Deformations of arithmetically Cohen-Macaulay subvarieties of pn

We show that every arithmetically Cohen-Macaulay two-codimensional subscheme ofP ⁿ can be deformed to a reduced union of two-codimensional linear subvarieties. This problem (classical for curves with the name of Zeuthen problem) was solved for curves by F.Gaeta.     

6-Thia-1-aza-5λ5-phosphabicyclo[3.2.0]hept-3-ene und Isothiocyanatophosphin-sulfide aus (Methylidenamino)phosphinen,Schwefelkohlenstoff und Acetylen- oder Ethylen-Derivaten

6-Thia-l-aza-5λ⁵-phosphabicyclo[3.2.0]hept-3-enes and Isothiocyanatophosphine-sulfides from (Methylidenamino)phosphines, Carbon Disulfide, and Acetylene- or Ethylene Derivatives (Methylidenamino)phosphines react with carbon disulfide to 1,3,2-thiazaphosphete derivatives 2 . Acetylenedicarboxylates give with 2 6-thia-l-aza-5λ⁵-phosphabicyclo[3.2.0]hept-3-enes 4a , b , and acrylates yield isothio-cyanatophosphin-sulfides 5a – c . The structures of 4a and 5a are proven by an X-ray diffraction analysis.     

A highly active fungal β-glucosidase

A highly active thermostable β-glucosidase was purified to homogeneity from a strain ofTrichoderma sp. The enzyme was an extracellular glycoprotein and showed hydrolytic activity toward several β-glucosides. Cellobiose was found to be the substrate of choice for this enzyme. This finding could suggest future technological applications of the purified protein.     

Physical aging of a polyetherimide: Creep and DSC measurements

Creep and differential scanning calorimetry (DSC) measurements have been used to study the physical aging behavior of a polyetherimide. Isothermal aging temperatures ranged from 160°C to T_g with aging times ranging from 10 min to 8 days. The only measurable effect of physical aging on the short-time creep curves is a shift of the creep compliance to longer times. Andrade plots of the compliance versus the cube root of time are linear at short times with the slope β decreasing with increasing aging time to a constant value once equilibrium is reached. Log β³ is related directly to the degree to which the creep curves shift to longer times with physical aging, and is used in this work as a measure of physical aging. A reduced curve of log β³ versus log aging time is obtained for the aging temperatures investigated by appropriate vertical and horizontal shifts. The enthalpy change during aging increases linearly with the logarithm of the aging time, t_a, leveling off at equilibrium at values which increase with decreasing aging temperature. Hence, both nonequilibrium and equilibrium temperature shift factors can be calculated from the DSC data. Good agreement is observed between the equilibrium temperature shift factors obtained from the creep and DSC data. The temperature dependence of the nonequilibrium temperature shift factors is found to be an order of magnitude smaller than that of the equilibrium shift factors. The time scales to reach equilibrium for enthalpy and for mechanical measurements are found to be the same within experimental error. © 1995 John Wiley & Sons, Inc.     

Upward and downward heat and mass transfer with miniature periodically operating loop thermosyphons

Upward and downward two-phase heat and mass transfer has been considered in the present paper. The heat and mass transfer with the condenser located below the evaporator has been obtained by inserting an accumulator tank in the liquid line of a loop thermosyphon and enforcing a pressure pulsation. In previous papers these heat transfer devices have been called pulsated two phase thermosyphons (PTPT). A mini PTPT has been experimentally investigated. It has shown a stable periodic heat transfer regime weakly influenced by the position of the condenser with respect to the evaporator. In contrast a classical loop mini thermosyphon (diameter of connecting pipes 4 mm) did not achieve a stable functioning for the investigated level differences between evaporator and condenser lower than 0.37 m. The present study shows that the functioning of a PTPT device does not directly depend on the level difference or the presence of noncondensable gas. In order to obtain a natural circulation in mini or micro loops, a periodically operating heat transfer regime should therefore be considered.     

