Convergent Star Product Algebras on ‘ax+b’

We define nontempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product. The techniques used to achieved the latter come from symmetric spaces geometry and star representation theory.     

多个相异性矩阵的数据分析

本文给出了分析多个相异性矩阵的三种方法.首先找到了一种图表示,使我们对所有相异性矩阵有一个总体的了解;其次定义了一个新的相异性矩阵,它可以看作是对所有原始相异性矩阵的一个折衷处理;最后提出了一种MIMU方法.在文中我们还对由上述方法得到的坐标图进行了比较.     

Critical exponents,hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2 ₄ – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2 ₄ –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R _g ² >/<R _e ² >=0.14026±0.00007, <R _m ² >/<R _e ² >=0.43961±0.00034, and ^*=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent ₁=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for ₁. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R _g ² >/<R _e ² >=0.1599±0.0002 and ^*=0.2471±0.0003; since ^*>0, hyperscaling holds. The approach to ^* is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2 ₄ – for two-dimensional SAWs.     

Geometry and combinatorics of Julia sets of real quadratic maps

For real a correspondence is made between the Julia setB forz(z–)², in the hyperbolic case, and the set of-chains±(±(±..., with the aid of Cremer's theorem. It is shown how a number of features ofB can be understood in terms of-chains. The structure ofB is determined by certain equivalence classes of-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and-chains. Certain Julia sets associated with the Feigenbaum function and some theorems of Lanford are discussed.Supported by NSF grant No. MCS-8104862.Supported by NSF grant No. MCS-8203325.     

铜离子对烟草多酚氧化酶变性和复性影响的热力学研究(英)

在有无5 mmol·L^-1 CuSO₄存在的两种情况下，运用荧光光谱研究了烟草多酚氧化酶在盐酸胍诱导下的变性和复性平衡。烟草多酚氧化酶在6.0 mol·L^-1盐酸胍变性30 min(25 ℃)即完全失活。荧光光谱结果表明：铜离子能够提高烟草多酚氧化酶的结构稳定性和抗盐酸胍变性的能力，进而影响烟草多酚氧化酶在盐酸胍诱导下的变性和复性过程。没有外源铜存在的情况下，盐酸胍诱导的烟草多酚氧化酶变性和复性是一个可逆的二态过程；在5 mmol·L^-1 CuSO₄存在的条件下，由于结合了Cu²⁺的酶的中间态稳定性增加，显示特征荧光，结果显示，外源铜存在时，盐酸胍诱导的烟草多酚氧化酶变性和复性是一个可逆的三态过程。根据相应模型，进行了热力学计算。上述实验结果得到酶活性测定的进一步证实，在6 mol·L^-1盐酸胍中放置5，10，15，20，25，30 min，烟草多酚氧化酶的剩余活性分别为18.7%，11.7%，8.9%，6.6%，3.6%，0.06%，但在5 mmol·L^-1 CuSO₄存在的条件下，剩余活性则分别为60.3%，44.6%，42.5%，40.2%，25.6%，25.3%。     

Monitoring folding transitions of synthetic,branched-chain polypeptides by capillary zone electrophoresis

The coil/helix transition of a synthetic, branched-chain polymeric polypeptide (poly (Lys(Glu(1)-DL-Ala(3))EAK), 50-Lys residues long in the backbone, as a function of increasing molarities of methanol in solution, is here studied by both, circular dichroism (CD) and capillary zone electrophoresis. CD spectra showed that, at 75% v/v methanol, the transition from random coil to fully helical structure was obtained, in a pH 1.1 HCI solution in the presence of 20 mM NaCI. CZE studies, run in parallel, exhibited the classical unfolding to folding sigmoidal transition, with mid-point at 60% v/v methanol concentration, plateauing at ca. 80% v/v organic solvent. Surprisingly, though, such unfolding to folding transition was accompanied by an expansion, rather than a contraction, of the resulting ordered polypeptide. As the charge of the polypeptide (a pure polycation at a pH of 2.1 in CZE) was kept rigorously constant, a plot of the radius of the polymer along the sigmoidal transition clearly showed that the radius of gyration of the helical, structured polypeptide was in fact larger than that of the random coil. Such results were confirmed by molecular dynamics simulations, which indicated that the dimensions of such polypeptide, in alpha-helix configuration, were 8.5 nm (in length) and 3.2 nm (in diameter), whereas those of the corresponding random coil were 7.2 nm (in length) and 5.1 nm (length of shorter axis). It would thus appear that the randomized structure assumes the shape of a more compact object, roughly resembling a "rugby ball".     

Phenomenology of nonlocal cellular automata

Dynamical systems with nonlocal connections have potential applications to economic and biological systems. This paper studies the dynamics of nonlocal cellular automata. In particular, all two-state, three-input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings, although it is observed that sometimes a rule can have different dynamical behaviors with different wirings. The nonlocal cellular automata rule space is studied using a mean-field parametrization which is ideal for the situation of random wiring. Nonlocal cellular automata can be considered as computers carrying out computation at the level of each component. Their computational abilities are studied from the point of view of whether they contain many basic logical gates. In particular, I ask the question of whether a three-input cellular automaton rule contains the three fundamental logical gates: two-input rules AND and OR, and one-input rule NOT. A particularly interesting edge-of-chaos nonlocal cellular automaton, the rule 184, is studied in detail. It is a system of coupled selectors or multiplexers. It is also part of the Fredkin's gate—a proposed fundamental gate for conservative computations. This rule exhibits irregular fluctuations of density, large coherent structures, and long transient times.     

Combined Chemical Modification and Collision Induced Unfolding Using Native Ion Mobility-Mass Spectrometry Provides Insights into Protein Gas-Phase Structure

Native mass spectrometry is now an important tool in structural biology. Thus, the nature of higher protein structure in the vacuum of the mass spectrometer is an area of significant interest. One of the major goals in the study of gas-phase protein structure is to elucidate the stabilising role of interactions at the level of individual amino acid residues. A strategy combining protein chemical modification together with collision induced unfolding (CIU) was developed and employed to probe the structure of compact protein ions produced by native electrospray ionisation. Tractable chemical modification was used to alter the properties of amino acid residues, and ion mobility-mass spectrometry (IM-MS) utilised to monitor the extent of unfolding as a function of modification. From these data the importance of specific intramolecular interactions for the stability of compact gas-phase protein structure can be inferred. Using this approach, and aided by molecular dynamics simulations, an important stabilising interaction between K6 and H68 in the protein ubiquitin was identified, as was a contact between the N-terminus and E22 in a ubiquitin binding protein UBA2.     

Physical Dimensions/Units and Universal Constants: Their Invariance in Special and General Relativity

The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing mechanics and electrodynamics, it naturally leads one, besides the dimensions of length and time, to the fundamental units of action $\mathfrak{h}$, electric charge q, and magnetic flux ?. Also, $q\times ?=\text{action}$ and $q/?=1/\text{resistance}$ are known. These results of classical physics suggests to look into the corresponding quantum aspects of q and ? (and also of $\mathfrak{h}$): The electric charge occurs exclusively in elementary charges e, whereas the magnetic flux can have any value; in specific situations, however, in superconductors of type II at very low temperatures, ? appears quantized in the form of fluxons (Abrikosov vortices). And $\mathfrak{h}$ leads, of course, to the Planck quantum h. Thus, one is directed to superconductivity and, because of the resistance, to the quantum Hall effect. In this way, the Josephson and the quantum Hall effects come into focus quite naturally. One goal is to determine the behavior of the fundamental constants in special and in general relativity.