Reactions of Tungsten Propargyl and Allenyl Complexes with Hydrido Triosmium Cluster: Molecular and Crystal Structure of Cp(CO)2[P(OMe)3]W(μ, η1, η2-CH2CH=CH)OS3(CO)10H and H2(CH2CH = CH)2Os6(CO)20

Reactions of H₂Os₃(CO)₁₀, 3, with the monophosphite-substituted and non-substituted tungsten propargyl and allenyl carbonyl complexes Cp(CO)₂LWCH₂C≡CH (1a, L = CO; 1b, L = P(OMe)₃) and Cp(CO)₂LWCH = C = CH₂ (2a, L = CO; 2b, L = P(OMe)₃) were investigated. In the reaction of 1b with 3, a tetranuclear complex 4b is obtained. The molecules of 4b crystallize as Cp(CO)₂[P(OMe)₃]W(μ, η¹, η²-CH₂CH=CH)(μ-H)Os₃(CO)_l0 in space group PI with a = 9.490 (4), b = 13.072 (7), c = 13.770 (9) Å, α = 91.89 (5), β = 106.71 (5), γ = 104.07(4)°, V = 1577(2) ų, Z = 2. In the reaction of 2a with 3, from the reaction mixture exposed to air followed by workup using silica-gel packed column chromatography, a complex consisting of two triosmium clusters bridged by a hexadiene ligand from the coupling of allenyl ligand was obtained. The molecules of the hexanuclear complex crystallize as [CH₂CH = CH)₂(μH)₂OS₆(CO)₂₀in space group P2₁/c with a = 14.448 (7), b = 13.689 (4), c = 19.224 (4) Å, β = 107.14(3)°, V = 3633 (2) Å Z = 4.     

A MNDO study of carbon clusters with specifically fitted parameters

Summary A MNDO method with new parameters for carbon clusters is presented. The parameters in the new sets are specifically tuned to fit the properties of small carbon clusters, C₂, C₃, C₅ and C₇–C₁₀, and buckminsterfullerene, C₆₀. The validity of these MNDO parameters is verified by experimental data. The calculated (with new parameters) IR spectra of C₆₀ and the heat of formation, geometry and IR spectra of C₇₀ agree satisfactorily with observed data. Heats of formation of other fullerenes, from C₂₀ to C₈₄, and C₆₀O are evaluated. The resulting heats of formation of the isomers of C₇₆ and C₈₄ are reliable and their relative stability is in excellent agreement with other reports. The predicted IR spectra of several fullerenes, C₂₄(C_6v ), C₂₈(T _d ), C₃₂(D₃), C₃₆(D_6h ), C₅₀(C_5h ) and C₈₀(D_5d ) are provided to aid assignments of experimental spectra.     

Synthesis of Some New 6,8‐Disubstituted 7,8‐Dihydropyrimido[2,3:4,3]pyrazolo[1,5‐a]pyrimidines and 6,7,8‐Trisubstituted Pyrimido[2,3:4,3]Pyrazolo[1,5‐a]Pyrimidine Derivatives

Cyclization of 5‐cyano‐1,6‐dihydro‐4‐methyl‐2‐phenyl‐6‐thioxopyrimidine 4 with excess of 85% hydrazine hydrate afforded the 3‐amino‐4‐methyl‐6‐phenylpyrazolo[3,4‐d]pyrimidine 5 , which can react with appropriate Mannich base derivatives 13a‐c and chalcones 27a,b to yield the corresponding 6,8‐disubstituted 7,8‐dihydropyrimido[2,3:4,3]pyrazolo[1,5‐a]pyrimidines 15a‐c and 30a,b , respectively. On the other hand, the 6,7,8‐trisubstituted pyrimido[2,3:4,3]pyrazolo[1,5‐a]pyrimidine derivatives 8a‐g, 20a‐e, 36 and 38 were obtained by treatment of compound 5 with appropriate 1,3‐diketones 6a‐g , 3‐dimethylamino‐1‐(substituted)prop‐2‐enones 18a‐e , 3‐aminocrotononitrile 3 , and ethoxymethylenemalononitrile 37 under acidic condition, respectively.     

Complexity analysis of a linear complementarity algorithm based on a Lyapunov function

We consider a path following algorithm for solving linear complementarity problems with positive semi-definite matrices. This algorithm can start from any interior solution and attain a linear rate of convergence. Moreover, if the starting solution is appropriately chosen, this algorithm achieves a complexity of O( L}) iterations, wherem is the number of variables andL is the size of the problem encoding in binary. We present a simple complexity analysis for this algorithm, which is based on a new Lyapunov function for measuring the nearness to optimality. This Lyapunov function has itself interesting properties that can be used in a line search to accelerate convergence. We also develop an inexact line search procedure in which the line search stepsize is obtainable in a closed form. Finally, we extended this algorithm to handle directly variables which are unconstrained in sign and whose corresponding matrix is positive definite. The rate of convergence of this extended algorithm is shown to be independent of the number of such variables.This research is partially supported by the U.S. Army Research Office, contract DAAL03-86-K-0171 (Center for Intelligent Control Systems), and by the National Science Foundation, grant NSF-ECS-8519058.     

The Wall Stresses and Insert Load in a Two‐Dimensional Flat‐bottomed Bin with an Equilateral Triangle Insert

The wall stresses and insert load in a two‐dimensional flat‐bottomed bin with a flow corrective insert were investigated. The static wall stress distributions produced by the granular solids were measured and compared with the theoretical prediction using the differential slice method. The variations in the dynamic wall stresses and the dynamic response of the insert load with time were obtained. The comparison of the experimental insert load to the theoretical prediction was demonstrated. In addition, the effect of the flow corrective insert upon the wall stress and insert load was investigated. As the insert half‐angle increases, the effect of disrupting the contact force network above the insert decreases, and the insert load produced by the granular solids increases. Employing the results obtained using stress measurements, the pulsation phenomena of wall stress and insert load in a bin with a triangle flow corrective insert may be further understood.