Minimum binding energy and size of the doubly muonic T3 molecule

The minimum energy and size of doubly muonic T₃ molecule in which two of the electrons are replaced by the much heavier muons are calculated by the well‐known variational method. The calculations show that the system possesses two minimum positions, one at a typically muonic distance and the second at the atomic distance. It is shown that at the muonic distance the effective charge, z_eff, is 2.88. We assumed a symmetrical planar vibrational model between two minima and an oscillation potential energy is approximated in this region. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 377–383, 2003     

Analysis of structure–properties relationship in nitrile‐butadiene rubber/phenolic resin/organoclay ternary nanocomposites using simple model system

The present study deals with the structure–property relationship of organoclay (OC) filled nanocomposites based on rubber blend comprising of nitrile‐butadiene rubber (NBR) and phenolic resin (PH). To obtain a better insight into the characteristics of the NBR/PH/OC hybrid system, a simple model system consisting of NBR/OC nanocomposites is also taken into consideration. A series of NBR/OC and NBR/PH/OC nanocomposites containing a wide range of OC concentrations (2.5–30 phr) are prepared by using traditional open two‐roll mill. Structural analysis performed by X‐ray diffraction (XRD), scanning electron microscope (SEM), and transmission electron microscope (TEM) exhibits mixed exfoliated and intercalated morphology at low OC content, below 7.5 phr, and a well‐ordered intercalated morphology at higher OC loading. It is shown that the dispersion of OC is also influenced by mixing time and order of mixing of components. Analysis of the cure characteristics, mechanical, and thermal properties of both the NBR/OC and NBR/PH/OC nanocomposites reveals that the OC is dispersed mainly in the NBR continuous phase, even though some is likely localized in the rubber–resin interface. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesis and characterization of optically active and organosoluble poly(amide-imide)s containing imidazole rings as pendent groups by direct polycondensation

Six new optically active poly(amide-imide)s(PAIs) 6a-f were prepared by direct polycondensation reaction of N-trimelli-tylimido-L-histidine 4 as a chiral diacid with various aromatic diamines 5a-f.Triphenyl phosphite(TPP)/pyridine(Py) in the presence of calcium chloride(CaCl2) and N-methyl-2-pyrrolidone(NMP) were successfully applied to direct polycondensation reaction.The resulting new polymers were in good yields,and had inherent viscosities ranging between 0.29 and 0.41 dL g-1 and were detected with elem...     

Finite 3-groups of class 3 whose elements commute with their automorphic images

A group G is an A-group if x ^α x =  xx ^α for all ${x\in G}A group G is an A-group if x ^α x =  xx ^α for all x ? G{x\in G} and all automorphisms α of G. Such groups have nilpotency class at most 3; we construct the first example having class precisely 3.     

A Two-parameter Family of Two-level Higher Order Difference Methods for the Two-dimensional Heat Equation

An algorithm for generating multi-parameter families of differenceoperators on rectangular grids to approximate linear partialdifferential equations has been developed. It has been appliedto construct a twelve-parameter, eighteen point, two-level familyfor the two-dimensional heat equation. Many familiar differenceoperators can be obtained as special cases. A complete analysisof all possibilities has not been attempted. Only the two-parametersubset that has O(h⁶) truncation errors has been studied indetail here. Truncated power series expansions of the operators are usedto construct Vandermonde matrices, whose inverses can be foundby use of familiar algorithms. These Vandermonde matrices constitutethe essential feature of the algorithm, permitting the methodto be used, with minor modifications, to establish differenceoperators that include boundary points; to deal with equationswith variable coefficients; and to deal with irregular (non-rectangular)nets. These possibilities indicate directions for the developmentof a digital computer algorithm to generate difference operatorsfor partial differential equations.     

