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We use the concept of spinor operator to study some aspects of the classical theory of surfaces in three dimensions. We show that a spinor operator representing a surface satisfies a pair of Dirac-like equations and that this spinor operator representation is a generalization of the Weierstrass representation of minimal surfaces. We also obtain spinor operator representations of a surface directly from its parameterization in terms of isothermal parameters, without the need of solving the pair of Dirac-like equations. We apply these results to minimal surfaces and their deformations and also show how they can be written in terms of quaternions and complex numbers. [ABSTRACT FROM AUTHOR]

We formulate and prove an analog of the classical Morse–Darboux lemma for the case of a surface with boundary. [ABSTRACT FROM AUTHOR]

We calculate q -dimension of k th Cartan power of fundamental representation Λ 0 , corresponding to affine root of affine simply laced Kac–Moody algebras, and show that in the limit q → 1 , and with natural renormalization, it is equal to universal partition function of Chern–Simons theory on three-dimensional sphere. [ABSTRACT FROM AUTHOR]

A good representation model of tolerance information is indispensable for achieving computer-aided tolerancing. Currently, the representation model used in industry is the EXPRESS model, while at the same time, a number of other kinds of representation models have been presented within the academia. The coexistence of different kinds of representation models generates a series of questions and discussions: can the EXPRESS model completely implement the representation of tolerance information semantics in an explicit, computer-readable, and computer-interpretable way? What challenges have been addressed to date by the presented representation models? What are the advantages and disadvantages of each representation model?What capabilities should an ideal representation model have? What are the potential research directions in tolerance information representation in the future? To approach these questions, a review of representation models of tolerance information is presented in this paper. An in-depth analysis of existing representation models is firstly provided. Then, the review makes a detailed comparison among them based on this analysis. Finally, some future research directions in tolerance information representation are suggested. [ABSTRACT FROM AUTHOR]

The article explores meaning of the term space, which refers to the main premise of the formation of the so-called spatial arts, which consists in affirming the possibility of the existence of forms that are built in three dimensions and in time, as described by the Russian State Academy of Artistic Sciences. It explores distinguish between space and formal means of expression in the spatial arts. It reports that surface serves as a boundary of space, which can be read either in front of the surface or behind it, or surface cuts into space, which is especially typical for intersecting planes.

The article explores meaning of the term representational arts, which speak about representation of any real object given form by a human being so that it serves as a sign of another real or imaginary object, as described by the Russian State Academy of Artistic Sciences. It mentions that the representing object, unlike a conventional sign, depicts using forms that are characteristic of its material and structure, a real or imagined visual appearance of the represented object. It reports the problem of representation coincides with the general problems of the construction of an aesthetic and artistic object.

The article explores meaning of the term representation, which in the broadest sense of the term means any real object given form by a human being so that it serves as a sign of another real or imaginary object, as described by the Russian State Academy of Artistic Sciences. It mentions that the representing object, unlike a conventional sign, depicts using forms that are characteristic of its material and structure, a real or imagined visual appearance of the represented object. It reports the problem of representation coincides with the general problems of the construction of an aesthetic and artistic object.

Let $S\subseteq \mathbb{P}^{d}$ be an anticanonically embedded surface of degree $d\geq 3$. In this note, we classify stable Ulrich bundles on $S$ of rank two. We also study their moduli spaces. [ABSTRACT FROM PUBLISHER]

This paper presents a Surface Geodesic Pattern (SGP) representation for matching textured 3D deformable surfaces. SGP encodes the local variations of the surface texture derivatives to extract local information from distinctive textural relationships contained in a geodesic neighborhood. Thus, SGP derives its strength from the fusion of surface texture and shape information at the data level in a way that is invariant to non-rigid deformations. We also propose Gabor Topography Wavelet (GTW) for direct feature extraction from the range data. Both features are combined using a multi-view sparse representation to achieve higher discrimination capability while matching non-rigid 3D surfaces. The performance of the proposed method is evaluated extensively on the Bosphorus face database, the FRGC v2 face database, and the PolyU contact-free hand database and the results are compared to state-of-the-art methods. Experimental results show the effectiveness and superiority of the proposed method in recognizing objects under non-rigid surface deformations. [ABSTRACT FROM AUTHOR]

