Effect of counterions on the activity of lipase in cationic water-in-oil microemulsions

This paper delineates how the different counterions affect the physicochemical properties of the aqueous aggregates and thereby the lipase activities at the interface of cationic water-in-oil microemulsions. To this end, we have synthesized a series of cetyltrimethylammonium-based surfactants, 1-14, having aliphatic, aliphatic with aromatic substitution at the alpha position, and aromatic carboxylate anion as the counterion. The physicochemical characterizations of these aqueous aggregates were done by conductometric, tensiometric, fluorometric techniques to determine counterion binding (beta), critical micelle concentration (cmc), and micropolarity at the microenvironment. It has been found that the activity of lipase mainly increases with hydrophobicity (which is directly proportional to the counterion binding (beta) of the surfactant) of the counterion and reaches a maximum when the beta value is around 0.5. Increase in hydrophobicity as well as beta leads to the attachment of more counterions at interface resulting in enhancement of interfacial area. Consequently, the enzyme may attain flexible secondary conformation at the augmented surface area and also allow larger population of substrates and enzyme molecules at the interface leading to the enhancement in lipase activity. After an optimum value of beta, further increase probably produces a steric crowding at the interface, hindering the smooth occupancy of enzyme and the substrate in this region leading to decrease of enzyme activity, while molecular surface area of the counterion did not show any virtual influence on the lipase activity. Thus, the variation in the counterion structure and hydrophobicity plays a crucial role in modulating the lipase activity.     

A new generalization of Aczél’s inequality and its applications to an improvement of Bellman’s inequality

A new generalized version of Aczél’s inequality is proved. This is a unified generalization of some known results. Moreover, the result is applied to the improvement of the well-known Bellman’s inequality.     

On transient development of surface waves

Summary An initial value investigation into the development of two-dimensional surface waves generated by a harmonically oscillating pressure acting on the free surface of a fluid of limited, unlimited and very shallow depth is made in this paper in considerable detail. A rigorous mathematical treatment of the problem is given with the aid of integral transform technique in conjunction with asymptotic methods. The limiting behaviour of the asymptotic solution as timet tends to infinity has been given due attention. It is shown that the ultimate steady state is attained in the case of physically realisable pressure distributions. Finally, a discussion of the wave motions including the main predictions of this theory is presented in some detail. A careful consideration has also been given to examine the validity of Lighthill's prediction regarding the steady state.     

Synthesis of homochiral bis (oxazolinyl) pyridine type ligands for asymmetric cyclopropanation reactions

Homochiral bis(oxazolinyl)pyridine type ligands were synthesized from (S)-valine and converted into their Cu(II) complexes. Reduction of these Cu(II) complexes into Cu(I) with diazoesters was studied by uv-vis and epr spectroscopy. The enantioselective cyclopropanation reaction was carried out using styrene as a model substrate.     

Variable Modified Chaplygin Gas in Anisotropic Universe with Kaluza-Klein Metric

In this work, we have considered Kaluza-Klein Cosmology for anisotropic universe where the universe is filled with Variable Modified Chaplygin Gas (VMCG). Here we find normal scalar field ? and the self interacting potential V(?) to describe the VMCG Cosmology. We have also graphically analyzed the geometrical parameters named Statefinder Parameters in anisotropic Kaluza-Klein model. Next, we have considered a Kaluza-Klein model of interacting VMCG with dark matter in the Einstein gravity framework. Here we construct the three dimensional autonomous dynamical system of equations for this interacting model with the assumption that the dark energy and the dark matter interacts between themselves and for that we also choose the interaction term. We convert that interaction term to its dimensionless form and perform stability analysis and solve them numerically. We obtain a stable scaling solution of the equations in Kaluza-Klein model and graphically represent solutions.     

A brief historical introduction to Euler's formula for polyhedra,topology, graph theory and networks

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Königsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real physical systems are included. We also mention some important and modern applications of graph theory or network problems from transportation to telecommunications. Graphs or networks are effectively used as powerful tools in industrial, electrical and civil engineering, communication networks in the planning of business and industry. Graph theory and combinatorics can be used to understand the changes that occur in many large and complex scientific, technical and medical systems. With the advent of fast large computers and the ubiquitous Internet consisting of a very large network of computers, large-scale complex optimization problems can be modelled in terms of graphs or networks and then solved by algorithms available in graph theory. Many large and more complex combinatorial problems dealing with the possible arrangements of situations of various kinds, and computing the number and properties of such arrangements can be formulated in terms of networks. The Knight's tour problem, Hamilton's tour problem, problem of magic squares, the Euler Graeco-Latin squares problem and their modern developments in the twentieth century are also included.     

A brief historical introduction to matrices and their applications

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer’s Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical networks. It contains a wide variety of important materials accessible to college and even high school students and teachers at all levels.     

Gravitational collapse in higher dimensional Husain space–time

We investigate exact solution in higher dimensional Husain model for a null fluid source with pressure p and density ρ are related by the following relations (i) p  =  kρ, (ii) (variable modified Chaplygin) and (iii) p  =  kρ^α (polytropic). We have studied the nature of singularity in gravitational collapse for the above equations of state and also for different choices of the of the parameters k and B namely, (i) k  =  0, B  =  constant (generalized Chaplygin), (ii) B  =  constant (modified Chaplygin). It is found that the nature of singularity is independent of these choices of different equation of state except for variable Chaplygin model. Choices of various parameters are shown in tabular form. Finally, matching of Szekeres model with exterior Husain space–time is done.