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On the rational cohomology of mapping spaces and their realization problem
Abdelhadi Zaim 대한수학회 2023 대한수학회논문집 Vol.38 No.4
Let $f:X\rightarrow Y$ be a map between simply connected CW-complexes of finite type with $X$ finite. In this paper, we prove that the rational cohomology of mapping spaces map$(X,Y;f)$ contains a polynomial algebra over a generator of degree $N$, where $ N= $ max$ \lbrace i, \pi_{i }(Y)\otimes \mathbb{Q}\neq 0 \rbrace$ is an even number. Moreover, we are interested in determining the rational homotopy type of map$\left( \mathbb{S}^{n}, \mathbb{C} P^{m};f\right) $ and we deduce its rational cohomology as a consequence. The paper ends with a brief discussion about the realization problem of mapping spaces.
SOME PROPERTIES OF THE JULIA SETS OF QUADRATIC RATIONAL MAPS
Ahn, Young-Joon The Honam Mathematical Society 2007 호남수학학술지 Vol.29 No.2
In this paper, we give some properties of the dynamics of quadratic rational maps. Using the properties we present the algorithm for drawing the Julia sets of the quadratic rational maps. We illustrate that they are fractals by computer graphics.
SPACES OF CONJUGATION-EQUIVARIANT FULL HOLOMORPHIC MAPS
KAMIYAMA, YASUHIKO Korean Mathematical Society 2005 대한수학회보 Vol.42 No.1
Let $RRat_k$ ($CP^n$) denote the space of basepoint-preserving conjugation-equivariant holomorphic maps of degree k from $S^2$ to $CP^n$. A map f ; $S^2 {\to}CP^n$ is said to be full if its image does not lie in any proper projective subspace of $CP^n$. Let $RF_k(CP^n)$ denote the subspace of $RRat_k(CP^n)$ consisting offull maps. In this paper we determine $H{\ast}(RF_k(CP^2); Z/p)$ for all primes p.
고해상도 스테레오 위성영상의 3차원 정확도 평가 및 향상
정인준 ( In Jun Jeong ),이창경 ( Chang Kyung Lee ),윤공현 ( Kong Hyun Yun ) 대한원격탐사학회 2014 大韓遠隔探査學會誌 Vol.30 No.5
가장 대표적인 범용센서모델인 다항식비례모형(Rational Function Model)은 물리적 센서모형의 정확도에 견줄 수 있는 특성으로 인하여 상업용 위성영상의 센서모델링 기법에서 가장 많이 쓰이고 있다. RPCs를 이용하여 인공위성 영상의 3차원 위치를 결정할 수 있지만, 대축척의 지형도 제작시 정확도 측면에서 한계를 가지고 있다. 본 연구에서는 QuickBird-2, 인공위성 영상을 이용하여 지상기준점의 수량, 분포 및 다항식비례모형의 차수에 따른 정확도 분석을 수행하였다. 그 결과 1:25,000 축척의 지형도 제작시 수평위치 및 표고 허용오차 범위에 포함 될 수 있는 가능성을 확인하였다. The Rational Function Model has been used as a replacement sensor model in most commercial photogrammetric systems due to its capability of maintaining the accuracy of the physical sensor models. Although satellite images with rational polynomial coefficients have been used to determine three-dimensional position, it has limitations in the accuracy for large scale topographic mapping. In this study, high resolution stereo satellite images, QuickBird-2, were used to investigate how much the threedimensional position accuracy was affected by the No. of ground control points, polynomial order, and distribution of GCPs. As the results, we can confirm that these experiments satisfy the accuracy requirements for horizontal and height position of 1:25,000 map scale.
Jean-Baptiste Gatsinzi 대한수학회 2022 대한수학회논문집 Vol.37 No.1
We use $L_{\infty}$ models to compute the rational homotopy type of the mapping space of the component of the natural inclusion $i_{n,k}: \mathbb{C}P^n \hookrightarrow \mathbb{C}P^{n+k}$ between complex projective spaces and show that it has the rational homotopy type of a product of odd dimensional spheres and a complex projective space. We also characterize the mapping $ \aut_1 \mathbb{C}P^n \rightarrow \map ( \mathbb{C}P^n, \mathbb{C}P^{n+k}; i_{n,k}) $ and the resulting $G$-sequence.
