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Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…
This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family $h$ of rigid motions. Our extension…
Harmonicity of holomorphic maps between various subclasses of almost contact metric manifolds is discussed. Consequently, some new results are obtained. Also some known results are recovered, some of them are generalized and some of them…
Bifurcations in dynamical systems are often studied experimentally and numerically using a slow parameter sweep. Focusing on the cases of period-doubling and pitchfork bifurcations in maps, we show that the adiabatic approximation always…
We give several versions of local and global inverse mapping theorem for tame non necessarily smooth, mappings. Here tame mapping means a mapping which is subanalytic or, more generally, definable in some o-minimal structure. Our sufficient…
Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape…
Spherical harmonics of degree 4 are widely used in volumetric frame fields design due to their ability to reproduce octahedral symmetry. In this paper we show how to use harmonics of degree 3 (octupoles) for the same purpose, thereby…
In this paper we show that a surface in P^3 parametrized over a 2-dimensional toric variety T can be represented by a matrix of linear syzygies if the base points are finite in number and form locally a complete intersection. This…
The set \[ \Gamma {\stackrel{\rm def}{=}} \{(z+w,zw):|z|\leq 1,|w|\leq 1\} \subset {\mathbb{C}}^2 \] has intriguing complex-geometric properties; it has a 3-parameter group of automorphisms, its distinguished boundary is a ruled surface…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
In formal safety verification, many proposed algorithms use parametric set representations and convert the computation of the relevant sets into an optimization problem; consequently, the choice of parameterization and objective function…
The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…
We generalize the notions of $\beta$- and $\lambda$-maps to general selections of sublocales, obtaining different classes of localic maps. These new classes of maps are used to characterize almost normality, extremal disconnectedness,…
A basic issue in optimization, inverse theory,neural networks, computational chemistry and many other problems is the geometrical characterization of high dimensional functions. In inverse calculations one aims to characterize the set of…
Homology has long been accepted as an important computable tool for quantifying complex structures. In many applications, these structures arise as nodal domains of real-valued functions and are therefore amenable only to a numerical study…
We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…
A comprehensive framework for detection and characterization of overlapping intrinsic symmetry over 3D shapes is proposed. To identify prominent symmetric regions which overlap in space and vary in form, the proposed framework is decoupled…
This article presents a novel approach to identifying and classifying intersections for semantic and topological mapping. More specifically, the proposed novel approach has the merit of generating a semantically meaningful map containing…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…