Changes in the thermal expansion coefficient and isothermal compressibility in homological series of n-alcohols at 298 K are discussed. It is shown that only methanol exhibits abnormal behavior. Volumetric coefficients of hypothetical solvents such as pseudo-water and pseudo-methanol are determined. Internal pressure values of liquids are calculated. The internal pressure of pseudo-water exceeds that of water, whereas the situation is opposite for the cohesion energy density. 相似文献
Let χ = {χn}n=0∞ be the Haar system normalized in L2(0, 1) and M = {Ms}s=1∞ be an arbitrary, increasing sequence of nonnegative integers. For any subsystem of χ of the form {φk} = χS = {χn}n∈S, where S = S(M) = {nk}k=1∞ = {n ∈ V[p]: p ∈ M}, V[0] = {1, 2} and V[p] = {2p + 1, 2p + 2, …, 2p+1} for p = 1, 2, … a series of the form Σi=1∞aiφi with ai ↘ 0 is constructed, that is universal with respect to partial series in all classes Lr(0, 1), r ∈ (0, 1), in the sense of a.e. convergence and in the metric ofLr(0, 1). The constructed series is universal in the class of all measurable, finite functions on [0, 1] in the sense of a.e. convergence. It is proved that there exists a series by Haar system with decreasing coefficients, which has the following property: for any ? > 0 there exists a measurable function µ(x), x ∈ [0, 1], such that 0 ≤ µ(x) ≤ 1 and |{x ∈ [0, 1], µ(x) ≠ = 1}| < ?, and the series is universal in the weighted space Lµ[0, 1] with respect to subseries, in the sense of convergence in the norm of Lµ[0, 1]. 相似文献
where denotes a field of characteristic 0 and is an indeterminate. The universal central extension of was determined by Bremner. In this note, we give a presentation for via generators and relations, which highlights a certain symmetry over the alternating group . To obtain our presentation of , we use the realization of as the tetrahedron Lie algebra.
For a connected linear semisimple Lie group , this paper considers those nonzero limits of discrete series representations having infinitesimal character 0, calling them totally degenerate. Such representations exist if and only if has a compact Cartan subgroup, is quasisplit, and is acceptable in the sense of Harish-Chandra.
Totally degenerate limits of discrete series are natural objects of study in the theory of automorphic forms: in fact, those automorphic representations of adelic groups that have totally degenerate limits of discrete series as archimedean components correspond conjecturally to complex continuous representations of Galois groups of number fields. The automorphic representations in question have important arithmetic significance, but very little has been proved up to now toward establishing this part of the Langlands conjectures.
There is some hope of making progress in this area, and for that one needs to know in detail the representations of under consideration. The aim of this paper is to determine the classification parameters of all totally degenerate limits of discrete series in the Knapp-Zuckerman classification of irreducible tempered representations, i.e., to express these representations as induced representations with nondegenerate data.
The paper uses a general argument, based on the finite abelian reducibility group attached to a specific unitary principal series representation of . First an easy result gives the aggregate of the classification parameters. Then a harder result uses the easy result to match the classification parameters with the representations of under consideration in representation-by-representation fashion. The paper includes tables of the classification parameters for all such groups .
In this paper I consider a class of non-standard singular integrals motivated by potential theoretic and probabilistic considerations.
The probabilistic applications, which are by far the most interesting part of this circle of ideas, are only outlined in Section
1.5: They give the best approximation of the solution of the classical Dirichlet problem in a Lipschitz domain by the corresponding solution by finite differences.
The potential theoretic estimate needed for this gives rise to a natural duality between the Lp functions on the boundary ∂Ω and a class of functions A on Ω that was first considered by Dahlberg. The actual duality is given by ∫Ω S f(x)A(x)dx = (f, A) where S f(x) = ∫∂Ω |x − y|1−nf(y)dy is the Newtonian potential.
We can identify the upper half Lipschitz space with in the obvious way and express for an appropriate kernel K. It is the boundedness properties of the above (for , ) that is the essential part of this work. This relates with more classical (but still “rough”) singular integrals that have
been considered by Christ and Journé.
Lecture held in the Seminario Matematico e Fisico on March 14, 2005
Received: April 2007 相似文献
** Email: wching{at}hkusua.hku.hk
In this paper, we propose an Interactive hidden Markov model(IHMM). In a traditional HMM, the observable states are affecteddirectly by the hidden states, but not vice versa. In the proposedIHMM, the transitions of hidden states depend on the observablestates. We also develop an efficient estimation method for themodel parameters. Numerical examples on the sales demand dataand economic data are given to demonstrate the applicabilityof the model. 相似文献
A self-organized model with social percolation process is proposed to describe the propagations of information for different
trading ways across a social system and the automatic formation of various groups within market traders. Based on the market
structure of this model, some stylized observations of real market can be reproduced, including the slow decay of volatility
correlations, and the fat tail distribution of price returns which is found to cross over to an exponential-type asymptotic
decay in different dimensional systems.
Received 15 March 2000 相似文献