RAPID SYNTHESIS OF NOVEL OPTICALLY ACTIVE POLY(AMIDE-IMIDE)S DERIVED FROM N,N''''-(PYROMELLITOYL)-BIS-L-ALANINE DIACID CHLORIDE AND HYDANTOIN DERIVATIVES UNDER MICROWAVE IRRADIATION

Eight novel poly(amide-imide)s were synthesized under microwave irradiation by using a domestic microwaveoven from the polycondensation reactions of N.N'-(pyromellitoyl)-bis-L-alanine diacid chloride(1)with eight differentderivatives of hydantoin compounds(2a-h)in the presence of a small amount of a polar organic medium such as o-cresol.The polycondensation proceeded rapidly,compared with the conventional solution polycondensation and was completedwithin 8-10 min,producing a series of new poly(amide-imide)s(3a-h)with inherent viscosities about 0.35-0.68 dL/g inhigh yields.The obtained PAIs(3a-h)were fully characterized by means of FT-IR spectroscopy,elemental analyses,inherentviscosity(ηinh),solubility and specific rotation measurements.All of the resulting polymers show optical rotation and areoptically active.Thermal properties of the poly(amide-imide)s were investigated by using thermal gravimetric analysis(TGA).     

Reproducibility of the high-performance liquid chromatographic fingerprints obtained from two soybean cultivars and a selected progeny

Roots from soybean cultivars Williams 82 and Hartwig along with one of their progeny 14a, were extracted with non-polar, moderately polar, and highly polar solvent systems. Extracts were compared by thin-layer chromatography and by HPLC. Methanol extractions conducted at ambient temperature coupled with analysis by reversed-phase HPLC using UV detection provided the most representative sets of reproducible fingerprints. Further optimization of the overall protocol should allow for the profiling of different soybean cultivars when their roots are exposed to various environments and insults during early growth.     

RAPID SYNTHESIS OF NOVEL OPTICALLY ACTIVE POLY（AMIDE-IMIDE）S DERIVED FROM N,N′-（PYROMELLITOYL）-BIS-L-ALANINE DIACID CHLORIDE AND HYDANTOIN DERIVATIVES UNDER MICROWAVE IRRADIATION

Eight novel poly(amide-imide)s were synthesized under microwave irradiation by using a domestic microwaveoven from the polycondensation reactions of N,N′-(pyromellitoyl)-bis-L-alanine diacid chloride (1) with eight different derivatives of hydantoin compounds (2a-h) in the presence of a small amount of a polar organic medium such as o-cresol. The polycondensation proceeded rapidly, compared with the conventional solution polycondensation and was completed within 8-10min, producing a series of new poly(amide-imide)s (3a-h) with inherent viscosities about 0.35-0.68dL/g in high yields. The obtained PAIs (3a-h) were fully characterized by means of FT-IR spectroscopy, elemental analyses, inherent viscosity (ηinh), solubility and specific rotation measurements. All of the resulting polymers show optical rotation and are optically active. Thermal properties of the poly(amide-imide)s were investigated by using thermal gravimetric analysis(TGA).     

Nonlinear Quantum Optical Springs and Their Nonclassical Properties

The original idea of quantum optical spring arises from the requirement of quantization of the frequencyof oscillations in the Hamiltonian of harmonic oscillator. This purpose is achieved by consideringa spring whose constant (and so its frequency) depends on the quantum states of another system.
Recently, it is realized that by the assumption of frequencymodulation ofω toω(1+μa^\dagger a)^1/2the mentioned idea can be established.
In the present paper, we generalize the approach of quantum optical springwith particular attention to thedependence of frequency to the intensity of radiation fieldthatnaturally observes in thenonlinear coherent states}, from which we arrive ata physical system has been called by us as nonlinear quantum optical spring.Then, after the introduction of the generalized Hamiltonian of nonlinear quantum optical spring and it's solution,we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revivalin the distribution functions and squeezing parameters, as particular quantum features, will berevealed.     

POLYMERIZATION OF N,N''''-(PYROMELLITOYL)-BIS-L-LEUCINE DIACID CHLORIDE WITH HYDANTOIN DERIVATIVES BY MICROWAVE IRRADIATION

INTRODUCTIONRecently, there has been growing interest in applying microwave energy to synthetic organic chemistry[1-4],sample preparation for analysis[5], extraction of natural products from plants[6], waste treatment[7] and polymersynthesis[8-13]. The reactions involved in these applications are very fast and are completed within a short periodof time. Recently, we have used microwave irradiation for the synthesis of poly(amide-imide)s and poly(ester-imide)s[14-17].Recently more attentio…