Fermion number creation via electromagnetism

Let an external current, whose support is confined to the space-like slab |x ⁰| < T in two-dimensional spacetime, build up a localized charge density which vanishes for times |x ⁰| > T. We show that the zero mass Dirac quantum field reacts to this current by a c-number shift of the fermion number, i.e. Q _out=Q _in+Q, with , where q(x ⁰) denotes the total external charge. For the shift of the axial charge we obtain an extension of existing results.     

Weber potential from finite velocity of action?

The Weber potential energy U for charges q and q' separated by the distance R is U = (qq'/R)[1 – (dR/dt)²/2c²]. If this potential arises from a finite velocity c of energy transfer Q', where the retarded rate of transfer from q' to q is dQ(t-R/c)/dt = Q'[1 – (dR/dt)/c] and where the advanced rate from q to q' is dQ(t+R/c)/dt = Q'[1 + (dR/dt)/c], then the resultant time-average root-mean-square action is given by . Identifying Q' with the Coulomb potential energy qq'/R, the Weber potential is obtained. Using the same argument, Newtonian gravitation yields a corresponding Weber potential energy, qq'/R being replaced by ( - Gmm'/R).     

De Haas-van Alphen studies of electron-scattering in dilute copper-based alloys

We have used the de Haas-van Alphen (dHvA) effect to study the relaxation times of “neck” and “belly” electrons in copper containing a range of dilute heterovalent and transition-metal solutes. The scattering (Dingle) temperaturex is derived from the variation of signal amplitude with magnetic field at a fixed temperature. Values ofx are believed accurate to within 0.1°K in a range ofx _N(neck) from ≃0.4°K to ≃6°K andx _B(belly) from ≃0.2°K to ≃3°K. Our results may be summarized as follows:Heterovalent solutes (Zn, Cd, Al; up to 0.1 at. %) .Transition-metal solutes (Ni, Co, Fe, Mn, Cr; up to 0.05 at.-%) . An anomalous dependence of dHvA amplitude on magnetic field has been observed for belly oscillations in several very dilute Cu Cr alloys. This anomaly is both concentration and temperature-sensitive, and is probably related to the Kondo effect.     

Measurements of the electronic conductivities of In-doped CaZrO<Subscript>3</Subscript> by a DC polarization technique

The following hydrogen and oxygen concentration cells using the oxide protonic conductors, \textCaZ\textr_0.98\textI\textn_0.02\textO_{3 - d} {\text{CaZ}}{{\text{r}}_{0.98}}{\text{I}}{{\text{n}}_{0.02}}{{\text{O}}_{3 - \delta }} and \textCaZ\textr_0.9\textI\textn_0.1\textO_{3 - d} {\text{CaZ}}{{\text{r}}_{0.{9}}}{\text{I}}{{\text{n}}_{0.{1}}}{{\text{O}}_{{3} - \delta }} , as the solid electrolyte were constructed, and their polarization behavior was studied,

Observables and Statistical Maps

This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the -effect algebra of effects (fuzzy events) and the set of probability measures on a measurable space . An observable is defined, where is the value space of X. It is noted that there exists a one-to-one correspondence between states on and elements of and between observables and -morphisms from to . Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived.     

Changes in the Luminescent Properties of Humic Acids Induced by UV Radiation

Humic acids (HA) are complex, dark, paramagnetic biopolymers, ubiquitus in the soil and aquatic ecosystems. Due to their peculiar properties (multifluorophore system capable of excitation energy transfer, continuous featureless absorption over a wide spectral range, and paramagnetism), HA play an important role as an efficient target for UV solar radiation, O₂, and O₃—detrimental environmental factors which affect the Earth's biosphere. Photooxidation of HA causes changes in the absorption and luminescence properties of HA which may be of significant importance for environmental photophysics and photochemistry. We have studied effects of UV irradiation on the degradation of several commercial HA (Fluka, Merck, and Serva). Aqueous, aerated alkaline solutions of HA (0.1–0.4 g/L in 0.006–0.1 M Na₂CO₃) were irradiated with an electrodeless Hg (254-nm) lamp in a flow system during several hours. After different times of irradiation, solutions were assayed by means of fluorescence (Fl), absorption (UV–Vis), and chemiluminescence (CL) spectroscopy. The data obtained indicate that the free radical-mediated degradative photooxidation of HA macromolecules is accompanied by a very weak, long-lived chemiluminescence (340–800 nm), a gradual decrease in absorbancy with characteristic changes in color coefficients Q _4/6, Q _2.7/6.0, and Q _2.7/4.0, and an increase in the intensity of Fl emission (340- to 560-nm) and excitation (250- to 400-nm) spectra. Processes undergoing these changes are intrinsically associated with the generation of excited states and reactive oxygen species . These processes are expected to play a vital role in the natural environment, e.g., HA-photosensitized decomposition of xenobiotics and solar energy transfer in symbiotic hydrobionts.     