A calligram is an arrangement of words or letters that creates a visual image, and a compact calligram fits one word into a 2D shape. We introduce a fully automatic method for the generation of legible compact calligrams which provides a balance between conveying the input shape, legibility, and aesthetics. Our method has three key elements: a path generation step which computes a global layout path suitable for embedding the input word; an alignment step to place the letters so as to achieve feature alignment between letter and shape protrusions while maintaining word legibility; and a final deformation step which deforms the letters to fit the shape while balancing fit against letter legibility. As letter legibility is critical to the quality of compact calligrams, we conduct a large-scale crowd-sourced study on the impact of different letter deformations on legibility and use the results to train a letter legibility measure which guides the letter deformation. We show automatically generated calligrams on an extensive set of word-image combinations. The legibility and overall quality of the calligrams are evaluated and compared, via user studies, to those produced by human creators, including a professional artist, and existing works. [ABSTRACT FROM AUTHOR]

We give an inequality on the inertia of Hermitian matrices with some symmetry and discuss algebraic conditions for equality. The basic results also have various applications in the theories of graph decompositions, graph embeddings, and block designs. [ABSTRACT FROM AUTHOR]

We transform suitable smooth functions into hard bounds for the solution to boundary value and obstacle problems for elliptic partial differential equations based on the probabilistic Feynman-Kac representation. Unlike standard approximate solutions, hard solution bounds are intended to limit the location of the solution, possibly to a large extent, and, thus, have the potential to be very useful information. Our approach requires two main steps. First, the violation of sufficient conditions is quantified for the test function to be a hard bounding function. After extracting those violation terms from the Feynman-Kac representation, it remains to deal with a boundary value problem with constant input data. Although the probabilistic Feynman-Kac representation is employed, the resulting numerical method is deterministic without the need for sophisticated probabilistic numerical methods, such as sample paths generation of reflected diffusion processes. Throughout this article, we provide numerical examples to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Rubber ( Hevea brasiliensis ) plantations are one of the most important economic forest in tropical area. Retrieving leaf area index (LAI) and its dynamics by remote sensing is of great significance in ecological study and production management, such as yield prediction and post-hurricane damage evaluation. Thirteen HJ-1A/1B CCD images, which possess the spatial advantage of Landsat TM/ETM+ and 2-days temporal resolution of MODIS, were introduced to predict the spatial–temporal LAI of rubber plantation on Hainan Island by Nonlinear AutoRegressive networks with eXogenous inputs (NARX) model. Monthly measured LAIs at 30 stands by LAI-2000 between 2012 and 2013 were used to explore the LAI dynamics and their relationship with spectral bands and seven vegetation indices, and to develop and validate model. The NARX model, which was built base on input variables of day of year (DOY), four spectral bands and weight difference vegetation index (WDVI), possessed good accuracies during the model building for the data set of training ( N = 202, R 2 = 0.98, RMSE = 0.13), validation ( N = 43, R 2 = 0.93, RMSE = 0.24) and testing ( N = 43, R 2 = 0.87, RMSE = 0.31), respectively. The model performed well during field validation ( N = 24, R 2 = 0.88, RMSE = 0.24) and most of its mapping results showed better agreement ( R 2 = 0.54–0.58, RMSE = 0.47–0.71) with the field data than the results of corresponding stepwise regression models ( R 2 = 0.43–0.51, RMSE = 0.52–0.82). Besides, the LAI statistical values from the spatio-temporal LAI maps and their dynamics, which increased dramatically from late March (2.36 ± 0.59) to early May (3.22 ± 0.64) and then gradually slow down until reached the maximum value in early October (4.21 ± 0.87), were quite consistent with the statistical results of the field data. The study demonstrates the feasibility and reliability of retrieving spatio-temporal LAI of rubber plantations by an artificial neural network (ANN) approach, and provides some insight on the application of HJ-1A/1B CCD images, and data and methods for productivity study of rubber plantation in future. [ABSTRACT FROM AUTHOR]

