Effort estimates through project complexity

This paper reports the results obtained from use of project complexity parameters in modeling effort estimates. It highlights the attention that complexity has recently received in the project management area. After considering that traditional knowledge has consistently proved to be prone to failure when put into practice on actual projects, the paper endorses the belief that there is a need for more open-minded and novel approaches to project management. With a view to providing some insight into the opportunities that integrate complexity concepts into model building offers, we extend the work previously undertaken on the complexity dimension in project management. We do so analyzing the results obtained with classical linear models and artificial neural networks when complexity is considered as another managerial parameter. For that purpose, we have used the International Software Benchmarking Standards Group data set. The results obtained proved the benefits of integrating the complexity of the projects at hand into the models. They also addressed the need of a complex system, such as artificial neural networks, to capture the fine nuances of the complex systems to be modeled, the projects.     

Decay estimates of functions through singular extensions of vector-valued Laplace transforms

Let X be a Banach space and let f∈L^∞(R⁺;X) whose Laplace transform extends analytically to some region containing iR?{0}, possibly having a pole at the origin. In this paper, we give estimates of the decay of certain slight suitable modification of f in terms of the growth of its Laplace transform along the imaginary axis. This technique is applied to obtain decay estimates of smooth orbits of bounded C₀-semigroups whose infinitesimal generators have an arbitrary finite boundary spectrum. These results are close to those given recently by C.J.K. Batty and T. Duyckaerts.     

Density estimates for a random noise propagating through a chain of differential equations

We here provide two sided bounds for the density of the solution of a system of n differential equations of dimension d, the first one being forced by a non-degenerate random noise and the n−1 other ones being degenerate. The system formed by the n equations satisfies a suitable Hörmander condition: the second equation feels the noise plugged into the first equation, the third equation feels the noise transmitted from the first to the second equation and so on … , so that the noise propagates one way through the system. When the coefficients of the system are Lipschitz continuous, we show that the density of the solution satisfies Gaussian bounds with non-diffusive time scales. The proof relies on the interpretation of the density of the solution as the value function of some optimal stochastic control problem.     

Size estimates in thermography

We deal with the problem of recovery of an unknown inclusion located in a medium Ω by prescribing a heat flux on the boundary of Ω and measuring the corresponding temperature. In particular, we provide an upper and a lower bound on the size of the inclusion. We also show the validity and the accuracy of the method with some numerical examples.     

Some estimates in spaces

We consider a class of rearrangement invariant Banach Function Spaces recently appeared in a paper by the same authors, containing at the same time some Lorentz spaces Γ(ν), classical Lebesgue spaces and small Lebesgue spaces. We discuss the main properties coming directly from the norm, and, for certain values of the involved parameters, we prove some estimates of the norm of the associate space.     

Isoperimetric estimates in products

In a product M ₁ × M ₂ of Riemannian manifolds, the least perimeter required to enclose given volume among general regions is at least 1/√ 2 times that among regions of product form, assuming that the isoperimetric profiles of M ₁ and M ₂ are concave. This result sharpens earlier work of Grigor'yan, generalizes results of Bollobás and Leader and of Barthe, and yields a lower bound on the Cheeger isoperimetric constant of a product.     

Local error estimates in quadrature

A theoretical error estimate for quadrature formulas, which depends on four approximations of the integral, is derived. We obtain a bound, often sharper than the trivial one, which requires milder conditions to be satisfied than a similar result previously presented by Laurie. A selection of numerical tests with one-dimensional integrals is reported, to show how the error estimate works in practice.     

Reverse estimates in growth spaces

Let H(B _d ) denote the space of holomorphic functions on the unit ball B _d of ${{\mathbb{C}}^d}$ . Given a radial doubling weight w, we construct functions ${f, g\in H(B_1)}$ such that |f| + |g| is comparable to w. Also, we obtain similar results for B _d , d ≥ 2, and for circular, strictly convex domains with smooth boundary. As an application, we study weighted composition operators and related integral operators on growth spaces of holomorphic functions.     

Dual estimates in multiextremal problems

We propose a technique of improving the dual estimates in nonconvex multiextremal problems of mathematical programming, by adding some additional constraints which are the consequences of the original constraints. This technique is used for the problems of finding the global minimum of polynomial functions, and extremal quadratic and boolean quadratic problems. In the article one ecological multiextremal problem and an algorithm for finding the dual estimate for it also considered. This algorithm is based upon a scheme of decomposition and nonsmooth optimization methods.This paper was presented at the II. IIASA Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

Stability estimates in inverse scattering

An algorithm is given for calculating the solution to the 3D inverse scattering problem with noisy discrete fixed energy data. The error estimates for the calculated solution are derived. The methods developed are of a general nature and can be used in many applications: in nondestructive evaluation and remote sensing, in geophysical exploration, medical diagnostics, and technology.     

Pointwise gradient estimates in exterior domains

We consider a class of elliptic operators with unbounded coefficients in a smooth exterior domain Ω and we prove that the Cauchy-Neumann problem associated with admits, for any bounded and continuous initial datum, a unique bounded classical solution. We also provide pointwise gradient estimates for such a solution. Received: 5 July 2005; Revised: 20 December 2005     

Isoperimetric estimates in low-dimensional Riemannian products

Annals of Global Analysis and Geometry - Let $$(T^k,h_k)=(S_{r_1}^1\times S_{r_2}^1 \times \cdots \times S_{r_k}^1, dt_1^2+dt_2^2+\cdots +dt_k^2)$$ be flat tori, $$r_k\ge \cdots \ge r_2\ge...     

Reverse estimates in logarithmic Bloch spaces

We obtain sharp reverse estimates for the logarithmic Bloch spaces on the unit disk. As an application, we study composition operators with values in the space BMOA.