scholarly journals An Infinite Family of Compact, Complete, and Locally Affine k-Symplectic Manifolds of Dimension Three

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2159
Author(s):  
Fanich El Mokhtar ◽  
Essabab Said
Keyword(s):  
Symplectic Structure ◽  
Infinite Family ◽  
Symplectic Manifolds ◽  
Affine Group ◽  
Affine Manifolds ◽  
Group A

We study the complete, compact, locally affine manifolds equipped with a k-symplectic structure, which are the quotients of Rn(k+1) by a subgroup Γ of the affine group A(n(k+1)) of Rn(k+1) acting freely and properly discontinuously on Rn(k+1) and leaving invariant the k-symplectic structure, then we construct and give some examples and properties of compact, complete, locally affine two-symplectic manifolds of dimension three.

scholarly journals Black hole thermodynamics in Snyder phase space

2017 ◽  
Vol 14 (11) ◽  
pp. 1750164
Author(s):  
Sara Saghafi ◽  
Kourosh Nozari
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Phase Space ◽  
Symplectic Structure ◽  
Symplectic Manifolds ◽  
Black Hole Thermodynamics ◽  
Schwarzschild Black Hole ◽  
Noncommutative Phase Space ◽  
Physics Of Black Holes ◽  
First Time

By defining a noncommutative symplectic structure, we study thermodynamics of Schwarzschild black hole in a Snyder noncommutative phase space for the first time. Since natural cutoffs are the results of compactness of symplectic manifolds in phase space, the physics of black holes in such a space would be affected mainly by these cutoffs. In this respect, this study provides a basis for more deeper understanding of the black hole thermodynamics in a pure mathematical viewpoint.

scholarly journals Cubic Edge-Transitive Bi-$p$-Metacirculants

10.37236/6417 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Yan-Li Qin ◽  
Jin-Xin Zhou
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Cayley Graphs ◽  
Infinite Family ◽  
Group Of Automorphisms ◽  
Group A ◽  
Semisymmetric Graphs ◽  
Edge Transitive

A graph is said to be a bi-Cayley graph over a group $H$ if it admits $H$ as a group of automorphisms acting semiregularly on its vertices with two orbits. For a prime $p$, we call a bi-Cayley graph over a metacyclic $p$-group a bi-$p$-metacirculant. In this paper, the automorphism group of a connected cubic edge-transitive bi-$p$-metacirculant is characterized for an odd prime $p$, and the result reveals that a connected cubic edge-transitive bi-$p$-metacirculant exists only when $p=3$. Using this, a classification is given of connected cubic edge-transitive bi-Cayley graphs over an inner-abelian metacyclic $3$-group. As a result, we construct the first known infinite family of cubic semisymmetric graphs of order twice a $3$-power.

RATIONAL BLOW-DOWNS AND NONSYMPLECTIC 4-MANIFOLDS WITH ONE BASIC CLASS

2007 ◽  
Vol 09 (05) ◽  
pp. 681-690
Author(s):  
JONGIL PARK ◽  
KI-HEON YUN
Keyword(s):  
Symplectic Structure ◽  
Infinite Family ◽  
Basic Class ◽  
Simply Connected

We present a simple way to construct an infinite family of simply connected, nonspin, smooth 4-manifolds with one basic class which do not admit a symplectic structure with either orientation.

scholarly journals An invitation to singular symplectic geometry

2019 ◽  
Vol 16 (supp01) ◽  
pp. 1940008 ◽  
Author(s):  
Roisin Braddell ◽  
Amadeu Delshams ◽  
Eva Miranda ◽  
Cédric Oms ◽  
Arnau Planas
Keyword(s):  
Celestial Mechanics ◽  
Symplectic Geometry ◽  
Symplectic Structure ◽  
Symplectic Manifolds ◽  
Symplectic Structures ◽  
Contact Manifolds ◽  
Symplectic Forms

In this paper, we analyze in detail a collection of motivating examples to consider [Formula: see text]-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every [Formula: see text]-symplectic structure. At the end of the paper, we introduce the odd-dimensional analogue to [Formula: see text]-symplectic manifolds: [Formula: see text]-contact manifolds.

Riemannian-polarized k-symplectic manifolds

2021 ◽  
Vol 18 (12) ◽  
Author(s):  
Ismail Benali ◽  
Souhaila Elamine ◽  
Azzouz Awane
Keyword(s):  
Symplectic Structure ◽  
Complex Structure ◽  
Riemannian Metric ◽  
Symplectic Manifolds ◽  
Complex Case ◽  
Hermitian Structure ◽  
Complex Structures ◽  
Dimensional Manifold ◽  
Almost Complex

In this paper, we give an analogue of the Hermitian structure in the almost complex case, on an [Formula: see text]-dimensional manifold endowed with an almost [Formula: see text]-complex metric. Also, we study the compatibility between Riemannian metric and polarized [Formula: see text]-symplectic structure. Also, we study some properties of an almost [Formula: see text]-complex structure. Moreover, we give an equivalence between almost [Formula: see text]-complex structures, [Formula: see text]-almost tangent structures and [Formula: see text]-almost cotangent structures.

