Über die Randwertaufgabe im Zusammenhang mit kraftfreien Magnetfeldern im rotationssymmetrischen Fall

The question of the existence and uniqueness of the solutions of the system in case of rotational symmetry can be reduced to the question of the resolvibility of a nonlinear elliptic differential equation for α which contains an arbitrary function g(α). Under rather general suppositions the boundary values of α and the function g(α) are given by the boundary values of H⊥ and H φ (the component of H which is perpendicular to the boundary). From the theory of non-linear elliptic equations one obtains: In sufficiently small domains the boundary value problem has a unique solution. For large domains these exist estimations about the diameter and area which guarantee the existence and uniqueness of the solutions.     

Über stationäre,rotierende, inkompressible Plasmen mit minimalen inneren Verlusten

The condition that the Ohmic and the friction losses are minimized leads to the assumption that both the magnetic field H and the velocity field v are Trkal-fields. . In the rotationally symmetric, stationary case the boundary conditions and the condition that the toroidal part of v and H should vanish on the boundary, lead to a linear eigenvalue problem for α, β which in case of a rectangular domain easily can be resolved. It follows: .     

Kinetics and thermodynamics of the Li/Li+ couple in tetrahydrofuran at low temperatures (195–295 K)

Kinetic and thermodynamic (formal potential) data relating to the synthetically useful Li/Li⁺ couple in tetrahydrofuran (THF) solvent at a range of temperatures (196–295 K) are reported. Formal potentials, have been measured versus the standard reference electrode, in THF. At 295 K the following data have been obtained using a mathematical model to simulate the electro‐deposition (metal deposition and growth kinetics) processes of lithium (Li) on a platinum microelectrode; a of ?3.48 ± 0.005 V, = ?9.2 (±0.5) × 10^?4 V K^?1, the standard electrochemical rate constant, k₀ = 1 (± 0.1) × 10^?4 cm s^?1, transfer coefficient, α = 0.57 ± 0.03 and diffusion coefficient, D = 8.7 ± 0.1 × 10^?6 cm² s^?1. Copyright © 2007 John Wiley & Sons, Ltd.     

Crystal structures of 3‐methyl‐2(1H)‐quinoxalinone and three substituted derivatives

3‐Methyl‐2(1H)‐quinoxalinone and three derivatives (3,7‐dimethyl‐2(1H)‐quinoxalinone, 3‐methyl‐6,7‐dichloro‐2(1H)‐quinoxalinone and 3‐methyl‐7‐nitro‐2(1H)‐quinoxalinone) have been synthesised and analysed by ¹H NMR and IR spectral spectroscopies. The crystal structures have been determined at room temperature from X‐ray single crystal diffraction data for three of them and from powder diffraction data for the nitro derivative. 3‐Methyl‐2(1H)‐quinoxalinone crystallises in the P2₁/c monoclinic system, 3,7‐dimethyl‐2(1H)‐quinoxalinone in the Pbca orthorhombic system and the two others compounds in the P$\overline {1} $ triclinic system. For the nitro derivative, C? H$\cdots $ N short contacts are established between the carbon of the methyl and the double bounded nitrogen of the ring. For the three other compounds N? H$\cdots $ O hydrogen bonds involve the atoms of the heterocyclic ring. Copyright © 2011 John Wiley & Sons, Ltd.     

The reaction of •OH with O2, the decay of O and the pKa of HO – interrelated questions in aqueous free‐radical chemistry

In the reactions of ozone with organic compounds in aqueous solution, O is an abundant intermediate. A basic aspect of its conversion into ^?OH is addressed here. The reactions O^?? + O₂ ? O (1), H⁺ + O^?? ? ^?OH (8), ^?OH + O₂ ? HO (6), and H⁺ + O ? HO (5) are interconnected by a thermodynamic cycle. For equilibria (1) and (8) reliable equilibrium constants, and hence Gibbs energies are available (ΔG⁰(1) = ?32 kJ mol^?1, ΔG⁰(8) = 67 kJ mol^?1). For reaction (6), a Gibbs energy of ΔG⁰(6) = 47 kJ mol^?1 (K₆ = 10^?8.2 M) has now been calculated by G1. From the thermodynamic cycle one hence arrives at ΔG⁰(5) = ?12 kJ mol^?1. This relates to pK_a(HO) = ?2.1. Thus, the HO radical is a very strong acid. This value agrees with a value of ?2.0 obtained from the Bielski and Schwarz relationship for pK_a values of O_xH_y compounds. Reaction (6) must be very slow, 0.1 < k₆ < 10⁴ M^?1 s^?1. Copyright © 2010 John Wiley & Sons, Ltd.     

