Weber electrodynamics: part III. mechanics,gravitation

Weber electrodynamics predicts the Kaufmann-Bucherer experiments and the fine structure energy level splitting of the H-atom (neglecting spin) without mass change with velocity (i.e., mass ). The Weber potential for the gravitational case yields Newtonian mechanics, confirming Mach's principle. It provides a cosmological condition yielding an estimated radius of the universe of 8 × 10⁹ light years. Despite these successes, the independent evidence for Kaufmann mechanics, where mass changes with velocity (i.e., mass ) is convincing. Perhaps a slight alteration may make the Weber theory compatible with Kaufmann mechanics.     

Thermoelectric power of YBa2Cu3Ox in equilibrium with gas phases

Thermoelectric power (TP) and electrical conductivity (EC) measurements were performed for YEa₂Cu₃O_x at 1128 K under controlled oxygen partial pressure varying between 50 and 10⁵ Pa. Three regimes are observed for the electrical properties. At low both TP and EC remain constant with . In the medium range sharp changes of both electrical parameters occur; TP changes sign from positive above 4×10² Pa to negative below this value. In the high region (>7.6×10³ Pa) TP vs log exhibits two slopes; 5.1 below 1.5×10⁴ Pa and 8.4 above this value. The slopes can be discussed in terms of the defect structure involving singly and doubly ionized oxygen vacancies below and above 7.6×10³ Pa, respectively.     

Glueball Spectroscopy in Regge Phenomenology

We show that linear Regge trajectories for mesons and glueballs, and the cubic mass spectrum associated with them, determine a relation between the masses of the meson and the scalar glueball, , which implies MeV. We also discuss relations between the masses of the scalar, tensor and 3^-- glueballs, , which imply MeV.     

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

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.     

Energy dependence of the charge exchange reaction from muonic hydrogen to oxygen

The charge exchange reaction of negative muons from the atom to oxygen has been measured in gaseous mixtures of H₂ + O₂. The measurements were performed at three different relative oxygen concentrations ranging from 0.2% to 0.8% and total pressures 3.5–15 bar. A mean transfer rate of , describing the transfer from the ground state of thermalized atoms to oxygen, was determined. In order to investigate the energy dependence of the transfer rate, Monte Carlo simulations of the thermalization and the muon transfer were carried out. The comparison of measured and simulated time spectra yielded an epithermal transfer rate =3.9 10¹¹ s^-1 in the energy interval 0.12–0.22 eV. The analysis with the model of Two components shows that all measured time spectra can be reproduced with the same set of parameters.     

The Chern classes of Sobolev connections

AssumeF is the curvature (field) of a connection (potential) onR ⁴ with finiteL ² norm . We show the chern number (topological quantum number) is an integer. This generalizes previous results which showed that the integrality holds forF satisfying the Yang-Mills equations. We actually prove the natural general result in all even dimensions larger than 2.     

Influence of Torsional Vibrations on the Photoluminescence Characteristics of Dye Solutions

The influence of torsional vibrations of fluorophore molecule on polarization spectra and absorption/emission vibronic band profiles of isotropic dye solutions has been considered. Basing on the concept of luminescence center (LC) and assuming that (1) electronic transitions in the LC may be assisted by torsion-vibrational excitations, and (2) reorientations of the LC can be described in terms of Stokes–Einstein rotational diffusion, the formula for time-dependent emission anisotropy, as a function of excitation, , and observation, frequencies has been obtained. It comprises depolarization by combined reorientations of the fluorophore molecule, i.e., its torsional vibrations with respect to the LC, and rotational diffusion of the LC. This approach is a generalization of the appropriate results obtained earlier by Ehrenberg and Rigler and, independently, by Chuang and Isenthal. The considered model has specific property that the torsional vibrations appear both as depolarizing factor for and as shaping factor for absorption/emission bands, resulting in the variation of the emission anisotropy across appropriate band profiles. This is demonstrated graphically using numerical results obtained for a simplified, one-dimensional torsional oscillator. It is also shown that observed absorption and emission spectra of coumarin solutions can be reproduced using this model with appropriate potentials for restoring forces.     

