Super <Emphasis Type="Italic">D</Emphasis>-Differentiation for <Emphasis Type="Italic">R</Emphasis><Superscript> ∞ </Superscript>-Supermanifolds

The concept of ‘D-Differentiation’, which, in the context of smooth manifolds, generalises Lie and covariant differentiation, is extended to R ^∞-supermanifolds under the name of ‘Super D-Differentiation’. This is done by defining new (non-linear) mappings, called ‘μ-mappings’ and by relating their non-linearity to the Leibniz rule that a derivation must satisfy when it acts on a tensor product. The resulting axiomatics, which is basis-independent and coordinate-free, is then expressed in a general basis (not necessarily holonomic). Super Lie and Super covariant differentiation are, amongst others, special cases of Super D-Differentiation. In particular, the transformation rules for the connection coefficients and the commutation coefficients of non-holonomic bases are obtained. These special cases are found to be in agreement with the DeWitt Super covariant and Super Lie derivatives.      

Refining search terms for nanotechnology

The ability to delineate the boundaries of an emerging technology is central to obtaining an understanding of the technology’s research paths and commercialization prospects. Nowhere is this more relevant than in the case of nanotechnology (hereafter identified as “nano”) given its current rapid growth and multidisciplinary nature. (Under the rubric of nanotechnology, we also include nanoscience and nanoengineering.) Past efforts have utilized several strategies, including simple term search for the prefix nano, complex lexical and citation-based approaches, and bootstrapping techniques. This research introduces a modularized Boolean approach to defining nanotechnology which has been applied to several research and patenting databases. We explain our approach to downloading and cleaning data, and report initial results. Comparisons of this approach with other nanotechnology search formulations are presented. Implications for search strategy development and profiling of the nanotechnology field are discussed.

Chiral soliton model vs. pentaquark structure for Θ(1540)

The exotic baryon Θ⁺(1540 MeV) is visualized as an expected (iso) rotational excitation in the chiral soliton model. It is also argued as a pentaquark baryon state in a constituent quark model with strong diquark correlations. I contrast these two points of view; observe the similarities and differences between the two pictures. Collective excitation, the characteristic of chiral soliton model, points toward small mixing of representations in the wake ofSU (3) breaking. In contrast, constituent quark models prefer near ‘ideal’ mixing, similar to ω-φ mixing.     

Spontaneous emission in dielectric nanoparticles

An analytical expression is obtained for the radiative-decay rate of an excited optical center in an ellipsoidal dielectric nanoparticle (with sizes much less than the wavelength) surrounded by a dielectric medium. It is found that the ratio of the decay rate A _nano of an excited optical center in the nanoparticle to the decay rate A _bulk of an excited optical center in the bulk sample is independent of the local-field correction and, therefore, of the adopted local-field model. Moreover, the expression implies that the ratio A _nano/A _bulk for oblate and prolate ellipsoids depends strongly on the orientation of the dipole moment of the transition with respect to the ellipsoid axes. In the case of spherical nanoparticles, a formula relating the decay rate A _nano and the dielectric parameters of the nanocomposite and the volumetric content c of these particles in the nanocomposite is derived. This formula reduces to a known expression for spherical nanoparticles in the limit c ≪ 1, while the ratio A _nano/A _bulk approaches unity as c tends to unity. The analysis shows that the approach used in a number of papers {H. P. Christensen, D. R. Gabbe, and H. P. Jenssen, Phys. Rev. B 25, 1467 (1982); R. S. Meltzer, S. P. Feofilov, B. Tissue, and H. B. Yuan, Phys. Rev. B 60, R14012 (1999); R. I. Zakharchenya, A. A. Kaplyanskii, A. B. Kulinkin, et al., Fiz. Tverd. Tela 45, 2104 (2003) [Phys. Solid State 45, 2209 (2003)]; G. Manoj Kumar, D. Narayana Rao, and G. S. Agarwal, Phys. Rev. Lett. 91, 203903 (2003); Chang-Kui Duan, Michael F. Reid, and Zhongqing Wang, Phys. Lett. A 343, 474 (2005); K. Dolgaleva, R. W. Boyd, and P. W. Milonni, J. Opt. Soc. Am. B 24, 516 (2007)}, for which the formula for A _nano is derived merely by substituting the bulk refractive index by the effective refractive index of the nanocomposite must be revised, because the resulting ratio A _nano/A _bulk turns out to depend on the local-field model. The formulas for the emission and absorption cross sections σ_nano for nanoparticles are derived. It is shown that the ratios σ_nano/σ_bulk and A _nano/A _bulk are not equal in general, which can be used to improve the lasing parameters. The experimentally determined and theoretically evaluated decay times of metastable states of dopant rare-earth ions in crystalline YAG and Y₂O₃ nanoparticles are compared with the corresponding values for bulk crystals of the same structure. Original Russian Text ? K.K. Pukhov, T.T. Basiev, Yu.V. Orlovskii, 2008, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 88, No. 1, pp. 14–20.     