Über ein weiteres Variationsprinzip im Zusammenhang mit kraftfreien Magnetfeldern

Im Anschluß an ein von Woltjer [1] diskutiertes Variationsproblem wird gezeigt: Die Euler-Lagrange-Gleichungen des Variationsproblems mit der Nebenbedingung wo H = rot A gesetzt ist, sind die Differentialgleichungen der kraftfreien Magnetfelder mit variablem α. Die Nebenbedingung läßt sich für alle Felder H erfüllen, die keinen singulären Punkt mit H = 0 in dem betrachteten Volumen V haben. In persuance of a variational principle discussed by Woltjer [1] it is shown that the Euler-Lagrange-equations of the variational problem with the secondary condition where H = rot A are the differential equations of the force-free magnetic fields with a variable scalar α. The secondary condition can be accomplished for all magnetic fields which do not contain singular points with H = 0 in the volume V under consideration.     

Na‐site energy of P2‐type NaxM O2 (M = Mn and Co)

P2‐type Na_xM O₂ (M = Mn and Co) is a promising cathode material for low‐cost sodium ion secondary batteries. In this structure, there are two different crystallographic Nai (i = 1 and 2) sites with different Coulomb potential $ (\varphi _i)$ provided by M^4–x and O^2–. Here, we experimentally determine a difference ${(\rm \Delta }\varepsilon \equiv \varepsilon _1 - \varepsilon _2)$ of Na‐site energies ${(}\varepsilon _i \equiv e\varphi {\kern 1pt} _i)$ based on the temperature dependence of the site occupancies. We find that ${\rm \Delta }\varepsilon \;{=}\;56\;{K}$ for Na_0.52MnO₂ is significantly smaller than 190 K for Na_0.59CoO₂. We interpret the suppressed ${\rm \Delta }\varepsilon $ in Na_0.52MnO₂ in terms of the screening effect of the Na⁺ charge. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Trends in properties of para‐substituted 3‐(phenylhydrazo)pentane‐2,4‐diones

Trends between the Hammett's σ_p and related normal , inductive σ_I, resonance σ_R, negative and positive polar conjugation and Taft's σ_p° substituent constants and the distance, δ_{N? H} NMR chemical shift, oxidation potential (E_p/2°x, measured in this study by cyclic voltammetry (CV)) and thermodynamic parameters (pK, ΔG⁰, ΔH⁰ and ΔS⁰) of the dissociation process of unsubstituted 3‐(phenylhydrazo)pentane‐2,4‐dione (HL₁) and its para‐substituted chloro (HL₂), carboxy (HL₃), fluoro (HL₄) and nitro (HL₅) derivatives were recognized. The best fits were found for σ_p and/or in the cases of , δ_{N? H} and E_p/2°x, showing the importance of resonance and conjugation effects in such properties, whereas for the above thermodynamic properties the inductive effects (σ_I) are dominant. HL₂ exists in the hydrazo form in DMSO solution and in the solid state and contains an intramolecular H‐bond with the distance of 2.588(3) Å. It was also established that the dissociation process of HL_1–5 is non‐spontaneous, endothermic and entropically unfavourable, and that the increase in the inductive effect (σ_I) of para‐substitutents (? H < ? Cl < ? COOH < ? F < ? NO₂) leads to the corresponding growth of the distance and decrease of the pK and of the changes of Gibbs free energy, of enthalpy and of entropy for the HL_1–5 acid dissociation process. The electrochemical behaviour of HL_1–5 was interpreted using theoretical calculations at the DFT/HF hybrid level, namely in terms of HOMO and LUMO compositions, and of reactivities induced by anodic and cathodic electron‐transfers. Copyright © 2010 John Wiley & Sons, Ltd.     

