Base subsets of symplectic Grassmannians

Let V and V′ be 2n-dimensional vector spaces over fields F and F′. Let also Ω: V× V→ F and Ω′: V′× V′→ F′ be non-degenerate symplectic forms. Denote by Π and Π′ the associated (2n−1)-dimensional projective spaces. The sets of k-dimensional totally isotropic subspaces of Π and Π′ will be denoted by and ${\mathcal G}'_{k}$, respectively. Apartments of the associated buildings intersect and by so-called base subsets. We show that every mapping of to sending base subsets to base subsets is induced by a symplectic embedding of Π to Π′.     

The arithmetic and combinatorics of buildings for

In this paper, we investigate both arithmetic and combinatorial aspects of buildings and associated Hecke operators for with a local field. We characterize the action of the affine Weyl group in terms of a symplectic basis for an apartment, characterize the special vertices as those which are self-dual with respect to the induced inner product, and establish a one-to-one correspondence between the special vertices in an apartment and the elements of the quotient .

We then give a natural representation of the local Hecke algebra over acting on the special vertices of the Bruhat-Tits building for . Finally, we give an application of the Hecke operators defined on the building by characterizing minimal walks on the building for .

     

超长建筑物爆炸泄压特性的试验研究

本文报导了在长径比等于7的7m3长方体试验装置内用液化石油气作的大量试验．定量地给出了液化石油气浓度、点火位置、点火源能量、泄压口封盖物和可燃气局部分布等因素对泄放爆炸压力的影响规律。     

新疆山地森林鸟类的分布及食性和营巢特征的初步研究

通过对新疆山地森林鸟类的考察和研究,将其归结为137种另30亚种,对其分布特征、栖境、食性、营巢进行了研究,并发现鸟类的分布对山地森林的发育情况呈现出某种一致性.     

Hybrid Siloxane-Based Nano Building Blocks for Optical Applications: Optimization of the Synthetic Procedures by Spectroscopic Analysis

Diphenylsilanediol (DPDO) reacts with triethoxysilane (TREOS) in anhydrous conditions and in the presence of pyridine, to form complex mixtures of linear and cyclic condensation products which were identified by ²⁹Si NMR and ATR/FTIR spectroscopies. The distribution of products can be varied by modifying the reaction conditions. Spectroscopic analysis allowed to identify the optimal reagents ratio and concentration for the production of hetero-condensation products minimizing the number of residual –OH groups whose presence would affect the performance of optical waveguides based on the synthesised nano building blocks.     

Compactification of Strictly Convex Real Projective Structures

In this paper we compactify the space of convex real projective structures, known as Hitchin’s component in a representation variety. We give geometric meanings to the boundary points.Mathematics Subject Classifications (2000). 51M10, 57S25.     

MB-GNG: Addressing drawbacks in multi-objective optimization estimation of distribution algorithms

We examine the model-building issue related to multi-objective estimation of distribution algorithms (MOEDAs) and show that some of their, as yet overlooked, characteristics render most current MOEDAs unviable when addressing optimization problems with many objectives. We propose a novel model-building growing neural gas (MB-GNG) network that is specially devised for properly dealing with that issue and therefore yields a better performance. Experiments are conducted in order to show from an empirical point of view the advantages of the new algorithm.     

Expected Sums of General Parking Functions

A (u₁, u₂, . . . )-parking function of length n is a sequence (x₁, x₂, . . . , x_n) whose order statistics (the sequence (x₍₁₎, x₍₂₎, . . . , x_(n)) obtained by rearranging the original sequence in non-decreasing order) satisfy x_(i) u_(i). The Gonarov polynomials g _n (x; a₀, a ₁, . . . , a _n-1) are polynomials biorthogonal to the linear functionals (a _i) Dⁱ, where (a) is evaluation at a and D is differentiation. In this paper, we give explicit formulas for the first and second moments of sums of u-parking functions using Gonarov polynomials by solving a linear recursion based on a decomposition of the set of sequences of positive integers. We also give a combinatorial proof of one of the formulas for the expected sum. We specialize these formulas to the classical case when u _i=a+ (i-1)b and obtain, by transformations with Abel identities, different but equivalent formulas for expected sums. These formulas are used to verify the classical case of the conjecture that the expected sums are increasing functions of the gaps u_i+1 - u_i. Finally, we give analogues of our results for real-valued parking functions.AMS Subject Classification: 05A15, 05A19, 05A20, 05E35.     

Trees, parking functions, syzygies, and deformations of monomial ideals

For a graph , we construct two algebras whose dimensions are both equal to the number of spanning trees of . One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ring modulo certain powers of linear forms. We describe the set of monomials that forms a linear basis in each of these two algebras. The basis elements correspond to -parking functions that naturally came up in the abelian sandpile model. These ideals are instances of the general class of monotone monomial ideals and their deformations. We show that the Hilbert series of a monotone monomial ideal is always bounded by the Hilbert series of its deformation. Then we define an even more general class of monomial ideals associated with posets and construct free resolutions for these ideals. In some cases these resolutions coincide with Scarf resolutions. We prove several formulas for Hilbert series of monotone monomial ideals and investigate when they are equal to Hilbert series of deformations. In the appendix we discuss the abelian sandpile model.

     

Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings

In this paper we shall show that the boundary of the hyperbolic building considered by M. Bourdon admits Poincaré type inequalities. Then by using Heinonen-Koskela's work, we shall prove Loewner capacity estimates for some families of curves of and the fact that every quasiconformal homeomorphism is quasisymmetric. Therefore by these results, the answer to questions 19 and 20 of Heinonen and Semmes (Thirty-three YES or NO questions about mappings, measures and metrics, Conform Geom. Dyn. 1 (1997), 1-12) is NO.