SU(5) Higgs problem with adjoint + vector representations

Recently Kim has given a general method, using group-invariant orbit parameters, for determining the energy and residual symmetry of the Higgs potential minimum. In this paper we illustrate the method by working out the case of a quartic SU(5) Higgs potential with $\text{5}$ and $\text{24}$ higgsons. In this method the Gell-Mann-Slansky conjecture concerning possible little groups of the potential minimum takes a geometric form, which is verified for our case. The results are used to discuss the hierarchical symmetry breaking of SU(5) grand unification theory. We generalize our results to the SU(N) adjoint + vector models, which are all closely related.     

Physico-chemical studies on Gum Dhawa (Anogeissus latifoliaWall.)

Summary The p_H of an aqueous solution of Gum Dhawa (Anogeissus latifoliaWall.) is 2.68 and it is sensitive to p_H changes. The absence of the sulphate and the presence of a slight trace of phosphate, confirms the view that the acidity is due to the presence of carboxyl groups, which are formed by the hydrolysis of the gum. The hydrogen ion activity increases up to a concentration of 3% and beyond this point it attains a steady value. The sp. cond. is zero at the zero concentration and the relation between sp. cond. and up to 3% concentration is linear and afterwards it attains a steady value. It has been found by experimental observation that the gum solution has got no buffering capacity. Neutralization curves with NaOH and Ba(OH)₂ show that the combination with alkali takes place in equivalent proportion. The viscosity of the gum solution always increases with increasing p_H on the addition of HCl. The viscosity increase with NaOH is slow in the beginning, but after p_H 4.2 it rises rapidly, attains a maximum and steeply falls off near p_H 6.7. Now it decreases slowly and again a deviation is noted at 10.5. The viscosity is maximum near about the neutralization point. This is due to the stretched chain of the polymer unit. The fall in viscosity is explained by the folding chain theory in conjunction with mass action or common ion effect and due to the destruction of the proteins, by concentrated NaOH, which forms a complex with carbohydrate polymer.The authors wish to thank Dr.R. C. Mehrotra, Professor and the Head of the Chemistry Department, for providing all facilities for this work. Our thanks are also due to the Ministry of Education, Government of India, for the award of a research scholarship to one of us (V.K.S.).     

Theory of the photoelastic effect in ZnO,ZnS and CdS crystals

It has been a general opinion that the Clausius-Mossotti dielectric theory is not capable of explaining the observed photoelastic behaviour of partially ionic crystals.However in the present communication we show that by making account of the variation of polarizabilities under compressive stress within the framework of the Clausius-Mossotti theory it is possible to obtain a reasonable agreement with experimental data on the photoelastic behaviour of ZnO, ZnS and CdS crystals.     

Jacobson radical of skew polynomial rings and skew group rings

LetR be a ring and σ an automorphism ofR. We prove the following results: (i)J(R _σ[x])={Σ_ir_i x ⁱ:r₀∈I∩J(R]), r _i∈I for alliε 1} whereI↪ {r∈R:rx ∈J(R _Σ[x])|s= (ii)J(R _σ<x>)=(J(R _σ<x>)∩R)_σ<x>. As an application of the second result we prove that ifG is a solvable group such thatG andR, + have disjoint torsions thenJ(R)=0 impliesJ(R(G))=0.     

Sizes and electronic polarizabilities of divalent ions in crystals

The Pauling’s form for the overlap repulsive energy is used to calculate the sizes of isoelectronic divalent ions in MgO, CaS, SrSe and BaTe crystals by minimising the next nearest neighbour repulsive interaction. The radii calculated by this method differ significantly from the conventional sets of ionic radii in a consistent way, being larger for cations and smaller for anions. The polarizability-radius cube relation is also utilized to calculate the electronic polarizabilities of ions. The electronic polarizabilities, thus obtained agree with the values determined from the refractivity measurements.     

Effect of the crystal potential on electronic polarizabilities of ions in alkaline earth chalcogenides

The electronic polarizabilities of ions in alkaline earth chalcogenides are estimated by taking account of the effect of the crystalline potential. The polarizabilities thus obtained are found to present a good agreement with experimental data. It has been shown that the polarizabilities and radii of alkaline earth and chalcogenide ions follow the polarizability-radius cube relation approximately well.     

Comparative reinvestigation of the interaction of phonons with Wannier and Frenkel excitons in crystalline solids

The interaction of lattice vibrations with excitons in inorganic and organic semiconductors/insulators is reinvestigated. These results expose the comparative nature of exciton—phonon interaction in the two types of solids and produce two new coupling functions useful for Frenkel exciton—phonon interaction.     

Tracking of transplanted mesenchymal stem cells labeled with fluorescent magnetic nanoparticle in liver cirrhosis rat model with 3-T MRI

In vivo visualization of transplanted stem cells with noninvasive technique is essential for the monitoring of cell implantation, homing and differentiation. At present, superparamagnetic iron oxide (SPIO) is most commonly used for cell labeling. However, stem cells lack phagocytic capacity and transfection agent is required for sufficient internalization of SPIO for cellular imaging. However, the potential hazards of transfection agents are not fully investigated. Instead of SPIO, we used commercially available new tagging material, fluorescent magnetic nanoparticle (MNP) containing rhodamine B isothiocyanate within a silica shell (Biterials, Seoul, Korea). This tagging material does not require transfection agents for the cell labeling. In addition to that, the core of this MNP is composed of ferrite and the inner portion of silica shell contains fluorescent materials, therefore, it has both magnetic and optical features. This study was designed to track intrasplenically injected bone marrow mesenchymal stem cells (MSCs) labeled with fluorescent MNP in liver cirrhosis rat model with 3-T magnetic resonance equipment. We compared magnetic resonance imaging (MRI) of livers in rats which were injected with non-labeled stem cells or labeled stem cells with MNP or SPIO. We found that the respective liver-to-muscle contrast-to-noise ratios at 3 and 5 h after MNP or SPIO-labeled stem cell injection was significantly lower than that of pre-injection and non-labeled group. There was no significant difference between MNP-labeled group and SPIO-labeled group. We can effectively detect intrasplenically injected MNP-labeled MSCs in an experimental rat model of liver cirrhosis with 3-T MRI.