Degree theory on oriented infinite dimensional varieties and the Morse number of minimal surfaces spanning a curve in ℝn

The algebraic number of disc minimal surfaces spanning a wire in ₃ is defined and shown to be equal to one.The author wishes to acknowledge the support of the NSF.     

Molecular structure of 1,2,4-triazole

The molecular structure of 1,2,4-triazole has been determined by gas phase electron diffraction. The intemuclear distances and bond angles were obtained by applying a least-squares analysis to the experimental intensity. The bond distances (r_g) and bond angles were N₁-N₂ = 1.380 ± 0.010 Å, N₂C₃ = 1.329 ± 0.009 Å, C₃-N₄ = 1.348 ± 0.009 Å, N₁-C₅ = 1.377 ± 0.004 Å, N₄C₅ = 1.305 Å (calculated value). N-H = 0.990 Å, C-H = 1.054 Å, ∠N₁N₂C₃ = 102.7± 0.5°, ∠N₂C₃N₄ = 113.8 ± 1.3°, ∠N₂N₁C₅ = 108.9 ± 0.8°, ∠H₁N₁N₂ = 110.9°, ∠H₂C₃N₄ = 119.2°, ∠H₃C₅N₁ = 131.0°, ∠C₃N₄C₅ = 105.7° (calculated value) and ∠N₄C₅N₁ = 108.7° (calculated value).     

The high resolution mass spectrum of 2-acetamido-1,3,4,6-tetra-O-acetyl-2-deoxy-α-D-glucopyranose

2-Acetamido-1,3,4,6-tetra-O-acetyl-2-deoxy-α-D-glucopyranose (I), and its analogs specifically mono (trideuterioacetylated) at O-1 (III), at N-2 (II), at O-4 (IV) and at O-6 (V), have been examined by high-resolution mass spectrometry. From the elemental compositions of the fragment ions, the mass-number shifts resulting from deuterium incorporation and analysis of metastable transitions, it has been possible to specify in detail the fragmentation pathways undergone by this molecule. The principal degradations of I proceed by initial rapid decomposition of the molecular ion (whose intensity is insignificant) by three routes: (i) by loss of the C-1 acetoxyl group as a radical to give the glycosyl cation (a), (ii) by loss of the 1-acetyl group as a radical to give an acyclic ion m/e 346 (b) and (iii) by loss of a C-6 fragment and acetic acid derived from the 3-acetate group to give m/e 241 (c).     

An additivity principle for Goldie rank

LetA be a noetherian ring. In generalA will not admit a classical Artinian ring of quotients. Yet a problem in enveloping algebras leads one to consider the possible embedding ofA in a prime ringB which is finitely generated as a left and a rightA module. Under certain additional technical assumptions, it is shown that the setS of regular elements ofA is regular inB and is an Ore set in bothA andB withS ⁻¹ A andS ⁻¹ B Artinian. This enables one to establish the following additivity principle for Goldie rank. Let {P ₁,P ₂, …P ₁} be the set of minimal primes ofA. Then under the above conditions it is shown that there exist positive integersz ₁,z ₂, …,z, such that , where rk denotes Goldie rank. This applies to the study of primitive ideals in the enveloping algebra of a complex semisimple Lie algebra. This paper was written while the authors were guests of the Institute for Advanced Studies, The Hebrew University of Jerusalem. The first author was on leave of absence from the Centre Nationale de la Recherche Scientifique, France.     

High electron mobility in solution-cast and vapor-deposited phenacyl-quaterthiophene-based field-effect transistors: toward N-type polythiophenes

New carbonyl-functionalized quaterthiophenes, 5,5' '-diperfluorophenylcarbonyl-2,2':5',2' ':5' ',2' '-quaterthiophene [DFCO-4T], 5,5' '-diphenyl-2,2':5',2' ':5' ',2' '-quaterthiophene [DPCO-4T], and a polymer having the same basic motif as DFCO-4T, poly{1,4-bis[(3'-n-octyl-2,2'-dithiophene)carbonyl]-2,3,5,6-tetrafluorobenzene} [P(COFCO-4T)], have been synthesized, characterized, and the crystal structures of the molecules determined. Field-effect transistors fabricated with vapor-deposited and solution-cast films of DFCO-4T exhibit very high Ion:Ioff current ratios (up to 108) and electron mobilities up to approximately 0.51 and approximately 0.25 cm2.V-1.s-1, respectively. Solution-cast blends of P(COFCO-4T) and DFCO-4T (1:1 weight ratio) exhibit an electron mobility of approximately 0.01 cm2.V-1.s-1 (Ion:Ioff = 104).     

Conformational dependence of the electrostatic potential-derived charges of dopamine: Ramifications in molecular mechanics force field calculations in the gas phase and in aqueous solution

The electrostatic potential-derived charges for the catecholamine neurotransmitter dopamine were calculated at the STO-3G and 6-31G* basis sets for six different molecular conformations. The degree of variance of the charges with changing conformations was examined. The 6-31G* basis set produced charges that were more sensitive to changes in conformation than those derived from the STO-3G electrostatic potentials. The implication of the charge variations in molecular mechanics calculations was also investigated. The molecular mechanics results in the gas phase exhibited a variance depending upon the charge set used. The force field calculations varied much less when aqueous solvation was included in the calculations through a continuum model. © 1993 John Wiley & Sons, Inc.     

Autonomous intelligent agents for accelerated materials discovery

We present an end-to-end computational system for autonomous materials discovery. The system aims for cost-effective optimization in large, high-dimensional search spaces of materials by adopting a sequential, agent-based approach to deciding which experiments to carry out. In choosing next experiments, agents can make use of past knowledge, surrogate models, logic, thermodynamic or other physical constructs, heuristic rules, and different exploration–exploitation strategies. We show a series of examples for (i) how the discovery campaigns for finding materials satisfying a relative stability objective can be simulated to design new agents, and (ii) how those agents can be deployed in real discovery campaigns to control experiments run externally, such as the cloud-based density functional theory simulations in this work. In a sample set of 16 campaigns covering a range of binary and ternary chemistries including metal oxides, phosphides, sulfides and alloys, this autonomous platform found 383 new stable or nearly stable materials with no intervention by the researchers.

We present an end-to-end computational system for autonomous materials discovery.     

Bronsted acid-promoted olefin aziridination and formal anti-aminohydroxylation

A straightforward synthesis of aziridines is reported from an electron-rich azide (alkyl or aryl azide), electron-deficient olefin, and triflic acid in cold acetonitrile. The only coproduct of the reaction is dinitrogen (N2). Active ester substrates bearing a nucleophilic carbonyl engage the putative protonated aziridine intermediate to produce the product of olefin aminohydroxylation in which the nitrogen is benzyl protected and the oxygen is acylated. The possibility that a triazoline need not be an intermediate in aziridine production is advanced.     

A localized basis that allows fast and accurate second-order Moller-Plesset calculations

We present a method for computing a basis of localized orthonormal orbitals (both occupied and virtual), in whose representation the Fock matrix is extremely diagonal dominant. The existence of these orbitals is shown empirically to be sufficient for achieving highly accurate second-order Moller-Plesset (MP2) energies, calculated according to Kapuy's method. This method (which we abbreviate KMP2) involves a different partitioning of the n-electron Hamiltonian and scales at most quadratically, with potential for linearity, in the number of electrons. As such, we believe the KMP2 algorithm presented here could be the basis of a viable approach to local-correlation calculations.