Positive values of non-homogeneous indefinite quadratic forms of type (1, 4)

Let Г_r,n—r denote the infimum of all number Г > 0 such that for any real indefinite quadratic form inn variables of type (r, n—r), determinantD ≠ 0 and real numbers c₁; c₂,…, c_n, there exist integersx ₁,x₂,…,x_n satisfying 0 < Q(x₁+c₁,x₂ + c₂,…,x_n + c_n) ≤(Г|Z > |)^1/n. All the values of Г_r,n—r are known except for г_1,4. Earlier it was shown that 8 ≤Г_1,4 ≤16. Here we improve the upper bound to get Г_1,4 < 12.     

Equivalence of the angular forces in the lattice dynamics of fcc metals

The expressions for the Clark, Gazis and Wallis type of angular forces are rederived in the caseof fcc metals. These expressions are now foundtobe equivalent to the deLauney type of angular forces.     

Investigation of anomalons in He fragments

We have studied the mean free path of He fragments from projectile beams of Ar, Fe and Kr of energy 1 ? E ?2A GeV at different distances $\text{(L ? 2.5}\text{cm}\text{)}$ from their production point and found that they are the same, independent of their (i) energy, (ii) target size, (iii) target excitation, (iv) He multiplicities and (v) production angles.     

Transfer of charge in liquid alloys

Hard sphere diameters of liquid alkali metal alloys (Na-Cs and K-Rb) are calculated at 373 K ensuring the minimum Helmholtz free energy of the system. These diameters are then used to fix the packing density of the alloy. On alloying, the hard sphere diameters of Na in Na-Cs and K in K-Rb alloys expand whereas those of Cs and Rb contract.     

Angular forces in the lattice dynamics of b.c.c. metals

The lattice dynamics of the b.c.c. lattice has been investigated using the central and the angular forces which are in general rotationally invariant. It has been observed that the four force constants are related to three elastic constants only. Dispersion curves for sodium were calculated and were found to be in excellent agreement with experiment.     

n-dimensional array languages and description of crystal symmetry—I

Following the general linguistic approach proposed by Narasimhan to pattern recognition we proposed two generative models,viz., the matrix models and the more powerful two-dimensional array models. In this paper we generalize the matrix models ton-dimensions and establish that then-dimensional matrix models are closed under union, concatenation, Kleene closure, ∈-free homomorphism, inverse homomorphism and intersection with regular matrices. Symmetry operations such as translation, reflection and half-turn are examined.     

Spatially Homogeneous Bianchi Type-I Universes with Variable G and Λ

In this paper, we have studied the cosmological models of Bianchi type-I universes in a different basic form filled with bulk viscous fluid, in the presence of time-dependent gravitational as well as cosmological constants. A set of new exact cosmological solutions have been obtained in both full and truncated causal theories. These solutions are suitable for describing the evolution of the universe in its early stages. The physical and dynamical consequences have been discussed in detail.     

Organocatalytic Green Approach Towards the Fabrication of Fused Benzo N,N‐containing Heterocycles Facilitated by Ultrasonic Irradiation

The development of a metal‐free protocol for transformations in organic synthesis offers a significant potential environmental benefit. This article reports the exploration of meglumine, a nontoxic and biodegradable amino sugar, as an organocatalyst for the synthesis of biologically active 1H‐dibenzo[b,e][1,4]diazepin‐1‐ones, highly regioselective benzimidazole derivatives and derivatives of quinoxalines. Operational simplicity, mild reaction conditions, shorter reaction times, and use of green solvents are the highlights of this protocol. The advantage of ultrasonic irradiation has been significantly explored for the synthesis of the aforesaid compounds. Furthermore, the multifaceted use of o‐phenylenediamine has also been accentuated in the study.     

Effect of ZnO/CdO on the structure and electrical conductivity in Li2O·MO·Bi2O3·B2O3 glasses (M=Zn, Cd)

Studies of structural and electrical properties have been carried out on a number of glasses with wide ranging compositions in the glass systems Li₂O·MO·Bi₂O₃·B₂O₃ (where M=Zn or Cd), in order to understand the effect of transition metal (TM) ions on the structure of these glasses. The density and molar volume measurements have also been made to understand the structural changes occurring in these glasses. The dc conductivity measured in the temperature range 423-623 K obeys Arrhenius law. It increases with increase in Li₂O/MO ratio. The results of infrared spectra indicate that TM ions (Zn²⁺ or Cd²⁺) behave as network former in the present system. Boron exists in both tri- and tetra-hedral units in these glasses and no boroxol ring formation takes place in the glass structure. Values of theoretical optical basicity have also been reported.     

Comprehensive Understanding of the Eco‐Friendly Synthesis of Zeolites: Needs of 21st Century Sustainable Chemical Industries

Zeolites have taken a leading position in petrochemical, fine, and bulk chemical industries due to their porous architecture, pore sizes, tunable acidity, and thermal stability. Various strategies of zeolites preparation, including template‐free, solvent‐free, and toxic mineral‐free strategies are summarized. Moreover, the zeolite synthesis using naturally occurring minerals and sustainable natural templates is also discussed, which involves the synthesis of nanocrystalline zeolites of different framework structures using plant‐based natural templates and biomass‐derived renewable chemicals. Overall this personal account provides the fundamentals of various sustainable synthetic strategies reported in the literature for the synthesis of zeolites with suitable examples that will be useful for the students and will motivate experienced researchers to develop various novel sustainable methods for the synthesis of zeolites and other inorganic materials of industrial relevance.