1311 Submissions

[5] viXra:1311.0192 [pdf] replaced on 2014-05-20 17:46:37

Effective Dynamic Iso-Sphere Inopin Holographic Rings: Inquiry and Hypothesis

Authors: Nathan O. Schmidt
Comments: 19 pages, 5 figures, accepted in Algebras, Groups and Geometries

In this preliminary work, we focus on a particular iso-geometrical, iso-topological facet of iso-mathematics by suggesting a developing, generalized approach for encoding the states and transitions of spherically-symmetric structures that vary in size. In particular, we introduce the notion of "effective iso-radius" to facilitate a heightened characterization of dynamic iso-sphere Inopin holographic rings (IHR) as they undergo "iso-transitions" between "iso-states". In essence, we propose the existence of "effective dynamic iso-sphere IHRs". In turn, this emergence drives the construction of a new "effective iso-state" platform to encode the generalized dynamics of such iso-complex, non-linear systems in a relatively straightforward approach of spherical-based iso-topic liftings. The initial results of this analysis are significant because they lead to alternative modes of research and application, and thereby pose the question: do these effective dynamic iso-sphere IHRs have application in physics and chemistry? Our hypothesis is: yes. To answer this inquiry and assess this conjecture, this developing work should be subjected to further scrutiny, collaboration, improvement, and hard work via the scientific method in order to advance it as such.
Category: Topology

[4] viXra:1311.0059 [pdf] submitted on 2013-11-09 05:09:59

Only Simply Connected Space is Homeomorphic to Sphere

Authors: Dmitri Martila
Comments: 1 Page.

Simple but strict talk about homeomorphism in topology. The World. Shape. The Beginning and End are shown.
Category: Topology

[3] viXra:1311.0031 [pdf] replaced on 2014-02-08 15:45:08

Exterior and Interior Dynamic Iso-Sphere Holographic Rings with an Inverse Iso-Duality

Authors: Nathan O. Schmidt
Comments: 13 pages, 2 figures, accepted by the Hadronic Journal

In this preliminary work, we use a dynamic iso-unit function to iso-topically lift the "static" Inopin holographic ring (IHR) of the unit sphere to an interconnected pair of "dynamic iso-sphere IHRs" (iso-DIHR), where the IHR is simultaneously iso-dual to both a magnified "exterior iso-DIHR" and de-magnified ``interior iso-DIHR". For both the continuously-varying and discretely-varying cases, we define the dynamic iso-amplitude-radius of one iso-DIHR as being equivalent to the dynamic iso-amplitude-curvature of its counterpart, and conversely. These initial results support the hypothesis that a new IHR-based mode of iso-geometry and iso-topology may be in order, which is significant because the interior and exterior zones delineated by the IHR are fundamentally "iso-dual inverses" and may be inferred from one another.
Category: Topology

[2] viXra:1311.0030 [pdf] replaced on 2013-11-20 19:31:09

Mandelbrot Iso-Sets: Iso-Unit Impact Assessment

Authors: Reza Katebi, Nathan O. Schmidt
Comments: 14 pages, 2 figures, accepted in the Hadronic Journal

In this introductory work, we use Santilli's iso-topic lifting as a cutting-edge platform to explore Mandelbrot's set. The objective is to upgrade Mandelbrot's complex quadratic polynomial with iso-multiplication and then computationally probe the effects on this revolutionary fractal. For this, we define the "iso-complex quadratic polynomial" and engage it to generate a locally iso-morphic array of "Mandelbrot iso-sets" by varying the iso-unit, where the connectedness property is topologically preserved in each case. The iso-unit broadens and strengthens the chaotic analysis, and authorizes an enhanced classification and demystification such complex systems because it equips us with an additional degree of freedom: the new Mandelbrot iso-set array is an improvement over the traditional Mandelbrot set because it is significantly more general. In total, the experimental results exemplify dynamic iso-spaces and indicate two modes of topological effects: scale-deformation and boundary-deformation. Ultimately, these new and preliminary developments spark further insight into the emerging realm of iso-fractals.
Category: Topology

[1] viXra:1311.0016 [pdf] submitted on 2013-11-02 15:03:09

Toward a Topological Iso-String Theory in 4D Iso-Dual Space-Time: Hypothesis and Preliminary Construction

Authors: Nathan O. Schmidt
Comments: 34 pages, 7 figures, accepted in the Hadronic Journal

We propose a preliminary framework that engages iso-triplex numbers and deformation order parameters to encode the spatial states of Iso Open Topological Strings (Iso-OTS) for fermions and the temporal states of Iso Closed Topological Strings (Iso-CTS) for bosons, where space and time are iso-dual. The objective is to introduce an elementary Topological Iso-String Theory (TIST) that complies with the holographic principle and fundamentally represents the twisting, winding, and deforming of helical, spiral, and vortical information structures---by default---for attacking superfluidic motion patterns and energy states with iso-topic lifting. In general, these preliminary results indicate a cutting-edge, flexible, consistent, and powerful iso-mathematical framework with considerable representational capability that warrants further examination, collaboration, construction, and discipline.
Category: Topology