RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.     

On two epireflective subcategories of the category of 2T 0-fuzzy bitopological spaces

In the space of absolutely summable sequences the total variation of a sequence becomes a natural norm, and is a measure of smoothness. This norm is preserved by the so-called LU LU-smoothers, in that the variation of the image plus the variation of the difference is equal to the variation of the original sequence. This surprising property is useful for strategies for the removal of impulsive and other random noise. Strong shape preserving properties of these smoothers are derived in the process of proving this. The results shed light on similar properties of the popular median smoothers, as well as their sometimes enigmatic behaviour.     

A Closed Formula for the Riemann Normal Coordinate Expansion

We derive an integral representation whichencodes all coefficients of the Riemann normalcoordinate expansion and also a closed formula for thosecoefficients.     

关于一类波方程的非线性本征值问题的注记

本文推广[1]中关于问题[Ⅰ] 的无穷多对本征值,本征函数存在性定理到p>2的情形.当p=2时,所考虑的空间是Hilbert空间,可利用相应线性算子的本征函数展开;当p>2时,我们的工作空间是Banach空间.我们利用空间L~p和其对偶空间L~p(?)上的Hausdorff-Young不等式对泛函数估值,从而证明了相应的定理.     

LETTER: String Theory and an Integrable Model in Two-Dimensional Gravity with Dynamical Torsion

The integrability character of an integrable model of two-dimensional gravity with bosonic string coupling in Riemann-Cartan space is studied in the present letter. The equations of motion in the model are reduced to a nonlinear integrable equation. The general numerical solutions of this equation are found. In addition, the exact solution of scalar curvature is obtained.     

A new compactness type topological property

By a gauge on a topological space we shall mean a mapping that assigns each element in the space an open neighbourhood. We investigate some topological properties which can be characterized using gauges. The main property we will consider is the gauge compactness. Some problems and possible future work are listed at the end of the paper.     

Perfect Fluids: Field-theoretical Description and Gauge Symmetry Issue

We show that combinations of (in general,non-linear) two- and threeform fields, analogous to theMaxwell (one-form) field, completely describe perfectfluids, including the rotating ones. In the non-rotating case, the two-form field is sufficient, and afree three-form field proves to be equivalent toappearance of the cosmological term in Einstein'sequations (the square-root non-linearity correspondingto = 0). The gauge degrees of freedombreak down when a rotation is included, but even whenthey exist, there fails to be realized an equivalence ofthe two-form field and the massless scalar one recently claimed by Weinberg.     

Energy and Relativistic Clock Rates in Five Dimensions

In the framework of a Kaluza-Klein-like scheme, based on a five-dimensional Riemannian space in which energy plays the role of the fifth dimension, we discuss a class of solutions of the five-dimensional Einstein equations in vacuum, which allows us to recover the energy-dependent phenomenological metric for gravitation, recently derived from the analysis of some experimental data concerning the slowing down of clock rates in the gravitational field of Earth.     

两面针植物中的新生物碱7-去甲6-甲氧基-5,6-二氢白屈菜红碱的晶体结构

从两面针植物中分离得新生物碱7-去甲-6-甲氧基-5,6-二氢白屈菜红碱(C~2~1H~1~0O~5N的单晶结构已用直接法解出:空间群为P2t/c,晶能参数:a=14.213(7),b=17.347(3),c=7.513(9)A,β=101.40(13)°,z=4。对I≥3σ(I)的1876个独立反射, 用全矩阵最小二乘法修正到R=0.096和Rπ=0.077(单位权重)。     

Some Extremal Properties of Section Spaces of Banach Bundles and Their Duals,II

Let π : E → X be a real Banach bundle with section space Γ(π), where X is a compact Hausdorff space. We complete the characterization of weak-* and sequential weak-* points of continuity in the unit ball of Γ(π) ? for certain classes of bundles (which include the trivial ones), which was begun in an earlier paper. The proofs avoid the use of vector measures.