Generalized Variational Problems and Euler–Lagrange equations

This paper introduces three new operators and presents some of their properties. It defines a new class of variational problems (called Generalized Variational Problems, or GVPs) in terms of these operators and derives Euler–Lagrange equations for this class of problems. It is demonstrated that the left and the right fractional Riemann–Liouville integrals, and the left and the right fractional Riemann–Liouville, Caputo, Riesz–Riemann–Liouville and Riesz–Caputo derivatives are special cases of these operators, and they are obtained by considering a special kernel. Further, the Euler–Lagrange equations developed for functional defined in terms of the left and the right fractional Riemann–Liouville, Caputo, Riesz–Riemann–Liouville and Riesz–Caputo derivatives are special cases of the Euler–Lagrange equations developed here. Examples are considered to demonstrate the applications of the new operators and the new Euler–Lagrange equations. The concepts of adjoint differential operators and adjoint differential equations defined in terms of the new operators are introduced. A new class of generalized Lagrangian, Hamiltonian, and action principles are presented. In special cases, these formulations lead to fractional adjoint differential operators and adjoint differential equations, and fractional Lagrangian, Hamiltonian, and action principle. Thus, the new operators introduce a generalized approach to many problems in classical mechanics in general and variational calculus in particular. Possible extensions of the subject and the concepts discussed here are also outlined.     

Dielectric properties of iron doped calcium copper titanate,CaCu<Subscript>3</Subscript>Ti<Subscript>3.9</Subscript>Fe<Subscript>0.1</Subscript>O<Subscript>12</Subscript> ceramic

Dielectric properties of iron doped CaCu₃Ti₄O₁₂ (CCTO), viz. CaCu₃Ti_3.9Fe_0.1O₁₂ (CCTFO) prepared by a novel semi-wet route have been investigated. X-ray diffraction of powder sintered at 900 °C show formation of single phase solid solution. Energy dispersive X-ray spectroscopy (EDX) confirmed the presence of CuO rich phase at grain boundaries of CCTFO. Nature of dielectric relaxation observed above room temperature is studied using complex plane impedance analysis and modulus spectroscopy. It has been found that out of the two relaxations reported earlier above room temperature, one occurring at lower temperature is due to grainboundaries interfacial polarization.     

Zinc oxide nanoparticles augment CD4, CD8, and GLUT‐4 expression and restrict inflammation response in streptozotocin‐induced diabetic rats

This study evaluated the biochemical, molecular, and histopathological mechanisms involved in the hypoglycaemic effect of zinc oxide nanoparticles (ZnONPs) in experimental diabetic rats. ZnONPs were prepared by the sol–gel method and characterised by scanning and transmission electron microscopy (SEM and TEM). To explore the possible hypoglycaemic and antioxidant effect of ZnONPs, rats were grouped as follows: control group, ZnONPs treated group, diabetic group, and diabetic + ZnONPs group. Upon treatment with ZnONPs, a significant alteration in the activities of superoxide dismutase, glutathione peroxidase, and the levels of insulin, haemoglobin A1c, and the expression of cluster of differentiation 4+ (CD4+), CD8+ T cells, glucose transporter type‐4 (GLUT‐4), tumour necrosis factor, and interleukin‐6 when compared to diabetic and their control rats. ZnONPs administration to the diabetic group showed eminent blood glucose control and restoration of the biochemical profile. This raises their active role in controlling pancreas functions to improve glycaemic status as well as the inflammatory responses. Histopathological investigations showed the non‐toxic and therapeutic effect of ZnONPs on the pancreas. TEM of pancreatic tissues displayed restoration of islets of Langerhans and increased insulin‐secreting granules. This shows the therapeutic application of ZnONPs as a safe anti‐diabetic agent and to have a potential for the control of diabetes.Inspec keywords: nanoparticles, transmission electron microscopy, cellular biophysics, sugar, nanomedicine, nanofabrication, zinc compounds, molecular biophysics, biochemistry, tumours, enzymes, biomedical materials, biological organs, blood, diseases, patient treatment, II‐VI semiconductors, wide band gap semiconductors, scanning electron microscopy, sol‐gel processing, semiconductor growthOther keywords: molecular mechanisms, histopathological mechanisms, zinc oxide nanoparticles, experimental diabetic rats, hypoglycaemic effect, antioxidant effect, control group, diabetic group, CD4+, CD8+ T cells, glucose transporter type‐4, control rats, GLUT‐4 expression, streptozotocin‐induced diabetic rats, biochemical mechanisms, safe antidiabetic agent, inflammation response, sol‐gel method, transmission electron microscopy, scanning electron microscopy, SEM, TEM, superoxide dismutase, glutathione peroxidase, insulin levels, haemoglobin A1c, differentiation 4+ T cells, tumour necrosis factor, interleukin‐6, blood glucose control, pancreas functions, glycaemic status, therapeutic effect, pancreatic tissues, Langerhans islets, insulin‐secreting granules, ZnO     

