The strong coupling constant: Its theoretical derivation from a geometric approach to hadron structure

Since more than a decade, abi-scale, unified approach to strong and gravitational interactions has been proposed, that uses the geometrical methods of general relativity, and yielded results similar to strong gravity theory's. We fix our attention, in this note, on hadron structure, and show that also the strong interaction strength _S, ordinarily called the (perturbative) coupling-constant square, can be evaluated within our theory, and found to decrease (increase) as the distancer decreases (increases). This yields both the confinement of the hadron constituents (for large values ofr) and their asymptotic freedom (for small values ofr inside the hadron): in qualitative agreement with the experimental evidence. In other words, our approach leads us, on a purely theoretical ground, to a dependence of _S onr which had been previously found only on phenomenological and heuristic grounds. We expect the above agreement to be also quantitative, on the basis of a few checks performed in this paper, and of further work of ours on calculating meson mass spectra.     

A Family of Fifth-Order Runge-Kutta Pairs

The construction of a Runge-Kutta pair of order with the minimal number of stages requires the solution of a nonlinear system of order conditions in unknowns. We define a new family of pairs which includes pairs using function evaluations per integration step as well as pairs which additionally use the first function evaluation from the next step. This is achieved by making use of Kutta's simplifying assumption on the original system of the order conditions, i.e., that all the internal nodes of a method contributing to the estimation of the endpoint solution provide, at these nodes, cost-free second-order approximations to the true solution of any differential equation. In both cases the solution of the resulting system of nonlinear equations is completely classified and described in terms of five free parameters. Optimal Runge-Kutta pairs with respect to minimized truncation error coefficients, maximal phase-lag order and various stability characteristics are presented. These pairs were selected under the assumption that they are used in Local Extrapolation Mode (the propagated solution of a problem is the one provided by the fifth-order formula of the pair). Numerical results obtained by testing the new pairs over a standard set of test problems suggest a significant improvement in efficiency when using a specific pair of the new family with minimized truncation error coefficients, instead of some other existing pairs.

     

Quantum-chemical study of C<Subscript>n</Subscript>F2<Subscript><Emphasis Type="Italic">n</Emphasis>+2</Subscript> conformers. Structure and IR spectra

Quantum-chemical calculations of the geometrical structure and vibrational spectra of C_nF_2n+2 oligomers (n = 5–8) in the chain and branched conformations are reported. The lengthening of the chain of C_nF_2n+2 does not substantially affect the geometrical parameters of the oligomers. In all cases under study, the most optimal structure of the molecule is a zigzag chain with bond lengths R(C-C) = 1.53 –1.54 and R(C-F) = 1.36 –1.34 ; the chain is rolled into a helix, which makes an angle of 17° with the plane. The IR spectra are sensitive to the structural deficiency of oligomers C_nF_2n+2 associated with the lateral trifluoromethyl groups formed in the chain; the spectra can be used for revealing defects of this type in the structure of polytetrafluoroethylene (PTFE). The possibility of defects associated with the lateral CF₃ groups in the structure of PTFE and its low-temperature modifications is explained based on the calculated total energies of C_nF2 _n+2.Original Russian Text Copyright © 2004 by L. N. Ignatieva, A. Yu. Beloliptsev, S. G. Kozlova, and V. M. BuznikTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 632–643, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

[Co(3,3-tri)(men)Cl][ZnCl_4]和[Co(3,3-tri)(cmen)Cl][ZnCl_4]两体系配合物的合成及两经式异构体的晶体结构

分别合成了 [Co(3, 3-tri)(men)Cl][ZnCl4]、[Co(3, 3-tri)(cmen)Cl][ZnCl4] (3, 3-tri = N-(3-胺基丙基)-1, 3-丙二胺,men = N-甲基乙二胺,cmen = 1, 2-二胺基-丙烷) 2体系的部分配合物异构体,用单晶 X-射线衍射分析方法解析了2异构体的晶体结构。其中 [Co(3, 3-tri)(men)Cl][ZnCl4] 体系的一异构体Ⅰ的化学简式为 CoCl(C9H27N5)ZnCl4,晶体属正交晶系,空间群 Pca21,a = 16.788(2),b = 7.964(1),c = 14.416(2) 牛琕 =1927.3(4) ?,Dc = 1.747 g/cm3,Z = 4,F(000) = 1032,Mr = 506.91,R = 0.0352,wR =0.0935;[Co(3, 3-tri)(cmen)Cl]2+ 体系的一异构体Ⅱ的化学简式为 CoCl(C9H27N5)ZnCl4稨2O, 晶体属三斜晶系,空间群 P ,a = 9.511(3), b = 9.972(3),c = 11.694(3) 牛琣 = 68.367(5),b = 85.196(6),?= 86.580(5),V = 1026.9(5)?3,Dc = 1.698 g/cm3,Z = 2,F(000) = 536,Mr = 524.92,R = 0.0494,wR = 0.1180。两异构体中 Co3+ 为六配位,晶胞中对映体比例均为1:1。在配合物异构体Ⅰ和Ⅱ中,三元胺以经式排布,三元胺配体(3, 3-tri)仲胺上的氢相对于Cl分别处于顺位(syn-)和反位(anti-);二元胺配体氮(或邻位碳)取代的胺基氮原子(N*)与三元胺配体中的仲氮原子分别处于对位(trans(N*))和邻位(cis(N*))。     

