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 International Journal of Astronomy and Astrophysics (IJAA) , 2014, DOI: 10.4236/ijaa.2014.41025 Abstract: From evolutionary miniaturization activation of ancestral larger genes stocks, an electromagnetic field derivate from cancer microscopic collision events participates in the elaboration of geometric complexes and chiral biomolecules that serve to build bodies with embryoid print as it develops during gestation. This miniaturization platform literally allows us to see what would otherwise remain completely invisible. In concordance with our observations collision extreme chaos generates in space time interval geometric scalable invariant extreme order. To determine whether our predictions are valid, we select Mars one of the planets with highest rate collision impact craters. The idea that impact events produce major geological effects that go far beyond the production of craters has recently been emphasized. We wonder if we could predict geometric chiral triangular hexagonal complexes in Martian landscape similar to those documented at microscopic, macroscopic, megascopic levels. We resolved to investigate the geomorphology patterns of more than 4000 collision impact craters in Mars landscape using images from Google Mars platforms, and HIRISE (High resolution imaging science experiment camera from the University of Arizona) based on a pattern recognition images algorithm we identified Mars mosaic order area (MOA). MOA is a circular cluster of overlap craters organized in apparent visible cycle sequential order oriented counterclockwise and consisting of nine craters that structure visible and measurable geometry in interface with biosignature morphologies in their interior not having been previously documented. Crater, therefore,
 Mathias Rousset Mathematics , 2013, Abstract: This paper considers space homogenous Boltzmann kinetic equations in dimension $d$ with Maxwell collisions (and without Grad's cut-off). An explicit Markov coupling of the associated conservative (Nanbu) stochastic $N$-particle system is constructed, using plain parallel coupling of isotropic random walks on the sphere of two-body collisional directions. The resulting coupling is almost surely decreasing, and the $L_2$-coupling creation is computed explicitly. Some quasi-contractive and uniform in $N$ coupling / coupling creation inequalities are then proved, relying on $2+\alpha$-moments ($\alpha >0$) of velocity distributions; upon $N$-uniform propagation of moments of the particle system, it yields a $N$-scalable $\alpha$-power law trend to equilibrium. The latter are based on an original sharp inequality, which bounds from above the coupling distance of two centered and normalized random variables $(U,V)$ in $\R^d$, with the average square parallelogram area spanned by $(U-U_\ast,V-V_\ast)$, $(U_\ast,V_\ast)$ denoting an independent copy. Two counter-examples proving the necessity of the dependance on $>2$-moments and the impossibility of strict contractivity are provided. The paper, (mostly) self-contained, does not require any propagation of chaos property and uses only elementary tools.
 Boletín de la Sociedad Espa？ola de Cerámica y Vidrio , 2004, Abstract: The elastic interactions generated by the presence of a biperiodic network, more precisely hexagonal, of misfit dislocations in the interfacing of a thin bicristal have been simulated numerically while considering an anisotropic elasticity for each crystal. The representation of the normal equi-stress near the dislocation segments and near of the triple node of hexagonal cell permits to detect the stress concentration zone du to elastic field for InAs/(111)GaAs system, because, in the category of semiconductors, this is an ideal system which exhibit the presence of edge dislocations type parallels to the free surfaces by S.T.M.[1]. Las interacciones elásticas generadas por la presencia de una red biperiódica, de dislocaciones en la interfase de un bicristal han sido simuladas numéricamente, considerando elasticidad anisotropa para cada cristal. La representación de las tensiones próximas a las dislocaciones y del nodo triple de la celda hexagonal, permite detectar la zona de concentración de tensiones debido al campo elástico para el sistema InAS/(111) GaAS, ya que, en los semiconductores, éste es un sistema ideal que muestra la presencia de dislocaciones paralelas a las superficies libres por S.T.M.[1].
 Cancer Management and Research , 2011, Abstract: Jairo A Díaz, Mauricio F Murillo, Alvaro BarreroDepartment of Pathology, Hospital Departmental Villavicencio, Hospital Departmental Granada, Medicine School, University Cooperative of Colombia, Villavicencio, Meta, ColombiaAbstract: We have documented self-assembled geometric triangular chiral crystal complexes (GTCHC) and a framework of collagen vascular invariant geometric attractors in cancer tissues. This article shows how this system evolves in time. These structures are incorporated together and evolve in different ways. When the geometric core is stable, and the tissue architecture collapses, fragmented components emerge, which reveal a hidden interior identifying how each molecule is reassembled into the original mold, using one common connection, ie, a fractal self-similarity that guided the system from the beginning. GTCHC complexes generate ejected crystal comet tail effects and produce strange helicity states that arise in the form of spin domain interactions. As the crystal growth vibration stage progresses, biofractal echo images converge in a master-built construction of embryoid bodies with enolase-selective immunopositivity in relation to clusters of triangular chiral cell organization. In our electro-optic collision model, we were able to predict and replicate all the characteristics of this complex geometry that connects a physical phenomenon with the signal patterns that generate biologic chaos. Intrinsically, fractal geometry makes spatial correction errors embrace the chaotic system in a way that permits new structures to emerge, and as a result, an ordered self-assembly of embryoid bodies with neural differentiation at the final stage of cancer development is a predictable process. We hope that further investigation of these structures will lead not only to a new way of thinking about physics and biology, but also to a rewarding area in cancer research.Keywords: embryoid bodies, cancer, electro-optic collision model
 PLOS ONE , 2007, DOI: 10.1371/journal.pone.0001282 Abstract: The present study describes and documents self-assembly of geometric triangular chiral hexagon crystal like complex organizations (GTCHC) in human pathological tissues.The authors have found this architectural geometric expression at macroscopic and microscopic levels mainly in cancer processes. This study is based essentially on macroscopic and histopathologic analyses of 3000 surgical specimens: 2600 inflammatory lesions and 400 malignant tumours. Geometric complexes identified photographically at macroscopic level were located in the gross surgical specimen, and these areas were carefully dissected. Samples were taken to carry out histologic analysis. Based on the hypothesis of a collision genesis mechanism and because it is difficult to carry out an appropriate methodological observation in biological systems, the authors designed a model base on other dynamic systems to obtain indirect information in which a strong white flash wave light discharge, generated by an electronic device, hits over the lines of electrical conductance structured in helicoidal pattern. In their experimental model, the authors were able to reproduce and to predict polarity, chirality, helicoid geometry, triangular and hexagonal clusters through electromagnetic sequential collisions. They determined that similar events among constituents of extracelular matrix which drive and produce piezoelectric activity are responsible for the genesis of GTCHC complexes in pathological tissues. This research suggests that molecular crystals represented by triangular chiral hexagons derived from a collision-attraction event against collagen type I fibrils emerge at microscopic and macroscopic scales presenting a lateral assembly of each side of hypertrophy helicoid fibers, that represent energy flow in cooperative hierarchically chiral electromagnetic interaction in pathological tissues and arises as a geometry of the equilibrium in perturbed biological systems. Further interdisciplinary studies must be carried out to reproduce, manipulate and amplify their activity and probably use them as a base to develop new therapeutic strategies in cancer.
