Effect of ‘Transannular Transmission’ in Dibenzo-18-Crown-6

The effect of the nature of the substituent in the monosubstituted derivatives of dibenzo-18-crown-6 on the reactivity and direction of the electrophilic substitution reaction of the unsubstituted benzene ring has been determined. This transfer is carried out via the macrocycle and therefore is called transannular transmission. The possible mechanism of this transmission is discussed.     

Functional connectedness and Darboux property of multivalued functions

To 80^th birthday of Paul Erds     

Semistable measures and limit theorems on real andp-adic groups

For any locally compact groupG, we show that any locally tight homomorphism from a real directed semigroup intoM ¹ (G) (semigroup of probability measures onG) has a shift which extends to a continuous one-parameter semigroup. IfG is ap-adic algebraic group then the above holds even iff is not locally tight. These results are applied to give sufficient conditions for embeddability of some translate of limits of sequences of the form {v _n ^kn } and M ¹ (G) such that ()= ^M , for somek>1 and AutG (cf. Theorems 2.1, 2.4, 3.7).     

Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant

Summary This work is concerned with the existence and uniqueness of a class of semimartingale reflecting Brownian motions which live in the non-negative orthant of ^d . Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the orthant the process behaves like a Brownian motion with a constant drift and covariance matrix, and at each of the (d-1)-dimensional faces that form the boundary of the orthant, the bounded variation part of the process increases in a given direction (constant for any particular face) so as to confine the process to the orthant. For historical reasons, this pushing at the boundary is called instantaneous reflection. In 1988, Reiman and Williams proved that a necessary condition for the existence of such a semimartingale reflecting Brownian motion (SRBM) is that the reflection matrix formed by the directions of reflection be completely-L. In this work we prove that condition is sufficient for the existence of an SRBM and that the SRBM is unique in law. It follows from the uniqueness that an SRBM defines a strong Markov process. Our results have potential application to the study of diffusions arising as approximations tomulti-class queueing networks.Research supported in part by NSF Grants DMS 8657483, 8722351 and 9023335, and a grant from AT&T Bell Labs. In addition, R.J. Williams was supported in part during the period of this research by an Alfred P. Sloan Research Fellowship     

Theoretical Study on the Structures and Electronic Spectra of the Derivatives of C_(60)-P-2,4,6-Triphenyl Borazinc

1 INTRODUCTION The electron-transfer reaction of C60 derivatives, especially light-induced electron-transfer reaction, has been an active research field for a long time. Many researches are focused on the long-live charge- separated state caused by electron-transfer[1]. And several electron-transfers between electron donor and C60 or intramolecular electron-transfer have been confirmed. As an example, TTF-C60 is proved to be a short-live charge-separated compound[2].Due to the excelle…     

Aminomethylation of (ω-alkylthioalkyl)phenols

The reactions of ()-alkylthioalkyl)phenols with formaldehyde and secondary amines afforded the corresponding aminomethyl derivatives, in which the dimethylamino group may be replaced by the alkylthio group.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1504–1507, June, 1996.     

Characterization of the normal distribution by constant regression of quadratic statistics on linear statistics

This paper contains applications of theorems of [1] for quadratic statistics which have constant regression on linear statistics. Two theorems are proved. The first is a sufficient condition which assumes that the characteristic function of a sample is an entire function. The second gives a new characterization of the normal distribution.     

Mixed strategy solutions forN-person quadratic games

Mixed strategy -equilibrium points are given forN-person games with cost functions consisting of quadratic, bilinear, and linear terms and strategy spaces consisting of closed balls in Hilbert spaces. The results are applied to linear-quadratic differential games with no information and quadratic integral constraints on the control functions.This work was supported by a Commonwealth of Australia, Postgraduate Research Award.     

Linear combination of concomitants of order statistics with application to testing and estimation

Summary Let (X ₁,Y ₁), (X ₂,Y ₂),…, (X _n,Y _n) be i.i.d. as (X, Y). TheY-variate paired with therth orderedX-variateX _rn is denoted byY _rn and terms the concomitant of therth order statistic. Statistics of the form are considered. The asymptotic normality ofT _n is established. The asymptotic results are used to test univariate and bivariate normality, to test independence and linearity ofX andY, and to estimate regression coefficient based on complete and censored samples.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)