Gravitationskollaps und Lichtgeschwindigkeit im Gravitationsfeld

An elementary criterion of the stability of a matter sphere against gravitational collapse is given by the circular velocity condition of POINCARÉ : In a space with a spherically symmetric gravitation potential ? (r) and with a spherically symmetric metric gik (e.g., a SCHWARZSCHILD space time) the circular velocity V^* of a particle on the surface r = R of the matter-sphere must be (This condition is a consequence of the virial theorem and of the POINCARÉ theorem.) - However, EINSTEIN 's axiom of causality implies that this velocity V^* must be smaller than the local velocity of light v: V^*2 < v². And this local velocity v is a function of the gravitation potential ?, too: v = v [?]. In the case of NEWTON 's or EINSTEIN 's theory the spherically symmetric gravitation potential is given by the NEWTON ian function ? = fM/r. In the special theory of relativity, we would have v = c (c = EINSTEIN 's fundamental velocity) and grr = 1. Therefore, the specialrelativistic stability condition is R > fMc^?2. - But in the NEWTON ian theory v is depending of the gravitation potential and depends of the boundary condition for the light propagation, also. According to the ansatz of LAPLACE (1799) we have: (emanation-theory of light). But, according to SOLDNER (1801), we have Therefore, we are finding in the case of LAPLACE the same condition R > fMc^?2 as in the SRT. But, in the case of SOLDER 's ansatz non condition for stability is resulting. - In the general relativistic theories the local velocity of light is given by EINSTEIN 's expression According to EINSTEIN 's theory of “static gravitation” (1911/12) we have grr = 1 and therefore the formula and according to the GRT (with - g_ω = grr^?1) we have the formula Therefore, the Hilbert-Laue condition r= R > 3fMc^?2 results as stability condition. From the gravo-optical point of view, in GRT and for the classical ansatz of LAPLACE “black-holes” with bounding states of light result for R ≤ 2fM^?2. But, no “black-holes” are existing according to SOLDNER 's ansatz. However, in GRT each black-hole must be a “collapsar”. But according to the classical theory of LAPLACE we have uncollapsed “black- holes” for the domain .     

Thermochemistry,bond energies and internal rotor barriers of methyl sulfinic acid,methyl sulfinic acid ester and their radicals

Sulfur–Oxygen containing hydrocarbons are formed in oxidation of sulfides and thiols in the atmosphere, on aerosols and in combustion processes. Understanding their thermochemical properties is important to evaluate their formation and transformation paths. Structures, thermochemical properties, bond energies, and internal rotor potentials of methyl sulfinic acid CH₃S(?O)OH, its methyl ester CH₃S(?O)OCH₃ and radicals corresponding to loss of a hydrogen atom have been studied. Gas phase standard enthalpies of formation and bond energies were calculated using B3LYP/6‐311G (2d, p) individual and CBS‐QB3 composite methods employing work reactions to further improve accuracy of the ${\Delta} _{{\bf f}} H_{{\bf 298}}^{{\bf o}} $ . Molecular structures, vibration frequencies, and internal rotor potentials were calculated. Enthalpies of the parent molecules CH₃S(?O)OH and CH₃S(?O)OCH₃ are evaluated as ?77.4 and ?72.7 kcal mol^?1 at the CBS? QB3 level; Enthalpies of radicals C^?H₂? S(?O)? OH, CH₃? S^?(?O)₂, C^?H₂? S(?O)? OCH₃ and CH₃? S(?O)? OC^?H₂ (CBS‐QB3) are ?25.7, ?52.3, ?22.8, and ?26.8 kcal mol^?1, respectively. The CH₃C(?O)O—H bond dissociation energy is of 77.1 kcal mol^?1. Two of the intermediate radicals are unstable and rapidly dissociate. The CH₃S(?O)? O. radical obtained from the parent CH₃? S(?O)? OH dissociates into methyl radical (${\bf CH}_{{\bf 3}}^{{\bf .}} $ ) plus SO₂ with endothermicity (ΔH_rxn) of only 16.2 kcal mol^?1. The CH₃? S(?O)? OC^?H₂ radical dissociates into CH₃? S^?=O and CH₂=O with little or no barrier and an exothermicity of ?19.9 kcal mol^?1. DFT and the Complete Basis Set‐QB3 enthalpy values are in close agreement; this accord is attributed to use of isodesmic work reactions for the analysis and suggests this combination of B3LYP/work reaction approach is acceptable for larger molecules. Copyright © 2010 John Wiley & Sons, Ltd.     

