Journal articles: 'Rational degree'

1

Denker, William A., and Gary J. Herron. "Generalizing rational degree elevation." Computer Aided Geometric Design 14, no. 5 (June 1997): 399–406. http://dx.doi.org/10.1016/s0167-8396(96)00036-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Nguyen Dat, Dang. "EXTENDED DEGREE OF RATIONAL MAPS." Journal of Science Natural Science 64, no. 6 (June 2019): 23–30. http://dx.doi.org/10.18173/2354-1059.2019-0027.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Oja, Peeter. "Low degree rational spline interpolation." BIT Numerical Mathematics 37, no. 4 (December 1997): 901–9. http://dx.doi.org/10.1007/bf02510359.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Coskun, Izzet, and Eric Riedl. "Normal bundles of rational curves on complete intersections." Communications in Contemporary Mathematics 21, no. 02 (February 27, 2019): 1850011. http://dx.doi.org/10.1142/s0219199718500116.

Full text

Abstract:

Let [Formula: see text] be a general Fano complete intersection of type [Formula: see text]. If at least one [Formula: see text] is greater than [Formula: see text], we show that [Formula: see text] contains rational curves of degree [Formula: see text] with balanced normal bundle. If all [Formula: see text] are [Formula: see text] and [Formula: see text], we show that [Formula: see text] contains rational curves of degree [Formula: see text] with balanced normal bundle. As an application, we prove a stronger version of the theorem of Tian [27], Chen and Zhu [4] that [Formula: see text] is separably rationally connected by exhibiting very free rational curves in [Formula: see text] of optimal degrees.

APA, Harvard, Vancouver, ISO, and other styles

5

BJÖRKLUND, JOHAN. "REAL ALGEBRAIC KNOTS OF LOW DEGREE." Journal of Knot Theory and Its Ramifications 20, no. 09 (September 2011): 1285–309. http://dx.doi.org/10.1142/s0218216511009248.

Full text

Abstract:

In this paper, we study rational real algebraic knots in ℝP3. We show that two real rational algebraic knots of degree ≤ 5 are rigidly isotopic if and only if their degrees and encomplexed writhes are equal. We also show that any smooth irreducible knot which admits a plane projection with less than or equal to four crossings has a rational parametrization of degree ≤6. Furthermore an explicit construction of rational knots of a given degree with arbitrary encomplexed writhe (subject to natural restrictions) is presented.

APA, Harvard, Vancouver, ISO, and other styles

6

Matsuoka, Takashi, and Fumio Sakai. "The degree of rational cuspidal curves." Mathematische Annalen 285, no. 2 (October 1989): 233–47. http://dx.doi.org/10.1007/bf01443516.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Krajnc, Marjeta, Karla Počkaj, and Vito Vitrih. "Construction of low degree rational motions." Journal of Computational and Applied Mathematics 256 (January 2014): 92–103. http://dx.doi.org/10.1016/j.cam.2013.07.014.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Downs, T. "A degree property of rational matrices." Linear Algebra and its Applications 72 (December 1985): 73–84. http://dx.doi.org/10.1016/0024-3795(85)90143-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Chardin, M., S. H. Hassanzadeh, and A. Simis. "Degree of rational maps versus syzygies." Journal of Algebra 573 (May 2021): 641–62. http://dx.doi.org/10.1016/j.jalgebra.2021.01.001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Leviatan, D., and D. S. Lubinsky. "Degree of Approximation by Rational Functions with Prescribed Numerator Degree." Canadian Journal of Mathematics 46, no. 3 (June 1, 1994): 619–33. http://dx.doi.org/10.4153/cjm-1994-033-1.

Full text

Abstract:

AbstractWe prove a Jackson type theorem for rational functions with prescribed numerator degree: For continuous functions f: [—1,1] —> ℝ with ℓ sign changes in (—1,1), there exists a real rational function Rℓ,n(x) with numerator degree ℓ and denominator degree at most n, that changes sign exactly where f does, and such thatHere C is independent of f, n and ℓ, and ωφ is the Ditzian-Totik modulus of continuity. For special functions such as f(x) = sign(x)|x|α we consider improvements of the Jackson rate.

APA, Harvard, Vancouver, ISO, and other styles

11

HASSELBLATT, BORIS, and JAMES PROPP. "Degree-growth of monomial maps." Ergodic Theory and Dynamical Systems 27, no. 5 (October 2007): 1375–97. http://dx.doi.org/10.1017/s0143385707000168.