Classical r-matrices and compatible Poisson brackets for coupled KdV systems

The formalism of classical r-matrices is used to construct families of compatible Poisson brackets for some nonlinear integrable systems connected with Virasoro algebras. We recover the coupled KdV [1] and Harry Dym [2] systems associated with the auxiliary linear problem 1 $$\sum\limits_{i = 0}^N {\lambda '\left( {a_i \frac{{{\text{d}}^{\text{2}} }}{{{\text{dx}}^2 }} + {\text{u}}_{\text{i}} } \right)} \psi = 0$$ .     

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.     

Diffusion of proton in alumina-rich nonstoichiometric magnesium aluminate spinel

The phenomenon of the diffusion of proton and deuteron in a single crystal of magnesium aluminate spinel was studied by infrared absorption. The chemical diffusion coefficient of proton was determined by the relaxation time of the absorption intensity upon the substitution of deuteron with proton. The temperature dependence of the chemical diffusion coefficient of proton for was expressed as . The chemical diffusion coefficient of proton was found to be independent of the composition of spinel and of the atmosphere. Paper presented at the 11th Euro Conference on the Science and Technology of Ionics, Batz-sur-Mer, Sept. 9–15 2007.     

Normal ordering and quantum groups

The irreducible R-matrices associated with the quantum Liouville and sine-Gordon equations were classified by the su(2) index l, 2l integer. We find that the associated quantum field theories must have the following equal time operator product expansions in the lattice approximation

Parity-violating neutron spin rotation in hydrogen and deuterium

We calculate the (parity-violating) spin-rotation angle of a polarized neutron beam through hydrogen and deuterium targets, using pionless effective field theory up to next-to-leading order. Our result is part of a program to obtain the five leading independent low-energy parameters that characterize hadronic parity violation from few-body observables in one systematic and consistent framework. The two spin-rotation angles provide independent constraints on these parameters. Our result for np spin rotation is $\frac{1} {\rho }\frac{{d\varphi _{PV}^{np} }} {{dl}} = \left[ {4.5 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {2g^{\left( {^3 S_1 - ^3 P_1 } \right)} + g^{\left( {^3 S_1 - ^3 P_1 } \right)} } \right) - \left[ {18.5 \pm 1.9} \right] rad MeV^{ - \frac{1} {2}} \left( {g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 2} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right)$\frac{1} {\rho }\frac{{d\varphi _{PV}^{np} }} {{dl}} = \left[ {4.5 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {2g^{\left( {^3 S_1 - ^3 P_1 } \right)} + g^{\left( {^3 S_1 - ^3 P_1 } \right)} } \right) - \left[ {18.5 \pm 1.9} \right] rad MeV^{ - \frac{1} {2}} \left( {g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 2} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right), while for nd spin rotation we obtain $\frac{1} {\rho }\frac{{d\varphi _{PV}^{nd} }} {{dl}} = \left[ {8.0 \pm 0.8} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^1 P_1 } \right)} + \left[ {17.0 \pm 1.7} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^3 P_1 } \right)} + \left[ {2.3 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {3g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 1} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right)$\frac{1} {\rho }\frac{{d\varphi _{PV}^{nd} }} {{dl}} = \left[ {8.0 \pm 0.8} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^1 P_1 } \right)} + \left[ {17.0 \pm 1.7} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^3 P_1 } \right)} + \left[ {2.3 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {3g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 1} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right), where the g ^(X-Y), in units of $MeV^{ - \frac{3} {2}}$MeV^{ - \frac{3} {2}}, are the presently unknown parameters in the leading-order parity-violating Lagrangian. Using naıve dimensional analysis to estimate the typical size of the couplings, we expect the signal for standard target densities to be $\left| {\frac{{d\varphi _{PV} }} {{dl}}} \right| \approx \left[ {10^{ - 7} \ldots 10^{ - 6} } \right]\frac{{rad}} {m}$\left| {\frac{{d\varphi _{PV} }} {{dl}}} \right| \approx \left[ {10^{ - 7} \ldots 10^{ - 6} } \right]\frac{{rad}} {m} for both hydrogen and deuterium targets. We find no indication that the nd observable is enhanced compared to the np one. All results are properly renormalized. An estimate of the numerical and systematic uncertainties of our calculations indicates excellent convergence. An appendix contains the relevant partial-wave projectors of the three-nucleon system.     

