Studies of the compositions of Pd(II) hydrolysis products

The characterization of the clusters formed on alkaline hydrolysis of [PdCl₄]^2– was performed using¹⁷O,²³Na,³⁵Cl,¹³³Cs NMR and UV spectroscopy. The chemical composition of the clusters was found to be [Pd(OH)₂] _n ·nNaCl. No mononuclear oxo- or hydroxocomplexes were detected. The spatial structure of the clusters is stabilized by alkali metal cations.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 675–679, April, 1993.     

An infinite family of simply connected flag-transitive tilde geometries

We consider tilde-geometries (orT-geometries), which are geometries belonging to diagrams of the following shape: Here the rightmost edge stands for the famous triple cover of the classical generalized quadrangle related to the group Sp₄(2). The automorphism group of the cover is the nonsplit extension 3·Sp₄(2) – 3 ·S ₆. Five examples of flag-transitiveT-geometries were known. These are rank 3 geometries related to the groupsM ₂₄ (the Mathieu group),He (the Held group) and and 3⁷·Sp₆(2) (a nonsplit extension); a rank 4 geometry related to the Conway groupCo ₁ and a rank 5 geometry related to the Fischer-Griess Monster groupF ₁. In the present paper we construct an infinite family of flag-transitiveT-geometries and prove that all the new geometries are simply connected. The automorphism group of the rankn geometry in the family is a nonsplit extension of a 3-group by the symplectic group Sp_2n (2). The rank of the 3-group is equal to the number of 2-dimensional subspaces in ann-dimensional vector space over GF(2).     

Spin effects in instanton models

Nonperturbative nolocal structure of QCD vacuum is well described by instanton model. Specific helicity and flavor structure of zero modes of quarks, in instanton field allows simultaneously to explain some important features of low-and high-energy hadron phenomemology. The basic characteristics of hadron spectrum, partonic sum rules, heavyquark potential etc within the instanton liquid model are briefly discussed.     

Some remarks on metaplectic cusp forms and the correspondences of Shimura and Waldspurger

The simple relation between representations of the covering groups of SL₂ and GL₂ makes it possible to fuse and extend the recent metaplectic results of Shimura, Waldspurger, Flicker, and ourselves. By giving a new (purely local andL-function theoretic) treatment of the Waldspurger-Shintani correspondence, we also simplify some of Waldspurger’s original results.     

A New Distribution Function for Risk Analysis

This paper presents an alternative to the beta continuous probability distribution for risk analysis. Particular attention has been given to two major applications of distributions, namely project management risk and critical path analysis (PERT). In conjunction with the beta, the triangular and normal distributions are frequently employed in order to give sufficient robustness to risk analysis. The beta distribution, as used in PERT, has a major theoretical implementation flaw. The new distribution was developed to give a possible alternative method of assessing risk. It is shown that the requirement to estimate the most pessimistic variate may be replaced by the probability to exceed the mode. Proposals for other simplifications in risk analysis are discussed. Practical means to validate the most appropriate distributions for risk analysis are outlined, and a cost-data case study is included.     

Existence and Stability for Spherical Crystals Growing in a Supersaturated Solution

We consider the growth of a spherical crystal in a supersaturatedsolution. In the first part, existence and uniqueness resultsfor radially symmetric growth are obtained, provided that thesupersaturation is not too large; conversely, when the far-fieldsupersaturation exceeds a critical value, it is shown that theradially symmetric solution ceases to exist in finite time.In the second part, we examine the linear stability of a radiallysymmetric similarity solution (in which the radius grows ast?) to shape perturbations. The results are compared with previousquasi-static analyses, and, in particular, the critical radiusat which the crystal becomes unstable is found to be largerfor small supersaturations, but smaller for large supersaturations,than those predicted by the quasi-static analysis