Banzhaf Measures for Games with Several Levels of Approval in the Input and Output

An axiomatic characterization of ‘a Banzhaf score’ notion is provided for a class of games called (j,k) simple games with a numeric measure associated to the output set, i.e., games with n players, j ordered qualitative alternatives in the input level and k possible ordered quantitative alternatives in the output. Three Banzhaf measures are also introduced which can be used to determine a player's ‘a priori’ value in such a game. We illustrate by means of several real world examples how to compute these measures. Research partially supported by Grant BFM 2003-01314 of the Science and Technology Spanish Ministry and the European Regional Development Fund.     

关于亚纯函数的分解

讨论了一类亚纯函数的分解 ,推广了整函数的相关结果 .证明了有理函数与超越整函数的复合不可能为具有非常数多项式为模的拟周期函数 .     

On the Expansion of Ramanujan's Continued Fraction

If Ramanujan's continued fraction (or its reciprocal) is expanded as a power series, the sign of the coefficients is (eventually) periodic with period 5. We give combinatorial interpretations for the coefficients from which the result is immediate. We make use of the quintuple product identity, which we prove.     

On the Rogers--Ramanujan Periodic Continued Fraction

In the paper, the convergence properties of the Rogers--Ramanujan continued fraction $$1 + \frac{qz}{1 + \tfrac{q^2 z}{1 + \cdots}}$$ are studied for q = exp (2 π i τ), where τ is a rational number. It is shown that the function H _q to which the fraction converges is a counterexample to the Stahl conjecture (the hyperelliptic version of the well-known Baker--Gammel--Wills conjecture). It is also shown that, for any rational τ, the number of spurious poles of the diagonal Padé approximants of the hyperelliptic function H _q does not exceed one half of its genus.     

识同思异——澳洲会计师公会总裁麦雅理对话银行家鲍里斯

我要先知道“相同想法”是什么,然后我再去思考不同做法。     

On the Expansion of a Continued Fraction of Gordon

We show that when certain infinite products associated with a continued fraction of Basil Gordon are expanded as power series, the sign of the coefficients is periodic, with period 8.     

m-continued Fraction Expansions of Multi-Laurent Series

The simple continued fraction expansion[7] of a single real number gives the best solution to its rational approximation problem.     

On the Generalized Rogers–Ramanujan Continued Fraction

On page 26 in his lost notebook, Ramanujan states an asymptotic formula for the generalized Rogers–Ramanujan continued fraction. This formula is proved and made slightly more precise. A second primary goal is to prove another continued fraction representation for the Rogers–Ramanujan continued fraction conjectured by R. Blecksmith and J. Brillhart. Two further entries in the lost notebook are examined. One of them is an identity bearing a superficial resemblance to the generating function for the generalized Rogers–Ramanujan continued fraction. Thus, our third main goal is to establish, with the help of an idea of F. Franklin, a partition bijection to prove this identity.     

A Type of Hyperelliptic Continued Fraction

Based on hints of Tschebychev, a continued fraction is described which gives an effective algorithm for calculating the torsion, if finite, of divisors D − D⁻ on a hyperelliptic curve of genus ≥2, where D is an effective divisor of degree 2 and D⁻ denotes the image of D under the hyperelliptic involution. The difficulties involved in extending the algorithm to divisors of degree ≥3 are briefly discussed.     

同一个色多项式图的结构特征问题

研究了图的色多项式,给出了用图的结构特征描述的色多项式表达式.     

Fraction of solid angle subtended by the detector to the source

A general formula for the solid angle subtended by the detector to the radioactive source is derived.     

Matrix Continued Fraction for the Resolvent Function of the Band Operator

The aim of this paper is the expansion of a matrix function in terms of a matrix-continued fraction as defined by Sorokin and Van Iseghem. The function under study is the Weyl function or resolvent function of an operator, given in the standard basis by a bi-infinite band matrix, with p subdiagonals and q superdiagonals, where the p + q – 1 intermediate diagonals are zero. The main goal of this paper is to find, for the moments, an explicit form in terms of the coefficients of the continued fraction, called genetic sums, which lead to a generalization of the notion of a Stieltjes continued fraction. These results are extension of some results already found for the vector case (p = 1) and are a step in the direction towards the solution of the direct and inverse spectral problem. The actual computation of the approximants of the given function as the convergents of the continued fraction is shown to be effective. Some possible extensions are considered.     

关于Psi函数的连分式估计及其应用（英文）

建立了Psi函数的连分式估计.作为应用,我们获得了Euler-Mascheroni常数的更高阶估计.     

On a Continued Fraction Formula of Wall

We study the combinatorics of a continued fraction formula due to Wall. We also derive the orthogonality of little q-Jacobi polynomials from this formula, as Wall did for little q-Laguerre polynomials.     

Note on a Continued Fraction of Ramanujan

Ramanujan, who loved continued fractions, recorded many of his formulas in his two notebooks. The 25th entry in Chapter 12 of Notebook II is a continued fraction involving a quotient of gamma function products. We are going to give a new proof of Entry 25, which, incidently, is the least difficult of all Ramanujan's continued fraction formulas involving quotients of gamma function products. In our proof, we make use of a hypergeometric formula of his.