Independence of Yang-Mills Equations with Respect to the Invariant Pairing in the Lie Algebra

It is proved that the Euler–Lagrange equations of a Yang-Mills type Lagragian is independent with respect to the chosen pairing in the Lie algebra. Moreover, the Hamilton-Cartan equations of these Lagrangians are obtained and proved to be also independent with respect to the pairing. PACS Numbers 2003: 02.20.Qs, 02.20.Sv, 02.20.Tw, 02.40.Ma, 02.40.Vh, 11.10.Ef, 11.15.Kc Mathematics Subject Classification 2000: Primary 70S15, Secondary 58A20, 58E15, 58E30, 70S05, 70S10, 81T13     

Asymptotic singular behaviour of inhomogeneous cosmologies in Einstein-Maxwell-dilaton-axion theory

We present the study of exact inhomogeneous cosmological solutions to a four-dimensional low energy limit of string theory containing non-minimal interacting electromagnetic, dilaton and axion fields. We focus at Einstein-Rosen solutions of Einstein-Maxwell-dilaton-axion equations. Several cases are analyzed and some of them have asymptotically velocity-term dominated (AVTD) singularities.     

Plane Symmetric Viscous Fluid Cosmological Models with Varying <Emphasis Type="Italic">Λ</Emphasis>-Term

Plane symmetric viscous fluid cosmological models of the universe with a variable cosmological term are investigated. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density whereas the coefficient of shear viscosity is to be proportional to rate of expansion in the model. We have also obtained a special model in which the shear viscosity is assumed to be zero. The cosmological constant Λ is found to be a decreasing function of time and a positive which is supported by results from recent supernovae Ia observations. Some physical and geometric properties of the models are also discussed.     

Intra-Channel Collision of Dual-Power Law Optical Solitons

The intra-channel collision of optical solitons, with dual-power law nonlinearity, is studied in this paper by the aid of quasi-particle theory. The perturbation terms that are considered in this paper are the nonlinear gain and saturable amplifiers along with filters. The suppression of soliton-soliton interaction, in presence of these perturbation terms, is acheived. The numerical simulations support the quasi-particle theory. OCIS codes: 060.2310; 060.4510; 060.5530; 190.3270; 190.4370.     

Dynamic Entanglement and Separability Criteria for Quantum Computing Bit States

A theoretical framework is demonstrated to evaluate the degree of entanglement of bit states in quantum computing. Separability of general superposition of Hilbert space unit vectors is discussed, and criteria in amplitude as well as in phase are derived. By these criteria the possibility of different quantum gates such as controlled not (CN), controlled controlled not (CCN), controlled rotation (CR), and controlled phase shift (CPS), to create the entanglement is examined. Furthermore, the selection of measurement mode external to the quantum system is incorporated in the formula using Kronecker delta (δ _kx ), introducing the concept of dynamic entanglement. With this the process of wavefunction collapse upon measurement is understood as the result of the activation of the dynamic entanglement. A firefly in a box model is used to show a pure state of ontological uncertainty, which is in a dynamically entangled state in Hilbert space.     

Investigations on Pd:SnO2/porous silicon structures for sensing LPG and NO2 gas

P-type porous silicon (PS) structure has been prepared by anodic electrochemical etching process under optimized conditions. Photoluminescence studies of the PS structure show emission at longer wavelengths (red) for the excitation at 365 nm. Scanning electron microscope investigations of the PS surface confirm the formation of uniform porous structure, and the pore diameter have been estimated as 25 μm. Pd:SnO₂/PS/p-Si heterojunction with top gold ohmic contact developed by conventional methods has been used as the sensor device. Sensing properties of the device towards liquefied petroleum gas (LPG) and NO₂ gas have been investigated in an indigenously developed sensor test rig. The response and recovery characteristics of the sensor device at different operating temperatures show short response time for LPG. From the studies, maximum sensitivity and optimum operating temperature of the device towards LPG and NO₂ gas sensing has been estimated as 69% at 180 °C and 52% at 220 °C, respectively. The developed sensor device shows a short response time of 25 and 57 s for sensing LPG and NO₂ gases, respectively. Paper presented at the Third International Conference on Ionic Devices (ICID 2006), Chennai, Tamilnadu, India, Dec. 7–9, 2006.     