As the number of space-borne SAR sensors increases, a rising number of different SAR acquisition modes is in use, resulting in a higher variation within the image products. This variability in acquisition geometry, radiometry, and last but not least polarimetry raises the need for a consistent SAR image description incorporating all available sensors and acquisition modes. This paper therefore introduces the framework of the Kennaugh elements to comparably represent all kinds of multi-scale, multi-temporal, multi-polarized, multi-frequency, and hence, multi-sensor data in a consistent mathematical framework. Furthermore, a novel noise model is introduced that estimates the significance and thus the (polarimetric) information content of the Kennaugh elements. This facilitates an advanced filtering approach, called multi-scale multi-looking, which is shown to improve the radiometric accuracy while preserving the geometric resolution of SAR images. The proposed methodology is finally demonstrated using sample applications that include TerraSAR-X (X-band), Envisat-ASAR, RADARSAT-2 (C-band) and ALOS-PALSAR (L-band) data as well as the combination of all three frequencies. Thus the suitability of the Kennaugh element framework for practical use in proved for advanced SAR remote sensing. [ABSTRACT FROM AUTHOR]

The accurate representation of terrestrial CO 2 uptake (GPP) using Monteith’s approach requires a frequent and site-specific parameterization of the model inputs. In this work, an optimization of this approach has been carried out by adjusting the inputs ( f APAR , PAR and ε ) for the study area, peninsular Spain, a typical Mediterranean region. The daily GPP images have been calculated for 2008 and 2011 with a 1-km spatial resolution and validated by comparison with in situ GPP estimates from the eddy covariance data (direct validation) and by inter-comparison with the MODIS GPP product. The direct validation has evidenced an excellent agreement with correlations up to 0.98 in 2008 and 0.92 in 2011 in some sites. The inter-comparison has shown that the two GPP products are consistent temporally. However, a slightly decrease of the correlation has been observed in some areas. The validation has also shown that our optimized GPP product accounts better for the water stress than the MODIS product. The analysis of the explanatory power of the model in terms of its inputs shows, as expected, that PAR and f APAR are the most relevant inputs. The f APAR plays a major role on GPP estimation when the vegetation phenology maximum is not reached during solar solstice. Finally, it has been shown that the influence of the water stress, associated with the water shortage typical of Mediterranean landscapes, has to be evaluated accurately in order to explain the GPP inter-annual variability. [ABSTRACT FROM AUTHOR]

A width and color based geometric active deformable model is proposed for road network extraction from remote sensing images with minimal human interception. Orientation and width of road are computed from a single manual seed point, from which the propagation starts both right and left hand directions of the starting point, which extracts the interconnected road network from the aerial or high spatial resolution satellite image automatically. Here the propagation (like water flow in canal with defined boundary) is restricted with color and width of the road. Road extraction is done for linear, curvilinear (U shape and S shape) roads first, irrespective of width and color. Then, this algorithm is improved to extract road with junctions in a shape of L, T and X along with center line. Roads with small break or disconnected roads are also extracts by a modified version of this same algorithm. This methodology is tested and evaluated with various remote sensing images. The experimental results show that the proposed method is efficient and extracting roads accurately with less computation time. However, in complex urban areas, the identification accuracy declines due to the various sizes of obstacles, over bridges, multilane etc. [ABSTRACT FROM AUTHOR]

A new greedy-based multiquadric method (MQ-G) has been developed to perform LiDAR-derived ground data reduction by selecting a certain amount of significant terrain points from the raw dataset to keep the accuracy of the constructed DEMs as high as possible, while maximally retaining terrain features. In the process of MQ-G, the significant terrain points were selected with an iterative process. First, the points with the maximum and minimum elevations were selected as the initial significant points. Next, a smoothing MQ was employed to perform an interpolation with the selected critical points. Then, the importance of all candidate points was assessed by interpolation error (i.e. the absolute difference between the interpolated and actual elevations). Lastly, the most significant point in the current iteration was selected and used for point selection in the next iteration. The process was repeated until the number of selected points reached a pre-set level or no point was found to have the interpolation error exceeding a user-specified accuracy tolerance. In order to avoid the huge computing cost, a new technique was presented to quickly solve the systems of MQ equations in the global interpolation process, and then the global MQ was replaced with the local one when a certain amount of critical points were selected. Four study sites with different morphologies (i.e. flat, undulating, hilly and mountainous terrains) were respectively employed to comparatively analyze the performances of MQ-G and the classical data selection methods including maximum z-tolerance (Max-Z) and the random method for reducing LiDAR-derived ground datasets. Results show that irrespective of the number of selected critical points and terrain characteristics, MQ-G is always more accurate than the other methods for DEM construction. Moreover, MQ-G has a better ability of preserving terrain feature lines, especially for the undulating and hilly terrains. [ABSTRACT FROM AUTHOR]

