Dynamical models of molecular chains and efficient integration algorithms

Chains of point masses and chains of rigid bodies are used to model biological polymers. To investigate their dynamics we propose a method which allows an efficient realization of the constraints jointly with a simple and accurate integration of the free rigid body motion. The method is quite effective to evolute the geodesic flow of a rigid body chain and the global performance depends on the computational complexity of the algorithms used to compute the interaction forces. Our approach is suitable to describe a chain of rigid bodies immersed in a thermal bath. In the method we propose, the constraints are realized by hard springs whose elastic constant is set to maximize the energy dissipation rate of a Runge–Kutta integrator scheme. Moreover the use of local Lagrangian coordinates is introduced using the possibility of a continuous change of chart, such that the distance from the coordinate singularities is the highest possible. For a chain of point masses the numerical results are checked with another method where the constraints are exactly realized by means of Lagrangian coordinates. When the chain is subject to regular interactions potentials plus a thermal bath the exact and approximate constraints realization provide comparable results.     

Independence over arbitrary sets in NSOP1 theories

We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP₁ theory. We deduce symmetry of Kim-independence and the independence theorem for Lascar strong types.     

Magnetic domain wall motion by current injection in CoPt nanowires consisting of notches

Magnetic domain wall behaviors in CoPt nanowires consisting of multiple pairs of notches were investigated by experimental measurements as well as by micromagnetic modeling. The nanowires were fabricated by ion-beam sputter deposition and e-beam lithography where one to three triangular shaped notches were installed at an interval of 1 μm. Based on the evaluated I–V characteristics, we observed that differential resistance curves showed two peaks with a local minimum at around zero current; the domain wall was trapped between the current ranges within these two peaks. As the number of notch was increased, the resistance of the nanowire became larger.     

Integral transform and convolution of analytic functionals on abstract Wiener space

Yeh defined a convolution of functionals on classical Wiener space and investigated the relationship between the Fourier-Wiener transforms of functionals in certain classes and the Fourier-Wiener transform of their convolution. Yoo extended Yeh's results to abstract Wiener space. In this paper, we introduce the intergal transform and convolution of analytic functionals on abstract Wiener space. And we establish the relationship between the integral transforms of exponential type of analytic functionals and the integral transform of theor convolution. Also we obtain Parseval's and Plancherel's relations for those functionals from this relationship. The main results of Yeh and Yoo then follow from our results as corollaries.     

On the de Bruijn-Newman constant

If λ(0) denotes the infimum of the set of real numbers λ such that the entire function Ξλ represented by

     

Controllability and Hedgibility of Black-Scholes Equations with <Emphasis Type="Italic">N</Emphasis> Stocks

This paper is to investigate the controllability and observability properties of linear and certain nonlinear Black-Scholes (B-S) type equations consisting of N stocks in an appropriate bounded domain I of ℝ₊ ^N . In this model both the stock volatility and interest rate are influenced by the stock prices and the control which is related to the hedging ratio in option pricing of finance is distributed over a subdomain of I. The proof of the controllability result for the linear B-S equations relies on the suitable observability inequality for the associated adjoint problem, and for the nonlinear model, fixed point technique is applied. Our result leads to that the dynamic hedgibility in finance is proved in the context of controllability theory.     

Green’s Function for Second Order Elliptic Equations in Non-divergence Form

We construct the Green function for second order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition and the domain has C^1,1 boundary. We also obtain pointwise bounds for the Green functions and its derivatives.