Computer modeling of optical shadow-casting processor

Computing employing optical signal presupposes information being encoded optically. Many digital optical computing system employs pixel patterns to represent different logic level. Cellular logic, symbolic substitution, morphological and image processing could be performed on such pattern-coded information. Such systems have generally been analyzed by geometric optics. In this work, we propose to model such computing systems using laws of electromagnetic propagation. Results predicted by both geometric optics and the computer model are provided for a pattern-coded full adder/subtracter implementation. The model is general enough to be extended to other systems with more complicated coding pattern and could serve as design tool for optimizing a computing system using pattern-coded logic.     

Minimal submanifolds of hyperbolic spaces via harmonic morphisms

In this paper we give a method for constructing complete minimal submanifolds of the hyperbolic spaces H ^m . They are regular fibres of harmonic morphisms from H ^m with values in Riemann surfaces.     

Chemical cleavage reactions of DNA on solid support: application in mutation detection

Background  

The conventional solution-phase Chemical Cleavage of Mismatch (CCM) method is time-consuming, as the protocol requires purification of DNA after each reaction step. This paper describes a new version of CCM to overcome this problem by immobilizing DNA on silica solid supports.     

Box-Trees and R-Trees with Near-Optimal Query Time

Abstract. A box-tree is a bounding-volume hierarchy that uses axis-aligned boxes as bounding volumes. The query complexity of a box-tree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing box-trees with small worst-case query complexity with respect to queries with axis-parallel boxes and with points. We also prove lower bounds on the worst-case query complexity for box-trees, which show that our results are optimal or close to optimal. Finally, we present algorithms to convert box-trees to R-trees, resulting in R-trees with (almost) optimal query complexity.     

A model for peak formation in the two-phase equations

We present a hyperbolic-elliptic model problem related to the equations of two-phase fluid flow. The model problem is solved numerically, and properties of its solution are presented. The model equation is well-posed when linearized around a constant state, but there is a strong focusing effect, and very large solutions exist at certain times. We prove that the model problem has a smooth solution for bounded times.

     

The effect of nonlinearity on unstable zones of Mathieu equation

Mathieu equation is a well-known ordinary differential equation in which the excitation term appears as the non-constant coefficient. The mathematical modelling of many dynamic systems leads to Mathieu equation. The determination of the locus of unstable zone is important for the control of dynamic systems. In this paper, the stable and unstable regions of Mathieu equation are determined for three cases of linear and nonlinear equations using the homotopy perturbation method. The effect of nonlinearity is examined in the unstable zone. The results show that the transition curves of linear Mathieu equation depend on the frequency of the excitation term. However, for nonlinear equations, the curves depend also on initial conditions. In addition, increasing the amplitude of response leads to an increase in the unstable zone.     

Synthesis of novel imidazo[1,2-a]pyridines with potent activity against herpesviruses

[reaction: see text] Synthesis of a novel imidazopyridine with potent activity against herpes simplex viruses is presented. Several synthetic approaches that describe the introduction of a C-3 pyrimidine substituent on the imidazopyridine core via construction of the pyrimidine or Stille coupling are outlined. Methodology for efficient installation of C-8 amine substituents was developed. The outlined strategies provide a high-yielding, scalable route that is amenable to rapid analogue synthesis.