ASYMPTOTIC ANALYSIS OF SKOLEM’S EXPONENTIAL FUNCTIONS

Asymptotic Variation of L Functions of One-variable Exponential Sums

Fix an integer d ≥ 3. Let A be the dimension-d affine space over the algebraic closure Q of Q, identified with the coefficient space of degree-d monic polynomials f(x) in one variable x. For any f(x) in A(Q), let Q(f) be the field generated by coefficients of f in Q. For each prime p coprime to d, pick an embedding from Q to Qp, once and for all. Let P be the place in Q(f) lying over p specifie...

Limit summability of ultra exponential functions

In [1] we uniquely introduced ultra exponential functions (uxpa) and denednext step of the serial binary operations: addition, multiplication and power.Also, we exhibited the topic of limit summability of real functions in [2,3]. Inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. Finally, we pose an unsolved problem aboutthem.

Asymptotic analysis of the exponential penalty trajectory in linear programming

We consider the linear program rain { c'x: Ax ~< b } and the associated exponential penalty function fr(x) = c'x + rEexp [ ( A ~ bi)/r]. For r close to 0, the unconstrained minimizer x(r) offr admits an asymptotic expansion of the form x (r) = x* + rd* + *l(r) where x* is a particular optimal solution of the linear program and the error term ~(r) has an exponentially fast decay. Using duality t...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Asymptotic approximation of exponential integrals

1 Preliminaries 1 1.1 What this is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Big-O and small-o notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.4 Definition: Asymptotic approximation ...