$ {\rm{V}}_2 {\rm{O}}_5^ + $ {\rm{V}}_2 {\rm{O}}_5^ + " border="0"> reaction with C2H4: theoretical considerations of experimental findings

Density functional calculations have been performed for the reactions towards ethylene considering atomic and molecular oxygen loss, oxygen transfer and association reactions. The oxygen transfer channel to ethylene is energetically favourable in contrast to the oxygen loss. This is in agreement with the experimental results [1] which show that does not lose atomic oxygen during the collision induced dissociation at thermal energies. A radical cation mechanism based on structure-reactivity relation of cluster is proposed to explain oxygen transfer channel indicating that this reaction is size selective.     

Multipoint Series of Gromov–Witten Invariants of CP1

We derive explicit formulas for the multipoint series of in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of . We also obtain explicit formulas for the Hodge integrals , in the cases i=0 and 1.     

On Continuous and Differential Hochschild Cohomology

We show that there are canonical isomorphisms between Hochschild cohomology spaces , where is the algebra of smooth functions on a manifold M and the space of skew multivector fields over M. This implies that continuous and differential deformation theories of coincide.     

The low-temperature afterglow in N2–ε·CH4 gas mixtures

The influence of the small methane impurities on the pure nitrogen afterglow was studied in DC flowing plasma reactor in wide range of methane concentrations (0.01–400 ppm) at different wall temperatures of the reactor observation part (77–300 K). The relative vibrational distributions of states have been calculated from the recorded spectra in pure nitrogen. We observed strong quenching of the nitrogen pink afterglow at methane concentrations of a few ppm, however the pink afterglow intensity was growing up at the methane concentrations under 1 ppm. Simultaneously, the maximum pink afterglow intensity was observable at later decay times with the increase of the methane concentration. At low wall temperatures, especially at later decay times, we observed extremely high sensitivity of the pure nitrogen to the methane pretence in the discharge. Thus we are able to detect the methane concentrations in order of 0.01 ppm. We also observed the higher transitions of the CN violet system which are usually observed in the spectra of space emission sources. The method detecting hydrocarbon and fluorocarbon impurities in pure nitrogen is based on the results of the above mentioned experiments. We present first results of some experiments studying the polyhydrocarbon destruction rates measured by this new sensitive method. Finally, we designed also the simple kinetic model describing the processes during the afterglow in the N₂–·CH₄ mixture.     

Zero Energy Modes of Massless Fermions in S3R Spacetime

The Dirac-type equation on topology is worked out and the complete set of solutions in the particular physical case of the zero-energy modes of the massless field quanta is derived. Unlike the Minkowskian case, the 1/2fermionic vacua on the manifold is made of nontrivial static modes of defined chirality.     

Empirical formulas for the fermion spectra and Yukawa matrices

We present empirical relations that connect the dimensionless ratios of low energy fermion masses for the charged lepton, up-type quark and down-type quark sectors and the CKM elements: and . Explaining these relations from first principles imposes strong constraints on the search for the theory of flavor. We present a simple set of normalized Yukawa matrices, with only two real parameters and one complex phase, which accounts with precision for these mass relations and for the CKM matrix elements and also suggests a simpler parametrization of the CKM matrix. The proposed Yukawa matrices accommodate the measured CP-violation, giving a particular relation between standard model CP-violating phases, . According to this relation the measured value of is close to the maximum value that can be reached, for . Finally, the particular mass relations between the quark and charged lepton sectors find their simplest explanation in the context of grand unified models through the use of the Georgi-Jarlskog factor.Received: 31 July 2004, Revised: 22 September 2004, Published online: 9 November 2004     

Er-Yb Codoped Ferroelectrics for Controlling Visible Upconversion Emissions

Under a 980 nm laser pumping, quenching of green upconversion (UC) emission accompanied with enhancement of red UC emission observed was dominated by the energy back-transfer (EBT) process in Er³⁺ and Yb³⁺ co-doped PbTiO₃, BaTiO₃, and SrTiO₃ polycrystalline powders. The efficiency of the EBT process depends not only on Yb³⁺ concentration but also on level match of the doped Er³⁺ and Yb³⁺ ions caused by the crystal fields with different symmetries. Our UC emission spectra and X-ray diffraction confirm that the centrosymmetric crystal field arising from reducing tetragonality causes level match of transition of Er³⁺ and of Yb³⁺. This level match is responsible for enhancing red UC emission.     

