p-adic analysis and their applications is used distributions, measure, integrals, L-function other generalized functions. In addition, among the many ways to investigate construct generating functions for special polynomials numbers, one of most important techniques Fermionic integral over \(\mathbb{Z}\)p. this paper, we introduce new numbers arising from on First, as generalizations Changhee o...

We prove that stationary Gromov-Witten invariants of P1 arise as the Eynard-Orantin invariants of the spectral curve x = z + 1/z, y = ln z. As an application we show that tautological intersection numbers on the moduli space of curves arise in the asymptotics of large degree Gromov-Witten invariants of P1.

and Applied Analysis 3 If p, 1/q ∈ Z, then solutions f : N0 → Z of the difference equation 1.7 are called the Lucas sequences see, e.g., 24 ; in some special cases they are given specific names; that is, the Fibonacci numbers p −1, q −1, f 0 0, and f 1 1 , the Lucas numbers p −1, q −1, f 0 2, and f 1 1 , the Pell numbers p −2, q −1, f 0 0, and f 1 1 , the Pell-Lucas or companion Lucas numbers p...

Discrete sets of numbers related to some irrational number , called the-integers Z , are a natural tool to describe quasicrystals. We prove that, when is a quadratic Pisot unit, the set Z is a group isomorphic to the set of integers Z.

Let X be a Brownian motion defined on the line (with X(0)=0) and let Y be an independent Brownian motion defined on the nonnegative real numbers. For all t ≥ 0, we define the iterated Brownian motion (IBM), Z, by setting Z t ∆ = X(Y t). In this paper we determine the exact uniform modulus of continuity of the process Z.

• If m > n, the exact quotient of two n-bit numbers cannot be an m-bit number. • Let x, y ∈ Mn. x = y ⇒ |x/y − 1| ≥ 2−n. We call a breakpoint a value z where the rounding changes, that is, if t1 and t2 are real numbers satisfying t1 < z < t2 and ◦t is the rounding mode, then ◦t(t1) < ◦t(t2). For “directed” rounding modes (i.e., towards +∞, −∞ or 0), the breakpoints are the FP numbers. For round...

Main theorems of the article concern the problem of M. Atiyah on possible values of l2-Betti numbers. It is shown that all non-negative real numbers are l2-Betti numbers, and that “many” (for example all non-negative algebraic) real numbers are l2-Betti numbers of aspherical manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to an aspherical m...

The papers [23], [24], [4], [5], [2], [20], [21], [9], [1], [22], [13], [15], [16], [12], [10], [11], [17], [14], [25], [3], [7], [6], [19], and [8] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: X denotes a complex Banach algebra, w, z, z1, z2 denote elements of X, k, l, m, n denote natural numbers, s1, s2, s3, s, s ′ denote sequences of...

Using covariant density functional theory with the DDME2 and labeling single-particle energy orbitals by Nilsson quantum numbers, a search for particle-hole (p-h) excitations connected to appearance of shape coexistence is performed $Z=38$ 84. Islands are found near magic numbers $Z=82$ $Z=50$, restricted in regions around relevant neutron midshells $N=104$ $N=66$, respectively, accordance well...

All vector spaces and so forth here will be defined over the complex numbers. If z = x+i y is a complex number, where x, y are real numbers, then the complex conjugate of z is denoted z and defined to be x− i y. The complex conjugate of a sum or product of complex numbers is equal to the corresponding sum or product of complex conjugates. The modulus of a complex number z is the nonnegative rea...