Third Hankel determinant for starlike and convex functions with respect to symmetric points

The objective of this paper is to obtain best possible upper bound to the $H_{3}(1)$  Hankel determinant for starlike and convex functions with respect to symmetric points, using Toeplitz determinants

Coefficient inequality for transforms of certain subclass of analytic functions

The objective of this paper is to obtain the best possible sharp upper bound for the second Hankel functional associated with the kth root transform [f(zk)]1/k of normalized analytic function f(z) when it belongs to certain subclass of analytic functions, defined on the open unit disc in the complex plane using Toeplitz determinants

An upper bound to the second Hankel determinant for pre-starlike functions of order α

The objective of this paper is to obtain an upper bound to the second Hankel determinant  for the function f and its inverse belonging to the class of pre-starlike functions of order alpha (0 ≤ alpha ≤ 1), using Toeplitz determinants

Real-time detection of cruciform extrusion by single-molecule DNA nanomanipulation

During cruciform extrusion, a DNA inverted repeat unwinds and forms a four-way junction in which two of the branches consist of hairpin structures obtained by self-pairing of the inverted repeats. Here, we use single-molecule DNA nanomanipulation to monitor in real-time cruciform extrusion and rewinding. This allows us to determine the size of the cruciform to nearly base pair accuracy and its kinetics with second-scale time resolution. We present data obtained with two different inverted repeats, one perfect and one imperfect, and extend single-molecule force spectroscopy to measure the torque dependence of cruciform extrusion and rewinding kinetics. Using mutational analysis and a simple two-state model, we find that in the transition state intermediate only the B-DNA located between the inverted repeats (and corresponding to the unpaired apical loop) is unwound, implying that initial stabilization of the four-way (or Holliday) junction is rate-limiting. We thus find that cruciform extrusion is kinetically regulated by features of the hairpin loop, while rewinding is kinetically regulated by features of the stem. These results provide mechanistic insight into cruciform extrusion and help understand the structural features that determine the relative stability of the cruciform and B-form states

The Effect of Suction/Injection on Free Convection in a Micropolar Fluid Saturated Porous Medium under Convective Boundary Condition

AbstractIn this article, the influence of the convective boundary condition of free convection flow over a permeable vertical plate in porous medium saturated with a micropolar fluid is investigated. In order to analyze all the essential features, the transformed nonlinear conservation equations are worked out numerically by Spectral Quasi-Linearisation Method. By insisting the comparison between suction and injection effects, the physical quantities of the flow and its characteristics are exhibited graphically and quantitatively with various parameters

COEFFICIENT INEQUALITY FOR CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS

Abstract The objective of this paper is to an obtain an upper bound to the second Hankel determinant |a 2 a 4 − a 2 3 | for the function f , belonging to a certain subclass of analytic functions, using Toeplitz determinants

Similarity Solution for Free Convection Flow of a Micropolar Fluid under Convective Boundary Condition via Lie Scaling Group Transformations

The free convective flow of an incompressible micropolar fluid along permeable vertical plate under the convective boundary condition is investigated. The Lie scaling group of transformations is applied to get the similarity representation for the system of partial differential equations and then the resulting systems of equations are solved using spectral quasi-linearisation method. A quantitative comparison of the numerical results is made with previously published results for special cases and the results are found to be in good agreement. The results of the physical parameters on the developments of flow, temperature, concentration, skinfriction, wall couple stress, heat transfer, and mass transfer characteristics along vertical plate are given and the salient features are discussed