Constructing Large 2D Lattices Out of DNA-Tiles

The predictable nature of deoxyribonucleic acid (DNA) interactions enables assembly of DNA into almost any arbitrary shape with programmable features of nanometer precision. The recent progress of DNA nanotechnology has allowed production of an even wider gamut of possible shapes with high-yield and error-free assembly processes. Most of these structures are, however, limited in size to a nanometer scale. To overcome this limitation, a plethora of studies has been carried out to form larger structures using DNA assemblies as building blocks or tiles. Therefore, DNA tiles have become one of the most widely used building blocks for engineering large, intricate structures with nanometer precision. To create even larger assemblies with highly organized patterns, scientists have developed a variety of structural design principles and assembly methods. This review first summarizes currently available DNA tile toolboxes and the basic principles of lattice formation and hierarchical self-assembly using DNA tiles. Special emphasis is given to the forces involved in the assembly process in liquid-liquid and at solid-liquid interfaces, and how to master them to reach the optimum balance between the involved interactions for successful self-assembly. In addition, we focus on the recent approaches that have shown great potential for the controlled immobilization and positioning of DNA nanostructures on different surfaces. The ability to position DNA objects in a controllable manner on technologically relevant surfaces is one step forward towards the integration of DNA-based materials into nanoelectronic and sensor devices.     

Investigating isomerization reactions in solid state by using simultaneous high overtone pumping and Raman detection

Formation of the unstable cis-formic acid in solid argon matrix is induced by direct excitation of the 6<--0 transition of the nu(OH) vibration of the trans-formic acid. The experiment utilizes strongly focused laser beam that produces relatively high isomerization rate despite the low cross section of the absorption. Raman spectroscopy in a backscattering geometry is used for detection of the reactants and the products. This experimental arrangement allow us to use the same laser source for simultaneous pumping and Raman excitation, and it also guarantees that the excited and probed volumes overlap. The presented method has a high potential for solid state investigations of chemical reactions on the ground electronic state.     

Industrial impulse noise: Crest factor as an additional parameter in exposure measurements

A procedure to measure industrial impulse noise was developed that provides information on both the equivalent noise level and impulsiveness. Impulsiveness of the signal was defined as the difference between the A-weighted peak level and the root-mean-square level. This difference, also known as a crest factor, varies in time, so the cumulative distribution function was used to describe the probability to achieve a certain value of impulsiveness. A telemetric sampling system carried by the worker was used to take measurements at a shipyard. The sample duration of 10 minutes was considered sufficient to cover welders', platers', and grinders' different work phases. The total number of 10 minute samples was 123. The welders were exposed to the most impulsive noise, whereas the grinders were exposed to the highest equivalent noise level. The present paper describing a procedure to measure industrial impulse noise comprises part of a follow-up study on the effects of noise on hearing.     

Singular Indefinite Sturm-Liouville Operators with a Spectral Gap

Singular Sturm-Liouville operators with the indefinite weight sgn(·) and a symmetric potential which has a positive limit at ∞ have a gap in the essential spectrum. Under an additional condition it is shown that in this gap are no eigenvalues. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient Markets and Contingent Claims Valuation: An Information Theoretic Approach

This research article shows how the pricing of derivative securities can be seen from the context of stochastic optimal control theory and information theory. The financial market is seen as an information processing system, which optimizes an information functional. An optimization problem is constructed, for which the linearized Hamilton–Jacobi–Bellman equation is the Black–Scholes pricing equation for financial derivatives. The model suggests that one can define a reasonable Hamiltonian for the financial market, which results in an optimal transport equation for the market drift. It is shown that in such a framework, which supports Black–Scholes pricing, the market drift obeys a backwards Burgers equation and that the market reaches a thermodynamical equilibrium, which minimizes the free energy and maximizes entropy.     

An indefinite Laplacian on a rectangle

In this note, we investigate the nonelliptic differential expression

$$A = - div\operatorname{sgn} \nabla $$

on a rectangular domain Ω in the plane. The seemingly simple problem of associating a self-adjoint operator with the differential expression A in L²(Ω) is solved here. Such indefinite Laplacians arise in mathematical models of metamaterials characterized by negative electric permittivity and/or negative magnetic permeability.

     

Spectral analysis of singular ordinary differential operators with indefinite weights

In this paper we develop a perturbation approach to investigate spectral problems for singular ordinary differential operators with indefinite weight functions. We prove a general perturbation result on the local spectral properties of selfadjoint operators in Krein spaces which differ only by finitely many dimensions from the orthogonal sum of a fundamentally reducible operator and an operator with finitely many negative squares. This result is applied to singular indefinite Sturm-Liouville operators and higher order singular ordinary differential operators with indefinite weight functions.     

Elliptic boundary value problems with λ-dependent boundary conditions

In this paper second order elliptic boundary value problems on bounded domains Ω⊂Rn with boundary conditions on ∂Ω depending nonlinearly on the spectral parameter are investigated in an operator theoretic framework. For a general class of locally meromorphic functions in the boundary condition a solution operator of the boundary value problem is constructed with the help of a linearization procedure. In the special case of rational Nevanlinna or Riesz-Herglotz functions on the boundary the solution operator is obtained in an explicit form in the product Hilbert space L²(Ω)⊕(L²m(∂Ω)), which is a natural generalization of known results on λ-linear elliptic boundary value problems and λ-rational boundary value problems for ordinary second order differential equations.     

A characterization of the eigenvalues of Schrödinger operators with Dirichlet and Neumann boundary conditions

The eigenvalues of the self-adjoint Schrödinger operators on a bounded domain with Dirichlet and Neumann boundary conditions are characterized by the singularities of an associated Dirichlet-to-Neumann map and its inverse, respectively. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)