An ab initio study of CX3‐substitution (X = H,F, Cl,Br, I) effects on the static electric polarizability and hyperpolarizability of diacetylene

We report a systematic ab initio and density functional theory (DFT) study of the electric properties of the X₃C? C≡C? C≡C? H (X = H, F, Cl, Br, and I) sequence of substituted diacetylenes. We rely on finite‐field Møller–Plesset perturbation theory and coupled‐cluster calculations with large, flexible basis sets. Our best values at the second‐order Møller–Plesset perturbation theory level for the mean dipole polarizability and second hyperpolarizability are $\overline {{\alpha} } $ /e²aE = 64.46 (? CH₃), 65.59 (? CF₃), 110.11 (? CCl₃), 138.90 (? CBr₃), 184.98 (? CI₃) and $\overline {{\gamma} } $ /e⁴aE = 21020 (? CH₃), 13469 (? CF₃), 32708 (? CCl₃), 57599 (? CBr₃), and 105251 (? CI₃). For comparison, the analogous MP2 values for diacetylene [P.Karamanis and G.Maroulis, Chem. Phys. Lett. 2003 , 376, 403.] are $\overline {{\alpha} } $ /e²aE = 49.17, and $\overline {{\gamma} } $ /e⁴aE = 16227. For the mean first hyperpolarizability we report $\overline {{\beta} } $ /e³aE = ?205.8 (? CH₃), ?55.7 (? CF₃), 120.8 (? CCl₃), 443.8 (? CBr₃), and 725.4 (? CI₃). Copyright © 2010 John Wiley & Sons, Ltd.     

Cosmic Antiproton Spectrum at the Top of the Atmosphere Derived from the New Scaling Model

The new scaling variable model explains the scaling behavior of p + p → p + X inclusive reactions at ISR energies. The cosmic antiproton spectrum has been derived from this model using the primary proton spectrum of RYAN et al. The derived antiproton-proton flux ratio lies within the upper limit value of BOGOMOLOV et al. and CHEN. The estimated antiproton spectrum follows the relation where the antiproton energy E_p is expressed in GeV and the intensity in units (cm² sec sr GeV)^?1.     

Synthesis,properties, and solvatochromism of 1,3‐dimethyl‐5‐{(thien‐2‐yl)‐[4‐(1‐piperidyl) phenyl]methylidene}‐(1H,3H)‐pyrimidine‐2,4,6‐trione

A new merocyanine dye, 1,3‐Dimethyl‐5‐{(thien‐2‐yl)‐[4‐(1‐piperidyl)phenyl]methylidene}‐ (1H, 3H)‐pyrimidine‐2,4,6‐trione 3 , has been synthesized by condensation of 2‐[4‐(piperidyl)benzoyl]thiophene 1 with N,N′‐dimethyl barbituric acid 2 . The solvatochromic response of 3 dissolved in 26 solvents of different polarity has been measured. The solvent‐dependent long‐wavelength UV/Vis spectroscopic absorption maxima, v_max, are analyzed using the empirical Kamlet–Taft solvent parameters π* (dipolarity/polarizability), α (hydrogen‐bond donating capacity), and β (hydrogen‐bond accepting ability) in terms of the well‐established linear solvation energy relationship (LSER): (1) The solvent independent coefficients s , a , and b and (v_max)₀ have been determined. The McRae equation and the empirical solvent polarity index, E_T(30) have been also used to study the solvatochromism of 3 . Copyright © 2007 John Wiley & Sons, Ltd.     

Observation of stimulated Raman scattering in polar tetragonal crystals of barium antimony tartrate trihydrate,Ba[Sb2((+)C4H2O6)2]·3H2O

The non‐centrosymmetric polar tetragonal (P 4₁) barium antimony tartrate trihydrate, Ba[Sb₂((+)C₄H₂O₆)₂]·3H₂O, was found to be an attractive novel semi‐organic crystal manifesting numerous χ ⁽²⁾‐ and χ ⁽³⁾‐nonlinear optical interactions. In particular, with picosecond single‐ and dual‐wavelength pumping SHG and THG via cascaded parametric four‐wave processes were observed. High‐order Stokes and anti‐Stokes lasing related to two SRS‐promoting vibration modes of the crystal, with ω_SRS1 ≈ 575 cm^?1 and ω_SRS2 ≈ 2940 cm^?1, takes place. Basing on a spontaneous Raman investigation an assignment of the two SRS‐active vibration modes is discussed.

     

Sea Level Muon Spectrum Derived from the All Particle Primary Spectrum of GRIGOROV et al.

