(<Emphasis Type="Italic">p</Emphasis> + 1)-Algebra for a super <Emphasis Type="Italic">p</Emphasis>-brane: the Nambu bracket reformulation

We express the covariant actions of a super p-brane and the corresponding equations of motion, in flat and curved superspaces, in terms of the Nambu (p + 1)-brackets. These brackets make the (p + 1)-algebra structure of a super p-brane manifest. For the flat superspace, this reconstruction of the action also allows reformulating it in terms of two sets of differential forms.     

Semiclassical bosonic <Emphasis Type="Italic">D</Emphasis>-brane boundary states in curved spacetime

In this paper we discuss the existence of quantum D-brane states in the strong gravitational field and in the presence of a constant Kalb-Ramond field. A semiclassical string quantization method in which the spacetime metric g _AB and the constant antisymmetric Kalb-Ramond field b _AB are treated exactly is employed. In this framework, the semiclassical D-branes are defined at the first order perturbation around the trajectory of the center-of-mass of a string. The set of equations the semiclassical D-branes must satisfy in a general strong gravitational field are given. These equations are solved in the AdS background where it is shown that a D-brane coherent state exists if the operators that project the string fields onto the corresponding Neumann and Dirichlet directions satisfy a set of algebraic constraints. A second set of equations that should be satisfied by the projectors in order that the semiclassical state be compatible with the global structure of the D-brane are derived in the particle limit of a string in the torsionless AdS background.     

<Emphasis Type="Italic">V</Emphasis>-<Emphasis Type="Italic">A</Emphasis> sum rules with <Emphasis Type="Italic">D</Emphasis> = 10 operators

The difference of vector and axial-vector charged current correlators is analyzed by means of QCD sum rules. The contribution of 10-dimensional 4-quark condensates is calculated and its value is estimated within the framework of the factorization hypothesis. It is compared to the result obtained from an operator fit of Borel sum rules in the complex q ²-plane, calculated from experimental data on hadronic -decays. This fit gives accurate values of the light quark condensate and the quark-gluon mixed condensate. The size of the high-order operators and the convergence of the operator series are discussed.Received: 10 May 2004, Revised: 7 September 2004, Published online: 18 November 2004     

Analysis of the spectrum of the Zn-like Kr VII ion: Highly excited 4<Emphasis Type="Italic">p</Emphasis>4<Emphasis Type="Italic">d</Emphasis> and 4<Emphasis Type="Italic">p</Emphasis>5<Emphasis Type="Italic">s</Emphasis> configurations

The spectrum of the Zn-like Kr VII ion, excited in a capillary discharge and recorded with a high resolution in the wavelength range of 300–1000 Å, was studied. Previously performed identification of the transitions from the levels of the 4s4f, 4s5s, 4s5p, and 4s5d configurations is confirmed and extended, and the energies of these levels are specified. The (4p ²+4s4d)?4p4d and (4p ²+4s5s)?4p5s transitions are identified for the first time, and the energies of all the levels of the 4p4d and 4p5s configurations are determined. The results of the analysis performed are confirmed by semiempirical calculations in terms of the Hartree-Fock method. These results are also shown to conform to the experimental data obtained for lighter ions of the Zn I isoelectronic sequence.     

Multiple two-variable <Emphasis Type="Italic">p</Emphasis>-adic <Emphasis Type="Italic">q-L</Emphasis>-function and its behavior at <Emphasis Type="Italic">s</Emphasis> = 0

The objective of this paper is to construct a multiple p-adic q-L-function of two variables which interpolates multiple generalized q-Bernoulli polynomials. By using this function, we solve a question of Kim and Cho. We also define a multiple partial q-zeta function which is related to the multiple q-L-function of two variables. Finally, we give a finite-sum representation of the multiple p-adic q-L-function of two variables and prove a multiple q-extension of the generalized formula of Diamond and Ferrero-Greenberg.     