scholarly journals An Energy Bound in the Affine Group

2020 ◽  
Author(s):  
Giorgis Petridis ◽  
Oliver Roche-Newton ◽  
Misha Rudnev ◽  
Audie Warren
Keyword(s):  
Affine Group ◽  
Affine Transformations ◽  
Constant Multiple ◽  
General Field ◽  
Finite Set ◽  
Group A ◽  
Point Set ◽  
Energy Bound ◽  
Line Meeting ◽  
Plane Point

Abstract We prove a nontrivial energy bound for a finite set of affine transformations over a general field and discuss a number of implications. These include new bounds on growth in the affine group, a quantitative version of a theorem by Elekes about rich lines in grids. We also give a positive answer to a question of Yufei Zhao that for a plane point set $P$ for which no line contains a positive proportion of points from $P$, there may be at most one line, meeting the set of lines defined by $P$ in at most a constant multiple of $|P|$ points.

scholarly journals Elliptic singularities on log symplectic manifolds and Feigin–Odesskii Poisson brackets

2017 ◽  
Vol 153 (4) ◽  
pp. 717-744 ◽  
Author(s):  
Brent Pym
Keyword(s):  
Symplectic Form ◽  
Symplectic Structure ◽  
Transversality Condition ◽  
Symplectic Manifolds ◽  
Poisson Brackets ◽  
Poisson Structures ◽  
Elliptic Point ◽  
Surface Singularities ◽  
Complex Symplectic

A log symplectic manifold is a complex manifold equipped with a complex symplectic form that has simple poles on a hypersurface. The possible singularities of such a hypersurface are heavily constrained. We introduce the notion of an elliptic point of a log symplectic structure, which is a singular point at which a natural transversality condition involving the modular vector field is satisfied, and we prove a local normal form for such points that involves the simple elliptic surface singularities$\widetilde{E}_{6},\widetilde{E}_{7}$and$\widetilde{E}_{8}$. Our main application is to the classification of Poisson brackets on Fano fourfolds. For example, we show that Feigin and Odesskii’s Poisson structures of type$q_{5,1}$are the only log symplectic structures on projective four-space whose singular points are all elliptic.

scholarly journals Coisotropic Submanifolds in b-symplectic Geometry

2020 ◽  
pp. 1-32
Author(s):  
Stephane Geudens ◽  
Marco Zambon
Keyword(s):  
Normal Form ◽  
Symplectic Geometry ◽  
Symplectic Structure ◽  
Symplectic Manifolds ◽  
Coisotropic Submanifolds ◽  
Form Theorem ◽  
Degeneracy Locus ◽  
Normal Form Theorem

Abstract We study coisotropic submanifolds of b-symplectic manifolds. We prove that b-coisotropic submanifolds (those transverse to the degeneracy locus) determine the b-symplectic structure in a neighborhood, and provide a normal form theorem. This extends Gotay’s theorem in symplectic geometry. Further, we introduce strong b-coisotropic submanifolds and show that their coisotropic quotient, which locally is always smooth, inherits a reduced b-symplectic structure.

Electron microscopic radioautographic studies on the incorporation of 3H proline in the glomerular basement membrane (GBM) in antistreptococcal-cell-membrane (SCM) injected mice

1984 ◽  
Vol 42 ◽  
pp. 188-189
Author(s):  
R.P. Nayyar ◽  
C.F. Lange ◽  
J. L. Borke
Keyword(s):  
Body Weight ◽  
Cell Membrane ◽  
Basement Membrane ◽  
Glomerular Basement Membrane ◽  
Mesangial Matrix ◽  
Electron Microscopic ◽  
Group A ◽  
Injection Protocol

Streptococcal cell membrane (SCM) antiserum injected mice show a significant thickening of glomerular basement membrane (GBM) and an increase in mesangial matrix within 4 to 24 hours of antiserum administration (1,2,3). This study was undertaken to evaluate the incorporation of 3H proline into glomerular cells and GBM under normal and anti-SCM induced conditions. Mice were administered, intraperitoneally, 0.1 ml of normal or anti-SCM serum followed by a 10 µC/g body weight injection of 3H proline. Details of the preparation of anti-SCM (Group A type 12 streptococcal pyogenes) and other sera and injection protocol have been described elsewhere (2). After 15 minutes of isotope injection a chase of cold proline was given and animal sacrificed at 20 minutes, 1,2,4,8,24 and 48 hours. One of the removed kidneys was processed for immunofluorescence, light and electron microscopic radioautographic studies; second kidney was used for GBM isolation and aminoacid analysis.

An ultrastructural study of sertoli cells in two geographically isolated populations of Aphanius dispar

1992 ◽  
Vol 50 (1) ◽  
pp. 548-549
Author(s):  
Taber A. Ba-Omar ◽  
Philip F. Prentis
Keyword(s):  
Ultrastructural Level ◽  
Uranyl Acetate ◽  
Freshwater Teleost ◽  
Isolated Populations ◽  
En Bloc ◽  
The North ◽  
Group A ◽  
Ultrathin Sections ◽  
Group B ◽  
Geographically Isolated

We have recently carried out a study of spermiogenic differentiation in two geographically isolated populations of Aphanius dispar (freshwater teleost), with a view to ascertaining variation at the ultrastructural level. The sampling areas were the Jebel Al Akhdar in the north (Group A) and the Dhofar region (Group B) in the south. Specimens from each group were collected, the testes removed, fixed in Karnovsky solution, post fixed in OsO, en bloc stained with uranyl acetate and then routinely processed to Agar 100 resin, semi and ultrathin sections were prepared for study.

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