Conformal invariance and scalar-tensor theories

A new generalisation of Einstein’s theory is proposed which is invariant under conformal mappings. Two scalar fields are introduced in addition to the metric tensor field, so that two special choices of gauge are available for physical interpretation, the ‘Einstein gauge’ and the ‘atomic gauge’. The theory is not unique but contains two adjustable parameters ζ anda. Witha=1 the theory viewed from the atomic gauge is Brans-Dicke theory (ω=−3/2+ζ/4). Any other choice ofa leads to a creation-field theory. In particular the theory given by the choicea=−3 possesses a cosmological solution satisfying Dirac’s ‘large numbers’ hypothesis.     

Geometries and electronic structures of Ga<Subscript>2</Subscript>Se<Subscript>3</Subscript>, Ga<Subscript>3</Subscript>Se<Subscript>2</Subscript> and their anions. Theoretical insights

We hereby report a theoretical study on the equilibrium geometries, electronic structures and harmonic vibrational frequencies of Ga₂Se₃, Ga₃Se₂ and their anions. The ground and low-lying excited states of Ga₂Se₃⁻, Ga₂Se₃, Ga₃Se₂⁻ and Ga₃Se₂ are studied at the B3LYP and/or MP2 and CCSD(T) levels in conjunction with 6-311+G(d) and 6-311+G(2df) one particle basis sets. Ga₂Se₂⁻ adopts the C_2v kite geometry while Ga₂Se₃ has a ‘V’ geometry. Ga₃Se₂⁻ has a three-dimensional ‘D_3h ’ geometry and Ga₃Se₂ prefers the three-dimensional ‘C_2v ’ structure. Electron detachment energies from the ground electronic states of the anions to several neutral states are reported and discussed. At CCSD(T)//MP2 level, the adiabatic electron affinity (AEA) of Ga₂Se₃ is calculated to be 3.23 eV when using the 6-311+G(2df) basis set and that of Ga₃Se₂ is 2.77 eV with the 6-311+G(d) basis set. The findings of this research are analyzed and compared with gallium oxide and sulfide analogues.     

Einsteinian gravity from a topological action

The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a ‘vacuum degeneracy’. By modifying the duality via a scale breaking term, we demonstrate that only Einstein’s equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of ‘dark energy’ as well as ‘dark matter’ modeled by a torsion induced quintaxion.     

Factors affecting the superconductivity in the process of depositing Nd1.85Ce0.15CuO4-δ by the pulsed electron deposition technique

On SrTiO₃ single crystal substrate, by using the pulsed electron deposition technique, the high-quality electron doped Nd_1.85Ce_0.15CuO_4−δ superconducting film was successfully fabricated. After careful study on the R-T curves of the obtained samples deposited with different substrate temperatures, thicknesses, annealing methods and pulse frequencies, the effects of them on the superconductivity of the films were found, and the reasons were also analyzed. Additionally, by using the same model of the pulsed laser deposition technique, the relation between the target-to-substrate distance and the deposition pressure was drawn out as a quantitative one. Supported by the Key Project of Zhejiang Provincial Natural Science Foundation (Grant No. Z605131), the ‘100 Talents Project’ of Chinese Academy of Sciences, the Creative Research Group of National Natural Science Foundation of China (Grant No. 60321001) and the National Natural Science Foundation of China (Grant No. 60571029)     

Co<Superscript>2+</Superscript> Ions in ZnO powders as seen by Magnetic Resonance

This is a report of an X-band electronic paramagnetic resonance (EPR) study of Zn_1−x Co _x O (x = 1 and 3%) powders at various temperatures (10–200 K). EPR spectroscopy is a powerful tool to study the complex magnetic state and the Co ionic state, their local environment and interactions as well. These samples are interesting to study in order to understand how ‘Co doping’ produces ferromagnetism in ZnO₂, making it a promising ferromagnetic semiconductor at room temperature.     