Ion exchange equilibrium between cation exchange membranes and aqueous solutions of K+/Na+, K+/Ca2+, and Na+/Ca2+

Equilibrium between synthetic ion exchangers and solutions of cations has been the subject of this investigation. Competitive ion exchange reactions were studied for two cation exchange membranes (CMX and CRP) involving K⁺, Na⁺, and Ca²⁺ ions. The ionic strength of the equilibrating solutions was maintained constant, but the molar fraction varied; all experiments were conduced with nitrate as nonexchanging anions at 25 °C. Adsorption isotherm for the three binaries systems: K⁺/Na⁺, K⁺/Ca²⁺, and Na⁺/Ca²⁺ were studied. The obtained results show that potassium was the most strongly sorbed and the selectivity order for CMX and CRP membranes is K⁺>Ca²⁺>Na⁺ at 0.1 M, under the experimental conditions. Selectivity coefficients , , and for the three binaries and for the two membranes were determined at an ionic strength of 0.1 M and at a constant temperature of 25 °C. We remark that all the selectivity coefficient values are quite different from the unit. Ternary equilibrium was taken for the Ca²⁺/K⁺/Na⁺ system. It was found that binary selectivity data could be successfully used to predict the ternary ion exchange equilibrium.     

Energy cost of negative pion production on deuterium-tritium target

The negative pion production by deuterons (T ₀=0.8 GeV/nucl.) was calculated for a cylindrical gaseous deuterium-tritium target (the density of DT-mixture is=0.5). Revised cross sections of nucleon-nucleus interaction were used in a Monte Carlo simulation and multiple nucleon-nuclei collisions were taken into account. The energy cost of negative pion production is in the cylindrical target 30 m long and in diameter, while the energy of nucleous escaping from this target is _N=76% of the initial energy of the deuteron beam. For the target with a shaped surface, the volume of which (V=0.32 m³) is only 8.5% of the previous volume, the following parameters were obtained and _N=78%.     

Background-free detection of trapped ions

We demonstrate a Doppler cooling and detection scheme for ions with low-lying D levels which almost entirely suppresses scattered laser light background, while retaining a high fluorescence signal and efficient cooling. We cool a single ion with a laser on the $^{2}\mathrm{S}_{\mbox{\tiny$1/2$}}\leftrightarrow {^{2}\mathrm{P}}_{\mbox{\tiny$1/2$}}$ transition as usual, but repump via the $^{2}\mathrm{P}_{\mbox{\tiny$3/2$}}$ level. By filtering out light on the cooling transition and detecting only the fluorescence from the $^{2}\mathrm{P}_{\mbox{\tiny$3/2$}}\rightarrow {^{2}\mathrm{S}}_{\mbox{\tiny$1/2$}}$ decays, we suppress the scattered laser light background count rate to 1 s^?1 while maintaining a signal of 29000 s^?1 with moderate saturation of the cooling transition. This scheme will be particularly useful for experiments where ions are trapped in close proximity to surfaces, such as the trap electrodes in microfabricated ion traps, which leads to high background scatter from the cooling beam.     

Infrared multiple photon dissociation spectroscopy of transition metal oxide cluster cations

Infrared spectra in the range of 530–1400 cm^–1 are presented for tantalum oxide cluster cations (x = 3, 4 and 6). These spectra are obtained via multiple photon dissociation (MPD) spectroscopy of free cluster cations moving in a molecular beam. The IR spectra for are compared to spectra of as well as to the experimental data available for vanadium oxide cluster cations from IR-MPD spectroscopy. For and the IR spectra exhibit very strong similarities (including the band positions), whereas absorption bands in are relatively blue-shifted by about 20–40 cm^–1.     

On the Schrödinger equation and the eigenvalue problem

If _k is thek ^th eigenvalue for the Dirichlet boundary problem on a bounded domain in ⁿ , H. Weyl's asymptotic formula asserts that , hence . We prove that for any domain and for all . A simple proof for the upper bound of the number of eigenvalues less than or equal to - for the operator –V(x) defined on ⁿ (n3) in terms of is also provided.Research partially supported by a Sloan Fellowship and NSF Grant No. 81-07911-A1