Parameterization of the spectra of configurations 3<Emphasis Type="Italic">p</Emphasis>4<Emphasis Type="Italic">f</Emphasis> and 3<Emphasis Type="Italic">p</Emphasis>5<Emphasis Type="Italic">f</Emphasis> of a phosphorus ion P II. Gyromagnetic ratios

In the one-configuration approximation, in the formalism of irreducible tensor operators, and in the intermediate (real) coupling scheme, numerical values of the fine-structure parameters are determined for the 3p4f and 3p5f highly excited configurations of the P II phosphorus ion with the energy-operator matrix in the LK-coupling approximation. With these values of the fine-structure parameters, the energy-operator matrix is numerically diagonalized in the LS-coupling approximation. The gyromagnetic ratios calculated in both basis sets in the absence of a field are compared with one another, as well as with their vector counterparts and the experimental g-factors available for the 3p4f configuration. The experimental and theoretical g-factors calculated with the LS basis set are in good agreement with the sole exception of the ³ F ₂ level. Note that the calculation of g-factors from the Zeeman splitting in the linear region totally confirmed their agreement with the values calculated in the LS basis set (g _LS ) in the absence of a field. The gyromagnetic ratios are the main objectives of this and previous papers, especially for configurations for which experimental data are absent. Apart from the g-factors, the specific features of Zeeman splitting (the crossings and anticrossings of magnetic components) in the 3p5f configurations were determined. These data are to be compared with results of future experiments. Comparison of gyromagnetic ratios calculated in the intermediate coupling scheme with their vector counterparts showed that most levels of the configurations studied are closer than in the LK-coupling scheme.     

Energy dependence of Cronin momentum in saturation model for <Emphasis Type="Italic">p</Emphasis> + <Emphasis Type="Italic">A</Emphasis> and <Emphasis Type="Italic">A</Emphasis> + <Emphasis Type="Italic">A</Emphasis> collisions

The energy dependence of the Cronin momentum for p + A and A + A collisions in the saturation model are calculated. This dependence is consistent with simple dimensional considerations and can be used to test the validity of the saturation model. It gives the possibility to distinguish the different variants of the saturation model with precise experimental data and to measure the x dependence of the saturation momentum.     

Tsallis <Emphasis Type="Italic">p</Emphasis>,<Emphasis Type="Italic">q</Emphasis>-deformed Touchard polynomials and Stirling numbers

In this paper, we develop and investigate a new two-parametrized deformation of the Touchard polynomials, based on the definition of the NEXT q-exponential function of Tsallis. We obtain new generalizations of the Stirling numbers of the second kind and of the binomial coefficients and represent two new statistics for the set partitions.     

<Emphasis Type="Italic">p</Emphasis>-Nuclearity in a New Perspective

In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25.     

Powerful diode nanosecond current opening switch made of <Emphasis Type="Italic">p</Emphasis>-silicon (<Emphasis Type="Italic">p</Emphasis>-SOS)

The nanosecond semiconductor diode-based opening switch (SOS-diode) capable of switching currents with densities up to several tens of kiloamperes per cubic centimeter represents a p⁺p’Nn⁺ silicon structure fabricated by the deep simultaneous diffusion doping (to about 200 μm) of n-Si by Al and B from one side and P from the other. In the SOS mode, first a short pulse of forward current passes through the diode and then a fast-growing pulse of reverse voltage is applied. A resulting pulse of reverse current carries away injected holes and thereby forms a plasma front in the p’ layer, which moves toward the p’N junction. When the hole concentration in the flow exceeds the dopant concentration in the p’ layer, a space charge region arises in this layer, the resistivity of the diode increases sharply, and the current switches to a load connected parallel to the diode. Early results concerning an alternative configuration of the SOS diode are presented. Here, the diode was made by the rapid simultaneous diffusion of B and P from the opposite sides of a p-Si wafer to a depth of 60-80 μm. If a short pulse of forward current is passed through such a p⁺pn⁺ structure and a pulse of reverse voltage is then applied, a plasma front arising in the p⁺ region moves toward the p⁺p interface through the heavily doped (i.e., low-resistivity) p⁺ region. Having crossed this interface, the front passes into a low-doped region, where the hole concentration in the flow becomes much higher than the dopant concentration and a space charge region causing the current to pass to the load forms at once. It is shown experimentally that, all other things being the same, the time of current breaking in the p-SOS-diode is roughly twice as short as in the conventional n-SOS-diode, switched currents are considerably lower, and the fabrication technique of p-SOS-diodes is much simpler. Ways of optimizing the design of the semiconductor structure of the p-SOS-diode to further raise the speed are outlined.     

