Search results for "General Mathematics"

COMPLEX CONVEXITY AND VECTOR-VALUED LITTLEWOOD–PALEY INEQUALITIES

2003

Let 2 p 0s uch thatfHp(X) (� f(0)� p + λ (1 −| z| 2 ) p−1 � f � (z)� p dA(z)) 1/p ,f or all f ∈ H p (X). Applications to embeddings between vector-valued BMOA spaces defined via Poisson integral or Carleson measures are provided.

Explicit expressions for Sturm-Liouville operator problems

1987

Throughout this paper H will denote a complex separable Hilbert space and L(H) denotes the algebra of all bounded linear operators on H. If T lies in L(H), its spectrum σ(T) is the set of all complex numbers z such zI–T is not invertible in L(H) and its compression spectrum σcomp(T) is the set of all complex numbers z such that the range (zI-T)(H) is not dense in H ([3, p. 240]). This paper is concerned with the Sturm–Liouville operator problemwhere λ is a complex parameter and X(t), Q, Ei, Fi for i = l,2, and t∈[0,a], are bounded operators in L(H). For the scalar case, the classical Sturm-Liouville theory yields a complete solution of the problem, see [4], and [7]. For the finite-dimension…

On the fractional integral of Weyl inL p

1994

Carleson's counterexample and a scale of Lorentz-BMO spaces on the bitorus

2005

We introduce a full scale of Lorentz-BMO spaces BMO L p,q on the bidisk, and show that these spaces do not coincide for different values ofp andq. Our main tool is a detailed analysis of Carleson's construction in [C].

Numerical Recovery of Source Singularities via the Radiative Transfer Equation with Partial Data

2013

The inverse source problem for the radiative transfer equation is considered, with partial data. Here we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$ where $X_{V}$ is the partial data solution operator to the radiative transfer equation. The numerical scheme is based in part on a forward solver designed by F. Monard and G. Bal. We will see that one can detect quite well the visible singularities of an internal optical source $f$ for generic anisotropic $k$ and $\sigma$, with or without noise added to the accessible data $X_{V}f$. In particular, we use a truncated Neumann series to estimate $X_{V}$ and $X_{V}^{*}$, which provides a good approximation of $X_{V}^{*…

A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

2015

Variational methods are commonly used to solve noise removal problems. In this paper, we present an augmented Lagrangian-based approach that uses a discrete form of the L1-norm of the mean curvature of the graph of the image as a regularizer, discretization being achieved via a finite element method. When a particular alternating direction method of multipliers is applied to the solution of the resulting saddle-point problem, this solution reduces to an iterative sequential solution of four subproblems. These subproblems are solved using Newton’s method, the conjugate gradient method, and a partial solution variant of the cyclic reduction method. The approach considered here differs from ex…

A Stochastic Algorithm Based on Fast Marching for Automatic Capacitance Extraction in Non-Manhattan Geometries

2014

WOS:000346854900026 (Nº de Acesso Web of Science) We present an algorithm for two- and three-dimensional capacitance analysis on multidielectric integrated circuits of arbitrary geometry. Our algorithm is stochastic in nature and as such fully parallelizable. It is intended to extract capacitance entries directly from a pixelized representation of the integrated circuit (IC), which can be produced from a scanning electron microscopy image. Preprocessing and monitoring of the capacitance calculation are kept to a minimum, thanks to the use of distance maps automatically generated with a fast marching technique. Numerical validation of the algorithm shows that the systematic error of the algo…

Curvelet-based method for orientation estimation of particles

2013

A method based on the curvelet transform is introduced for estimating from two-dimensional images the orientation distribution of small anisotropic particles. Orientation of fibers in paper is considered as a particular application of the method. Theoretical aspects of the suitability of this method are discussed and its efficiency is demonstrated with simulated and real images of fibrous systems. Comparison is made with two traditionally used methods of orientation analysis, and the new curvelet-based method is shown to perform clearly better than these traditional methods.

The interplay between the guidance from the digital learning environment and the teacher in supporting folding back

2022

AbstractPrevious studies have proposed that students’ mathematical understanding develops dynamically through the process known as folding back, in which learners revisit earlier forms of understanding and use them to build even deeper levels of mathematical understanding. Digital learning environments, where students can manipulate representations, are often used to enable students to notice properties, patterns, or rules. When working in such an environment, students usually receive support from the environment and the teacher. The interplay between these different sources of support is important according to previous studies. In this study, we examine this interplay in the case of foldin…

"Writing to Learn or Learning to Write". A Critical Review of "English as a Foreign Language" (EFL) Teaching Practices in Writing in Saudi Universiti…

2020

Developing proficiency in English writing has always been a challenge for L2 learners in general and Saudi learners in particular. Despite the widespread presence of English departments as a result of the sharp rise of Saudi universities in the previous decade, the numbers of outcomes or achievements in terms of skills are very discouraging. This paper aims to study this issue closely by investigating the most crucial elements that are likely to explain this weakness by reviewing the related empirical and theoretical studies in the Saudi context. This paper also aims to present to researchers a quick reference as to how English writing skills have evolved in Saudi Arabia in the recent past,…