Smoothness

Given a metric continuum X, we consider the following hyperspaces of X: 2 X , Cn(X) and Fn(X) (n ∈ N). Let F 1 (X) = {{x} : x ∈ X}. A hyperspace K(X) of X is said to be rigid, provided that for every homeomorphism h : K(X) → K(X), we have h(F 1 (X)) = F 1 (X). In this paper, we study conditions under which a continuum X has a rigid hyperspace Cn(X). Among others, we consider families of continua, such as dendroids, Peano continua, hereditarily indecomposable continua and smooth fans.

A novel three-dimensional gray-level interpolation method called the Directional Coherence Interpolation (DCI) is presented in the paper. The principal advantage of the proposed approach is that it leads to significantly higher visual quality in 3D rendering when compared with traditional image interpolation methods. The basis of DCI is a form of directional image-space coherence. DCI interpolates the missing image data along the maximum coherence directions (MCD), which are estimated from the local image intensity yet constrained by a generic smoothness term. In order to further improve both the algorithm efficiency and robustness, we also propose to apply a pyramidal search strategy for MCD estimation. This coarse-to-fine scheme requires less computation time by starting with the reduced amount of data and propagating searching results to finer resolutions. DCI can incorporate image shape and structure information without the prior requirement of explicit representation of object ...

In interpretation of seismic data the resolution and smoothness of the envelope of the seismic trace is an important property to have. This paper introduces a new method of envelope generation for seismic traces that is based on the concept of normalized total gradient (NTG) that found many useful applications in interpretation of potential field data and is considered in that field of study to be better resolved and smoother than envelopes obtained using the well known complex trace concept based on Hilbert transform. The NTG method defines a seismic trace by finite Fourier sine series. It then converts the seismic trace into an analytical trace in a manner similar to complex seismic trace analysis. As this trace is made of partial derivatives of a new function defined from the trace itself it is indeed a gradient vector and its envelope is therefore called "total gradient". The division of the total gradient by its average over time forms the "normalized total gradient" (NTG). In this study we investigate in general the use and effectiveness of the NTG method to calculate envelope of seismic data. Thereby, we particularly consider the importance of the choice of parameters to obtain stable results. It then compares the results of the NTG method with those obtained from the Hilbert transform method for synthetic as well as field data. Although these two methods are closely related, it is shown that only for an adequate choice of parameters do the envelopes obtained by using the NTG method are better resolved and smoother than those are obtained using the Hilbert transform. The NTG method can therefore be used as a quantitative tool in separating individual reflections from those which are made of interfering composite reflections since it clearly reveals local maximum points of the reflections.

In interpretation of seismic data the resolution and smoothness of the envelope of the seismic trace is an important property to have. This paper introduces a new method of envelope generation for seismic traces that is based on the concept of normalized total gradient (NTG) that found many useful applications in interpretation of potential field data and is considered in that field of study to be better resolved and smoother than envelopes obtained using the well known complex trace concept based on Hilbert transform. The NTG method defines a seismic trace by finite Fourier sine series. It then converts the seismic trace into an analytical trace in a manner similar to complex seismic trace analysis. As this trace is made of partial derivatives of a new function defined from the trace itself it is indeed a gradient vector and its envelope is therefore called "total gradient". The division of the total gradient by its average over time forms the "normalized total gradient" (NTG). In this study we investigate in general the use and effectiveness of the NTG method to calculate envelope of seismic data. Thereby, we particularly consider the importance of the choice of parameters to obtain stable results. It then compares the results of the NTG method with those obtained from the Hilbert transform method for synthetic as well as field data. Although these two methods are closely related, it is shown that only for an adequate choice of parameters do the envelopes obtained by using the NTG method are better resolved and smoother than those are obtained using the Hilbert transform. The NTG method can therefore be used as a quantitative tool in separating individual reflections from those which are made of interfering composite reflections since it clearly reveals local maximum points of the reflections.

This paper presents a new subdivision scheme that operates over an infinite triangulation, which is regular except for a single extraordinary vertex. The scheme is based on the quartic three-directional Box-spline scheme, and is guaranteed to generate C2 limit functions whenever the valency n of the extraordinary vertex is in the range 4⩽n⩽20. The new scheme differs from the commonly

The characterization of optimization problems over continuous parameter spaces plays an important role in optimization. A form of "fitness landscape" analysis is often carried out to describe the problem space in terms of modality, smoothness and variable separability. The outcomes of this analysis can then be used as a measure of problem difficulty and to predict the behaviour of a given algorithm. However, the metric value estimates of the landscape characterization are dependent upon the representation scheme adopted and the sampling method used. Consequently, the development of a complete classification of problem structure and complexity has proven to be challenging. In this paper, we continue this line of research. We present a methodology for the characterization of two dimensional numerical optimization problems. In our approach, data extracted during the search process is analyzed and the dependency of the results to the nominated sampling method are corrected. We show via computational simulations that the calculated metric values using our approach are consistent with the results from random experiments. As such, this study provides a first step towards the on-line calculation of fitness landscape characterization metrics and the development of empirical performance models of search algorithms. Advances in these areas would provide answers to the algorithm selection and portfolio configuration problems.