Conformational analysis of allyl halides from the calculation of indirect spin-spin coupling

A theoretical study on the conformation of allyl halides from the calculation of nuclear spin-spin coupling constants by adopting the finite perturbation theory (FPT), is carried out in terms of the self-consistent, semi-empirical INDO (intermediate neglect of differential overlap) approximation of molecular orbital theory. Results of the calculations performed using ‘s’ and ‘p’ valence orbitals alone (‘sp’ basis) at INDO level approximation seem to replicate the experimental trend quite satisfactorily. Despite the overall agreement of the theoretical values with the experimental ones, the uncertainties in the INDO parametrization scheme lead to overestimation of certain coupling constants. The calculations also show that the orientation of the coupled protons with respect to the substituent halogen atom is an important factor to be considered.     

Interplay of superconductivity and magnetism in presence of inter sub-lattice effect in cuprates

In the present communication, we report a model Hamiltonian to study the interplay between the two long range orders of anti-ferromagnetism (AFM) and superconductivity (SC) in cuprate superconductors in presence of the intersite pairing effect. The BCS type but non-phonon pairing mechanism is considered among the electrons of two equivalent ‘Cu’ sites. The pairing among the electrons of two nearest neighbour non-equivalent ‘Cu’ sites is included in the Hamiltonian and its effect on the interplay of SC and AFM is investigated. The Hamiltonian is solved by the Green’s function method and the corresponding gap equations are calculated and solved selfconsistently. The influence of model parameters like AFM coupling (λ), SC couling (λ ₁) and the coupling (λ ₂) for intersite superconducting interactions on the gaps (SC and AFM) are studied numerically and the results are reported.     

Conformal Proper Times According to the Woodhouse Causal Axiomatics of Relativistic Spacetimes

On the basis of the Woodhouse causal axiomatics, we show that conformal proper times and an extra variable in addition to those of space and time, together give a physical justification for the ‘chronometric hypothesis’ of general relativity. Indeed, we show that, with a lack of these latter two ingredients and of this hypothesis, clock paradoxes exist for which the unparadoxical asymmetry cannot be recovered when using the ‘clock and message functions’ only. These proper times originate from a given conformal structure of the spacetime when ascribing different compatible projective structures to each Woodhouse particle, and then, each defines a specific Weylian ‘sheaf structure’. In addition, the proper time parameterizations are defined via path-dependent conformal scale factors, which act like sockets for any kind of physical interaction and also represent the values of the variable associated with the extra dimension.     

Multidisciplinary cognitive content of nanoscience and nanotechnology

This article examines the cognitive evolution and disciplinary diversity of nanoscience/nanotechnology (nano research) as expressed through the terminology used in titles of nano journal articles. The analysis is based on the NanoBank bibliographic database of 287,106 nano articles published between 1981 and 2004. We perform multifaceted analyses of title words, focusing on 100 most frequent words or phrases (terms). Hierarchical clustering of title terms reveals three distinct time periods of cognitive development of nano research: formative (1981–1990), early (from 1991 to 1998), and current (after 1998). Early period is characterized by the introduction of thin film deposition techniques, while the current period is characterized by the increased focus on carbon nanotube and nanoparticle research. We introduce a method to identify disciplinary components of nanotechnology. It shows that the nano research is being carried out in a number of diverse parent disciplines. Currently, only 5% of articles are published in dedicated nano-only journals. We find that some 85% of nano research today is multidisciplinary. The case study of the diffusion of several nano-specific terms (e.g., “carbon nanotube”) shows that concepts spread from the initially few disciplinary components to the majority of them in a time span of around a decade. Hierarchical clustering of disciplinary components reveals that the cognitive content of current nanoscience can be divided into nine clusters. Some clusters account for a large fraction of nano research and are identified with such parent disciplines as the condensed matter and applied physics, materials science, and analytical chemistry. Other clusters represent much smaller parts of nano research, but are as cognitively distinct. In the decreasing order of size, these fields are: polymer science, biotechnology, general chemistry, surface science, and pharmacology. Cognitive content of research published in nano-only journals is the closest to nano research published in condensed matter and applied physics journals.     

