extremal cases for a class of symmetry measures. We show that the centers of the John and Löwner ellipsoids can be far apart and we give the optimal order for the extremal distance between the two centers. 相似文献
17.
东金文 《中国科学A辑(英文版)》2001,44(11):1373-1380
In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple
proof of the conclusion that every stationary Markov process is a generalized convex combination of stationary ergodic Markov
processes. A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding
stationary Markov process is time ergodic and every stationary distribution is a generalized convex combination of such extremal
ones. We then consider space ergodicity for spin flip particle systems. We prove space shift ergodicity and mixing for certain
extremal invariant measures for a class of spin systems, in which most of the typical models, such as the Voter Models and
the Contact Models, are included. As a consequence of these results we see that for such systems, under each of those extremal
invariant measures, the space and time means of an observable coincide, an important phenomenon in statistical physics. Our
results provide partial answers to certain interesting problems in spin systems. 相似文献
18.
Omri Sarig 《Geometric And Functional Analysis》2010,19(6):1757-1812
Consider a complete hyperbolic surface which can be partitioned into countably many pairs of pants whose boundary components
have lengths less than some constant. We show that any infinite ergodic invariant Radon measure for the horocycle flow is
either supported on a single horocycle associated with a cusp, or corresponds canonically to an extremal positive eigenfunction
of the Laplace–Beltrami operator. 相似文献
19.
It is well known that solutions of ordinary differential equations are continuously dependent on finite-dimensional parameters in equations. In this paper we study the dependence of solutions and eigenvalues of second-order linear measure differential equations on measures as an infinitely dimensional parameter. We will provide two fundamental results, which are the continuity and continuous Fréchet differentiability in measures when the weak? topology and the norm topology of total variations for measures are considered respectively. In some sense the continuity result obtained in this paper is the strongest one. As an application, we will give a natural, simple explanation to extremal problems of eigenvalues of Sturm–Liouville operators with integrable potentials. 相似文献
20.
For general potentials we prove that every canonical Gibbs measure on configurations over a manifold X is quasi‐invariant w.r.t. the group of diffeomorphisms on X. We show that this quasi‐invariance property also characterizes the class of canonical Gibbs measures. From this we conclude that the extremal canonical Gibbs measures are just the ergodic ones w.r.t. the diffeomorphism group. Thus we provide a whole class of different irreducible representations. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献