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As it is well-known, the geometry of curve in three-dimensions is actually characterized by Frenet vectors. In this paper, we obtain Smarandache curves by using cone frame formulas in null cone Q3 . Also, we give an example related to these curves.
In this paper, we give Smarandache curves according to the asymptotic orthonormal frame in null cone Q2. By using cone frame formulas, we present some characterizations of Smarandache curves and calculate cone frenet invariants of these curves. Also, we illustrate these curves with an example.
As it is well-known, the geometry of curve in three-dimensions is actually characterized by Frenet vectors. In this paper, we obtain Smarandache curves by using cone frame formulas in null cone Q3 . Also, we give an example related to these curves.
The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. TheMathematical Combinatorics (International Book Series) is a fully refereed international book series with an ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandachemulti-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astrophysics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either in theoretical exploration or further experiments, while some parts of these problems may be found useful for scholarly stimulation.The present book is also intended for young physics and mathematics fellows who will perhaps find the unsolved problems described here are at least worth pondering. If this book provides only a few highlights of plausible solutions, it is merely to keep the fun of readers in discovering the answers by themselves. Bon voyage!
In this paper, we study the Smarandache curves according to the asymptotic orthonormal frame in Null Cone Q3. By using cone frame formulas, we obtain some characterizations of the Smarandache curves and introduce cone frenet invariants of these curves.
800x600 Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} Smarandache Geometries as generalizations of Finsler, Riemannian, Weyl, and Kahler Geometries. A Smarandache geometry (SG) is a geometry which has at least one smarandachely denied axiom (1969). An axiom is said smarandachely denied (S-denied) if in the same space the axiom behaves differently (i.e., validated and invalided; or only invalidated but in at least two distinct ways). Thus, as a particular case, Euclidean, Lobachevsky-Bolyai-Gauss, and Riemannian geometries may be united altogether, in the same space, by some SGs. These last geometries can be partially Euclidean and partially non-Euclidean. The novelty of the SG is the fact that they introduce for the first time the degree of negation in geometry, similarly to the degree of falsehood in fuzzy or neutrosophic logic. For example an axiom can be denied in percentage of 30 Also SG are defined on multispaces, i.e. unions of Euclidean and non-Euclidean subspaces, or unions of distinct non-Euclidean spaces. As an example of S-denying, a proposition , which is the conjunction of a set i of propositions, can be invalidated in many ways if it is minimally unsatisfiable, that is, such that the conjunction of any proper subset of the i is satisfied in a structure, but itself is not. Here it is an example of what it means for an axiom to be invalidated in multiple ways [2] : As a particular axiom let's take Euclid's Fifth Postulate. In Euclidean or parabolic geometry a line has one parallel only through a given point. In Lobacevskian or hyperbolic geometry a line has at least two parallels through a given point. In Riemannian or elliptic geometry a line has no parallel through a given point. Whereas in Smarandache geometries there are lines which have no parallels through a given point and other lines which have one or more parallels through a given point (the fifth postulate is invalidated in many ways). Therefore, the Euclid's Fifth Postulate (which asserts that there is only one parallel passing through an exterior point to a given line) can be invalidated in many ways, i.e. Smarandachely denied, as follows: - first invalidation: there is no parallel passing through an exterior point to a given line; - second invalidation: there is a finite number of parallels passing through an exterior point to a given line; - third invalidation: there are infinitely many parallels passing through an exterior point to a given line.
Computer-aided diagnosis (CAD) in medicine is the result of a large amount of effort expended in the interface of medicine and computer science. As some CAD systems in medicine try to emulate the diagnostic decision-making process of medical experts, they can be considered as expert systems in medicine.