The incompressible Navier–Stokes equations from black hole membrane dynamics

We consider the dynamics of a d+1 space–time dimensional membrane defined by the event horizon of a black brane in (d+2)-dimensional asymptotically Anti-de Sitter space–time and show that it is described by the d-dimensional incompressible Navier–Stokes equations of non-relativistic fluids. The fluid velocity corresponds to the normal to the horizon while the rate of change in the fluid energy is equal to minus the rate of change in the horizon cross-sectional area. The analysis is performed in the Membrane Paradigm approach to black holes and it holds for a general non-singular null hypersurface, provided a large scale hydrodynamic limit exists. Thus we find, for instance, that the dynamics of the Rindler acceleration horizon is also described by the incompressible Navier–Stokes equations. The result resembles the relation between the Burgers and KPZ equations and we discuss its implications.     

On one-eighth law in unforced two-dimensional turbulence

We critically revisit the various attempts to prove one-eighth law in two-dimensional (2D) turbulence and reconcile them. Herein, the one-eighth law has been proved for unforced 2D incompressible high Reynolds number turbulence. An exact expression of the time derivative of two-point second order velocity correlation function is also derived for the enstrophy cascade dominated regime.     

Nuclear spin selection rules in chemical reactions by angular momentum algebra

The detailed selection rules for reactive collisions reported by Quack using molecular symmetry group are derived by using angular momentum algebra. Instead of the representations of the permutation-inversion group for both nuclear spin and rovibronic coordinate wavefunctions, those of the rotation group for nuclear spin wavefunction only are used. The method allows more straightforward derivation of Quack’s results and further extension of the calculation for separating elementary reactions and application to higher proton systems.     

Peculiarities of the Porous Structure of Aluminosilicate Mesoporous Substances Obtained in The Presence of Biotemplates

Supramolecular structures of lecithin occurred to be the template in the synthesis of mesoporous aluminosilicates; using of various combinations of lecithin and cetyltrimethyl-ammonium bromide or octadecylamine as templating agents allowed to obtain mesoporous substances with pores up to 100 Å, as well as biporous materials in aluminosilicate system. In the presence of glucose oxidase and cetyltrimethyl-ammonium bromide combinations aluminosilicate substances with complex porous structure were shown to be formed (pore size distributions exhibited 3 peaks, corresponding 3 effective size of mesopores in the 30–100 Å range). The investigation of sorption of glucose oxidase on obtained aluminosilicate mesoporous substances was carried out, the results obtained allowus to consider such materials as prospect for creation high capable and selective sorbents for biomolecules sorption, as well as active elements of chemical and biosensors.     

A Taxonomy of Static Modules with Examples

The objective of this note is to study properties of static and adstatic modules that are linked to generated, cogenerated, presented, copresented, self-static, self-tilting, *-, *^s-, and n-star modules. Several numerical examples in various situations of ?_n-static modules are presented.     

Performance analysis of different modulation formats in 4-channel CATV transmission system using OADM

In this paper we have analyzed the performance of different modulation formats for a four-channel WDM CATV system using optical ad drop multiplexers and the impact of frequency and wavelength on Q-value, and eye opening is observed for added and dropped channels at different lengths.     

On certain spaces of vector measures of bounded variation

If (Σ,X) is a measurable space and X a Banach space we investigate the X-inheritance of copies of ?_∞ in certain subspaces Δ(Σ,X) of bvca(Σ,X), the Banach space of all X-valued countable additive measures of bounded variation equipped with the variation norm. Among the consequences of our main theorem we get a theorem of J. Mendoza on the X-inheritance of copies of ?_∞ in the Bochner space L₁(μ,X) and other of the author on the X-inheritance of copies of ?_∞ in bvca(Σ,X).     

Determining tension parameters in rational gamma-spline interpolation

Inspired by the classic γ-spline, we propose a method for constructing a G² rational γ-spline curve that interpolates a given set of distinct ordered data-points (planar or spatial). The only input of our method is just these data-points. We also present a procedure to solve the key problem of determining the tension parameters γ_i which are computed in terms of exponential functions that determine the eccentricities of the common conic osculants at the junction points while keeping in geometrical agreement with data-points. This allows the resulting curve to be modified in the close vicinity of each data-point.