Full text

Abstract:

AbstractFor projectivizations of rational maps, Bellon and Viallet defined the notion of algebraic entropy using the exponential growth rate of the degrees of iterates. We want to call this notion to the attention of dynamicists by computing algebraic entropy for certain rational maps of projective spaces (Theorem 6.2) and comparing it with topological entropy (Theorem 5.1). The particular rational maps we study are monomial maps (Definition 1.2), which are closely related to toral endomorphisms. Theorems 5.1 and 6.2 that imply that the algebraic entropy of a monomial map is always bounded above by its topological entropy, and that the inequality is strict if the defining matrix has more than one eigenvalue outside the unit circle. Also, Bellon and Viallet conjectured that the algebraic entropy of every rational map is the logarithm of an algebraic integer, and Theorem 6.2 establishes this for monomial maps. However, a simple example using a monomial map shows that a stronger conjecture of Bellon and Viallet is incorrect, in that the sequence of algebraic degrees of the iterates of a rational map of projective space need not satisfy a linear recurrence relation with constant coefficients.

APA, Harvard, Vancouver, ISO, and other styles

12

Manes, Michelle. "ℚ-rational cycles for degree-2 rational maps having an automorphism." Proceedings of the London Mathematical Society 96, no. 3 (November 24, 2007): 669–96. http://dx.doi.org/10.1112/plms/pdm044.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Canci, Jung Kyu, and Solomon Vishkautsan. "Quadratic maps with a periodic critical point of period 2." International Journal of Number Theory 13, no. 06 (December 5, 2016): 1393–417. http://dx.doi.org/10.1142/s1793042117500786.

Full text

Abstract:

We provide a complete classification of possible graphs of rational preperiodic points of endomorphisms of the projective line of degree 2 defined over the rationals with a rational periodic critical point of period 2, under the assumption that these maps have no periodic points of period at least 7. We explain how this extends results of Poonen on quadratic polynomials. We show that there are exactly 13 possible graphs, and that such maps have at most nine rational preperiodic points. We provide data related to the analogous classification of graphs of endomorphisms of degree 2 with a rational periodic critical point of period 3 or 4.

APA, Harvard, Vancouver, ISO, and other styles

14

Fusi, Davide. "On rational varieties of small rationality degree." Advances in Geometry 18, no. 4 (October 25, 2018): 483–94. http://dx.doi.org/10.1515/advgeom-2017-0059.

Full text

Abstract:

Abstract We prove a stronger version of a criterion of rationality given by Ionescu and Russo. We use this stronger version to define an invariant for rational varieties (we call it rationality degree), and we classify rational varieties for small values of the invariant.

APA, Harvard, Vancouver, ISO, and other styles

15

Oara, Cristian, and Andras Varga. "Minimal Degree Coprime Factorization of Rational Matrices." SIAM Journal on Matrix Analysis and Applications 21, no. 1 (January 1999): 245–78. http://dx.doi.org/10.1137/s0895479898339979.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Hajja, Mowaffaq. "Radical and rational means of degree two." Mathematical Inequalities & Applications, no. 4 (2003): 581–93. http://dx.doi.org/10.7153/mia-06-54.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Ferjančič, Karla, Marjeta Knez, and Vito Vitrih. "On C2 rational motions of degree six." Journal of Computational and Applied Mathematics 388 (May 2021): 113324. http://dx.doi.org/10.1016/j.cam.2020.113324.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Lubbes, Niels. "Minimal degree rational curves on real surfaces." Advances in Mathematics 345 (March 2019): 263–88. http://dx.doi.org/10.1016/j.aim.2019.01.019.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Rees, M. "Components of degree two hyperbolic rational maps." Inventiones Mathematicae 100, no. 1 (December 1990): 357–82. http://dx.doi.org/10.1007/bf01231191.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Schicho, Josef. "The parametric degree of a rational surface." Mathematische Zeitschrift 254, no. 1 (March 28, 2006): 185–98. http://dx.doi.org/10.1007/s00209-006-0941-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Rault, Patrick X. "On uniform bounds for rational points on rational curves of arbitrary degree." Journal of Number Theory 133, no. 9 (September 2013): 3112–18. http://dx.doi.org/10.1016/j.jnt.2013.03.008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

D’Mello, Shane. "Classification of real rational knots of low degree in the 3-sphere." Journal of Knot Theory and Its Ramifications 26, no. 04 (April 2017): 1750020. http://dx.doi.org/10.1142/s0218216517500201.

