Grand unified model with a stable proton and no axion problem

We present a grand unified model of the strong, electromagnetic and weak interactions based on a local SU(8)_L×SU(8)_R gauge theory which possesses a global U(8)_L × U(8)_R invariance. We break the symmetry down to the standard SU(3)_C × SU(2)_L × U(1) model, with the proton remaining stable and the left-handed neutrinos obliged to remain massless. A novel feature of our model is the simultaneous absence of both strong CP violations and of axions.     

Electric polarization and dielectric behaviour in dc electric fields of fused KNO2 in phase II at room temperature

On application of dc electric fields to a sample of KNO₂ (99.9% pure) fused between two heavily nickel plated copper plates the sample does not acquire the potential difference equal to the applied emf even though there is no external potential drop in the circuit. Also a very large capacitance of the order of 3000μF is obtained for this sample which is attributed to interfacial polarization effect. An equivalent circuit is given to explain the dc electrical behaviour of the sample. The idea of solid state battery does not seem to be applicable in the case of fused KNO₂. The large value of the capacitance for dc fields in series with large voltage-dependent resistance is the cause of the slow discharge of the condenser.     

Final state gluon effects in charmed meson decays

In the valence-quark c-decay scheme the decay $\text{D}{}^0\text{→}\text{K}{}^0\text{π}{}^0$ is expected to be strongly suppressed. We suggest that final state soft gluon exchange may account for the rather large branching ratio recently measured for this process, and study two-body decays of charmed mesons in our new scheme.     

Flavor-changing electromagnetic vertex in a non-linear Rξ gauge

We calculate the general transition q_i → q_j + γ for arbitrary quark flavors in a non-linear R_ξ gauge. The reduced number of Feynman diagrams as well as simplified Ward identities greatly facilitates this calculation. A general result with intermediate quarks of arbitrary mass is presented and the special cases s → d + γ as well as s → d + gluon are discussed.     

Simple synthesis of 2-acetyl-5,8-dimethoxy-3,4-dihydronaphthalene,a key intermediate for the synthesis of optically active anthracycliones

2-Acetyl-5,8-dimethoxy-3,4-dihydronaphthalene is synthesised easily·starting from 2-acetyl-5,8-dimethoxytetralone.     

Electrical conductivity of binary sulphates of lithium sulphate

To engineer lithium sulphate based material with high ionic conductivity at lowest possible temperature, the electrical conductivity of binary sulphates of Li₂SO₄ with Na₂SO₄, K₂SO₄, MgSO₄, ZnSO₄ and Ag₂SO₄ has been measured in the temperature range from 513 K to 773 K. The results are interpreted on the basis of different phases present therein. Li₂SO₄:Ag₂SO₄(40:60) mol % has high ionic conductivity = 2.17×10^-3(ohm cm)^-1 at 606 K which could be utilized in power sources.     

Theoretical study of small clusters of manganese-doped gallium oxide: Mn(GaO)n and Mn2(GaO)n with n?=?1?7

Structures, electronic and magnetic properties of Mn and Mn₂ doped stoichiometric (GaO) _n clusters with n = 1−7 are studied in the framework of density functional theory. Doping of a Mn atom is found to be energetically favorable in (GaO) _n clusters and the equilibrium configurations are found to be determined by the metal–oxygen interactions. Mn prefers to maximize the number of Mn–O bonds by selecting a Ga site in the cluster which increases its coordination with oxygen. Addition of a Mn atom in Mn(GaO) _n clusters results into the ground state to be either ferromagnetic or antiferromagnetic depending on the Mn coordination number and the Mn–Mn bond-length in the given Mn₂(GaO) _n cluster.     

A Fixed Point Theorem in Intuitionistic Fuzzy Metric Spaces by Using New Commutativity Condition

We prove a common fixed point theorem for discontinuous,noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces by using a new commutativity condition.We validate our main result by an example.     

One interesting family of diophantine triplets

In this note properties of two sequences generated by the recurrence relation G _n+2 = 4G _n+1 ? G _n , are studied. It is shown that one of the sequences leads to a family of diophantine triplets. Some interesting properties of these sequences are also established.