<Emphasis Type="Italic">p</Emphasis>-adic Superspaces and Frobenius

The notion of a p-adic superspace is introduced and used to give a transparent construction of the Frobenius map on p-adic cohomology of a smooth projective variety over (the ring of p-adic integers), as well as an alternative construction of the crystalline cohomology of a smooth projective variety over (finite field with p elements). Partly supported by NSF grant No. DMS 0505735.     

Substituent Dependent Optical Properties of <Emphasis Type="Italic">p</Emphasis>-phenyl Substituted ethenyl-<Emphasis Type="Italic">E</Emphasis>-thiophenes

Various electron donor and acceptor substituted (NO₂, CN, Cl, H, OCH₃, NH₂) p-phenyl ethenyl-E- thiophenes (1–6) were synthesized and substituent dependent optical properties (dipole moment, transition dipole moment, oscillator strength, optical band gap, hyperpolarizability) were studied using Solvatochromism and Density functional theory. It is shown that thiophene acts as a weak electron donor in presence of an electron withdrawing p-phenyl substituent (NO₂, CN, Cl), whereas thiophene acts as a weak electron acceptor in presence of an electron donating p-phenyl substituent (OCH₃, NH₂). In comparison to ethenyl thiophene 4, the HOMO-LUMO energy band gap is decreased upon increasing the electron donating or electron withdrawing capacity of p-phenyl substituent. From the excited state dipole moment calculation, it is shown that the excited state is highly dipolar for nitro and amino compounds 1 and 6, whereas compounds 2–5 show a non-polar excited state. As compared to the ethenyl thiophene 4, the first hyperpolarizability (β) increases upon substitution either with a strong electron withdrawing or strong electron donating p-phenyl substituent. A large β value is found for p-nitro phenyl ethenyl-E-thiophene and p-amino phenyl ethenyl-E- thiophene. Overall, these studies provide useful information in understanding the optical properties of phenyl and heterocyclic based ethenyl systems.     

Dielectron widths of the <Emphasis Type="Italic">S</Emphasis>-, <Emphasis Type="Italic">D</Emphasis>-vector bottomonium states

The dielectron widths of Y(nS)(n = 1, …, 7) and vector decay constants are calculated using the relativistic string Hamiltonian with a universal interaction. For Y(nS) (n = 1, 2, 3) the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For Y(10580) and Y(11020) a good agreement with experiment is reached only if the 4S-3D mixing (with a mixing angle θ = 27°± 4°) and 6S-5D mixing (with θ = 40°±5°) are taken into account. The possibility to observe higher “mixed D-wave” resonances, $ \tilde \Upsilon $ \tilde \Upsilon (n ³ D ₁) with n = 3, 4, 5 is discussed. In particular, $ \tilde \Upsilon $ \tilde \Upsilon (≈11120), originating from the pure 5³ D ₁ state, can acquire a rather large dielectron width, ∼130 eV, so that this resonance may become manifest in the e ⁺ e ⁻ experiments. On the contrary, the widths of pure D-wave states are very small, Γ _ee (n ³ D ₁)≤ 2 eV.     

Decay properties of new <Emphasis Type="Italic">D</Emphasis>-mesons

We consider radiative and pionic decays of the new D _s -mesons in the framework of a phenomenologically motivated approach. Present data on ratios of the two kinds of decays can be described without explicitly using a 4-quark component. Most probably, the isospin violation in decays of different D _s -mesons is not universal, and the binding potential should be different from Coulombic. New precise measurements may provide further clarification for the nature of the D _s excited states.Received: 10 March 2004, Published online: 14 September 2004PACS: 14.40.Lb Charmed mesons - 13.20.Fc Decays of charmed mesons - 13.25.Ft Decays of charmed mesons     

<Emphasis Type="Italic">D</Emphasis> instanton on the linear-dilaton background

It is shown that, in addition to a standard asymptotically flat D instanton, IIB superstring theory contains an instanton-type excitation on the linear-dilaton background. The new solution is asymptotically flat, but the dilaton grows linearly at infinity. The total action of this configuration diverges, but the instanton action proper becomes finite upon subtracting an infinite background contribution.     

