磷酰化氨基酸自聚成肽的FTIR研究

本文通过对傅里叶变换红外光谱（ＦＴＩＲ）技术研究证明了磷酰化氨基酸可以知聚成肽，并由此说明了在仿生化成肽反应过程中，磷（酰化）起着十分重要的作用，同时了说明了ＦＴＩＲ技术为仿生化的过程研究提供了新的研究方法。     

Phonon Dispersion in Polyadenylic Acid

A study of the normal modes of vibration and their dispersion in polyadenylic acid based on the Urey–Bradley force field is reported. It gives a better interpretation of FTIR spectra as compared with the valence force field. Characteristic features of dispersion curves such as regions of high density‐of‐states, repulsion, and character mixing of dispersive modes are discussed. Predictive valuzes of heat capacity as a function of temperature are reported.     

Skorokhod decomposition of reflected diffusions on bounded Lipschitz domains with singular non-reflection part

Let be a compact set with interior G. Let L ¹ (G,dx), >0 dx-a.e. on G, and m:=dx. Let A=(a _ij ) be symmetric, and globally uniformly strictly elliptic on G. Let be such that ; f, , is closable in L ² (G,m) with closure ( ^r ,D( ^r )). The latter is fulfilled if satisfies the Hamza type condition, or _i L ¹ _loc (G,dx), 1id. Conservative, non-symmetric diffusion processes X _t related to the extension of a generalized Dirichlet form where satisfies are constructed and analyzed. If G is a bounded Lipschitz domain, H ^1,1 (G), and a _ij D( ^r ), a Skorokhod decomposition for X _t is given. This happens through a local time that is uniquely associated to the smooth measure 1_{{ Tr ()>0}} d, where Tr denotes the trace and the surface measure on G.This research has been financially supported by TMR grant HPMF-CT-2000-00942 of the European Union. Mathematics Subject Classification (2000): 60J60, 60J55, 31C15, 31C25, 35J25     

Goodness-Of-Fit Tests Based on Estimated Expectations of Probability Integral Transformed Order Statistics

New goodness-of-fit tests, based on bootstrap estimated expectations of probability integral transformed order statistics, are derived for the location-scale model. The resulting test statistics are location and scale invariant, and are sensitive to discrepancies at the tails of the hypothesized distribution. The limiting null distributions of the test statistics are derived in terms of functionals of a certain Gaussian process, and the tests are shown to be consistent against a broad family of alternatives. Critical points for all sample sizes are provided for tests of normality. A simulation study shows that the proposed tests are more powerful than established tests such as Shapiro-Wilk, Cramér-von Mises and Anderson-Darling, for a wide range of alternative distributions.     

En route to Background Independence: Broken split-symmetry,and how to restore it with bi-metric average actions

The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Average Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a ‘bi-metric’ ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein–Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring: In the ultraviolet they emanate from a non-Gaussian fixed point, and in the infrared they loose all symmetry violating contributions inflicted on them by the non-invariant functional RG equation. As an application, we compute the scale dependent spectral dimension which governs the fractal properties of the effective QEG spacetimes at the bi-metric level. Earlier tests of the Asymptotic Safety conjecture almost exclusively employed ‘single-metric truncations’ which are blind towards the difference between quantum and background fields. We explore in detail under which conditions they can be reliable, and we discuss how the single-metric based picture of Asymptotic Safety needs to be revised in the light of the new results. We shall conclude that the next generation of truncations for quantitatively precise predictions (of critical exponents, for instance) is bound to be of the bi-metric type.     

High resolution study of the six lowest doubly excited vibrational states of PH2D

The five lowest doubly excited deformational vibrational bands ν₄ + ν₆, 2ν₆, ν₃ + ν₄, ν₃ + ν₆, and 2ν₃ of PH₂D have been recorded for the first time using a Bruker 120 HR interferometer with a resolution 0.0033 cm⁻¹ and analysed. Some transitions belonging to a very weak band 2ν₄ have been also assigned. From the fit 24 and 86, respectively, diagonal and resonance interaction parameters were obtained which reproduce 1089 upper energy levels obtained from more than 4600 assigned transitions with the rms deviation of 0.00059 cm⁻¹.     

Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions

Some Hardy-type integral inequalities in general measure spaces, where the corresponding Hardy operator is replaced by a more general Volterra type integral operator with kernel , are considered. The equivalence of such inequalities on the cones of non-negative respective non-increasing functions are established and applied.

     

Existence and uniqueness of the solution,separation for certain second order elliptic differential equation

In this paper, we study conditions under which Schrodinger type operators with a matrix potential is separated and Schrodinger equation has a unique solution in the weighted space L_2,k(Rⁿ)^l, where l is any natural number and k ε C¹(Rⁿ) is a positive function     

A brief historical introduction to Euler's formula for polyhedra,topology, graph theory and networks

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Königsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real physical systems are included. We also mention some important and modern applications of graph theory or network problems from transportation to telecommunications. Graphs or networks are effectively used as powerful tools in industrial, electrical and civil engineering, communication networks in the planning of business and industry. Graph theory and combinatorics can be used to understand the changes that occur in many large and complex scientific, technical and medical systems. With the advent of fast large computers and the ubiquitous Internet consisting of a very large network of computers, large-scale complex optimization problems can be modelled in terms of graphs or networks and then solved by algorithms available in graph theory. Many large and more complex combinatorial problems dealing with the possible arrangements of situations of various kinds, and computing the number and properties of such arrangements can be formulated in terms of networks. The Knight's tour problem, Hamilton's tour problem, problem of magic squares, the Euler Graeco-Latin squares problem and their modern developments in the twentieth century are also included.