Chelate polymers: II. Some novel transition metals complexes with azomethine‐containing siloxanes and their polyesters

New Schiff bases of 2,4‐dihydroxybenzaldehyde with siloxane‐α,ω‐diamines having different numbers of siloxane units in the chain have been synthesized and characterized by spectroscopy, elemental and thermal analyses. These azomethines were found to form complexes readily with copper(II), nickel(II), cobalt(II), cadmium(II) and zinc(II). From IR and UV–Vis studies, the phenolic oxygen and imine nitrogen of the ligand were found to be the coordination sites. Thermogravimetric analysis (TGA) data indicate the chelates to be more stable than the corresponding ligands. The melting points increase with shortening of the siloxane segment from azomethine, as well as the result of complexation. The chelates obtained were covalently inserted in polymeric linear structures by polycondensation through the OH‐difunctionalized ligand with 1,3‐bis(carboxypropyl)tetramethyldisiloxane. Direct polycondensation, assisted either by acetic anhydride or N,N′‐dicyclohexylcarbodiimide as dehydrating agent and the complex 4‐(dimethylamino)pyridinium 4‐toluenesulfonate as catalyst, was used for the synthesis of these compound types. The structures of the polymers obtained were confirmed by IR, UV and ¹H NMR. Characterization was undertaken by TGA, solubility tests and viscosity measurements. Copyright © 2003 John Wiley & Sons, Ltd.     

Influence of heat treatment conditions on the porosity changes of sulfonated styrene/divinylbenzene copolymers

Sulfonic cation exchangers with two ion exchange group concentrations (0.5 and 2.4 mmol/g, samples A and B, respectively) were obtained by sulfonation of a porous styrene (S) and divinylbenzene (DVB) copolymer with chlorosulfonic acid. Strong thermal decomposition of the sulfonated copolymer A, accompanied by significant changes in its porous structure, starts at ca. 400°C. The char has no sulfonic groups. After heat treatment at 400°C in steam, a sorbent was obtained (yield 65%) that shows higher phenol sorption than the untreated sample when related to the bed volume. The chlorosulfonic derivatives of the initial copolymer were less thermally resistant than the sulfonic ones obtained by hydrolysis. Pyrolysis of the cation exchanger B, in its H+ and Ca²⁺ forms, was carried out at 900°C (yield of both chars close to 30%). By subsequent steam activation at 800°C to a 50% burn-off of the char, sorbents with well-developed, but distinctly different, porous structures were obtained. The activated char from the sulfonated copolymer in its hydrogen form was highly microporous and indicated an effective surface area of 1180 m²/g. However, because of a low contribution of mesopores, its ability to adsorb phenol from the liquid phase was not very high. The activated char from the calcium-doped copolymer, indicating a smaller surface area (580 m²/g) but characterized by a well-developed mesoporosity, was a better sorbent for phenol. © 1994 John Wiley & Sons, Inc.     

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

Nanostructured polymetallaynes of controlled length: Synthesis and characterization of oligomers and polymers from 1,1′‐bis‐(ethynyl)4,4′‐biphenyl bridging Pt(II) or Pd(II) centers

The reactivity of square planar palladium(II) and platinum(II) complexes in trans or cis configuration, namely trans or cis‐[dichlorobis(tributylphosphine)platinum(II)] and trans‐[dichlorobis(tributylphosphine)palladium(II)] with 1,1′‐bis(ethynyl) 4,4′‐biphenyl, DEBP, leading to π‐conjugated organometallic oligomeric and polymeric metallaynes, was investigated by a systematic variation of the reaction conditions. The formation of polymers and oligomers with defined chain length [? M(PBu₃)₂ (C?C? C₆H₄? C₆H₄? C?C? )]_n (n = 3–10 for the oligomers, n = 20–50 for the polymers) depends on the configuration of the precursor Pt(II) and Pd(II) complexes, the presence/absence of the catalyst CuI, and the reaction time. A series of model reactions monitored by XPS, GPC, and NMR ³¹P spectroscopy showed the route to modulate the chain growth. As expected, the nature of the transition metal (Pt or Pd) and the molecular weight of the polymers markedly influence the photophysical characteristics of the polymetallaynes, such as optical absorption and emission behavior. Polymetallaynes with nanostructured morphology could be obtained by a simple casting procedure of polymer solutions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3311–3329, 2007