Full text

Abstract:

In this paper, we classify, up to rigid isotopy, real rational knots of degrees less than or equal to [Formula: see text] in a real quadric homeomorphic to the 3-sphere. We also study their connections with rigid isotopy classes of real rational knots of low degree in [Formula: see text] and classify real rational curves of degree 6 in the 3-sphere with exactly one ordinary double point.

APA, Harvard, Vancouver, ISO, and other styles

23

Maniatis, Yiorgo N. "Ontology, epistemology and politics in Plato’s Republic." ΣΧΟΛΗ. Ancient Philosophy and the Classical Tradition 15, no. 2 (2021): 468–500. http://dx.doi.org/10.25205/1995-4328-2021-15-2-468-500.

Full text

Abstract:

In the present work I examine the rational relationship that exists among the ontology, the epistemology, and the politics in Plato’s Republic, and to what degree these three theories support each other with rational foundations. In particular, this study examines to what degree the platonic ontology and epistemology support rationally and sufficiently the platonic political theory of the φιλόσοφοι-βασιλεῖς of the ἀρίστη πολιτεία in the Republic.

APA, Harvard, Vancouver, ISO, and other styles

24

CASTRAVET, ANA-MARIA. "RATIONAL FAMILIES OF VECTOR BUNDLES ON CURVES." International Journal of Mathematics 15, no. 01 (February 2004): 13–45. http://dx.doi.org/10.1142/s0129167x0400220x.

Full text

Abstract:

Let C be a smooth projective complex curve of genus g≥2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1. For any k≥1, we find all the irreducible components of the space of rational curves on M, of degree k. In particular, we find the maximal rationally connected fibrations of these components. We prove that there is a one-to-one correspondence between moduli spaces of rational curves on M and moduli spaces of rank 2 vector bundles on ℙ1×C.

APA, Harvard, Vancouver, ISO, and other styles

25

Song, Jinfang, and Yaoqiu Kuang. "An Analysis on Female Education Level, Income and Fertility Rate in China." E3S Web of Conferences 251 (2021): 01088. http://dx.doi.org/10.1051/e3sconf/202125101088.

Full text

Abstract:

The present population economic theories are all established at a hypothesis: parents are fully rational in decisions at every birth. The hypothesis is actually contradicted with the reality. This paper attempts to explain the fertility behavior of persons with different cultural degrees and income levels without the fully rational hypothesis. The paper puts forward a hypothesis that fertility rate has negative correlation with cultural degree, and proves it through two routes. One is higher cultural degree means longer education duration, which must occupy female reproductive period. The other route is that persons who get higher cultural degree are generally more rational, therefore less accidental pregnancy and childbearing occur.

