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Vessels are complex structures in the body that have been studied extensively in multiple representations. While voxelization is the most common of them, meshes and parametric models are critical in various applications due to their…
It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain…
A frame independent formulation of analytical mechanics in the Newtonian space-time is presented The differential geometry of affine values i.e., the differential geometry in which affine bundles replace vector bundles and sections of one…
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…
Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of…
This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the…
The correspondence between two geometrical descriptions of the KP-hierarchy, one by discrete surface and another by difference analogue of differential geometry, is given.
Differentiable rendering is a technique to connect 3D scenes with corresponding 2D images. Since it is differentiable, processes during image formation can be learned. Previous approaches to differentiable rendering focus on mesh-based…
Sufficient conditions are determined on the parameters such that the generalized and normalized Bessel function of the first kind and other related functions belong to subclasses of starlike and convex functions defined in the unit disk…
The theory of algebraic-geometric codes has been developed in the beginning of the 80's after a paper of V.D. Goppa. Given a smooth projective algebraic curve X over a finite field, there are two different constructions of error-correcting…
A 3-parameter family of helical tubular surfaces obtained by screw revolving a circle provides a useful pedagogical example of how to study geodesics on a surface that admits a 1-parameter symmetry group, but is not as simple as a surface…
Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given…
We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules over a topological ring K. This calculus…
Traditionally, robots are regarded as universal motion generation machines. They are designed mainly by kinematics considerations while the desired dynamics is imposed by strong actuators and high-rate control loops. As an alternative, one…
An invex function generalizes a convex function in the sense that every stationary point is a global minimizer. Recently, invex functions and their subclasses have attracted attention in signal processing and machine learning. However,…
We continue the analysis in [3] of matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus [5]. We amend and improve some…
Differential geometry is powerful tool to analyze the vapor-liquid critical point on the surface of the thermodynamic equation of state. The existence of usual condition of the critical point $\left( \partial p/\partial V\right) _{T}=0$…
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…