Glass ceramics containing ferroelectric phases

Glass ceramics prepared by controlled crystallization of glasses produce fine dispersion of crystallites in a glassy matrix. Glasses containing a mjor portion of constituents of a ferroelectric phase produce crystallites of ferroelectric phase in glass through a suitable heat treatment. The amount of network former in the initial glass has a profound influence on its crystallization behaviour and microstructure of the resulting ferroelectric glass ceramics. The value of dielectric constant and the nature of ferroelectric to paraelectric transition depend on the crystallite size and volume fraction of the ferroelectric phase. These glass ceramics are transparent for crystallite size less than 0·1μm and exhibit large quadratic-electro-optic effect.     

Comparison of lantadenes content and toxicity of different taxa of the lantana plant

Three taxa of the lantana plant (Lantana camara var.Aculeata) I (white-pink), II (yellow-pink), and III (yellow-red)-differed in the content of lantadenes and compounds X, Y, and Z. Lantadene A, lantadene B, and lantadene C were the major lantadenes of taxon III. It contained small amounts of lantadene D. Taxa I and II contained very small amounts of lantadene A and lantadene B. Compounds X, Y, and Z were the major constituents of taxa I and II, and they constituted 59% and 92% of the total constituents in these taxa, respectively. Ingestion of lantana leaf powder of taxon III by male guinea pigs caused severe hepatotoxicity. Taxon I elicited mild hepatotoxicity in one out of six animals while taxon II was nontoxic. The biological and ecological significance of the presence of high amounts of compounds X, Y, and Z in taxa I and n is not known.     

Equivalent circuit models using CPE for impedance spectroscopy of electronic ceramics

Complex immittance (Impedance Z, Modulus M, Admittance Y, Permittivity ?) spectra for some equivalent circuit models involving resistances, capacitances and constant phase angle elements (CPE) are calculated for different ratios of the parameters. A comparison of experimentally obtained complex immittance plots with these diagrams greatly facilitates the search for the most appropriate equivalent circuit representing the electrical properties of electronic ceramics. An equivalent circuit for Ba_1-xSr_xTiO₃ (x = 0.35) ceramic system is developed by using these simulated plots.     

Mechanistic Modelling of the Catalytic Pyrolysis of Methylcyclohexane

A detailed chemical kinetic mechanism describing the thermal and catalytic cracking of methylcyclohexane over a 12CaO.7Al₂O₃ catalyst is presented. The model is based on balanced equations for both molecular and radical species describing an experimental fixed‐bed reactor system. The mechanistic model is based on overall first‐order decomposition kinetics, which satisfactorily describes experimental data. The simulated product distributions show a reasonably good agreement with the experimental results and confirm the hypothesis that the catalyst does not affect the pyrolysis mechanism and only increases the rate of the initiation steps.     

Dynamic analysis of flexible multi-body systems using mixed modal and tangent coordinates

This paper presents a mixed modal and tangent coordinate technique for computer aided analysis of flexible mechanical systems whose components undergo large translations and large rotations. In this model the configuration of a flexible component is identified by using two sets of generalized coordinates, namely rigid body and elastic coordinates. The rigid body coordinates define the location and orientation of a body axis, whereas the elastic coordinates define the displacement field of a component with respect to its body axis. The elastic coordinates are introduced by using finite element discretization to model flexible components with complex geometries. A modal analysis technique is used to identify the elastic mode shapes and to eliminate insignificant higher frequency modes. An orthonormalization of constraint Jacobian matrix associated with rigid body coordinates is used to identify the rigid body tangent coordinates. The resulting modal and tangent coordinates are used to develop an automated numerical integration scheme to solve the system differential and algebraic equations. Two numerical examples are considered to show the feasibility of dynamic analysis of flexible mechanical systems using this scheme.