We derive an asymptotic expansion as n → ∞ for a large range of coefficients of (f (z))n, where f(z) is a power series satisfying |f(z)| < f(|z|) for z ∈ C, z ∉R+. When f is a polynomial and the two smallest and the two largest exponents appearing in f are consecutive integers, we use the expansion to generalize results of Odlyzko and Richmond (1985) on log concavity of polynomials, and we prov...

We show that for a given holomorphic noncharacteristic surface S ∈ C, and a given holomorphic function on S, there exists a unique meromorphic solution of Burgers’ equation which blows up on S. This proves the convergence of the formal Laurent series expansion found by the Painlevé test. The method used is an adaptation of Nirenberg’s iterative proof of the abstract Cauchy-Kowalevski theorem. A...

A granular gas subjected to a permanent injection of energy is described by means of hydrodynamic equations derived from a moment expansion method. The method uses as reference function not a Maxwellian distribution f(M) but a distribution f(0)=Phif(M), such that Phi adds a fourth cumulant kappa to the velocity distribution. The formalism is applied to a stationary conductive case showing that ...

– A self-consistent variational theory for globules based on the uniform expansion method is presented. This method, first introduced by Edwards and Singh to estimate the size of a self-avoinding chain, is restricted to a good solvent regime, where two-body repulsion leads to chain swelling. We extend the variational method to a poor solvent regime where the balance between the two-body attract...

Given a set F of vertices of a connected graph G, we study the problem of testing the connectivity of G−F in polynomial time with respect to |F | and the maximum degree ∆ of G. We present two approaches. The first algorithm for this problem runs in O ( |F |∆2ε−1 log(|F |∆ε−1) ) time for every graph G with vertex expansion at least ε > 0. The other solution, designed for the class of graphs with...

We prove that a two-variable p-adic lq-function has the series expansion lp,q s, t, χ 2 q/ 2 F ∑F a 1, p,a 1 −1 a χ a qa/〈a pt〉 ∑∞ m 0 −s m F/〈a pt〉 mE∗ m,qF which interpolates the values lp,q −n, t, χ E∗ n,χn,q pt − pχn p 2 q/ 2 qp E∗ n,χn,q t , whenever n is a nonpositive integer. The proof of this original construction is due to Kubota and Leopoldt in 1964, although the method given in this ...

With the help of a simple variational procedure it is possible to convert the partial sums of order N of many divergent series expansions f(g) = ∑∞ n=0 ang n into partial sums ∑N n=0 bng −ωn, where 0 < ω < 1 is a parameter that parametrizes the approach to the large-g limit. The latter are partial sums of a strong-coupling expansion of f(g) which converge against f(g) for g outside a certain di...

We consider the following generalization of the seminal Erdős–Ko–Rado theorem, due to Frankl [5]. For some k ≥ 2, let F be a k-wise intersecting family of r-subsets of an n element set X, i.e. for any F1, . . . , Fk ∈ F , ∩ k i=1Fi 6= ∅. If r ≤ (k − 1)n k , then |F| ≤ ( n−1 r−1 ) . We prove a stability version of this theorem, analogous to similar results of Dinur-Friedgut, Keevash-Mubayi and o...

Uf(a,ß,Y,x): Universal-logic-module for ternary functions, based upon Reed-Muller expansion, i.e. aodulo-algebra expansion Uh(c,n,x): basic Universal-logic-module for ternary function«, based upon modulo-algebra expansion uh(5,n,x) t ® n x F]: column vector whose entries are the 3 values of f(x), arranged in Increasing order of y, n-1 yI x^ 1-0 LgCK)]: coefficient column vector based upon modul...

A perturbation algorithm using any time transformation is introduced. To account for the nonlinear dependence of the function, we exhibit the function f of the system in the differential equation. To this end, we introduce the transformation t t w f Te ) , ( , where f is a function that depends on t or w. The problems are solved with new time transformation: Linear damped vibration equation, cl...