Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion
2013
In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally when the pattern invades the domain as a trave…
Well-posedness of Prandtl equations with non-compatible data
2013
In this paper we shall be concerned with Prandtl's equations with incompatible data, i.e. with initial data that, in general, do not fulfil the boundary conditions imposed on the solution. Under the hypothesis of analyticity in the streamwise variable, we shall prove that Prandtl's equations, on the half-plane or on the half-space, are well posed for a short time.
Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring
2013
We introduce a new iterative scheme for solving linear ill-posed problems, similar to nonstationary iterated Tikhonov regularization, but with an approximation of the underlying operator to be used for the Tikhonov equations. For image deblurring problems, such an approximation can be a discrete deconvolution that operates entirely in the Fourier domain. We provide a theoretical analysis of the new scheme, using regularization parameters that are chosen by a certain adaptive strategy. The numerical performance of this method turns out to be superior to state-of-the-art iterative methods, including the conjugate gradient iteration for the normal equation, with and without additional precondi…
Rotationally symmetric 1-harmonic flows from D2 TO S 2: Local well-posedness and finite time blowup
2010
The 1-harmonic flow from the disk to the sphere with constant Dirichlet boundary conditions is analyzed in the case of rotational symmetry. Sufficient conditions on the initial datum are given, such that a unique classical solution exists for short times. Also, a sharp criterion on the boundary condition is identified, such that any classical solution will blow up in finite time. Finally, nongeneric examples of finite time blowup are exhibited for any boundary condition.
On the discrete linear ill‐posed problems
1999
An inverse problem of photo‐acoustic spectroscopy of semiconductors is investigated. The main problem is formulated as the integral equation of the first kind. Two different regularization methods are applied, the algorithms for defining regularization parameters are given. Diskrečiųjų blogai sąlygotų uždavinių klausimu Santrauka Darbe nagrinejamas foto‐akustines spektroskopijos puslaidininkiuose uždavinys, kuriame i vertinami nešeju difuzijos ir rekombinacijos procesai. Reikia atstatyti šaltinio funkcija f(x), jei žinoma antrosios eiles difuzijos lygtis ir atitinkamos kraštines salygos. Naudojantis matavimu, atliktu ivairiuose dažniuose, rezultatais sprendžiamas atvirkštinis uždavinys, kel…
Optimization of conducting structures by using the homogenization method
2002
Approximation and numerical realization of a class of optimization problems with control variables represented by coefficients of linear elliptic state equations is considered. Convergence analysis of well-posed problems is performed by using one- and two-level approximation strategies. The latter is utilized in an optimization layout problem for two conductive constituents, for which the necessary steps to transfer the well-posed problem into a computational form are described and some numerical experiments are given.
Multicomponent line profile restoring by means of ill-posed inverse task solution
2017
The investigation of the criteria of usage of the Tikhonov regularization method for multicomponent overlapping line profiles restoring was done by means of model task solution. The influence of the width and kind of the instrumental function, number of the components of the profile and distance between components are discussed.
Property (w) and perturbations II
2008
AbstractThis note is a continuation of a previous article [P. Aiena, M.T. Biondi, Property (w) and perturbations, J. Math. Anal. Appl. 336 (2007) 683–692] concerning the stability of property (w), a variant of Weyl's theorem, for a bounded operator T acting on a Banach space, under finite-dimensional perturbations K commuting with T. A counterexample shows that property (w) in general is not preserved under finite-dimensional perturbations commuting with T, also under the assumption that T is a-isoloid.
Property (w) and perturbations III
2009
AbstractThe property (w) is a variant of Weyl's theorem, for a bounded operator T acting on a Banach space. In this note we consider the preservation of property (w) under a finite rank perturbation commuting with T, whenever T is polaroid, or T has analytical core K(λ0I−T)={0} for some λ0∈C. The preservation of property (w) is also studied under commuting nilpotent or under injective quasi-nilpotent perturbations. The theory is exemplified in the case of some special classes of operators.
Distance measures for biological sequences: Some recent approaches
2008
AbstractSequence comparison has become a very essential tool in modern molecular biology. In fact, in biomolecular sequences high similarity usually implies significant functional or structural similarity. Traditional approaches use techniques that are based on sequence alignment able to measure character level differences. However, the recent developments of whole genome sequencing technology give rise to need of similarity measures able to capture the rearrangements involving large segments contained in the sequences. This paper is devoted to illustrate different methods recently introduced for the alignment-free comparison of biological sequences. Goal of the paper is both to highlight t…