Stochastic relaxed inertial forward-backward-forward splitting for monotone inclusions in Hilbert spaces

Computational Optimization and Applications - We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose...     

Measurable,nonleavable gambling problems

The optimal return function for a Borel measurable gambling problem with a bounded utility function was shown by Strauch (1967) to be universally measurable when the problem is leavable in the sense that the gambler may terminate play at any time. The same is shown here for the more general class of nonleavable problems. Research supported by National Science Foundation Grant DMS-8801085.     

Analysis of numerical integration in p-version finite element eigenvalue approximation

We study the effect of numerical integration when the p-version of the finite element method is used to approximate the eigenpairs of elliptic partial differential operators. We obtain optimal orders of convergence for approximate eigenvalues and eigenvectors under a certain set of requirements on the quadrature rules employed. This is the same set of conditions that has been shown (in an earlier work) to be sufficient for the optimal approximation of the solutions of the corresponding source problems.     

Studies towards the total synthesis of (−)-borrelidin: a strategy for the construction of the C11-C15 cyanodiene fragment and the utility of RCM for macrocyclization using model systems

We report here a methodology for the construction of a conjugated cyanodiene synthon and the propensity of such synthons to participate in the olefin metathesis reaction. To this end, we have developed a strategy for the construction of the C11-C15 fragment of borrelidin and demonstrated the utility of the RCM reaction in the preparation of the final macrolide. To our knowledge, this is the first example of a RCM with a nitrile functionality on a diene.     

Melt-polymerizable bisimido-bisphthalonitriles containing silicon,fluoro, and ether groups: Synthesis,characterization, and NMR study

Various melt-polymerizable bisimido-bisphthalonitrile polymer precursors were synthesized by the reaction of 4-aminophthalonitrile (4-APN) with bis(3,4-dicarboxyphenyl) dimethylsilane dianhydride (SIDA), 4,4′-hexafluoroisopropylidene diphthalic anhydride (6FDA), bis(3,4-dicarboxyphenyl)ether dianhydride (ODPA), and 3,3′, 4,4′-tetracarboxylichenzophen+ne dianhydride (BTDA) in an aprotic solvent. The synthesized monomers showed crystalline melting at 269 and 271°C. Elemental analysis, differential thermal analysis (DTA), infrared (IR), nuclear magnetic resonance (¹H-NMR) and mass spectral studies were carried out to characterize the synthesized monomers. Thermogravimetric analysis (TGA) of the synthesized monomers showed their thermal stability at 410–400°C. A detailed study and NMR investigation of the first step of condensation reaction was carried out and indicated the formation of a transient charge transfer complex. Thermal cyclization of the formed intermediate, however, gave the required monomers. A preliminary study demonstrated that melt-polymerization of the synthesized monomers gave thermallystable, tough polymers.     

Cis di-oxomolybdenum(VI) complexes with a tridentate ONO donor ligand; synthesis,X-ray crystal structure,spectroscopic properties and oxotransfer chemistry

The molybdenum complexes of Schiff base ligands viz. [MoO₂LH₂O] where L¹ = tris(hydroxymethyl)(salicylide-neamino)methane, L² = tris(hydroxymethyl)(2,3-dihydroxybenzylideneamino)methane and L³ = tris(hydroxymethyl)(2,3,4-trihydroxybenzylideneamino)methane have been synthesized and characterized by spectroscopic and electrochemical techniques. The X-ray crystal structure of the complex [MoO₂L¹H₂O] reveals a distorted octahedral geometry with one ligand and a water molecule coordinated to the MoO₂ center. No previous complex of this type contains a coordinated water molecule. The complex undergoes an oxotransfer in the presence of Bu₃P to form a -oxobridged molybdenum(V,V) dimer. This rules out Mo—S coordination as a prerequisite for oxotransfer in such molybdenum(VI) complexes.     

Heat-resistant polymers from melt-processable bisimido-bisphthalonitriles

Heat-resistant polymers which are processable into void-free components and suitable for composite applications have been synthesized by thermal/chemical polymerization of four newly developed bisimido-bisphthalonitriles containing silicon, ether, carbonyl, and hexafluoroisopropylidene groups. Thermal polymerization involving addition reactions was performed at 200–275°C for 2–10 h and then post-curing at 310°C for 10 h. Polymers VI, VII, VIII , and IX were obtained. The thermal polymerization was monitored using infrared spectroscopy. Thermal polymerization was also carried out in the presence of an aromatic diamine. A polyhexasocyclane ( V ) was synthesized by condensation polymerization of ether containing bisimido-bisphthalonitrile with 4,4′-diaminodiphenyl ether in solvent phenol. The synthesized polymers were evaluated for thermal stability using dynamic thermogravimetric analysis (TGA). Polymers VII, VIII, IX , and X showed thermal decomposition temperature in the range of 475–500°C in nitrogen and air atmosphere. The char yield of the polymers was in the range of 60–69% in nitrogen at 800°C. This study indicated that synthesized thermosetting polymers from ether and keto containing bisimido-bisphthalo-nitrile are potential candidates for development of graphite composites. © 1993 John Wiley & Sons, Inc.     

An algebraic approach to q-partial fractions and Sylvester denumerants

The Ramanujan Journal - In 1857, Sylvester established an elegant theory that certain counting functions (which he termed denumerants) are quasi-polynomials by decomposing them into periodic and...     

Improved highly efficient synthesis of α,β-acetylenic ketones. Nature of the intermediate from the reaction of lithium acetylide with boron trifluoride etherate

A wide variety of α,β-acetylenic ketones were synthesized in very high yields via an exceptionally facile intermolecular reaction of lithium alkynyltrifluoroborates and carboxylic acid anhydrides.     

Synthesis of Pyrimidine Annelated Heterocycles [1]. Regioselective Heterocyclization of 6-Cyclopent-2-enyl-5-hydroxy-1,3-dimethyl-pyrimidine-2,4( 1H, 3H)-dione and 5-Cyclopent-2-enyl-6-hydroxy-1,3-dimethylpyrimidine-2,4( 1H, 3H)-dione

Summary. Two hitherto unreported pyrimidine annelated heterocycles were synthesized from 6-cyclopent-2-enyl-5-hydroxy-1,3-dimethylpyrimidine-2,4(1H,3H)-dione and 5-cyclopent-2-enyl-6-hydroxy-1,3-dimethylpyrimidine-2,4(1H,3H)-dione by reaction with pyridine hydrotribromide or hexamethylenetetramine hydrotribromide. The first one was also obtained by reaction with concentrated sulfuric acid.Received October 28, 2002; accepted October 30, 2002 Published online June 2, 2003