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Embedding of a pseudo-point residual design into a Möbius plane

Agnes Hui Chan
1981 Discrete Mathematics  
Any S,(2, q+ 1, q2) is called a pseudo-point-residual design of order q, abbreviated by PPRD(q). Let A and I3 be two blocks ill E PPRD(q)M*.  ...  A Mobius plane M is an S,(3, q + 1, q* + 1) where q is a positive integer. Let 30 be a fixed point in M.  ...  In this paper we consider the dual of the Mobius plane problem and show the embedding of a pseudo-point-residual design of a Mobius plane.  ... 
doi:10.1016/0012-365x(81)90137-0 fatcat:tzu2qwta5rbnhna6m4olx5ioy4

Embedding of a pseudo-residual design into a Möbius plane

Agnes Hui Chan, D.K Ray-Chaudhuri
1982 Journal of combinatorial theory. Series A  
We define a design to be a pseudo-block-residual design of order q (abbreviated by PBRD(q)) if it has these parameters. We consider the reconstruction problem of a Mobius plane from a given PBRD(q).  ...  We show that any PBRD(q) D can be uniquely embedded into a Mobius plane if and only if D satisfies the r-tangency condition.  ...  If D is a pseudo-block-residual design of order q and satisfies the Tangency Condition, then D is uniquely embedded into a Mobius plane of order q.  ... 
doi:10.1016/0097-3165(82)90066-8 fatcat:akqtbyz7u5f7dfdyyldu32sxga

Liaison linkages

Matteo Gallet, Georg Nawratil, Josef Schicho
2017 Journal of symbolic computation  
Moreover, we provide a construction of hexapods with curves of maximal degree, which is based on liaison, a technique used in the theory of algebraic curves.  ...  The complete classification of hexapods - also known as Stewart Gough platforms - of mobility one is still open.  ...  Let D be the Möbius curve of A and let D be its residual curve. Then D is rational and of degree 6. Moreover D and D intersect in 14 points. polynomials, of the third Veronese embedding of P 2 C .  ... 
doi:10.1016/j.jsc.2016.08.006 fatcat:52nllfdcsjdqnccw5ourgx6asa

Modeling Shapes with Higher-Order Graphs: Methodology and Applications [chapter]

Chaohui Wang, Yun Zeng, Dimitris Samaras, Nikos Paragios
2013 Shape Perception in Human and Computer Vision  
Most existing methods address the influence of extrinsic factors by decomposing the transformation of the source shape (model) into two parts: one corresponding to the extrinsic factors and the other accounting  ...  In this chapter, we consider a methodology to circumvent the influence of extrinsic factors by exploiting shape properties that are invariant to them.  ...  More specifically, the original problem is decomposed into a linear subproblem, a higher-order pseudo-boolean subproblem and a set of local subproblems.  ... 
doi:10.1007/978-1-4471-5195-1_31 fatcat:t5ty2ffeffetnpdfn7lhfha55e

Dynamics of non-metric manifolds [article]

Alexandre Gabard, David Gauld
2011 arXiv   pre-print
An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.  ...  This produces many embedded copies of the Möbius band, so denote this surface by P short Möbius .  ...  Otherwise a small propagator is designed by aggregating to a chart countably many points picked in the non-dense orbits.  ... 
arXiv:1102.5684v1 fatcat:unx7zcu4krfkfbh65ixjor46t4

Fully Hyperbolic Neural Networks [article]

Weize Chen, Xu Han, Yankai Lin, Hexu Zhao, Zhiyuan Liu, Peng Li, Maosong Sun, Jie Zhou
2022 arXiv   pre-print
However, existing hyperbolic networks are not completely hyperbolic, as they encode features in a hyperbolic space yet formalize most of their operations in the tangent space (a Euclidean subspace) at  ...  Moreover, we also prove that linear transformation in tangent spaces used by existing hyperbolic networks is a relaxation of the Lorentz rotation and does not include the boost, implicitly limiting the  ...  point in a hyperbolic space, the tangent space at this point is a Euclidean subspace, all Euclidean neural operations can be easily adapted into this tangent space.  ... 
arXiv:2105.14686v3 fatcat:q4wofyt66vg4hm74ulmmduv574

Multi-step prediction of zero series and gap series of Riemann zeta function

Guohai Chen, Guiqiang Guo, Kaisheng Yang, Dixiong Yang
2021 Results in Physics  
zeta function from a new perspective of chaotic dynamics, and addresses the multi-step prediction of the zero series and gap series using the proposed EMD-ELM (empirical mode decomposition-extreme learning  ...  It is shown that the multi-step prediction of the zero series presents a fairly high accuracy while that of the gap series has an acceptable predicted accuracy, which implies that these series contains  ...  , until the original series is decomposed into q IMFs and a residue r q ( Eventually, one complex time series is decomposed into the sum of q IMFs and a residue, which possess different frequency component  ... 
doi:10.1016/j.rinp.2021.104449 fatcat:3ol7ojvshnbt3iqvozklf5itee

Paley and the Paley graphs [article]