Random-Cluster Representation of the Blume–Capel Model

The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume–Capel model. It has three parameters, a vertex parameter a, an edge parameter p, and a cluster weighting factor q. Stochastic comparisons of measures are developed for the ‘vertex marginal’ when q ∊ [1,2], and the ‘edge marginal’ when q ∊ [1,∞). Taken in conjunction with arguments used earlier for the random-cluster model, these permit a rigorous study of part of the phase diagram of the Blume–Capel model. Mathematics Subject Classification (2000): 82B20, 60K35.     

Solution of approximate gluon evolution equation for small-x at fixed ‘ρ’

A simple method has been applied to solve the approximate gluon evolution equation for small-x at fixedρ(≡√ln(x ₀/x)/ln[ln(Q ²/Λ²)/ln(Q ₀ ² /Λ²)]. Numerical comparison is made with the predictions from ‘double asymptotic scaling’ and fit. Better agreement is found between our solution and fit nearρ=1. The solution gives approximate double scaling in this region having ‘hard’ pomeron with small contamination.     

Continuity of a Quantum Stochastic Process

We investigate a quantum counterpart of the classical notion of a stochastic process continuous with probability one, and prove that the L ²-limit of quantum martingales ‘continuous with probability one’ is a quantum martingale ‘continuous with probability one’. Applications of this result to a number of concrete situations is presented.     

Interacting entropy-corrected holographic dark energy with apparent horizon as an infrared cutoff

In this work we consider the entropy-corrected version of interacting holographic dark energy (HDE), in the non-flat universe enclosed by apparent horizon. Two corrections of entropy so-called logarithmic ‘LEC’ and power-law ‘PLEC’ in HDE model with apparent horizon as an IR-cutoff are studied. The ratio of dark matter to dark energy densities u, equation of state parameter w _D and deceleration parameter q are obtained. We show that the cosmic coincidence problem is solved for interacting models. By studying the effect of interaction in EoS parameter of both models, we see that the phantom divide may be crossed and also understand that the interacting models can drive an acceleration expansion at the present and future, while in non-interacting case, this expansion can happen only at the early time. The graphs of deceleration parameter for interacting models, show that the present acceleration expansion is preceded by a sufficiently long period deceleration at past. Moreover, the thermodynamical interpretation of interaction between LECHDE and dark matter is described. We obtain a relation between the interaction term of dark components and thermal fluctuation in a non-flat universe, bounded by the apparent horizon. In limiting case, for ordinary HDE, the relation of interaction term versus thermal fluctuation is also calculated.     

On the Complete Classification of Unitary <Emphasis Type="Italic">N</Emphasis> = 2 Minimal Superconformal Field Theories

Aiming at a complete classification of unitary N = 2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate partition function of such a theory is indeed the partition function of a fully-fledged unitary N = 2 minimal model, subject to the assumptions that orbifolding is a ‘physical’ process and that the space-time supersymmetric A{\mathcal{A}} -D{\mathcal{D}} -E{\mathcal{E}} models are physical. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models then demonstrates that there exists a unitary N = 2 minimal model for every one of the allowed partition functions in the list obtained from Gannon’s work (Gannon in Nucl Phys B 491:659–688, 1997).     

Gamow state vectors as functionals over subspaces of the nuclear space

Exponentially decaying ‘Gamow state’ vectors are obtained from S-matrix poles in the lower half of the second sheet and are defined as functionals over a subspace of the nuclear space Φ. Exponentially growing ‘Gamow state’ vectors are obtained from S-matrix poles in the upper half of the second sheet and are defined as functionals over another subspace of Φ. On functionals over these two subspaces the dynamical group of time development splits into two semigroups.