On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Phase equilibria in the Ag4SSe–As2Se3 system

The phase diagram of the system Ag₄SSe–As₂Se₃ is studied by means of X-ray diffraction, differential thermal analyses and measurements of the microhardness and the density of the materials. The unit-cell parameters of the intermediate phases 3Ag₄SSe·As₂Se₃ (phase A) and Ag₄SSe·2As₂Se₃ (phase B) are determined as follows for phase A: a=4.495 Å, b=3.990 Å, c=4.042 Å, α=89.05°, β=108.98°, γ=92.93°; for phase B: a=4.463 Å, b=4.136 Å, c=3.752 Å, α=118.60°, β=104.46°, γ=83.14°. The phase 3Ag₄SSe·As₂Se₃ and Ag₄SSe·2As₂Se₃ have a polymorphic transition α?β consequently at 105 and 120°C. The phase A melts incongruently at 390°C and phase B congruently at the same temperature.     

Effect of viscosity on stationary phase stability in capillary column gas chromatography

With recent advances in column technology it is now possible to prepare highly efficient, very inert, and thermally stable capillary columns coated with nonpolar polysiloxane stationary phases. Unfortunately, the same degree of success has not been achieved for some of the more polar polysiloxane phases. A parameter that has been studied little in the past in relation to stationary phase film stability is the viscosity of the stationary phase. In this paper the efficiency and stability of coated columns are correlated to the viscosity of the phase. Due to their structure, the viscosity of the phenyl-containing polysiloxanes change rapidly with temperature and hence, thin-film coatings are not stable at elevated temperatures. By using high viscosity phenyl-containing methylphenylpolysiloxanes which were recently synthesized, efficient and stable columns have been prepared.     

Analytic continuation at first-order phase transitions

We study the analytic structure of thermodynamic functions at first-order phase transitions in systems with short-range interactions and in particular in the two-dimensional Ising model. We analyze the nature of the approximation of the d=2 system by anN × strip. Investigation of the structure of the eigenvalues of the transfer matrix in the vicinity of H=0 in the complexH plane allows us to define a new function which provides rapidly convergent approximations to the stable free energyf and its derivatives for allH 0. This new function is used for numerical calculation of the coefficients C_n in the power series expansions of the magnetizationm in the form m(H)=1 + C_n(H-H ₀ )ⁿ for various H₀ 0. The resulting series are studied by conventional methods. We confirm recent series analysis results on the existence of the droplet model type essential singularity at H=0. Evidence is found for a spinodal at H=H_sp(Ti < 0.     

Application of HPLC to measure vanadium in environmental,biological and clinical matrices

Vanadate and vanadium compounds exist in many environmental, biological and clinical matrices, and despite the need only limited progress has been made on the analysis of vanadium compounds. The vanadium coordination chemistry of different oxidation states is known, and the result of the characterization and speciation analysis depends on the subsequent chemistry and the methods of analysis. Many studies have used a range of methods for the characterization and determination of metal ions in a variety of materials. One successful technique is high performance liquid chromatography (HPLC) that has been used mainly for measuring total vanadium level and metal speciation. Some cases have been reported where complexes of different oxidation states of vanadium have been separated by HPLC. Specifically reversed phase (RP) HPLC has frequently been used for the measurement of vanadium. Other HPLC methods such as normal phase, anion-exchange, cation-exchange, size exclusion and other RP-HPLC modes such as, ion-pair and micellar have been used to separate selected vanadium compounds. We will present a review that summarizes and critically analyzes the reported methods for analysis of vanadium salts and vanadium compounds in different sample matrices. We will compare various HPLC methods and modes including sample preparation, chelating reagents, mobile phase and detection methods. The comparison will allow us to identify the best analytical HPLC method and mode for measuring vanadium levels and what information such methods provide with regard to speciation and quantitation of the vanadium compounds.     