Line segment detection in images is already a well-investigated topic, although it has received considerably less attention in 3D point clouds. Benefiting from current LiDAR devices, large-scale point clouds are becoming increasingly common. Most human-made objects have flat surfaces. Line segments that occur where pairs of planes intersect give important information regarding the geometric content of point clouds, which is especially useful for automatic building reconstruction and segmentation. This paper proposes a novel method that is capable of accurately extracting plane intersection line segments from large-scale raw scan points. The 3D line-support region, namely, a point set near a straight linear structure, is extracted simultaneously. The 3D line-support region is fitted by our Line-Segment-Half-Planes (LSHP) structure, which provides a geometric constraint for a line segment, making the line segment more reliable and accurate. We demonstrate our method on the point clouds of large-scale, complex, real-world scenes acquired by LiDAR devices. We also demonstrate the application of 3D line-support regions and their LSHP structures on urban scene abstraction. [ABSTRACT FROM AUTHOR]

In cartography the coordination of different map themes is directly linked to map generalization (Imhof, 1972). That means a good generalization result can only be achieved by a reasonable coordination of participated map themes and their associated generalization operations and algorithms. In the field of automated map generalization there exist only a few research papers (e.g. Gaffuri, 2006 and Monnot et al, 2007a) where a simultaneous generalization and coordination has been implemented. The objective of this paper is to investigate a generic set of cartographic relations which could exist between different map themes and to prove how they can be used for cartographic coordination. One approach to define and recognize cartographic relations during generalization is data enrichment (Neun, 2007). Following this approach an auxiliary data structure was used to implement a simultaneous generalization of "rivers" and "borders". This simple test case shows how cartographic relations can support the coordination of different map themes. [ABSTRACT FROM AUTHOR]

Increased attention to global climate change in recent years has resulted in a wide array of maps and geovisualizations that forecast various scenarios. Since many consequences of climate change are inherently geographic in nature, effective cartographic representations that depict these risks are valuable for planning and mitigation purposes. In particular, sea-level rise resulting from climate change calls attention to the numerous representation issues that warrant consideration for hazard and risk mapping in general, including categorizing and representing risk, selecting an appropriate level of realism, and displaying potential impacts of a hazard on human populations as well as on the natural and built environments. Using examples of potential inundation from sea-level rise at global, regional, and local scales, the authors propose a conceptual framework of key cartographic considerations for maps, Web-based mashups, and geovisualizations that depict risk. The cartographic framework presented here may be extended to other risks of an ambiguous or fuzzy nature and may be used to organize key future research areas for hazard or risk mapping in general. [ABSTRACT FROM AUTHOR]

It is explained why the generalizeddiscrete variable representationis variational neither with respect to the size (truncation) of thebasis set nor with respect to the selection of grid points. [ABSTRACT FROM AUTHOR]

Abstract: The correspondence between different versions of the Gauss–Weingarten equation is investigated. The compatibility condition for one version of the Gauss–Weingarten equation gives the Gauss–Mainardi–Codazzi system. A deformation of the surface is postulated which takes the same form as the original system but contains an evolution parameter. The compatibility condition of this new augmented system gives the deformed Gauss–Mainardi–Codazzi system. A Lax representation in terms of a spectral parameter associated with the deformed system is established. Several important examples of integrable equations based on the deformed system are then obtained. It is shown that the Gauss–Mainardi–Codazzi system can be obtained as a type of reduction of the self-dual Yang–Mills equations. [Copyright &y& Elsevier]

Piezoelectric materials with a doubly periodic array of cracks and rigid-line inclusions under far-field antiplane mechanical load and inplane electric load are investigated. By employing the conformal mapping technique and the elliptical function theory, an exact solution of the whole-field stress and electrical displacement is obtained. The closed-form formulae for the stress and electrical displacement intensity factors at the tips of cracks and rigid-line inclusions and the effective electroelastic moduli of the composites are presented. Some existing solutions can be regarded as degenerated cases of the present results. Numerical examples are provided to show the interesting electroelastic interaction between multiple cracks and multiple rigid-line inclusions. [ABSTRACT FROM AUTHOR]

