This paper is concerned with the problem of computing approximate D-optimal design for polynomial regression with analytic weight function on a interval [m0-a, mo+ a]. It is shown that the structure of the optimal design depends on a and weight function. Moreover, the optimal support points and weights are analytic functions of a at a = 0. We make use of a Taylor expansion to provide a recursiv...

We study the asymptotic behavior of the solutions related to a family of singularly perturbed linear partial differential equations in the complex domain. The analytic solutions obtained by means of a BorelLaplace summation procedure are represented by a formal power series in the perturbation parameter. Indeed, the geometry of the problem gives rise to a decomposition of the formal and analyti...

Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit probability distributions present in large random structures. “Singularity analysis” reviewed here provides constructive estimates that are applicable in several areas...

this paper presents an analytic procedure for the value added to different production levels with different policy options. the approach is stochastic and thus provides a framework for informed decision-making on productivity growth under uncertainty conditions. the model was applied to data collected from a firm and re-sults recommend that the firm should redevelop if in diversification and sy...

Many problems in physics and engineering with semi-infinite boundaries or interfaces are exactly solvable by the Wiener–Hopf technique. It has been used successfully in a multitude of different disciplines when the Wiener–Hopf functional equation contains a single scalar kernel. For complex boundary value problems, however, the procedure often leads to coupled equations which therefore have a k...

BACKGROUND/OBJECTIVES Meaningful profiling of pancreatic cancer samples is particularly challenging due to their complex cellular composition. Beyond tumor cells, surgical biopsies contain desmoplastic stroma with infiltrating inflammatory cells, adjacent normal parenchyma, and "non-pancreatic tissues". The risk of misinterpretation rises when the heterogeneous cancer tissues are sub-divided in...

VC-dimension is the measure of model complexity (capacity) used in VC-theory. The knowledge of the VC-dimension of an estima-2 tor is necessary for rigorous complexity control using analytic VC generalization bounds. Unfortunately, it is not possible to obtain the analytic estimates of the VC-dimension in most cases. Hence, it has been recently proposed to measure the VC-dimension of an estimat...

The procedure of solving nonstationary Schrödinger equations in the exact analytic form is elaborated on the basis of exactly solvable stationary models. The exact solutions are employed to study the nonadiabatic geometric phase at cyclic evolution of quantum systems.