Prime ideals in restricted differential operator rings

In this paper restricted differential operator rings are studied. A restricted differential operator ring is an extension of ak-algebraR by the restricted enveloping algebra of a restricted Lie algebra g which acts onR. This is an example of a smash productR #H whereH=u (g). We actually deal with a more general twisted construction denoted byR * g where the restricted Lie algebra g is not necessarily embedded isomorphically inR * g. Assume that g is finite dimensional abelian. The principal result obtained is Incomparability, which states that prime idealsP ₁ ⊆P ₂ ⊂R * g have different intersections withR. We also study minimal prime ideals ofR * g whenR is g-prime, showing that the minimal primes are precisely those having trivial intersection withR, that these primes are finite in number, and their intersection is a nilpotent ideal. Prime and primitive ranks are considered as an application of the foregoing results.     

Effects of diamines and their fluorinated groups on the color lightness and preparation of organosoluble aromatic polyimides from 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]‐hexafluoropropane

To investigate the position and amount of the CF₃ group affecting the coloration of polyimides (PIs), we prepared 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]hexafluoropropane ( 2 ) with four CF₃ groups with 2‐chloro‐5‐nitrobenzotrifluoride and 2,2‐bis(4‐hydroxyphenol)hexafluoropropane. A series of soluble and light‐colored fluorinated PIs ( 5 ) were synthesized from 2 and various aromatic dianhydrides ( 3a – 3f ). 5a – 5f had inherent viscosities ranging from 0.80 to 1.19 dL/g and were soluble in amide polar solvents and even in less polar solvents. The glass‐transition temperatures of 5 were 221–265 °C, and the 10% weight‐loss temperatures were above 493 °C. Their films had cutoff wavelengths between 343 and 390 nm, b* values (a yellowness index) ranging from 5 to 41, dielectric constants of 2.68–3.01 (1 MHz), and moisture absorptions of 0.03–0.29 wt %. In a comparison of the PI series 6 – 8 based on 2,2‐bis[4‐(4‐aminophenoxy)phenyl]hexafluoropropane, 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]propane, and 2,2‐bis[4‐(4‐aminophenoxy)phenyl]propane, we found that the CF₃ group close to the imide group was more effective in lowering the color; this means that CF₃ of 5 , 7 , and 8f was more effective than that of 6c . The color intensity of the four PI series was lowered in the following order: 5 > 7 > 6 > 8 . The PI 5f , synthesized from diamine 2 and 4,4′‐hexafluoroisopropylidenediphthalic anhydride, had six CF₃ groups in a repeated segment, so it exhibited the lightest color among the four series. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 922–938, 2003     

Novel,organosoluble, light‐colored fluorinated polyimides based on 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)biphenyl or 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)‐1,1′‐binaphthyl

Two series of fluorinated polyimides were prepared from 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)biphenyl ( 2 ) and 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)‐1,1′‐binaphthyl ( 4 ) with various aromatic dianhydrides via a conventional, two‐step procedure that included a ring‐opening polyaddition to give poly(amic acid)s, followed by chemical or thermal cyclodehydration. The inherent viscosities of the polyimides ranged from 0.54 to 0.73 and 0.19 to 0.36 dL/g, respectively. All the fluorinated polyimides were soluble in many polar organic solvents, such as N,N‐dimethylacetamide and N‐methylpyrrolidone, and afforded transparent and light‐colored films via solution‐casting. These polyimides showed glass‐transition temperatures in the ranges of 222–280 and 257–351 °C by DSC, softening temperatures in the range of 264–301 °C by thermomechanical analysis, and a decomposition temperature for 10% weight loss above 520 °C both in nitrogen and air atmospheres. The polyimides had low moisture absorptions of 0.23–0.58%, low dielectric constants of 2.84–3.61 at 10 kHz, and an ultraviolet–visible absorption cutoff wavelength at 351–434 nm. Copolyimides derived from the same dianhydrides with an equimolar mixture of 4,4′‐oxydianiline and diamine 2 or 4 were also prepared and characterized. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2416–2431, 2004     

Viscosity,particle size distribution,and structural investigation of tetramethyloxysilane/2‐hydroxyethyl methacrylate sols during the sol–gel process with acid and base catalysts

The tetramethoxysilane (TMOS)/2‐hydroxylethyl methacrylate (HEMA) hybrid gels were synthesized with acid and base catalysts, via the in situ polymerization of HEMA, with and without the cosolvent methanol. With methanol in the TMOS/HEMA sol, the enhanced esterification and depolymerization reactions of the silanols resulted in a slower growth of silica particles. The silica particles that were synthesized with an acid catalyst were less than 40 nm. The thermal resistance of the poly(2‐hydroxyethyl methacrylate) (PHEMA) chains was enhanced by the addition of colloidal silica. The Fourier transform infrared characterizations and the exothermal peaks on the differential scanning calorimetry traces of these hybrid gels indicated chemical hybridization occurring as a result of condensation of the colloid silica and PHEMA at higher temperatures. Hence, the residual weight content of the hybrid gel after its synthesis with the base catalyst was even higher than the content of TMOS in the hybrid sol. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3476–3486, 2004     