The article discusses the Helmholtz problem equation in the exterior of nonclosed surfaces with impedance boundary. It states that the boundary value problems for the three-dimensional Helmholtz equation were studied in the exterior of closed Lipschitz surfaces and in the exterior of smooth nonclosed screens. It tells that a normal vector exists everywhere on the Lipschitz surfaces. It says that a Lipschitz surfaces with a Lipschitz boundary that contains its limiting points, is the union of a finite number of such surfaces without common points, specifically without common boundary ones.

The non-invasive inspection of surfaces is a major issue in a wide variety of industries and research laboratories. The vast and increasing range of surface types, tolerance requirements and measurement constraints demanded during the last decades represents a major research effort in the development of new methods, systems and metrological strategies. The discreet dimensional evaluation the rugometric characterization and the profilometric inspection seem to be insufficient in many instances. The full microtopographic inspection has became a common requirement. Among the different systems developed, optical methods have the most important role and among those triangulation-based ones have gained a major status thanks to their flexibility, reliability and robustness. In this communication we will provide a brief historical review on the development of optical triangulation application to the dimensional inspection of objects and surfaces and on the work done at the Microtopography Laboratory of the Physics Department of the University of Minho, Portugal, in the development of methods and systems of optical triangulation-based microtopographic inspection of surfaces. [ABSTRACT FROM AUTHOR]

This is a reprinting of a paper by Roger Penrose, first published in a volume of conference proceedings in 1964, no longer easily accessible, in which he first presented the now-standard description of asymptotically flat spacetimes with the help of a conformal mapping, now called a Penrose transform. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Helmut Friedrich. [ABSTRACT FROM AUTHOR]

An essay is presented on the study of Byzantine cartography and geography which intends to think across some spatial constructs that are present in Byzantine narrative sources. It offers the Byzantine optic on geographical space at all scales and highlights the qualities of the geographic positionality of the Byzantine materiality and subject. The author relates his theory on Byzantine map-making and Byzantine spatiality in the works of Constantine Porphyrogenitus.

The possibility for diagnostics of a breathing crack type damage in a long cylindrical shell is examined. The damage is modeled by a notch that alters the cross-sectional geometry. The method of conformal mappings is used to solve the first main boundary-value problem of elasticity for domains in the form of an annular sector with and without a notch. The solutions are analyzed and compared to estimate the relative decrease in the stiffness of the shell because of the opening of the crack [ABSTRACT FROM AUTHOR]

The design of new map projections has up until now required mathematical and cartographic expertise that has limited this activity to a small group of specialists. This article introduces the background mathematics for a software-based method that enables cartographers to easily design new small-scale world map projections. The software is usable even by those without mathematical expertise. A new projection is designed interactively in an iterative process that allows the designer to graphically and numerically assess the graticule, the representation of the continents, and the distortion properties of the new projection. The method has been implemented in Flex Projector, a free and open-source application enabling users to quickly create new map projections and modify existing projections. We also introduce new tools that help evaluate the distortion properties of projections, namely a configurable acceptance index to assess areal and angular distortion, a derived acceptance visualization, and interactive profiles through the distortion space of a projection. To illustrate the proposed method, a new projection, the Cropped Ginzburg VIII projection, is presented. [ABSTRACT FROM AUTHOR]

This paper is concerned with the re-representation of a G1 composite rational Bézier curve. Although the rational Bézier curve segments that form the composite curve are G1 continuous at their joint points, their homogeneous representations may not be even C0 continuous in the homogeneous space. In this paper, an algorithm is presented to convert the G1 composite rational Bézier curve into a NURBS curve whose nonrational homogeneous representation is C1 continuous in the homogeneous space. This re-representation process involves reparameterization using Möbius transformations, smoothing multiplication and parameter scaling transformations. While the previous methods may fail in some situations, the method proposed in this paper always works. [ABSTRACT FROM AUTHOR]