Applying 2D algorithms for inverting the potential field data is more useful and efficient than their 3D counterparts, whenever the geologic situation permits. This is because the computation time is less and modeling the subsurface is easier. In this paper we present a 2D inversion algorithm for interpreting gravity data by employing a set of constraints including minimum distance, smoothness, and compactness. Using different combination of these constraints provide either smooth images of the underground geological structures or models with sharp geological boundaries. We model the study area by a large number of infinitely long horizontal prisms with square cross-sections and unknown densities. The final density distribution is obtained by minimizing an objective function that is composed of the model objective function and equality constraints, which are combined using a Lagrangian multipliers. Each block's weight depends on depth, a priori information on density and the allowed density ranges for the specified area. A MATLAB code has been developed and tested on a synthetic model consists of vertical and dipping dikes. The algorithm is applied with different combinations of constraints and the practical aspects are discussed. Results indicate that when a combination of constraints is used, the geometry and density distribution of both structures can be reconstructed. The method is applied on Zereshlu Mining Camp in Zanjan-Iran, which is well known for the Manganese ores. Result represents a high density distribution with the horizontal extension of about 30 m, and the vertical extension shows a trend in the E-W direction with a depth interval between 7 to 22 m in the east and 15 to 35 m in the west.

The aim of the paper is to establish (local) optimal embeddings of Besov spaces B^0,b_p,r involving only a slowly varying smoothness b. In general, our target spaces are outside of the scale of Lorentz-Karamata spaces and are related to small Lebesgue spaces. In particular, we improve results from [CGO11b], where the targets are (local) Lorentz-Karamata spaces. To derive such results, we apply limiting real interpolation techniques and weighted Hardy-type inequalities.

The strategic plan for establishing a vehicle weight monitoring net across Texas calls for deploying two technology types-piezoelectric and bending plate systems, and seeks to install weigh-in-motion (WIM) systems in roadways that are under new construction or reconstruction. Because the goal is to provide accurate truck weight data for pavement design, the strategic plan prefers deploying WIM installations on 500-ft continuously reinforced concrete pavements. While these pavements have, from experience, provided suitable stable foundations for WIM sensors, building a continuously reinforced concrete pavement is expensive. This project aimed to find less costly but equally viable alternatives for deploying WIM installations by developing guidelines for finding sections within existing asphalt concrete pavements that provide the level of smoothness, pavement support, and projected service life deemed suitable for weigh-inmotion sites, particularly for installations that use piezoelectric technology. Additionally, the project sought to evaluate the use of solar cells to power WIM systems, and wireless alternatives for data communication. These alternatives become particularly relevant in areas where bringing electrical and telephone wires to the site would add significantly to the cost of the WIM installation.

This paper presents a new subdivision scheme that operates over an infinite triangulation, which is regular except for a single extraordinary vertex. The scheme is based on the quartic three-directional Box-spline scheme, and is guaranteed to generate C 2 limit functions whenever the valency n of the extraordinary vertex is in the range 4 ≤ n ≤ 20. The new scheme differs from the commonly used subdivision schemes by the fact that it applies special subdivision rules near edges of the original triangulation, which emanate from the extraordinary vertex, and not only in the vicinity of the extraordinary vertex.

CONTENTS 1. Introduction 2. Rigorous Results about Conjugacies between Circle Maps 3. Some General Heuristic Remarks on Renormalization and Conjugacies 4. Computing the Conjugacies 5. Methods for Studying the Regularity 6. Numerical Implementation 7. Results 8. Some Bounds on the Regularity of Conjugacies 9. Conclusion 2000

The strategic plan for establishing a vehicle weight monitoring net across Texas calls for deploying two technology types – piezoelectric and bending plate systems, and seeks to install weigh-in-motion (WIM) systems in roadways that are under new construction or re-construction. Because the goal is to provide accurate truck weight data for pavement design, the strategic plan prefers deploying WIM installations on 500-ft continuously reinforced concrete pavements. While these pavements have, from experience, provided suitable stable foundations for WIM sensors, building a continuously reinforced concrete pavement is expensive. This project aimed to find less costly but equally viable alternatives for deploying WIM installations by developing guidelines for finding sections within existing asphalt concrete pavements that provide the level of smoothness, pavement support, and projected service life deemed suitable for weigh-in-motion sites, particularly for installations that use piezo...