The all particle primary spectrum of GRIGOROV et al. surveyed by HILLAS has been fitted by a power law fit of the form I_{all particle}(>E) = 1.3 E^?1.65 (cm² s sr)^?1 where E is the energy in GeV/nucleus. Using our recently determined conversion factor for protonnuclei flux ratio of equal energies the primary proton spectrum has been calculated and the result agrees with the Goddard Space Flight Centre primary proton spectrum data satisfactorily. The primary nucleon spectrum has also been calculated and follows the form N_nucleons(E) dE = 2.664 E^?2.75 dE (cm² s sr GeV/nucleon)^?1. Using this primary nucleon spectrum as the source of hadrons and accelerator data for various inclusive reactions viz. used for the estimation of hadronic energy moments in the frame work of FEYNMAN- Scaling, the differential meson spectra have been estimated. The meson atmospheric diffusion equation after Bugaev et al. has been considered for the derivation of sea level muon spectrum. The magnetic spectrograph data of Allkofer et al., Ayre et al., Green et al., and MUTRON group are in accord with the calculated muon spectrum.     

On the similarity solution of evolution equation u t =H(x,t, u,u x,u xx , ...)

Let $$\begin{gathered} u^* = u + \in \eta (x,{\text{ }}t,{\text{ }}u), \hfill \\ \hfill \\ \hfill \\ x^* = x + \in \xi (x, t, u{\text{),}} \hfill \\ \hfill \\ \hfill \\ {\text{t}}^{\text{*}} = {\text{ }}t + \in \tau {\text{(}}x,{\text{ }}t,{\text{ }}u), \hfill \\ \end{gathered}$$ be an infinitesimal invariant transformation of the evolution equation u _t =H(x,t,u,?u/?x,...,? ⁿ :u/?x ⁿ . In this paper we give an explicit expression for \(\eta ^{X^i }\) in the ‘determining equation’ $$\eta ^T = \sum\limits_{i = 1}^n {{\text{ }}\eta ^{X^i } {\text{ }}\frac{{\partial H}}{{\partial u_i }} + \eta \frac{{\partial H}}{{\partial u_{} }} + \xi \frac{{\partial H}}{{\partial x}} + \tau } \frac{{\partial H}}{{\partial t}},$$ where u _i =? ⁱ u/?x ⁱ . By using this expression we derive a set of equations with η, ξ, τ as unknown functions and discuss in detail the cases of heat and KdV equations.     

Perturbative renormalization of composite operators via flow equations II: Short distance expansion

We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive ₄ ⁴ . The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules.Supported by the Swiss National Science Foundation     

A novel probe for determination of electrical surface potential of surfactant micelles: N,N'‐di‐n‐octadecylrhodamine

The peculiarities of the structure of the fluorescent dye N,N'‐di‐n‐octadecylrhodamine advantage its using as an interfacial acid–base probe in aqueous micellar solution of colloidal surfactants. Two long hydrocarbon tails of the dye provide similar orientation of both cation and zwitterion on the micelle/water interface, with the ionizing group COOH exposed to the Stern region in all the systems studied. Further, the charge type of the acid–base couple, A⁺B^±, ensures similar values of the ‘intrinsic’ contribution, pK, to the ‘apparent’ pK value in micelles of different surfactants. This makes the indicator suitable for determination of electrical surface potentials, Ψ. The pKs have been obtained in cationic, anionic, zwitterionic, and nonionic surfactant systems, at various salt background. In total 17 systems were studied. At bulk counterion concentration of ca. 0.05 M, the pK values vary from 2.14 ± 0.07 in n–C₁₈H₃₇N(CH₃)Cl^– micelles to 5.48 ± 0.06 in n–C₁₆H₃₃OSONa⁺ micelles. The Ψ values, corresponding to the Stern region of micelles, have been evaluated as Ψ = 59.16 pK–pK for T = 298.15 K. The pK parameter was equated to the average value of 4.23 in nonionic surfactants (4.12–4.32, depending on the surfactant type). For cetyltrimethylammonium bromide and sodium n‐dodecylsulfate micelles, the Ψ values (±(7–11) mV) appeared to be +118 mV and at bulk Br^? concentration 0.019 M and ?76 mV at bulk Na⁺ concentration 0.020 M, respectively. This satisfactorily agrees with the theoretical values +111 and ?84 mV, estimated using the Oshima, Healy, and White equation for these well‐defined colloidal systems. Finally, not only absorption, but also fluorescence spectra display the same response to changes in bulk pH. Copyright © 2007 John Wiley & Sons, Ltd.