Trace Extensions,Determinant Bundles,and Gauge Group Cocycles

We study the geometry of determinant line bundles associated with Dirac operators on compact odd-dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated nonmultiplicative renormalized determinants.     

X分形晶格上Gauss模型的临界性质

采用实空间重整化群变换的方法,研究了2维和d(d>2)维X分形晶格上Gauss模型的临界性质.结果表明:这种晶格与其他分形晶格一样,在临界点处,其最近邻相互作用参量也可以表示为K=bqiqi(qi是格点i的配位数,bqi是格点i上自旋取值的Gauss分布常数)的形式;其关联长度临界指数v与空间维数d(或分形维数df)有关.这与Ising模型的结果存在很大的差异. 关键词： X分形晶格 重整化群 Gauss模型 临界性质     

Effect of end groups on complexation kinetics between cyclodextrins and guest polymers

α‐Cyclodextrin (α‐CD) has been complexed with various poly(ethylene glycol) (PEG) derivatives in aqueous solution. It has been found that the end groups of PEG derivatives affect the complexation kinetics greatly, but have only a little influence on the thermodynamic behavior. By increasing the hydrophobicity of end groups, the complexation speeds up rapidly. On the other hand, the bulky end groups slow down the threading of polymeric guests into the cavity of CD. By changing the hydrophobicity and the size of end groups, the complexation rate can be adjusted in the range of several orders of magnitudes, which should be quite useful in the design of new supramolecular systems. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2050–2057, 2006     

Detecting and Diagnostic Checking Multivariate Conditional Heteroscedastic Time Series Models

Two tests for multivariate conditional heteroscedastic models are proposed. One is based on the cross-correlations of standardized squared residuals and the other is a score (Lagrange multiplier) test. The cross-correlations test can be used to detect the presence of multivariate conditional heteroscedasticity whereas the other test can be used for diagnostic checking. Simulation studies on the size and power of the test statistics are reported. The application of the tests is illustrated by an example using the S & P 500 and Sydney All Ordinary Indexes.     

A Joint Integral Test for the Locations of Extrema for Brownian Motion

Let μ⁺(t) and μ⁻(t) be the locations of the maximum and minimum, respectively, of a standard Brownian motion in the interval [0,t]. We establish a joint integral test for the lower functions of μ⁺(t) and μ⁻(t), in the sense of Paul Lévy. In particular, it yields the law of the iterated logarithm for max(μ⁺(t),μ⁻(t)) as a straightforward consequence. Our result is in agreement with well-known theorems of Chung and Erdős [(1952) Trans. Amer. Math. Soc. 72, 179–186.], and Csáki, F?ldes and Révész [(1987) Prob. Theory Relat. Fields 76, 477–497].      

A common generalization for MV-algebras and Łukasiewicz–Moisil algebras

We introduce the notion of n-nuanced MV-algebra by performing a Łukasiewicz–Moisil nuancing construction on top of MV-algebras. These structures extend both MV-algebras and Łukasiewicz–Moisil algebras, thus unifying two important types of structures in the algebra of logic. On a logical level, n-nuanced MV-algebras amalgamate two distinct approaches to many valuedness: that of the infinitely valued Łukasiewicz logic, more related in spirit to the fuzzy approach, and that of Moisil n-nuanced logic, which is more concerned with nuances of truth rather than truth degree. We study n-nuanced MV-algebras mainly from the algebraic and categorical points of view, and also consider some basic model-theoretic aspects. The relationship with a suitable notion of n-nuanced ordered group via an extension of the Γ construction is also analyzed.     

Sets of permutations that generate the symmetric group pairwise

The paper contains proofs of the following results. For all sufficiently large odd integers n, there exists a set of ²n−1 permutations that pairwise generate the symmetric group Sn. There is no set of ²n−1+1 permutations having this property. For all sufficiently large integers n with n≡2mod4, there exists a set of ²n−2 even permutations that pairwise generate the alternating group An. There is no set of ²n−2+1 permutations having this property.     

Optical Glucose Monitoring Based on Femtosecond Two-Color Pulse Interferometry

We demonstrate the potential of femtosecond two-color pulse interferometry for in vitro optical glucose monitoring, by dispersion of the group refractive index in a glucose solution sample with respect to a red-color light and a blue-color light. By comparison with femtosecond one-color pulse interferometry, the basic performance of the present system with regard to sensitivity, quantitativeness, and tolerance to surrounding disturbances, is evaluated. The resulting accuracy and precision of glucose determination are 77 and 118mg/dl for 10-mm-sample-thickness, respectively. This near-common-path configuration of the two-color pulse light provides good stability to fluctuations of sample temperature, which is important in clinical applications. Considering the performance of femtosecond two-color pulse interferometry as an optical glucose sensor, a suitable measurement site for in vivo optical glucose monitoring is discussed.     

Microstructure effect on microtopography of chemically etched α + β Ti alloys

Microstructure effect on chemical etching behavior of the annealed Ti-6Al-4V and Ti-3Al-2.5V titanium (Ti) alloys was compared with that of unalloyed commercially pure titanium. The microstructural evolution of structure phases after annealing the titanium and its alloys at temperature near and above β transus and followed by furnace cooling to room temperature was studied using optical microscope, scanning electron microscope and X-ray diffraction techniques. The microstructure study illustrates that the heat treatment enhanced partitioning effect allows extensive formation of hemispherical and near spherical pits roughened surface to be readily acquired by chemically etching the annealed α + β titanium alloys. The kinetics of the chemical etching reaction process show a linear dependence on time. The annealed α + β titanium alloys that exhibit relatively lower weight loss and thickness reduction rate illustrate less chemical activity than the annealed unalloyed titanium.     

A New Family of Cyclic Difference Sets with Singer Parameters in Characteristic Three

We construct a new family of cyclic difference sets with parameters ((3 ^d – 1)/2, (3 ^{d – 1} – 1)/2, (3 ^{d – 2} – 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets.