15 citations · 125 across the 37 of their papers we have counts for
38 papers
Advances in the Geometry of the Ratio of Linear Points in the Desargues Affine Plane Skew Field
Orgest Zaka, James F. Peters
This paper introduces advances in the geometry of the ratio of either two or three points in a line in the Desargues affine plane, and we see this as a ratio of elements of skew fi…
Good Coverings of Proximal Alexandrov Spaces. Homotopic Cycles in Jordan Curve Theorem Extension
J. F. Peters, T. Vergili
This paper introduces proximal homotopic cycles, which lead to the main results in this paper, namely, extensions of the Mitsuishi-Yamaguchi Good Coverning Theorem with different f…
Homotopic Nerve Complexes with Free Group Presentations
J. F. Peters
This paper introduces homotopic nerve complexes in a planar Whitehead CW space and their Rotman free group presentations. Nerve complexes were introduced by P.S. Alexandrov during…
Fixed Point Property of Amenable Planar Vortexes
James F. Peters, Tane Vergili
This article introduces free group representations of planar vortexes in a CW space that are a natural outcome of results for amenable groups and fixed points found by M.M. Day dur…
Amiable and Almost Amiable Fixed Sets. Extension of the Brouwer Fixed Point Theorem
James F. Peters
This paper introduces shape boundary regions in descriptive proximity forms of CW (Closure-finite Weak) spaces as a source of amiable fixed subsets as well as almost amiable fixed…
Descriptive Fixed Set Properties for Ribbon Complexes
James F. Peters, Tane Vergili
This article introduces descriptive fixed sets and their properties in descriptive proximity spaces viewed in the context of planar ribbon complexes. These fixed sets are a byprodu…
Vortex Nerves and their Proximities. Nerve Betti Numbers and Descriptive Proximity
James F. Peters
This article introduces vortex nerve complexes in CW (Closure finite Weak) topological spaces, which first appeared in works by P. Alexandroff, H. Hopf and J.H.C. Whitehead during…
Ribbon Complexes & their Approximate Descriptive Proximities. Ribbon & Vortex Nerves, Betti Numbers and Planar Divisions
James F. Peters
This article introduces planar ribbons, Vergili ribbon complexes and ribbon nerves in Alexandroff-Hopf-Whitehead CW (Closure finite Weak) topological spaces. A {\em planar ribbon}…
Cardinality Estimations of Sets with Interval Uncertainties in Finite Topological Spaces
J. F. Peters, I. J. Dochviri
In this paper, we have established boundaries of cardinal numbers of nonempty sets in finite non- topological spaces using interval analysis. For a finite set with known cardi…
Ordered Line and Skew-Fields in the Desargues Affine Plane
Orgest Zaka, James F. Peters
This paper introduces ordered skew fields that result from the construction of a skew field over an ordered line in a Desargues affine plane. A special case of a finite ordered ske…
Ghrist Barcoded Video Frames. Application in Detecting Persistent Visual Scene Surface Shapes captured in Videos
Arjuna P. H. Don, James F. Peters
This article introduces an application of Ghrist barcodes in the study of persistent Betti numbers derived from vortex nerve complexes found in triangulations of video frames. A Gh…
Isomorphic-Dilations of the skew-fields constructed over parallel lines in the Desargues affine plane
Orgest Zaka, James F. Peters
This paper considers dilations and translations of lines in the Desargues affine plane. A dilation of a line transforms each line into a parallel line whose length is a multiple of…
Proximity Induced by Order Relations
M. Z. Ahmad, J. F. Peters
This paper introduces an order proximity on a collection of objects induced by a partial order using the Smirnov closeness measure on a Száz relator space. A Száz relator is a none…
Hyperconnected Relator Spaces. CW Complexes and Continuous Function Paths that are Hyperconnected
M. Z. Ahmad, J. F. Peters
This article introduces proximal cell complexes in a hyperconnected space. Hyperconnectedness encodes how collections of path-connected sub-complexes in a Alexandroff-Hopf-Whitehea…
Descriptive Unions. A Fibre Bundle Characterization of the Union of Descriptively Near Sets
M. Z. Ahmad, J. F. Peters
This paper introduces an extension of descriptive intersection and provides a framework for descriptive unions of nonempty sets. Fibre bundles provide structures that characterize…
Proximal Vortex Cycles and Vortex Nerves. Non-Concentric, Nesting, Possibly Overlapping Homology Cell Complexes
J. F. Peters
This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximi…
Descriptive Cellular Homology
M. Z. Ahmad, J. F. Peters
This article introduces descriptive cellular homology on cell complexes, which is an extension of J.H.C. Whitehead's CW topology. A main result is that a descriptive cellular compl…
Proximal Planar Shape Signatures. Homology Nerves and Descriptive Proximity
James F. Peters
This article introduces planar shape signatures derived from homology nerves, which are intersecting 1-cycles in a collection of homology groups endowed with a proximal relator (se…
Geodesics of Triangulated Image Object Shapes. Approximating Image Shapes via Rectilinear and Curvilinear Triangulations
M. Z. Ahmad, J. F. Peters
This paper introduces the geodesics of triangulated image object shapes. Both rectilinear and curvilinear triangulations of shapes are considered. The triangulation of image object…
Proximal Planar Shapes. Correspondence between Shapes and Nerve Complexes
James F. Peters
This article considers proximal planar shapes in terms of the proximity of shape nerves and shape nerve complexes. A shape nerve is collection of 2-simplexes with nonempty intersec…
Proximal Planar Cech Nerves. An Approach to Approximating the Shapes of Irregular, Finite, Bounded Planar Regions
J. F. Peters
This article introduces proximal Cech nerves and Cech complexes, restricted to finite, bounded regions of the Euclidean plane. A Cech nerve is a collection of intersecting ball…
Towards the neural code endowed in cortical microcolumns
Arturo Tozzi, James F. Peters, Ottorino Ori
This article reports on simulations that show how, starting with a form of neural lattice structure, it is possible to reversibly generate many alternative isomers with a lower str…
A Note on Computable Proximity of -Discs on the Digital Plane
J. F. Peters, K. Kordzaya, I. Dochviri
This paper investigates problems in the characterization of the proximity of digital discs. Based on the -metric structure for the 2D digital plane and using a Jacca…
Two Forms of Proximal Physical Geometry. Axioms, Sewing Regions Together, Classes of Regions, Duality, and Parallel Fibre Bundles
J. F. Peters
This paper introduces two proximal forms of Lenzen physical geometry, namely, an \emph{axiomatized strongly proximal physical geometry} that is built on simplicial complexes with t…