HEIGHT BOUND AND PREPERIODIC POINTS FOR JOINTLY REGULAR FAMILIES OF RATIONAL MAPS
이종규 대한수학회 2011 대한수학회지 Vol.48 No.6
Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly reg-ular pair. In this paper, we provide the same improvement for a jointly regular family: let h : <수식> be the logarithmic absolute height on the projective space, let r(f) be the D-ratio of a rational map f which is defined in [10] and let {f1,..., fk│ fl : A^n → A^n} be a finite set of poly-nomial maps which is defined over a number field K. If the intersection of the indeterminacy loci of f1,..., fk is empty, then there is a constant C such that <수식> where r = maxl=1,...,k (r(fl)).
HEIGHT BOUND AND PREPERIODIC POINTS FOR JOINTLY REGULAR FAMILIES OF RATIONAL MAPS
Lee, Chong-Gyu Korean Mathematical Society 2011 대한수학회지 Vol.48 No.6
Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly regular pair. In this paper, we provide the same improvement for a jointly regular family: let h : ${\mathbb{P}}_{\mathbb{Q}}^n{\rightarrow}{{\mathbb{R}}$ be the logarithmic absolute height on the projective space, let r(f) be the D-ratio of a rational map f which is de ned in [10] and let {$f_1,{\ldots},f_k|f_l:\mathbb{A}^n{\rightarrow}\mathbb{A}^n$} bbe finite set of polynomial maps which is defined over a number field K. If the intersection of the indeterminacy loci of $f_1,{\ldots},f_k$ is empty, then there is a constant C such that $ \sum\limits_{l=1}^k\frac{1}{def\;f_\iota}h(f_\iota(P))>(1+\frac{1}{r})f(P)-C$ for all $P{\in}\mathbb{A}^n$ where r= $max_{\iota=1},{\ldots},k(r(f_l))$.
Homotopical triviality of entire rational maps to even dimensional spheres
Suh, Dong-Youp Korean Mathematical Society 1996 대한수학회논문집 Vol.11 No.3
Let $G = Z_2$. Let X be any compact connected orientable nonsingular real algebraic variety of dim X = k = odd with the trivial G action, and let Y be the unit sphere $S^{2n-k}$ with the antipodal action of G. Then we prove that any G invariant entire rational map $f : x \times Y \to S^{2n}$ is G homotopically trivial. We apply this result to prove that any entire rational map $g : X \times RP^{2n-k} \to S^{2n}$ is homotopically trivial.
Periodic surface homeomorphisms and contact structures
Dheeraj Kulkarni,Kashyap Rajeevsarathy,Kuldeep Saha 대한수학회 2024 대한수학회지 Vol.61 No.1
In this article, we associate a contact structure to the conjugacy class of a periodic surface homeomorphism, encoded by a combinatorial tuple of integers called a marked data set. In particular, we prove that infinite families of these data sets give rise to Stein fillable contact structures with associated monodromies that do not factor into products to positive Dehn twists. In addition to the above, we give explicit constructions of symplectic fillings for rational open books analogous to Mori's construction for honest open books. We also prove a sufficient condition for the Stein fillability of rational open books analogous to the positivity of monodromy for honest open books due to Giroux and Loi-Piergallini.
SOME FIXED POINT RESULTS FOR TAC-SUZUKI CONTRACTIVE MAPPINGS
Mebawondu, Akindele A.,Mewomo, Oluwatosin T. Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.4
In this paper, we introduce the notion of modified TAC-Suzuki-Berinde type F-contraction and modified TAC-(${\psi}$, ${\phi}$)-Suzuki type rational mappings in the frame work of complete metric spaces, we also establish some fixed point results regarding this class of mappings and we present some examples to support our main results. The results obtained in this work extend and generalize the results of Dutta et al. [9], Rhoades [18], Doric, [8], Khan et al. [13], Wardowski [25], Piri et al. [17], Sing et al. [23] and many more results in this direction.