The Fixed Point of a Generalization of the Renormalization Group Maps for Self-Avoiding Paths on Gaskets

Let W(x,y) = ax ³+ bx ⁴+ f ₅ x ⁵+ f ₆ x ⁶+ (3 ax ²)² y+ g ₅ x ⁵ y + h ₃ x ³ y ² + h ₄ x ⁴ y ² + n ₃ x ³ y ³+a ₂₄ x ² y ⁴+a ₀₅ y ⁵+a ₁₅ xy ⁵+a ₀₆ y ⁶, and X = , , where the coefficients are non-negative constants, with a > 0, such that X ²(x,x ²)−Y(x,x ²) is a polynomial of x with non-negative coefficients. Examples of the 2 dimensional map Φ: (x,y)↦ (X(x,y),Y(x,y)) satisfying the conditions are the renormalization group (RG) maps (modulo change of variables) for the restricted self-avoiding paths on the 3 and 4 dimensional pre-gaskets. We prove that there exists a unique fixed point (x _f ,y _f ) of Φ in the invariant set . 2000 Mathematics Subject Classification Numbers: 82B28; 60G99; 81T17; 82C41.     

Parallel Plate Interferometer with a Reflecting Mirror for Measuring Angular Displacement

A parallel plate interferometer with a reflecting mirror for measuring angular displacement is proposed. A deflection angle of a beam caused by an angular displacement is amplified by use of a reflecting mirror to increase the optical path difference (OPD) in the plane-parallel plate, which provides high sensitivity of the phase measurement. Detection of light transmitted through the plane-parallel plate with a position sensitive detector (PSD) enables high accurate measurement of the initial angle of incidence to the plane-parallel plate with insensitivity to stray light. The improved parallel plate interferometer achieves a measurement repeatability of 10⁻⁸ rad.     

Phospholipid lung surfactant and nanoparticle surface toxicity: Lessons from diesel soots and silicate dusts

Because of their small size, the specific surface areas of nanoparticulate materials (NP), described as particles having at least one dimension smaller than 100 nm, can be large compared with micrometer-sized respirable particles. This high specific surface area or nanostructural surface properties may affect NP toxicity in comparison with micrometer-sized respirable particles of the same overall composition. Respirable particles depositing on the deep lung surfaces of the respiratory bronchioles or alveoli will contact pulmonary surfactants in the surface hypophase. Diesel exhaust ultrafine particles and respirable silicate micrometer-sized insoluble particles can adsorb components of that surfactant onto the particle surfaces, conditioning the particles surfaces and affecting their in vitro expression of cytotoxicity or genotoxicity. Those effects can be particle surface composition-specific. Effects of particle surface conditioning by a primary component of phospholipid pulmonary surfactant, diacyl phosphatidyl choline, are reviewed for in vitro expression of genotoxicity by diesel exhaust particles and of cytotoxicity by respirable quartz and aluminosilicate kaolin clay particles. Those effects suggest methods and cautions for assaying and interpreting NP properties and biological activities.     

Constraining extended theories of gravity using Solar System tests

Solar System tests give nowadays constraints on the estimated value of the cosmological constant, which can be accurately derived from different experiments regarding gravitational redshift, light deflection, gravitational time-delay and geodesic precession. Assuming that each reasonable theory of gravitation should satisfy Solar System tests, we use these limits on the estimated value of the cosmological constant to constrain extended theories of Gravity, which are nowadays studied as possible theories for cosmological models and provide viable solutions to the cosmological constant problem and the explanation of the present acceleration of the Universe. We obtain that the estimated values, from Solar System tests, for the parameters appearing in the extended theories of Gravity are orders of magnitude bigger than the values obtained in the framework of cosmologically relevant theories.