Pattern Matching with Swaps

Let a text string T of n symbols and a pattern string P of m symbols from alphabet Σ be given. A swapped version T′ of T is a length n string derived from T by a series of local swaps (i.e., t′_ℓ ← t_ℓ + 1 and t′_ℓ + 1 ← t_ℓ), where each element can participate in no more than one swap. The pattern matching with swaps problem is that of finding all locations i for which there exists a swapped version T′ of T with an exact matching of P in location i of T′. It has been an open problem whether swapped matching can be done in less than O(nm) time. In this paper we show the first algorithm that solves the pattern matching with swaps problem in time o(nm). We present an algorithm whose time complexity is O(nm^1/3 log m log σ) for a general alphabet Σ, where σ = min(m,Σ).     

The method of ascending symmetry for irreducible characters of finite groups

The irreducible characters of a finite group are determined uniquely by those of a minimal set of maximal subgroups. The method is based on the construction of all class functions which are irreducible characters on every maximal subgroup. These are generalized characters by a theorem of Brauer, so that the irreducible characters are obtained by checking the norm. An alternative characterization of irreducible characters, the Maximum Mixing Rule, works for all point symmetry groups, and its physical significance is discussed. As an example, the character tables for all point symmetry groups and crystal double-groups are constructed in this way.Bat-Sheva de Rothschild fellow for 1985     

A bond-order analysis of the mechanism for hydrated proton mobility in liquid water

Bond-order analysis is introduced to facilitate the study of cooperative many-molecule effects on proton mobility in liquid water, as simulated using the multistate empirical valence-bond methodology. We calculate the temperature dependence for proton mobility and the total effective bond orders in the first two solvation shells surrounding the H(5)O(2) (+) proton-transferring complex. We find that proton-hopping between adjacent water molecules proceeds via this intermediate, but couples to hydrogen-bond dynamics in larger water clusters than previously anticipated. A two-color classification of these hydrogen bonds leads to an extended mechanism for proton mobility.     

Channel inclusion of potassium and tetrachloroplatinate ions in a complex formed between 1,3-diamino-2-propanone and K2PtCl4 in an acidic medium

The crystalline complex dipotassium 1,3-diammonio-2-propanone tetrachloroplatinate trihydrate, formulated as K₂[(NH₃CH₂C)₂O][PtCl₄]₂ · 3H₂O, has been prepared while synthesizing complexes analogous tocis-dichlorodiamine Pt(II). Its structure is orthorhombic, space groupPnma,M _r = 896.1,F(000) = 1640,a = 8.428(4),b = 20.360(10),c = 12.141(7)A,V = 2083.3ų,Z = 4,D _x = 2.860 g cm^–3, (MoK _x) = 196 cm^–1, finalR = 0.083 for 1379 unique reflections. The structure consists of a very extended hydrogen bonded network which involves half of the PtCl₄ ^2– ions, the organic molecules and the water molecules of hydration, leaving large oval channels which accommodate potassium cations and tetrachloroplatinate anions. Within the channel the potassium and tetrachloroplatinate ions pack in columns extending along the a axis. The dense packing is rather reminiscent of that found in the neat salt where each potassium ion is surrounded by six chlorine atoms which describe a polyhedron of a distorted trigonal prism with K⁺ —C1 distances ranging between 3.163–3.187 Å. There is some indirect evidence for the formation of 1,3-diammonio-2-propanone dications which counterbalance the charges of half of the PtCl₄ ^2– ions by protonation of each of the amino nitrogens. The carbonyl oxygens, however, are involved only in a very weak O-C-O interactions along thea axis.     

3D Electron Diffraction Structure Determination of Terrylene,a Promising Candidate for Intermolecular Singlet Fission

Herein we demonstrate the prowess of the 3D electron diffraction approach by unveiling the structure of terrylene, the third member in the series of peri-condensed naphthalene analogues, which has eluded structure determination for 65 years. The structure was determined by direct methods using electron diffraction data and corroborated by dispersion-inclusive density functional theory optimizations. Terrylene crystalizes in the monoclinic space group P2₁/a, arranging in a sandwich-herringbone packing motif, similar to analogous compounds. Having solved the crystal structure, we use many-body perturbation theory to evaluate the excited-state properties of terrylene in the solid-state. We find that terrylene is a promising candidate for intermolecular singlet fission, comparable to tetracene and rubrene.