Controlling a bunch of multiple filaments by means of a beam diameter

We demonstrate a three orders of magnitude increase and stability in the backscattered fluorescence signal from nitrogen molecules by terawatt femtosecond laser pulse induced air filaments using a new method. The method is based on squeezing the initial beam diameter using a telescope. The effect of laser shot-to-shot fluctuations was included in numerical simulations by a random distribution of the initial intensity in both squeezed and non-squeezed beams. Statistical processing of the simulation results shows that the average diameter of plasma channels as well as the total amount of free electrons generated in a bunch of multiple filaments in air is larger in the squeezed beam. Shot-to-shot stability of the simulated plasma density increases in the squeezed beam. The change of this plasma density with propagation distance is in good qualitative agreement with the change of the range-corrected nitrogen fluorescence signal with distance. PACS 42.65.Jx; 42.60.Jf; 42.68.Ay; 42.68.Wt     

A note on strongly π-regular rings

Let R be an associative ring with unit and let N(R) denote the set of nilpotent elements of R. R is said to be stronglyπ-regular if for each x∈R, there exist a positive integer n and an element y∈R such that x ⁿ=x ^{n +1} y and xy=yx. R is said to be periodic if for each x∈R there are integers m,n≥ 1 such that m≠n and x ^m=x ⁿ. Assume that the idempotents in R are central. It is shown in this paper that R is a strongly π-regular ring if and only if N(R) coincides with the Jacobson radical of R and R/N(R) is regular. Some similar conditions for periodic rings are also obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

THE VALIDITY OF HIGH TEMPERATURE APPROXIMATION IN NMR SPECTROSCOPY AND ITS RELATED PROBLEMS

A large body of conspicuous publications [1] in recent years asserts that the high temperature approximation (HTA), a mostly tested and most widely used assumption in NMR spectroscopy and MRI technology, is invalid for concentrated samples in high magnetic fields such as for a proton COSY spectrum of water [1].     

Behaviors of the positive temperature coefficient of resistance of poly(styrene‐co‐n‐butylacrylate) filled with Ni‐plated core‐shell polymeric particles

Conductive composite films of poly(styrene‐co‐n‐butylacrylate) copolymers filled with low‐density, Ni‐plated core‐shell polymeric particles were prepared and their behaviors of positive temperature coefficient of resistance (PTCR) were investigated. When the conductive fillers in the composite film were loaded beyond the critical volume, 10 up to 25 vol %, composite films exhibited a unique electrical resistant transition behavior, which the electrical resistance rapidly increased by several orders of magnitude at the critical temperature. The PTCR transition temperature, in general, occurred before the glass transition temperature of polymer matrix. Further increased the conductive filler loading to 30 vol %, the overpacked conduction paths were formed in the entire composite and the PTCR effects became blurred. While the composite film treated with thermal cycle several times from room temperature up to 120 °C, the electrical resistivity increased accompanied with the shift of the PTCR transition to lower temperature. The reason might have been caused by the formed interfacial cracks within the composite film. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 322–329, 2007     

Highly soluble and optically transparent poly (ether imide)s based on 2,6‐ or 2,7‐bis(3,4‐dicarboxyphenoxy)naphthalene dianhydride and aromatic bis(ether amine)s bearing trifluoromethyl groups

Two series of novel fluorinated poly(ether imide)s (coded IIIA and IIIB ) were prepared from 2,6‐bis(3,4‐dicarboxyphenoxy)naphthalene dianhydride and 2,7‐bis(3,4‐dicarboxyphenoxy)naphthalene dianhydride, respectively, with various trifluoromethyl‐substituted aromatic bis(ether amine)s by a standard two‐step process with thermal or chemical imidization of the poly(amic acid) precursors. These fluorinated poly(ether imide)s showed good solubility in many organic solvents and could be solution‐cast into transparent, flexible, and tough films. These films were nearly colorless, with an ultraviolet–visible absorption edge of 364–386 nm. They also showed good thermal stability with glass‐transition temperatures of 221–298 °C, 10% weight loss temperatures in excess of 489 °C, and char yields at 800 °C in nitrogen greater than 50%. The 2,7‐substituted IIIB series also showed better solubility and higher transparency than the isomeric 2,6‐substituted IIIA series. In comparison with nonfluorinated poly (ether imide)s, the fluorinated IIIA and IIIB series showed better solubility, higher transparency, and lower dielectric constants and water absorption. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5909–5922, 2006