We consider social choice rules which select a lottery over outcomes for each profile of individual preferences. Agents are assumed to have preferences over lotteries satisfying the axioms of expected utility. We exhibit a large class of rules satisfying strategy-proofness. All these ...

In this paper we present results on asymptotic characteristics of multivariate function classes in the uniform norm. Our main interest is the approximation of functions with mixed smoothness parameter not larger than 1/2. Our focus will be on the behavior of the best m-term trigonometric approximation as well as the decay of Kolmogorov and entropy numbers in the uniform norm. It turns out that these quantities share a few fundamental abstract properties like their behavior under real interpolation, such that they can be treated simultaneously. We start with proving estimates on finite rank convolution operators with range in a step hyperbolic cross. These results imply bounds for the corresponding function space embeddings by a well-known decomposition technique. The decay of Kolmogorov numbers have direct implications for the problem of sampling recovery in L 2 in situations where recent results in the literature are not applicable since the corresponding approximation numbers are not square summable.

In this paper we propose new method for proving of global solutions for 3D Navier-Stokes equations. This complies an application to the Clay Institute Millennium Prize Navier Stokes Problem. The proposed method can be applied for investigation of global solutions for other classes of PDEs.

A general variational framework for image approximation and segmentation is introduced. By using a continuous "line-process" to represent edge boundaries, it is possible to formulate a variational theory of image segmentation and approximation in which the boundary function has a simple explicit form in terms of the approximation function. At the same time, this variational framework is general enough to include the most commonly used objective functions. Application is made to Mumford-Shah type functionals as well as those considered by Geman and others. Employing arbitrary L L L p p p norms to measure smoothness and approximation allows the user to alternate between a least squares approach and one based on total variation, depending on the needs of a particular image. Since the optimal boundary function that minimizes the associated objective functional for a given approximation function can be found explicitly, the objective functional can be expressed in a reduced form that depends only on the approximating function. From this a partial differential equation (PDE) descent method, aimed at minimizing the objective functional, is derived. The method is fast and produces excellent results as illustrated by a number of real and synthetic image problems.

In this paper we study the existence, stability and the smoothness of a bounded solution of the following nonlinear time-varying thermoelastic plate Equation with homogeneous Dirichlet boundary conditions    u tt + Δ 2 u + αΔθ = f 1 (t, u, θ) t ≥ 0, x ∈ Ω, θ t − βΔθ − αΔu t = f 2 (t, u, θ), t ≥ 0, x ∈ Ω, θ = u = Δu = 0, t ≥ 0, x ∈ ∂Ω, where α = 0, β > 0, Ω is a sufficiently regular bounded domain in R N (N ≥ 1) and f e 1 , f e 2 : R × L 2 (Ω) 2 → L 2 (Ω) define by f e (t, u, θ)(x) = f (t, u(x), θ(x)), x ∈ Ω are continuous and locally Lipschitz functions. First, we prove that the linear system (f 1 = f 2 = 0) generates an analyitic strongly continuous semigroups which decays exponentially to zero. Second, under some additional condition we prove that the non-linear system has a bounded solution which is exponentially stable, and for a large class of functions f 1 , f 2 this bounded solution is almost periodic. Finally, we use the analyticity of the semigroup generated by the linear system to prove the smoothness of the bounded solution.

When dominant information is available about a process, its corresponding spectral density will exhibit a variable order of smoothness. In such situations, calculating a nonparametric spectral estimate with a fixed smoothing parameter will lead to biased spectral estimates. We propose a simple method that allows the bandwidth of the spectral window in the smoothed periodogram running average procedure to vary

This paper outlines a method for solving the stereovision matching problem using edge segments as the primitives. In stereovision matching the following constraints are commonly used: epipolar, similarity, smoothness, ordering and uniqueness. We propose a new matching strategy under a fuzzy context in which such constraints are mapped. The fuzzy context integrates both Fuzzy Clustering and Fuzzy Cognitive Maps. With such purpose a network of concepts (nodes) is designed, each concept represents a pair of primitives to be matched. Each concept has associated a fuzzy value which determines the degree of the correspondence. The goal is to achieve high performance in terms of correct matches. The main findings of this paper are reflected in the use of the fuzzy context that allows building the network of concepts where the matching constraints are mapped. Initially, each concept value is loaded via the Fuzzy Clustering and then updated by the Fuzzy Cognitive Maps framework. This updating is achieved through the influence of the remainder neighboring concepts until a good global matching solution is achieved. Under this fuzzy approach we gain quantitative and qualitative matching correspondences. This method works as a relaxation matching approach and its performance is illustrated by comparative analysis against some existing global matching methods.