Gareth A. Jones
2017 arXiv   pre-print
This paper discusses some aspects of the history of the Paley graphs and their automorphism groups.  ...  If m ≥ 4 there are m − 1 points and blocks, each block has size (m − 2)/2, and any two blocks have (m − 4)/4 points in common. A block design with these properties is called a Hadamard design.  ...  More recently Klin, Kriger and Woldar [54] have used association schemes based on affine planes to construct pseudo-Paley graphs of order q = p 2 for odd primes p.  ... 
arXiv:1702.00285v1 fatcat:d6kuccqyrzanjhavjkardxoho4

Periodic discrete conformal maps [article]

U. Hertrich-Jeromin, I. McIntosh, P. Norman, F. Pedit
1999 arXiv   pre-print
Each point of the map corresponds to a line bundle over the spectral curve so that the map corresponds to a discrete subgroup of the Jacobi variety.  ...  As such, the DCM equation is a discrete soliton equation and we describe the dressing action of a loop group on the set of DCM's.  ...  Moreover it is an embedding, for when dλ = 0 we are at ramification points, which lie over the roots of m(λ) (and the point over λ = 0 when n is odd).  ... 
arXiv:math/9905112v1 fatcat:2cbgbrwneveiblaguoug3njtuy

Conformal tilings I: foundations, theory, and practice

Philip L. Bowers, Kenneth Stephenson
2017 Conformal Geometry and Dynamics  
This paper opens a new chapter in the study of planar tilings by introducing conformal tilings.  ...  Many of the motivations for studying tilings remain unchanged, not least being the pure beauty and intricacy of the patterns.  ...  Lastly, a special thanks to Maria Ramirez-Solano for digging so deeply into the regular pentagonal tiling and to her and Jean Savinien for arranging an exciting workshop on Non-standard hierarchical tilings  ... 
doi:10.1090/ecgd/304 fatcat:zvd6gxm4sjbdjhkv62vrc6lexi

Supersymmetry and Phenomenology of Heterotic and Type I Superstring Models [article]

D. J. Clements
2004 arXiv   pre-print
The first example has N=2 supersymmetry and includes a rank reduction of the D5 gauge groups as a result of using a freely acting Kaluza Klein shift Z_2^s. The second case is an N=1 model.  ...  One has a choice of sign epsilon=+/-1 from terms not related to the principle orbits by S and T transformations. This allows the breaking of supersymmetry with the introduction of antibranes.  ...  However, this closed string coupling has the interpretation of two one-point functions at the O9-planes with a propagator of 1 p 2 + m 2 . (1.0.2) The factor of 1 τ 4 2 can be converted into a momentum  ... 
arXiv:hep-th/0407091v1 fatcat:dbviug2uabfsvi5pzctao6mbcm

Schwarz Reflection Geometry II: Local and Global Behavior of the Exponential Map

Annalisa Calini, Joel Langer
2007 Experimental Mathematics  
A local normal form is obtained for geodesics in the space Λ = {Γ} of analytic Jordan curves in the extended complex plane with symmetric space multiplication Γ1 · Γ2 defined by Schwarzian reflection of  ...  Local geometric features of (Λ, ·) will be seen to reflect primarily the structure of the Witt algebra, while issues of global behavior of the exponential map will be viewed in the context of conformal  ...  Again, the geodesic Γ t runs into singularities (at −2, −1/2) long before it has a chance to fill up much of the plane.  ... 
doi:10.1080/10586458.2007.10129010 fatcat:npqhxjfaprfnpgpt4ieq3aag5y

General index, 1965-1974: Research announcements

1975 Bulletin of the American Mathematical Society  
A., On homeomorphisms of the plane, and their embedding in flows, 71, 381 Andrews, J.J. and Lomonaco, S.  ...  J., Pseudo-inverses of operators, 80, 325 Kanheim, A. G. and Rivlin, T.  ...  74, 639 Markley, Nelson G. and Anderson, William N., Jr., An application of Möbius inversion to a problem in topological dynamics, 79, 1027 Marrero, Osvaldo, Completion and embedding between pseudo (v,  ... 
doi:10.1090/s0002-9904-1975-13804-3 fatcat:atkshf2s7jfe3o7bgu62xbbbpy

Asymptotic behaviour of rational curves [article]

David Bourqui
2011 arXiv   pre-print
We investigate the asympotic behaviour of the moduli space of morphisms from the rational curve to a given variety when the degree becomes large.  ...  One of the crucial tools is the homogeneous coordinate ring of the variey. First we explain in details what happens in the toric case. Then we examine the general case.  ...  Let X be the projective plane blown up at four points (P i ) 1 i 4 in general position; then HCR(X) may be identified with the homogeneous coordinate rings of the Plücker embedding of the Grassmannian  ... 
arXiv:1107.3824v1 fatcat:ely2562yz5fkxcqm743iboxfem

Combinatorial designs

Douglas R. Stinson
2008 ACM SIGACT News  
Acknowledgments I have benefitted from the suggestions, comments and encouragement of  ...  The affine plane of order 3 constructed in Example 5.5 can be embedded into a projective plane of order 3 consisting of the following blocks: L 0,0 = {(0, 0), (1, 0), (2, 0), ∞ 1 } L 0,1 = {(0, 1), (1,  ...  The residual design is constructed by deleting all points in A 0 .  ... 
doi:10.1145/1466390.1466393 fatcat:ofdobskyynaqzl4jual5uswjp4
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