Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

The MATLAB™ toolbox MTEX provides a unique way to represent, analyse and interpret crystallographic preferred orientation, i.e. texture, based on integral (“pole figure”) or individual orientation (“EBSD”) measurements. In particular, MTEX comprises functions to import, analyse and visualize diffraction pole figure data as well as EBSD data, to estimate an orientation density function from either kind of data, to compute texture characteristics, to model orientation density functions in terms of model functions or Fourier coefficients, to simulate pole figure or EBSD data, to create publication ready plots, to write scripts for multiple use, and others. Thus MTEX is a versatile free and open-source software toolbox for texture analysis and modeling.

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Texture Analysis with MTEX - Free and Open Source Software Toolbox

Three-dimensional Problems of the Theory of Elasticity. By A. I. Lur’e.1964. (Interscience Publishers)

We give a methodology-oriented perspective on directional image analysis and rotation-invariant processing. We review the state of the art in the field and make connections with recent mathematical developments in functional analysis and wavelet theory. We unify our perspective within a common framework using operators. The intent is to provide image-processing methods that can be deployed in algorithms that analyze biomedical images with improved rotation invariance and high directional sensitivity. We start our survey with classical methods such as directional-gradient and the structure tensor. Then, we discuss how these methods can be improved with respect to robustness, invariance to geometric transformations (with a particular interest in scaling), and computation cost. To address robustness against noise, we move forward to higher degrees of directional selectivity and discuss Hessian-based detection schemes. To present multiscale approaches, we explain the differences between Fourier filters, directional wavelets, curvelets, and shearlets. To reduce the computational cost, we address the problem of matching directional patterns by proposing steerable filters, where one might perform arbitrary rotations and optimizations without discretizing the orientation. We define the property of steerability and give an introduction to the design of steerable filters. We cover the spectrum from simple steerable filters through pyramid schemes up to steerable wavelets. We also present illustrations on the design of steerable wavelets and their application to pattern recognition.

/pdf/transforms-and-operators-for-directional-bioimage-analysis-a-cz4ketezr8.pdf

Transforms and Operators for Directional Bioimage Analysis: A Survey

GROUPS AND GEOMETRIC ANALYSIS Integral Geometry, Invariant Differential Operators, and Spherical Functions (Pure and Applied Mathematics: A Series of Monographs and Textbooks)

We consider a left-linear analogue to the classical Riemann problem: Dau =0 inR n n u + = H(x)u +h(x )o n ju(x)j = O(jxj n 2 1 )a sjxj!1: For this purpose, we state a Borel-Pompeiu formula for the disturbed Dirac operatorDa = D +a with a paravectora and some functiontheoretical results. We reformulate the Riemann problem as an integral equation: Pau +HQau = h on ; where Pa = 1 (I +Sa )a ndQa = I Pa: We demonstrate that the essential part of the singular integral operator Sa which is constructed by the aid of a fundamental solution of D +a is just the singular integral operator S associated toD: In case Sa is simplyS and = R n 1 , then under the assumptions 1.H= P He and allH are real-valued, measurable and essentially bounded; 2. (1 +H(x))(1 +H(x)) and H(x) H(x) are real numbers for all x2R n 1 ; 3. the scalar part H0 of H fulls H0(x) >"> 0 for all x2R n 1 ; the Riemann problem is uniquely solvable in L2;C(R n 1 ) and the successive approximation

/pdf/on-the-left-linear-riemann-problem-in-clifford-analysis-4ptz74dwjg.pdf

On the left linear Riemann problem in Clifford analysis

This article is intended as a mathematical overview of the generalizations of analytic signals to higher-dimensional problems, as well as of their applications to and of their comparison on artificial and real-world image samples.

Generalized Analytic Signals in Image Processing: Comparison, Theory and Applications

We develop basic properties of solutions to the Dirac-Hodge and Laplace equations in upper half space endowed with the hyperbolic metric. Solutions to the Dirac-Hodge equation are called hypermonogenic functions, while solutions to this version of Laplace's equation are called hyperbolic harmonic functions. We introduce a Borel-Pompeiu formula forC
 1 functions and a Green's formula for hyperbolic harmonic functions. Using a Cauchy integral formula, we introduce Hardy spaces of solutions to the Dirac-Hodge equation. We also provide new arguments describing the conformal covariance of hypermonogenic functions and invariance of hyperbolic harmonic functions and introduce intertwining operators for the Dirac-Hodge operator and hyperbolic Laplacian.

Function theory for Laplace and Dirac-Hodge Operators in hyperbolic space

Continuous wavelet transformation: A novel approach for better detection of mud pulses

We introduce Szeg&#337; projections for Hardy spaces of monogenic functions defined on a bounded domain &#937; in &#8477;n. We use such projections to obtain explicit orthogonal decompositions for L2(b&#937;). As an application, we obtain an explicit representation of the solution of the Dirichlet problem for balls and half spaces with L2, Clifford algebra-valued, boundary datum.

/pdf/szego-projections-for-hardy-spaces-of-monogenic-functions-5apoz3g0yn.pdf

Swanhild Bernstein

Papers

On the left linear Riemann problem in Clifford analysis

Generalized Analytic Signals in Image Processing: Comparison, Theory and Applications

Function theory for Laplace and Dirac-Hodge Operators in hyperbolic space

Continuous wavelet transformation: A novel approach for better detection of mud pulses

Szegő projections for hardy spaces of monogenic functions and applications