We describe some new methods for obtaining a mathematical representation of a surface that approximates a scattered point cloud, {( x i, y i, z i) i = 1, . . . , N} without the use or need of normal vector data. The fitting surface is defined implicitly as the level set of a field function which is a linear combination of trivariate radial basis functions. Optimal approximations are based upon normalized least squares criteria which lead to eigenvalue/eigenvector characterizations. The normalized aspect allows for the exclusion of the need of normal vector estimates which is one of the unique features of this new method. Localizing techniques are introduced to allow for the efficient application of these new methods to large data sets. The use of a variety of radial basis functions are introduced through various examples that illustrate the performance and efficiency of the new methods. [ABSTRACT FROM AUTHOR]

Lens-shaped surfaces (with vertices of valence 2) arise for example in automatic quad-remeshing. Applying standard Catmull–Clark subdivision rules to a vertex of valence 2, however, does not yield a C1 surface in the limit. When correcting this flaw by adjusting the vertex rule, we discover a variant whose characteristic ring is z → z2. Since this conformal ring is of degree bi-2 rather than bi-3, it allows constructing a subdivision algorithm that works directly on the control net and generates C2 limit surfaces of degree bi-4 for lens-shaped surfaces. To further improve shape, a number of re-meshing and re-construction options are discussed indicating that a careful approach pays off. Finally, we point out the analogy between characteristic configurations and the conformal maps z4/ n, cos z and e z. [ABSTRACT FROM AUTHOR]

An approximate conformal mapping for an arbitrary region Ω bounded by a smooth curve Γ is constructed using the Schwarz-Christoffel mapping for a polygonal region in which Ω is embedded. An algorithm for finding this so-called outer polygon is presented. The resulting function is a conformal mapping from the upper half-plane or the unit disk to a region R, approximately equal to Ω. R is bounded by a C∞ curve, and since the mapping function originates from the Schwarz-Christoffel mapping and tangent polygons are used to determine it, important properties of Γ such as direction, linear asymptotes, and inflexion points are preserved in the boundary of R. The method makes extensive use of existing Schwarz-Christoffel software in both the determination of outer polygons and the calculation of function values. By the use suggested here, the capabilities of such well-written software are extended. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present a new way to calculate channel length shortening in saturation for standard bulk MOSFETs by solving 2D Poisson’s equation. Compared to most existing models, we use in our model only physically meaningful and geometry-independent fitting parameters, which gives our model a good scalability. 2D Poisson is solved in analytical closed form by applying the conformal mapping technique. This gives the model the advantage additionally to its application in circuit simulations to be useful in calculating device scaling behavior. Our model describes the output conductance of MOSFETs down to 50nm effective channel length very well. [Copyright &y& Elsevier]

Abstract: In this paper, a revitalization of conformal mapping methods applied to fluid flows in two dimensions is proposed. The present work addresses several important issues concerning their application for vortex particle flow solvers. Difficulties of past conformal based method are reviewed. One difficulty concerns the ability of a mapping procedure to represent complicated shapes. The present paper improves past algorithms to be able to map new shapes, including multiply connected domains. A new fast procedure allows transferring a set of points in the mapped simplified plane to the complicated domain and vice versa. After a mapping construction, it is demonstrated how basic exact solutions to potential flow problems with vortices can be put in a new form which provides a faster and more accurate computation than with distributed singularity methods. [Copyright &y& Elsevier]

Abstract: We study the temperature distribution around a cylindrical lava tube with an elliptical cross section. The steady-state heat equation is solved by assuming an unbounded medium and a uniform temperature of the tube wall. An analytical solution for the temperature field is obtained by the conformal mapping technique. It is found that the isothermal lines on the planes perpendicular to the tube are confocal ellipses. The heat flow in the medium surrounding the tube has hyperbolic field lines, while the curves on which the magnitude of heat flow is constant are Cassini ovals. At the tube wall, the heat flow density is proportional to the cubic root of the curvature of the wall. A solution is also obtained for a tube embedded in a half-space, when the size of the tube is small with respect to its depth. Formulae are given relating the heat flow at the surface of the half-space to the eccentricity and to the orientation of the major axis of the tube cross section, as well as to the temperature and the depth of the tube. For eccentricity equal to zero, all the formulae are reduced to those for a circular tube. [Copyright &y& Elsevier]

