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1.
Ever since the discovery of nucleic acids 150 years ago,[1] major achievements have been made in understanding and decrypting the fascinating scientific questions of the genetic code.[2] However, the most fundamental question about the origin and the evolution of the genetic code remains a mystery. How did nature manage to build up such intriguingly complex molecules able to encode structure and function from simple building blocks? What conditions were required? How could the precursors survive the unhostile environment of early Earth? Over the past decades, promising synthetic concepts were proposed providing clarity in the field of prebiotic nucleic acid research. In this Minireview, we show the current status and various approaches to answer these fascinating questions.  相似文献   
2.
This paper deals with a scalar conservation law in 1-D space dimension, and in particular, the focus is on the stability analysis for such an equation. The problem of feedback stabilization under proportional-integral-derivative (PID for short) boundary control is addressed. In the proportional-integral (PI for short) controller case, by spectral analysis, the authors provide a complete characterization of the set of stabilizing feedback parameters, and determine the corresponding time delay stability interval. Moreover, the stability of the equilibrium is discussed by Lyapunov function techniques, and by this approach the exponential stability when a damping term is added to the classical PI controller scheme is proved. Also, based on Pontryagin results on stability for quasipolynomials, it is shown that the closed-loop system subject to PID control is always unstable.  相似文献   
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A degenerate parabolic equation of convection-diffusion type has been proposed by Robert and Sommeria in [12] to describe the relaxation towards statistical equilibrium states in 2D incompressible perfect fluid dynamics. The paper is concerned with the Cauchy problem for this equation. The local existence of a variational soluation is obtained in using the decrease of the (negative) mixing entropy and Schauder theorem. A smoothing effect is used when proving the uniqueness of the variational solutions by youdovitch's method. Finally, global existence of solutions and their asymptotic convergence towards Gibbs states are shown for a large class of initial data.  相似文献   
6.
《Liquid crystals》2012,39(12):1763-1768
ABSTRACT

We report the synthesis of 7,7?-disubstituted 2,2?-methylenedioxy-1,1?-binaphthyls and demonstrate their application as chiral dopants in the nematic mixture MLC-6260 to produce highly twisted cholesteric phases. Especially mesogenic and/or polarizable groups in the 7,7?-positions of the bridged binaphthyls generate unusually high helical twisting powers.  相似文献   
7.
《Optimization》2012,61(6):1187-1201
ABSTRACT

Several optimization problems of modifying the weight of vertices in rooted trees, some of which are special cases of the inverse 1-median problem, are solved. Such problems arise in Very Large Scale Integration (VLSI) design of hardware security circuits, circuit synchronization, and analog-to-digital converters. These problems require assigning costly hardware (demands) to the leaves of rooted trees. One common property of these problems is that a resource allocated to an internal node can be shared by the entire sub-tree emanated at the node. Two types of problems are studied here. (1) A tree node employs an addition operation and the demands at the leaves are obtained by summing the resources allocated to nodes along the root-to-leaf paths. A linear-time bottom-up algorithm is shown to minimize the total resources allocated to tree nodes. (2) A tree’s node employs a multiplication operation and the demands at the leaves are obtained by multiplying the resources allocated to nodes along the root-to-leaf paths. A bottom-up dynamic programming algorithm is shown to minimize the total resources allocated to the tree’s nodes. While the above problems are usually solved by design engineers heuristically, this paper offers optimal solutions that can be easily programmed in CAD tools.  相似文献   
8.
《Optimization》2012,61(12):2269-2295
ABSTRACT

In this paper, we propose a best-response approach to select an equilibrium in a two-player generalized Nash equilibrium problem. In our model we solve, at each of a finite number of time steps, two independent optimization problems. We prove that convergence of our Jacobi-type method, for the number of time steps going to infinity, implies the selection of the same equilibrium as in a recently introduced continuous equilibrium selection theory. Thus the presented approach is a different motivation for the existing equilibrium selection theory, and it can also be seen as a numerical method. We show convergence of our numerical scheme for some special cases of generalized Nash equilibrium problems with linear constraints and linear or quadratic cost functions.  相似文献   
9.
ABSTRACT

The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed.  相似文献   
10.
Clustering is the problem of partitioning data into a finite number k of homogeneous and separate groups, called clusters. A good choice of k is essential for building meaningful clusters. In this paper, this task is addressed from the point of view of model selection via penalization. We design an appropriate penalty shape and derive an associated oracle-type inequality. The method is illustrated on both simulated and real-life data sets.  相似文献   
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