Kinetic-catalytic determination of traces of iron by the oxidative coupling reaction of 3-methyl-2-benzothiazolinone hydrazone with N,N-dimethylaniline

A new kinetic-catalytic method by the initial rate procedure for the determination of nanogram level of iron(III) is developed, which is based on its catalytic effect on the oxidative coupling of 3-methyl-2-benzothiazolinone hydrazone (MBTH) with N,N-dimethylaniline (DMA) to form an indamine dye (λ_max=590 nm) in the presence of hydrogen peroxide. Iron(II) is also determined, being oxidized to iron(III) by hydrogen peroxide. Calibration graphs obtained by the initial rate method are linear in the range 1–1000 ng ml⁻¹ Fe and as low as 10⁻⁸ M Fe(II, III) can easily be determined. The relative standard deviations are 6.6, 2.5 and 1.5% for ten determinations of 1, 20 and 60 ng ml⁻¹ of Fe(III), respectively. The method is applicable to the determination of iron in natural waters without preconcentration and separation.     

An investigation of dynamic mechanical, thermal, and electrical properties of housing materials for outdoor polymeric insulators

The present paper reports the results about a study of mechanical, thermal, dynamic mechanical and electrical properties of housing (weather shed) materials for outdoor polymeric insulators. Silicone rubber, ethylene-propylene-diene monomer (EPDM) and alloys of silicon-EPDM are known polymers for use as housing in high voltage insulators. The result of dynamical mechanical measurement shows that the storage modulus of blends enhances with increase EPDM in formulation. It can be seen from the result of TGA measurement that initial thermal degradation of silicone rubber improves by the effect of EPDM in blends. The blends of silicone-EPDM show good breakdown voltage strength compared to silicone rubber. Surface and volume resistance of silicone rubber improve by EPDM content. The mechanical properties of EPDM such as strength, modulus and elongation at break improve by silicone.     

Study of geometrical parameters in N-H...N type of hydrogen bonds

Geometrical parameters associated with N-H ... N types of hydrogen bonds have been analysed using crystal structure data on nucleic acids, amino acids and related compounds. Histograms depicting the frequency distribution of N-H ... N length (l) and H-N ... N angle (θ) have been drawn and conclusions on the favoured geometry of such bonds have been arrived at. The distribution ofl shows a pronounced maximum in the range between 2.9? and 3.0? with an overall average of 2.98 ?. The θ distribution shows a pronounced maximum for the hydrogen bond angle in the range 0°-10°, with a rapid fall-off in frequency for nonlinear hydrogen bonds. The frequency shows a cos⁶θ dependence as compared to cos²θ dependence term used earlier to predict the angular dependence of hydrogen bond potential energy in proteins and polypeptides.     

Ab initio study of Rg2I− (Rg = Ar,Kr, Xe)

The equilibrium geometries, vibrational frequencies, and dissociation energies of rare gas iodine clusters Rg₂I^?(Rg = Ar, Kr, Xe) were calculated at the Hartree–Fock (HF), second‐order Møller–Plesset (MP2), the coupled cluster method with single and double excitation and a noniterative correction for triple excitations method [CCSD(T)] levels. The title species have bent C_2v structure of about 60° angle. The electron correlation effects and relativistic effects on the geometry and stability were investigated at CCSD(T) level. Both effects stabilize title species. The calculated electron affinities are in good agreement with the experimental results available. The effect of high angular momentum functions (g and h) was studied. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Computational studies on glyceraldehyde and glycine Maillard reaction—I

Mechanisms for the initial stage of glyceraldehyde and glycine Maillard reaction under different pH conditions have been proposed, following usually the Hodge-scheme. Computations have been performed on the mechanisms at the standard state to test the possibility of the formation of different compounds, through evaluating the changes in Gibb's free energy during the reaction. Electronic energy changes during the reaction have also been evaluated. Glyceraldehyde+deprotonated glycine reaction has been found to be the most favorable for the formation of the Amadori rearrangement products in both gaseous and aqueous states. Due to the possibility of the production of both enol and keto forms of the Amadori rearrangement product, the rate of browning in glyceraldehyde+deprotonated glycine reaction is assumed to be faster than the others. Glyceraldehyde+unionized glycine reaction has been found to be more plausible for the formation of the keto form of the Amadori rearrangement products, particularly, in the gaseous phase. Glyceraldehyde+protonated glycine and glyceraldehyde+glycine zwitterion reactions are not favorable for the formation of the Amadori rearrangement products. Formation of hydroxyacetaldehyde from glyceralaldehyde, as one of the possible C2-fragmentation product, has been found to be favorable in the aqueous state.     

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.