Abstract: The computation of intersection and self-intersection loci of parametrized surfaces is an important task in Computer Aided Geometric Design. We address these problems via four resultants with separated variables; two of them are specializations of general multivariate resultants and the two others are specializations of determinantal resultants. We give a rigorous study in these four cases and provide new formulas in terms of Bezoutian matrix. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new method for the construction of parametric surfaces reproducing an object from a set of spatial data. We adopt a hybrid scheme, based on the Boolean sum of variable degree spline operators, which both interpolate a set of grid lines and approximate the data. As usual the variable degrees can be chosen to satisfy proper shape constraints. [Copyright &y& Elsevier]

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Several three-dimensional effects were observed in the performance monitoring data collected during excavation for the Ford Engineering Design Center in Evanston, Illinois. The elevations of the soil around the excavation varied and the excavator removed the soil in a nonuniform excavation process, both of which contributed to the observed three-dimensional (3D) effects. This paper describes the excavation support system and subsurface conditions at the site, summarizes the construction procedures, and presents the lateral soil movements measured by inclinometers, ground-surface movements measured by an automated total station, tilt of components of an adjacent structure, and forces in internal braces. These responses are compared with expected responses from current design methods. The 3D nature of the excavation resulted in smaller movements on the side of the excavation, where the retained soil was lowest, an unexpected pattern of axial strut loads and very slight damage to an exterior wall that paralleled one of the excavation walls. [ABSTRACT FROM AUTHOR]

We study the shape stability of disks moving in an external Laplacian field in two dimensions. The problem is motivated by the motion of ionization fronts in streamer-type electric breakdown. It is mathematically equivalent to the motion of a small bubble in a Hele-Shaw cell with a regularization of kinetic undercooling type, namely, a mixed Dirichlet-Neumann boundary condition for the Laplacian field on the moving boundary. Using conformal mapping techniques, linear stability analysis of the uniformly translating disk is recast into a single PDE which is exactly solvable for certain values of the regularization parameter. We concentrate on the physically most interesting exactly solvable and nontrivial case. We show that the circular solutions are linearly stable against smooth initial perturbations. In the transformation of the PDE to its normal hyperbolic form, a semigroup of automorphisms of the unit disk plays a central role. It mediates the convection of perturbations to the back of the circle where they decay. Exponential convergence to the unperturbed circle occurs along a unique slow manifold as time t → ∞. Smooth temporal eigenfunctions cannot be constructed, but excluding the far back part of the circle, a discrete set of eigenfunctions does span the function space of perturbations. We believe that the observed behavior of a convectively stabilized circle for a certain value of the regularization parameter is generic for other shapes and parameter values. Our analytical results are illustrated by figures of some typical solutions. [ABSTRACT FROM AUTHOR]

We present the results of two controlled studies comparing layered surface visualizations under various texture conditions. The task was to estimate surface normals, measured by accuracy of a hand-set surface normal probe. A single surface visualization was compared with the two-surfaces case under conditions of no texture and with projected grid textures. Variations in relative texture spacing on top and bottom surfaces were compared, as well as opacity of the top surface. Significant improvements are found for the textured cases over non-textured surfaces. Either larger or thinner top-surface textures, and lower top surface opacities are shown to give less bottom surface error. Top surface error appears to be highly resilient to changes in texture. Given the results we also present an example of how appropriate textures might be useful in volume visualization. [ABSTRACT FROM AUTHOR]

Abstract: Skeletons are important shape descriptors in object representation and recognition. Typically, skeletons of volumetric models are computed using iterative thinning. However, traditional thinning methods often generate skeletons with complex structures that are unsuitable for shape description, and appropriate pruning methods are lacking. In this paper, we present a new method for computing skeletons of volumetric models by alternating thinning and a novel skeleton pruning routine. Our method creates a family of skeletons parameterized by two user-specified numbers that determine respectively the size of curve and surface features on the skeleton. As demonstrated on both real-world models and protein images in bio-medical research, our method generates skeletons with simple and meaningful structures that are particularly suitable for describing cylindrical and plate-like shapes. [Copyright &y& Elsevier]

