Three-manifold invariants $${\hat{Z}}$$ (“Z-hat”), also known as homological blocks, are q-series with integer coefficients. Explicit form for is SU(2) group, supergroup SU(2|1) and orthosymplectic OSp(2|2). We focus on SO(3) group OSp(1|2) in this paper. Particularly, the change of variable relating link to plays a crucial role explicitly writing q-series.

Most recent models assuming the Higgs Boson is a pseudo-Nambu-Goldstone Boson (pNGb) are motivated by the indication from Standard Model fits that its mass is ≤ 200GeV .Starting from a modified SM. of Forshaw et. al. with a triplet boson added and a heavier Higgs Boson, we consider a pNGb model.This differs in several ways from most little Higgs models: apart from using only one loop, the cutof...

Following the U.S. Clean Air Act Amendments of 1990, electric utilities dramatically increased their utilization of low-sulfur coal from the Powder River Basin (PRB). Recent studies indicate that railroads hauling PRB coal exercise a substantial degree of market power and that relative price changes in the mining and transportation sectors were contributing factors to the observed pattern of in...

1 This paper gives a simple introduction to the SO(5) theory of high T c superconductivity. Current status and relation to experiments are summarized.

We conducted a series of bench-top experiments to examine accumulation of acidity in temperate snowpacks due to the deposition of SO 2 . To achieve this, SO 2 at concentrations of 45}85 ppbv was allowed to di!use into containers of snow at 03C for varying lengths of time, from 6 to 46 h. Depth pro"les of dissolved total sulfur (S(IV)#S(VI)) in the snow were measured and modeled with a coupled d...

The analog of the principal SO(3) subalgebra of a finite dimensional simple Lie algebra can be defined for any hyperbolic Kac Moody algebra g(A) associated with a symmetrizable Cartan matrix A, and coincides with the non-compact group SO(1, 2). We exhibit the decomposition of g(A) into representations of SO(1, 2); with the exception of the adjoint SO(1, 2) algebra itself, all of these represent...

The present article aims at developing simple realistic models in order to describe the gaseous removal process of SO(2) by absorption with and without chemical reaction in spray towers. Effects of droplet size, droplet velocity, superficial gas velocity, liquid flow rate and tower height on the performance of such a system are theoretically predicted. Model calculations bring out some very int...

Uptake of label from solutions containing (35)SO(2), H(35)SO(3) (-) and (35)SO(3) (2-) into mesophyll protoplasts, vacuoles, and chloroplasts isolated from young barley leaves was measured at different pH values. Uptake was fast at low pH, when the concentration of SO(2) was high, and low at high pH, when the concentration of SO(2) was low. When the resistance (R) of plasmalemma, tonoplast, and...

The potential-energy surface for has been computed at the HF/6-311G** and MP2/6-311G** levels. The calculated H É 2 results conÐrm that trans-planar HOSO is a transition state but not a stable structure. The decomposition channel for the HOSO adduct has been studied by analysing the transition states and stationary points. The kinetic stimulus for the rearrangement and dissociation of the radic...