Let f(z) be a function analytic in the complex domain C+∪C−∪(−1,+∞), real for real z and such that f(z), f2(z) are anti-Herglotz functions. In this paper we show that f(z) possesses simple upper and lower bounds given by rational functions. Our main tool is the analytic theory of continued fractions. An application to the theory of solutions of the Feigenbaum-Cvitanović equation is given.

We present a simple protocol for two-player secure circuit evaluation. The protocol enables players C and D to cooperate in the computation of f(x) while D conceals her data x from C and C conceals his circuit for f from D. The protocol is based on the technique of hiding information from an oracle [Abadi, Feigenbaum, Kilian, J. Comput. System Sci. 39(1):21{50, August, 1989].

In this paper, we develop a new approach to the construction of solutions of the Feigenbaum-Cvitanović equation whose existence was shown by H. Epstein. Our main tool is the analytic theory of continued fractions.

We establish Ramanujan-style congruences modulo certain primes $$\ell $$ between an Eisenstein series of weight k, prime level p and a cuspidal newform in the $$\varepsilon -eigenspace Atkin–Lehner operator inside space cusp forms k for $$\Gamma _0(p)$$ . Under mild assumption, this refines result Gaba–Popa. use these recent work Ciolan, Languasco third author on Euler–Kronecker constants, to q...

A method is developed here for doing multiple calculations of lattice sums when the lattice structure is kept fixed, while the molecular orientations or the molecules within the unit cells are altered. The approach involves a two-step process. In the first step, a multipole expansion is factored in such a way as to separate the geometry from the multipole moments. This factorization produces a ...

A so-called Renormalization Group (RG) analysis is performed in order to shed some light on why the density of prime numbers in N decreases like the single power of the inverse neperian logarithm. CERN–TH/2000–146 May 2000 Part I The most elementary proof of the Prime Numbers Theorem These few lines are not part of the proof. They simply show the history which has led to the starting point of o...

The prtnonation constant values of tryptophan were studied at 25 C. different ionic strengths. 0.1-1.0 moldm", and various ionic media of NaCIO, and N4N01, using a combination of spectrophotometrie andpotentiometric techniques. The general vend for the two protonation con Slant Vai net of tryptophan is in theorder of NaC104 > NaNO3 in different ionic media. The dependence of protonation constan...