This paper is the first of the author’s three articles on stability in the Liouville theorem on the Heisenberg group. The aim is to prove that each mapping with bounded distortion of a John domain on the Heisenberg group is close to a conformal mapping with order of closeness $$\sqrt {K - 1} $$ in the uniform norm and order of closeness K − 1 in the Sobolev norm L for all $$p < \tfrac{C}{{K - 1}}$$ . In the present article we study integrability of mappings with bounded specific oscillation on spaces of homogeneous type. As an example, we consider mappings with bounded distortion on the Heisenberg group. We prove that a mapping with bounded distortion belongs to the Sobolev class W , where p → ∞ as the distortion coefficient tends to 1. [ABSTRACT FROM AUTHOR]

In this paper, we prove Brennan's conjecture for conformal mappings f of the disk { z : | z| < 1} assuming that the Taylor coefficients of the function log( zf′( z)/ f( z)) at zero are nonnegative. We also obtain inequalities for the integral means over the circle | z| = r of the squared modulus of the function zf′( z)/ f( z). [ABSTRACT FROM AUTHOR]

We present a new, completely original exact method to determine the permeance between two opposing iron teeth. This configuration is important because it is often encountered in electrical machines and apparatus. The method is based on conformal mapping. The given "tooth-to-tooth" configuration is mapped into a simpler one, in which the same permeance can be analytically determined. We derive an explicit formula for this permeance, and confirm our results using the finite-element method. [ABSTRACT FROM AUTHOR]

Beginning in 1956, in order to obtain type criteria by quasiconformal (and more general) mappings f : G → G′, where G and G′ are domains in the plane or on Riemann surfaces, we considered at the regular points of f a length-area dilatation d depending not only on the dilatation quotient but also on the orientation of the characteristic ellipses [Andreian Cazacu, C, 1960, Sur les relations entre les fonctions caracteristiques de la pseudo-analyticitée. In: Lucrările celui de al IV-lea Congres al Matematicienilor Români, Bucureşti 1956 (Bucureşti: Editura Academiei Republicii Populare Române), pp. 82-85; Andreian Cazacu, C, 1957, Sur les transformations pseudo-analytiques. Revue de Mathematiques Pures et Appliquées, 2, 383-397; Andreian Cazacu, C, 1964, Sur l'application de la longueur extrémale dans la théorie des representations quasi-conformes. Mathematica (Cluj), 6(29), 1, 5-10; Andreian Cazacu, C, 1965, Sur un problème de L.I. Volkovyski. Revue Roumaine de Mathématiques Pures et Appliquées, 10, I, 43-63; Andreian Cazacu, C, 1971, Influence of the orientation of the characteristic ellipses on the properties of the quasiconformal mappings. In: Proceedings of the Romanian-Finnish Seminar on Teichmüller Spaces and Quasiconformal Mappings. Braşov 1969 (Bucharest: Publishing House of the Academy of the Socialist Republic of Romania), pp. 65-85; Andreian Cazacu, C , 1974, A generalization of the quasiconformality. In: Topics in Analysis, Colloquium on Mathematical Analysis, Jyväskylä 1970, Lecture Notes in Mathematics, Vol. 419 (Berlin-Heidelberg-New York: Springer-Verlag), pp. 4-17]. Last time the length-area dilatation found (under diverse names and notations) significant applications [Marković, V. and Mateljević, M., 1997, New versions of Grötzsch principle and Reich-Strebel inequality. Matematichki Vesnik, 49, 235-239; Marković, V. and Mateljević, M., 1999, New versions of the main inequality and uniqueness of harmonic maps. Journal d'Analyse Mathéematique, 79, 315-334; Gutlyanskij, V. and Martio, O., 2003, Conformality of a quasiconformal mapping at a point. Journal d'Analyse Mathematique, 91, 179-192] and the aim of this work is to point out its role in these researches, to establish connexions between old and new results. To simplify, we deal with domains in the plane since the essential is already evident in this frame. [ABSTRACT FROM AUTHOR]

In our previous paper (2003), we discussed the connected components of the space of surface group representations for any compact connected semisimple Lie group and any closed compact (orientable or nonorientable) surface. In this sequel, we generalize our results in two directions: we consider general compact connected Lie groups, and we consider all compact surfaces, including the ones with boundaries. We also interpret our results in terms of moduli spaces of flat connections over compact surfaces. [ABSTRACT FROM AUTHOR]