Kinetic Model for Solute Diffusion in Liquid Membrane Systems

In this study, a mathematical model for the kinetics of solute transport in liquid membrane systems (LMSs) has been formulated. This model merged the mechanisms of consecutive and reversible processes with a “semi-derived” diffusion expression, resulting in equations that describe solute concentrations in the three sections (donor, acceptor and membrane). These equations have been refined into linear forms, which are satisfying in the special conditions for simplification obtaining the important kinetic constants of the process experimentally

Macdonald operators and homological invariants of the colored Hopf link

Using a power sum (boson) realization for the Macdonald operators, we investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the homological invariants of the colored Hopf link, which include Khovanov-Rozansky homology as a special case. We prove the polynomiality of the invariants obtained by GIKV's proposal for arbitrary representations. We derive a closed formula of the invariants of the colored Hopf link for antisymmetric representations. We argue that a little amendment of GIKV's proposal is required to make all the coefficients of the polynomial non-negative integers.Comment: 31 pages. Published version with an additional appendi

Physical Properties of Pure and Nano Agdoped Liquid Crystalline Compounds Containing 1,3,4-Oxadizole Unit

Dielectric properties and other physical properties such as electrical conductivity (AC) and relaxation time or activation energy have been studied for two systems pure LC [V]6,6, [V]7,6, [V]8,6, [V]6,7, [V]7,7 and [V]8,7 and their doped with silver nanoparticles. The results show the increasing in real dielectric permittivity έ with increasing length terminal chain. So the real dielectric permittivity increasing with raising temperature. To compare between the values of at (400) Hz and (4000) Hz we observe these values at the low frequency are larger than that in high frequency. Generally, one can see that the doping of Ag nano particles effectively reduced the permittivity of the LC materials with its large electric dipole moment. The electrical conductivity value for pure LC samples in general increases  with increasing temperature. So we observed increasing of  electrical conductivity values at high frequency. The time scale is discussed in terms of the Arrhenius plot. Generally, with increasing the temperature the time period that spend by molecules at the transition state will increase. The activation energy Ea values show the increase in the activation energy to the doped systems.

BPS Monopole Equation in Omega-background

We study deformed supersymmetries in N=2 super Yang-Mills theory in the Omega-backgrounds characterized by two complex parameters $\epsilon_1, \epsilon_2$. When one of the $\epsilon$-parameters vanishes, the theory has extended supersymmetries. We compute the central charge of the algebra and obtain the deformed BPS monopole equation. We examine supersymmetries preserved by the equation.Comment: 14 pages, typos corrected, published version in JHE

N=2 Instanton Effective Action in Omega-background and D3/D(-1)-brane System in R-R Background

We study the relation between the ADHM construction of instantons in the Omega-background and the fractional D3/D(-1)-branes at the orbifold singularity of C \times C^2/Z_2 in Ramond-Ramond (R-R) 3-form field strength background. We calculate disk amplitudes of open strings connecting the D3/D(-1)-branes in certain R-R background to obtain the D(-1)-brane effective action deformed by the R-R background. We show that the deformed D(-1)-brane effective action agrees with the instanton effective action in the Omega-background.Comment: 35 pages, no figures, references adde

Macroscopic quantum fluctuations in noise-sustained optical patterns

We investigate quantum effects in pattern formation for a degenerate optical parametric oscillator with walk-off. This device has a convective regime in which macroscopic patterns are both initiated and sustained by quantum noise. Familiar methods based on linearization about a pseudoclassical field fail in this regime and new approaches are required. We employ a method in which the pump field is treated as a c-number variable but is driven by the c-number representation of the quantum subharmonic signal field. This allows us to include the effects of the fluctuations in the signal on the pump, which in turn act back on the signal. We find that the nonclassical effects, in the form of squeezing, survive just above the threshold of the convective regime. Further, above threshold, the macroscopic quantum noise suppresses these effects

Interactive Modelling of Buildings in Google Earth and GIS: a 3D Tool for Urban Planning (Tunjuk Island, Indonesia)

3D modelling of buildings in Google Earth in Batam city, Indonesia is very important for knowledge about facility, infrastructure, and others.Three-dimensional (3D) visualisations are an interesting method for representing model outcomes. This research In Tunjuk island with coordinate, at Latitude: 0.984123°, and Longitude: 104.225606°, with technical terms, there are two alternative routes for implementation, and they both share the same starting stage. In (Figure 5) visible visual measurements of the master plan that has been made has a length 141.99 metre and width 54.25 metre with location at Latitude 0.984593° and Longitude 104.228073°. In (Figure 5) visible visual measurements of the master plan that has been made has a length 92.96 metre and width 135.46  metre with location at Latitude 0.984593° and Longitude 104.228073°. This paper presented a rapid visualisation tool for supporting the joint decision making in evaluation of design/renewal proposals in Batam City, Tunjuk Island, Indonesia. 3D building using Google Earth (GE) and combaining Geographic Information System (GIS) system be done officially on a sampling or auditing basis by a professional body or by researchers, or it could be done by volunteers and user groups