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

DNA cruciform arms nucleate through a correlated but non-synchronous cooperative mechanism

Inverted repeat (IR) sequences in DNA can form non-canonical cruciform structures to relieve torsional stress. We use Monte Carlo simulations of a recently developed coarse-grained model of DNA to demonstrate that the nucleation of a cruciform can proceed through a cooperative mechanism. Firstly, a twist-induced denaturation bubble must diffuse so that its midpoint is near the centre of symmetry of the IR sequence. Secondly, bubble fluctuations must be large enough to allow one of the arms to form a small number of hairpin bonds. Once the first arm is partially formed, the second arm can rapidly grow to a similar size. Because bubbles can twist back on themselves, they need considerably fewer bases to resolve torsional stress than the final cruciform state does. The initially stabilised cruciform therefore continues to grow, which typically proceeds synchronously, reminiscent of the S-type mechanism of cruciform formation. By using umbrella sampling techniques we calculate, for different temperatures and superhelical densities, the free energy as a function of the number of bonds in each cruciform along the correlated but non-synchronous nucleation pathways we observed in direct simulations.Comment: 12 pages main paper + 11 pages supplementary dat

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

Coefficient inequality for certain subclass of analytic functions

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

COEFFICIENT INEQUALITY FOR MULTIVALENT BOUNDED TURNING FUNCTIONS OF ORDER α

The objective of this paper is to obtain the sharp upper bound to the H_2(p + 1), second Hankel determinant for p-valent (multivalent) analytic bounded turning functions (also called functions whose derivatives have positive real parts) of order α (0 ≤ α < 1), using Toeplitz determinants. The result presented here includes three known results as their special cases