X-ray and Thermal Analysis of Selected Drugs Containing Acetaminophen

Studies carried out by X-ray and thermal analysis confirmed that acetaminophen (paracetamol), declared by the manufacturers as an Active Pharmaceutical Ingredient (API), was present in all studied medicinal drugs. Positions of diffraction lines (2θ angles) of the studied drugs were consistent with standards for acetaminophen, available in the ICDD PDF database Release 2008. |Δ2θ| values were lower than 0.2°, confirming the authenticity of the studied drugs. Also, the values of interplanar distances d_hkl for the examined samples were consistent with those present in the ICDD. Presence of acetaminophen crystalising in the monoclinic system (form I) was confirmed. Various line intensities for API were observed in the obtained diffraction patterns, indicating presence of the preferred orientation of the crystallites in the examined samples. Thermal analysis of the studied substances confirmed the results obtained by X-ray analysis. Drugs containing only acetaminophen as an API have melting point close to that of pure acetaminophen. It was found that presence of other active and auxiliary substances affected the shapes and positions of endothermal peaks significantly. A broadening of endothermal peaks and their shift towards lower temperatures were observed accompanying an increase in the contents of additional substances being “impurities” in relation to the API. The results obtained by a combination of the two methods, X-ray powder diffraction (XRPD) and differential scanning calorimetry/thermogravimetry (DSC/TGA), may be useful in determination of abnormalities which can occur in pharmaceutical preparations, e.g., for distinguishing original drugs and forged products, detection of the presence of a proper polymorphic form or too low content of the active substance in the investigated drug.     

Improving resins for solid phase synthesis: incorporation of 1-[2-(2-methoxyethoxy)ethoxy]-4-vinyl-benzene

The preparation, characterisation and application of a series of non-grafted polystyrene (PS) resins containing a styrenic methoxypoly(ethylene glycol) (MPEG) derivative is presented. These novel PS-MPEG resins were designed to balance swelling and solvation with improved handling. The monomer, 1-[2-(2-methoxyethoxy)ethoxy]-4-vinyl-benzene, contained an inert phenyl ether linkage designed to provide broad chemical compatibility and stability, yet imparting all the favourable properties of the PEG group into the new resin, whilst maintaining a high loading capacity. The synthetic performance of the new resins compared very favourably to those of TentaGel™, ArgoGel™ and aminomethyl PS.     

Selective water sorbents for multiple applications, 3. CaCl2 solution confined in micro- and mesoporous silica gels: Pore size effect on the “solidification-melting” diagram

In this communication we present a low-temperature “solidification-melting” phase diagram for CaCl₂/H₂O solutions confined in KSK and KSM silica gels. At salt concentrations of 0–48 wt. %, the diagram has been found to lie below the diagram reported for the bulk system by 15–30°C. It shows a depression of the solution melting point due to its confinment to the pores. Several other peculiarities of melting and solidification in this system are also reported and discussed. Beside fundamental interest, the data obtained could be of importance in many commercial areas such as refrigeration, accumulation of low temperature heat, frost prevention in building materials,etc.     

IR spectroscopic study of the conformational lability of 4′-ethyl-4-cyanobiphenyl

The conformational lability of 4-ethyl-4-cyanobiphenyl molecules in solid crystal (SC) and isotropic liquid (IL) states was investigated by IR spectroscopic techniques (experiment and theory). IR absorption spectra were measured at 28°C–95°C in the frequency range 400 cm^–1–4000 cm^–1. Spectrum simulation was performed using the fragment method with allowance for the conformational fluctuations of molecules. The experimental and calculated spectra were compared and analyzed, and it was shown that in the IL, the samples are mixtures of conformers. The temperature changes in the spectra in the stated range are caused by the conformational lability of molecules.Original Russian Text Copyright © 2004 by L. M. Babkov, I. I. Gnatyuk, G. A. Puchkovskaya, and S. V. TrukhachevTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 3, pp. 398–405, May–June, 2004.     

Biomimetic formation of gramicidin S by dimerization-cyclization of pentapeptide precursor on solid support

The biomimetic formation of gramicidin S, cyclo(-d-Phe-Pro-Val-Orn-Leu-)₂, by the dimerization and cyclization of pentapeptide precursor without the protection of δ-amino group of the Orn residue was examined on a solid support. The cyclization of H-d-Phe-Pro-Val-Orn-Leu-oxime on a resin with an oxime group of 0.62 mmol/g in 1,4-dioxane directly gave gramicidin S in a 50% yield. The dimerization-cyclization mode on the solid support was similar to that of the biosynthesis of gramicidin S on an enzyme.