A Complete Set of Riemann Invariants

There are at most 14 independent real algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space. In the general case, these invariants can be written in terms of four different types of quantities: R , the real curvature scalar, two complex invariants I and J formed from the Weyl spinor, three real invariants I₆, I₇ and I₈ formed from the trace-free Ricci spinor and three complex mixed invariants K, L and M. Carminati and McLenaghan [5] give some geometrical interpretations of the role played by the mixed invariants in Einstein-Maxwell and perfect fluid cases. They show that 16 invariants are needed to cover certain degenerate cases such as Einstein-Maxwell and perfect fluid and show that previously known sets fail to be complete in the perfect fluid case. In the general case, the invariants I and J essentially determine the components of the Weyl spinor in a canonical tetrad frame; likewise the invariants I₆, I₇ and I₈ essentially determine the components of the trace-free Ricci spinor in a (in general different) canonical tetrad frame. These mixed invariants then give the orientation between the frames of these two spinors. The six real pieces of information in K, L and M are precisely the information needed to do this. A table is given of invariants which give a complete set for each Petrov type of the Weyl spinor and for each Segre type of the trace-free Ricci spinor This table involves 17 real invariants, including one real invariant and one complex invariant involving , and in some degenerate cases.     

Al,F-doped new perovskite lithium fast ion conductor Li3x La2/3−x□1/3−2x Ti1−y Al y O3−y F y (x=0.11)

Al, F-doped new perovskite lithium ion conductors (x=0.11) have been prepared by solid state reaction. It is found that a pure perovskite-structured phase with space group of P4mm(99) exits in the composition range of 0<y≤0.10. The sample with y=0.02 possesses the highest ionic conductivity of 1.06×10⁻³ S/cm at room temperature, and its decomposing voltage is 2.3 V. The factors affecting the conductivity of this system are discussed.     

An analytical expression for the specific capacity of lithium ion cells

The concentration of lithium ions in the cathode of lithium ion cells has been obtained by solving the materials balance equation $$\frac{{\partial c}}{{\partial t}} = \varepsilon ^{1/2} D\frac{{\partial ^2 c}}{{\partial x^2 }} + \frac{{aj_n (1--t_ + )}}{\varepsilon }$$ by Laplace transform. On the assumption that the cell is fully discharged when there are zero lithium ions at the current collector of the cathode, the discharge timet _d is obtained as $$\tau = \frac{{r^2 }}{{\pi ^2 \varepsilon ^{1/2} }}\ln \left[ {\frac{{\pi ^2 }}{{r^2 }}\left( {\frac{{\varepsilon ^{1/2} }}{J} + \frac{{r^2 }}{6}} \right)} \right]$$ which, when substituted into the equationC=It _d /M, whereI is the discharge current andM is the mass of the separator and positive electrode, an analytical expression for the specific capacity of the lithium cell is given as $$C = \frac{{IL_c ^2 }}{{\pi {\rm M}D\varepsilon ^{1/2} }}\ln \left[ {\frac{{\pi ^2 }}{2}\left( {\frac{{FDc_0 \varepsilon ^{3/2} }}{{I(1 - t_ + )L_c }} + \frac{1}{6}} \right)} \right]$$      

Elliptically polarized fields and responses

An ellipticaliy polarized field applied to a physical system and related responses are very common in physics. Due to the loss of symmetry, the response problems are very difficult to solve, and are usually described by nonlinear and unseparable equations. By introducing a time transformation=(1/)tan^–1(r tant), wherer is the ratio between the two components, one may reset the symmetry of the field. The equation

An exterior solution of the einstein field equations for a rotating infinite cylinder

We give here a new exact solution to the exterior Einstein field equations for a rotating infinite cylinder. The solution is characterized by an everywhere singular metric. In the Papapetrou canonical coordinates, the 3-force acting on a radially moving test particle is $f^\alpha = \left( {G\frac{m}{{\sqrt {\Gamma - \upsilon ^2 } }}{\text{ }}\frac{\lambda }{\rho },{\text{ 0,}} - \frac{m}{{\sqrt {\Gamma - \upsilon ^2 } }}{\text{ }}\frac{{C\upsilon }}{\rho }{\text{ }}} \right)$ where λ>0.f ¹ andf ³ are, respectively, the gravitational and Coriolis forces. The gravitational force is, therefore, repulsive.     

Secular-free solution up to third order of a model nonlinear equation for dispersive waves

The perturbation method of Lindstedt is applied to study the non linear effect of a nonlinear equation $$\nabla ^2 {\rm E} - \frac{1}{{c^2 }}\frac{{\partial ^2 {\rm E}}}{{\partial t^2 }} - \frac{{\omega _0^2 }}{{c^2 }}{\rm E} + \frac{{2v}}{{c^2 }}\frac{{\partial {\rm E}}}{{\partial t}} + E^2 \left[ {\frac{{\partial {\rm E}}}{{\partial t}} \times A} \right] = 0,$$ where (A. E)=0 andA,c, ω ₀ andν are constants in space and time. Amplitude dependent frequency shifts and the solution up to third order are derived.     

Laplace Sequences of Surfaces in Projective Space and Two-Dimensional Toda Equations

We find that the Laplace sequences of surfaces of period n in projective space P _n–1 have two types, while type II occurs only for even n. The integrability condition of the fundamental equations of these two types have the same form