Study of the vibrational spectra of SO2, H2O and D2O using the U(4) algebraic model

Using the U(4) algebraic model, in this work we report a study of the vibrational spectra of SO₂, H₂0¹⁸ and D₂O¹⁶. The inclusion of intermode couplings in algebraic models has been stated to give a deep insight into detailed spectroscopy for these bent XY₂ molecules. Improved set of algebraic parameters has been reported to provide improved RMS deviations for these molecules.     

An Inventory Model with Two-Component Demand Rate and Shortages

The article investigates a deterministic inventory system with two-component demand rate. The demand rate is stock-dependent down to a certain level and then constant. Shortages are allowed and are fully backlogged. The storage space is assumed to be limited. A flowchart is provided to solve a general system. To study the effects of changes in the system parameters on the average net profit a sensitivity analysis has been performed.     

An algebraic approach to the comparative study of the vibrational spectra of monofluoroacetylene (HCCF) and deuterated acetylene (HCCD)

Using the Lie algebraic method the vibrational energy levels of HCCF and HCCD are calculated for 102 and 110 vibrational bands, respectively, using the local Hamiltonian. A comparative study is made between the two. Better results are obtained than those published earlier from local mode analysis.     

Optical and static dielectric study of a terminally fluorinated liquid crystalline compound

Optical and static dielectric studies on a terminally fluorinated liquid crystalline compound have been carried out. Measurements of temperature variation of refractive indices of the compound are done by using thin prism method. A four-parameter model is validated by fitting the experimentally measured values of refractive indices, birefringence and average refractive indices of the compound with the theoretical ones. Refractive index and density data are utilized for determination of orientational order parameter. The temperature variation of dielectric permittivities of the compound are measured by a LCR meter.     

U (2) algebraic model applied to vibrational spectra of Nickel Metalloporphyrins

In this paper the highly excited stretching and bending vibrational energy levels of some Nickel Metalloporphyrin molecules are studied by U (2) algebraic model. Its application to Nickel Octaethyl Porphyrin, Nickel Tetra Phenyl Porphyrin and Nickel Porphyrin are presented with fewer algebraic fitting parameters. The highly excited stretching and bending vibrational energy levels of these molecules are showing the energy clustering spectrum.     

Vibrational spectroscopy of SnBr4 and CCl4 using Lie algebraic approach

The stretching and bending vibrational energies of SnBr₄ and CCl₄ are calculated in the one-dimensional framework. The dynamical symmetry group of tetrahedral molecule was taken into consideration to construct the model Hamiltonian in this framework. Casimir and Majorana invariant operators were also determined accordingly. Using the model Hamiltonian so constructed, we reported the vibrational energy levels of SnBr₄ and CCl₄ molecules accurately.      

The stability and stabilization of the motion of non-conservative mechanical systems

Two stability problems are solved. In the first, the stability of mechanical systems, on which dissipative, gyroscopic, potential and positional non-conservative forces (systems of general form) act, is investigated. The stability is considered in the case when the potential energy has a maximum at equilibrium. The condition for asymptotic stability is obtained by constructing Lyapunov's function. In the second problem, the possibility of stabilizing a gyroscopic system with two degrees of freedom up to asymptotic stability using non-linear dissipative and positional non-conservative forces is investigated. Stability of the gyroscopic system is achieved by gyroscopic stabilization. The stability conditions are obtained in terms of the system parameters. Cases when the gyroscopic stabilization is disrupted by these non-linear forces are indicated.     

Mixed-ligand fluorocuprates(II). Synthesis and characterisation of [CuF3L(H2O)2]− containing amino acids as coligands

Complex species of the type NH₄[CuF₃L(H₂O)₂] · nH₂O (L = glycine, n = 1; 1-alanine, n = 0) have been prepared by reacting hydrated copper(II) oxide, CuO · nH₂O, with the amino acids in the presence of bifluoride, HF₂ ^–, in aqueous solution. The order of addition of the ligands, fluoride and amino acids is crucial to the synthesis. A reaction solution pH lower than the isoelectric point of the respective amino acids seems to favour the formation of mixed-ligand fluoro complexes. Occurring as zwitterions, the amino acids in the complexes have been shown to be bonded to the copper(II) centre via the carboxyl (—COO^–) moiety representing an unexpected non-chelated form of the coligands. Magnetic moments and e.s.r. data are consistent with six-coordinate copper(II) complexes.     

丙二酰二腙衍生的二氧化二钼(Ⅵ)配合物的合成、表征和晶体结构

本文报道了二氧杂钼(Ⅵ)配合物[MoO₂(H₂L)(H₂O)]的合成、表征和分子结构。该配合物是由马来酰二腙配体双(2-羟基-1-萘醛)丙二酰二腙(H₄L)与双(乙酰丙酮)二氧钼(Ⅵ)在甲醇中以1∶1的物质的量之比反应得到的。通过各种光谱(如IR、MS和NMR)对该配合物进行了表征。通过单晶X射线晶体学确定了配合物的结构。该配合物属于单斜晶系P2₁/c空间群。金属中心具有扭曲的八面体配位环境,与H₂L^2-的1个甲亚胺氮原子、2个末端氧基团、H₂L^2-的2个氧原子和配位水分子的1个氧原子相连。     

Vibrational Spectroscopy of CH/CD Stretches in Propadiene: An Algebraic Approach

Using Hamiltonian based on Lie algebraic method, the stretching vibrational modes of C3H4 and C3D4 molecules are calculated up to higher overtones. The model appears to describe C-H and C-D stretching modes with less number of parameters. The locality parameter ξ confirms the highly local behaviour of the stretching modes of these molecules.