Search results for "Applied Mathematics"

Convergence for varying measures

2023

Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense.

Free-surface flows solved by means of SPH schemes with numerical diffusive terms

2010

A novel system of equations has been defined which contains diffusive terms in both the continuity and energy equations and, at the leading order, coincides with a standard weakly-compressible SPH scheme with artificial viscosity. A proper state equation is used to associate the internal energy variation to the pressure field and to increase the speed of sound when strong deformations/compressions of the fluid occur. The increase of the sound speed is associated to the shortening of the time integration step and, therefore, allows a larger accuracy during both breaking and impact events. Moreover, the diffusive terms allows reducing the high frequency numerical acoustic noise and smoothing …

Quantifying brain tumor tissue abundance in HR-MAS spectra using non-negative blind source separation techniques

2012

Given high-resolution magic angle spinning (HR-MAS) spectra from several glial tumor subjects, our goal is to differentiate between tumor tissue types by separating the different sources that contribute to the profile of each spectrum. Blind source separation techniques are applied for obtaining characteristic profiles for necrosis, highly cellular tumor and border tumor tissue and providing the contribution (abundance) of each of these tumor tissue types to the profile of each spectrum. The problem is formulated as a non-negative source separation problem. Non-negative matrix factorization, convex analysis of non-negative sources and non-negative independent component analysis methods are …

Constrained control of a nonlinear two point boundary value problem, I

1994

In this paper we consider an optimal control problem for a nonlinear second order ordinary differential equation with integral constraints. A necessary optimality condition in form of the Pontryagin minimum principle is derived. The proof is based on McShane-variations of the optimal control, a thorough study of their behaviour in dependence of some denning parameters, a generalized Green formula for second order ordinary differential equations with measurable coefficients and certain tools of convex analysis.

Locally Convex Quasi *-Algebras of Operators

2011

This note is mainly concerned with locally convex quasi C*-normed *-algebras which arise as completions of C*-algebras of operators under certain topologies. Their importance is made clear by the representation theory of abstract locally convex quasi C*-normed *-algebras, investigated in previous papers and whose basic aspects are also overviewed here.

On the Euler-Lagrange inequality of a convex variational integral in Orlicz spaces

1987

Fixed point theory for almost convex functions

1998

Traditionally, metric fixed point theory has sought classes of spaces in which a given type of mapping (nonexpansive, assymptotically or generalized nonexpansive, uniformly Lipschitz, etc.) from a nonempty weakly compact convex set into itself always has a fixed point. In some situations the class of space is determined by the application while there is some degree of freedom in constructing the map to be used. With this in mind we seek to relax the conditions on the space by considering more restrictive types of mappings.

Monotonicity and enclosure methods for the p-Laplace equation

2018

We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the $p$-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs, one of which is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.

Robust l2-gain control for 2D nonlinear stochastic systems with time-varying delays and actuator saturation

2013

Abstract This paper is concerned with the problems of stability analysis and l2-gain control for a class of two-dimensional (2D) nonlinear stochastic systems with time-varying delays and actuator saturation. Firstly, a convex hull representation is used to describe the saturation behavior, and a sufficient condition for the existence of mean-square exponential stability of the considered system is derived. Then, a state feedback controller which guarantees the resulting closed-loop system to be mean-square exponentially stable with l2-gain performance is proposed, and an optimization procedure to maximize the estimation of domain of attraction is also given. All the obtained results are for…

A constructive theory of shape

2021

We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of qualitatively similar shapes are constructed giving as input a finite ordered set of characteristic points (landmarks) and the value of a continuous parameter $\kappa \in (0,\infty)$. We prove that all shapes belonging to the same family are located within the convex hull of the landmarks. The theory is constructive in the sense that it provides a systematic means to build a mathematical model for any shape taken from the physical world. We illustrate this with a va…