A semiempirical calculation of the fine and Zeeman structure of 4<Emphasis Type="Italic">p</Emphasis>4<Emphasis Type="Italic">f</Emphasis> and 4<Emphasis Type="Italic">p</Emphasis>5<Emphasis Type="Italic">f</Emphasis> configurations of Ge I. Gyromagnetic ratios

The gyromagnetic ratios (g-factors) belong to the most important characteristics of atoms. For the 4p4f configuration of a germanium atom experimental values of g-factors are available only for four levels, while similar experimental data on the 4p5f configuration of Ge I are absent. Therefore, a theoretical study of the fine and Zeeman structures is topical for determining the gyromagnetic ratios. All the calculations are performed in the one-configuration approximation with the energy-operator matrix containing a maximum possible number of interactions, including magnetic: spin-orbit (own and other), spin-spin, and also orbitorbit interaction. The fine structure has been examined in three (LS, LK, and jK) approximations in order to establish the nature of coupling in the systems studied and the reliability of g-factors. Apart from the g-factors, in studying the Zeeman splitting, its specific features—the crossing and anticrossing fields of magnetic components— have been determined. A comparative analysis of g-factors was performed that showed that our results are in agreement with the available, albeit few in number, experimental data. At all stages, the corresponding energy-operator matrices were numerically diagonalized, i.e., all the results presented in the paper were obtained in the intermediate coupling scheme.     

Fermion superfluid with hybridized <Emphasis Type="Italic">s</Emphasis>- and <Emphasis Type="Italic">p</Emphasis>-wave pairings

Ever since the pioneering work of Bardeen, Cooper and Schrieffer in the 1950s, exploring novel pairing mechanisms for fermion superfluids has become one of the central tasks in modern physics. Here, we investigate a new type of fermion superfluid with hybridized s- and p-wave pairings in an ultracold spin-1/2 Fermi gas. Its occurrence is facilitated by the co-existence of comparable s- and p-wave interactions, which is realizable in a two-component ⁴⁰K Fermi gas with close-by s- and p-wave Feshbach resonances. The hybridized superfluid state is stable over a considerable parameter region on the phase diagram, and can lead to intriguing patterns of spin densities and pairing fields in momentum space. In particular, it can induce a phase-locked p-wave pairing in the fermion species that has no p-wave interactions. The hybridized nature of this novel superfluid can also be confirmed by measuring the s- and p-wave contacts, which can be extracted from the high-momentum tail of the momentum distribution of each spin component. These results enrich our knowledge of pairing superfluidity in Fermi systems, and open the avenue for achieving novel fermion superfluids with multiple partial-wave scatterings in cold atomic gases.     

Statistical properties of random environment of 1<Emphasis Type="Italic">D</Emphasis> quantum <Emphasis Type="Italic">N</Emphasis>-particles system in external field

The investigation of 1D quantum N-particle system (PS) with relaxation in the random environment under the influence of external field is conducted within the framework of the stochastic differential equation of the Langevin—Schrödinger (L—Sch) type. Using L—Sch equation, the 2D second-order nonstationary partial differential equation is found, which describes the quantum distribution in the environment, depending on the energy of nonperturbed 1D quantum N-PS and on the external field parameters. It is shown that the average value of the interaction potential between 1D disordered quantum N-PS and the external field, has the ultraviolet divergence. This problem is solved by the renormalization of the equation for the function of quantum distribution. It is shown that it has a sense of dimensional renormalization which is characteristic for the quantum field theory. Critical properties of the environment are investigated in detail. The possibility of the first-order phase transition in the environment distribution depending on amplitude of an external field is been shown.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Cosmology from <Emphasis Type="Italic">q</Emphasis>-theory

From a macroscopic theory of the quantum vacuum in terms of conserved relativistic charges (generically denoted by q ^(a) with label a), we have obtained, in the low-energy limit, a particular type of f(R) model relevant to cosmology. The macroscopic quantum-vacuum theory allows us to distinguish between different phenomenological f(R) models on physical grounds. The text was submitted by the authors in English.