 International Journal of Electronics and Computer Science Engineering , 2012, Abstract: In this paper, a multiband Fractal antenna having the shape of hexagonal is proposed. This hexagonal antenna is used for different wireless applications. Three iterations of the hexagonal fractal multiband antenna are examined. With this structure it is possible to configure the multiband frequency at various bands and return loss to obtain high gain. The Computer Simulation Technology Microwave Studio(CST MWS) software was used to design and analyze the antenna for different wireless applications at range 1-6GHz.
 Physics , 1995, DOI: 10.1016/0375-9601(95)00883-7 Abstract: The Hofstadter problem is studied on hexagonal lattice. We first establish a relation between the spectra for the hexagonal lattice and for its dual he triangular lattice. Following the idea of Faddeev and Kashaev, we then obtain the Bethe-ansatz equations for this system.
 Cancer Management and Research , 2011, DOI: http://dx.doi.org/10.2147/CMAR.S17402 Abstract: tercellular cancer collisions generate an ejected crystal comet tail effect with fractal interface embryoid body reassembly transformation Original Research (16854) Total Article Views Authors: Díaz JA, Murillo MF, Barrero A Published Date May 2011 Volume 2011:3 Pages 143 - 155 DOI: http://dx.doi.org/10.2147/CMAR.S17402 Jairo A Díaz, Mauricio F Murillo, Alvaro Barrero Department of Pathology, Hospital Departmental Villavicencio, Hospital Departmental Granada, Medicine School, University Cooperative of Colombia, Villavicencio, Meta, Colombia Abstract: We have documented self-assembled geometric triangular chiral crystal complexes (GTCHC) and a framework of collagen vascular invariant geometric attractors in cancer tissues. This article shows how this system evolves in time. These structures are incorporated together and evolve in different ways. When the geometric core is stable, and the tissue architecture collapses, fragmented components emerge, which reveal a hidden interior identifying how each molecule is reassembled into the original mold, using one common connection, ie, a fractal self-similarity that guided the system from the beginning. GTCHC complexes generate ejected crystal comet tail effects and produce strange helicity states that arise in the form of spin domain interactions. As the crystal growth vibration stage progresses, biofractal echo images converge in a master-built construction of embryoid bodies with enolase-selective immunopositivity in relation to clusters of triangular chiral cell organization. In our electro-optic collision model, we were able to predict and replicate all the characteristics of this complex geometry that connects a physical phenomenon with the signal patterns that generate biologic chaos. Intrinsically, fractal geometry makes spatial correction errors embrace the chaotic system in a way that permits new structures to emerge, and as a result, an ordered self-assembly of embryoid bodies with neural differentiation at the final stage of cancer development is a predictable process. We hope that further investigation of these structures will lead not only to a new way of thinking about physics and biology, but also to a rewarding area in cancer research.
 EURASIP Journal on Image and Video Processing , 2009, DOI: 10.1155/2009/248581 Abstract: This paper introduces triangular wavelets, which are two-dimensional nonseparable biorthogonal wavelets defined on the regular triangular lattice. The construction that we propose is a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. The resulting three oriented high-pass filters are symmetrically arranged on the lattice, while low-pass filters have hexagonal symmetry, thereby allowing an isotropic image processing in the sense that three detail components are distributed uniformly. Applying the triangular filter to images, we explore applications that truly benefit from the triangular wavelets in comparison with the conventional tensor product transforms.
 EURASIP Journal on Image and Video Processing , 2009, Abstract: This paper introduces triangular wavelets, which are two-dimensional nonseparable biorthogonal wavelets defined on the regular triangular lattice. The construction that we propose is a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. The resulting three oriented high-pass filters are symmetrically arranged on the lattice, while low-pass filters have hexagonal symmetry, thereby allowing an isotropic image processing in the sense that three detail components are distributed uniformly. Applying the triangular filter to images, we explore applications that truly benefit from the triangular wavelets in comparison with the conventional tensor product transforms.
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