APA, Harvard, Vancouver, ISO, and other styles

26

Hu, Qian-qian, and Guo-jin Wang. "Representing conics by low degree rational DP curves." Journal of Zhejiang University SCIENCE C 11, no. 4 (April 2010): 278–89. http://dx.doi.org/10.1631/jzus.c0910148.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Browning, Timothy, and Pankaj Vishe. "Rational curves on smooth hypersurfaces of low degree." Algebra & Number Theory 11, no. 7 (September 7, 2017): 1657–75. http://dx.doi.org/10.2140/ant.2017.11.1657.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Tent, Joan. "2-Length and rational characters of odd degree." Archiv der Mathematik 96, no. 3 (March 2011): 201–6. http://dx.doi.org/10.1007/s00013-011-0229-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Dietmann, Rainer. "Linear spaces on rational hypersurfaces of odd degree." Bulletin of the London Mathematical Society 42, no. 5 (July 30, 2010): 891–95. http://dx.doi.org/10.1112/blms/bdq052.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Harris, Joe, and Jason Starr. "Rational curves on hypersurfaces of low degree, II." Compositio Mathematica 141, no. 01 (December 1, 2004): 35–92. http://dx.doi.org/10.1112/s0010437x04001253.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Xu, Chunhui. "Rational behaviour and cooperation degree in competitive situations." International Journal of Systems Science 30, no. 4 (January 1999): 369–77. http://dx.doi.org/10.1080/002077299292326.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Busé, Laurent, Yairon Cid‐Ruiz, and Carlos D'Andrea. "Degree and birationality of multi‐graded rational maps." Proceedings of the London Mathematical Society 121, no. 4 (May 2, 2020): 743–87. http://dx.doi.org/10.1112/plms.12336.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Pérez-Dı́az, Sonia, and J. Rafael Sendra. "Computation of the degree of rational surface parametrizations." Journal of Pure and Applied Algebra 193, no. 1-3 (October 2004): 99–121. http://dx.doi.org/10.1016/j.jpaa.2004.02.011.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Freund, Michael. "The Degree of Rational Approximation to Meromorphic Functions." Zeitschrift für Analysis und ihre Anwendungen 7, no. 3 (1988): 193–202. http://dx.doi.org/10.4171/zaa/296.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Carpentier, Sylvain, Alberto De Sole, and Victor G. Kac. "Singular Degree of a Rational Matrix Pseudodifferential Operator." International Mathematics Research Notices 2015, no. 13 (June 10, 2014): 5162–95. http://dx.doi.org/10.1093/imrn/rnu093.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Siegele, J., D. F. Scharler, and H. P. Schröcker. "Rational motions with generic trajectories of low degree." Computer Aided Geometric Design 76 (January 2020): 101793. http://dx.doi.org/10.1016/j.cagd.2019.101793.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Ball, J. A., J. Kim, L. Rodman, and M. Verma. "Minimal-degree coprime factorizations of rational matrix functions." Linear Algebra and its Applications 186 (June 1993): 117–64. http://dx.doi.org/10.1016/0024-3795(93)90288-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Ball, Joseph A., and Jeongook Kim. "Stability and McMillan degree for rational matrix interpolants." Linear Algebra and its Applications 196 (January 1994): 207–32. http://dx.doi.org/10.1016/0024-3795(94)90325-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Ding, Zhiguo, and Michael E. Zieve. "Low-degree permutation rational functions over finite fields." Acta Arithmetica 202, no. 3 (2022): 253–80. http://dx.doi.org/10.4064/aa210521-12-11.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Im, Bo-Hae, and Michael Larsen. "Waring’s Problem for Rational Functions in One Variable." Quarterly Journal of Mathematics 71, no. 2 (February 3, 2020): 439–49. http://dx.doi.org/10.1093/qmathj/haz052.

Full text

Abstract:

Abstract Let $f\in{\mathbb{Q}}(x)$ be a non-constant rational function. We consider ‘Waring’s problem for $f(x)$,’ i.e., whether every element of ${\mathbb{Q}}$ can be written as a bounded sum of elements of $\{f(a)\mid a\in{\mathbb{Q}}\}$. For rational functions of degree $2$, we give necessary and sufficient conditions. For higher degrees, we prove that every polynomial of odd degree and every odd Laurent polynomial satisfies Waring’s problem. We also consider the ‘easier Waring’s problem’: whether every element of ${\mathbb{Q}}$ can be represented as a bounded sum of elements of $\{\pm f(a)\mid a\in{\mathbb{Q}}\}$.

APA, Harvard, Vancouver, ISO, and other styles

41

Korshunov, R. A. "Using the fictive points to transform entities in the process of map updating." Geodesy and Cartography 924, no. 6 (July 20, 2017): 17–24. http://dx.doi.org/10.22389/0016-7126-2017-924-6-17-24.

Full text

Abstract:

The method of transformation of a vectorized situation from remote-sensed data to digital map, using fictive points, by means of rational polynoms of different degrees is reported. Those points are not really existing corresponding points of entities and their images in the picture. Actually they are the intersections of appropriate corresponding lines both on the map and on the picture (photo). These lines have been drawn through the identical edges of contours and also new vectors, formed by fictive points. Those ones were used to calculate transform parameters of rational polynoms. We may take the degrees of polynoms (the numerator and denominator) separately from the first to the third degree. The degree of rational polynoms be applied depends on situation in the map and on the geometry of material in use. If any coefficient in particular polynoms of 1t, 2nd or 3d degree, making near zero contribution, useful to eliminate it. This enlarges degree of freedom in resolution. These parameters are used for transfer entity of actualization direct from picture on the digital map. Method was tested on the special maid application ad models and on real images and maps.

APA, Harvard, Vancouver, ISO, and other styles

42

Guedj, Vincent. "Ergodic properties of rational mappings with large topological degree." Annals of Mathematics 161, no. 3 (May 1, 2005): 1589–607. http://dx.doi.org/10.4007/annals.2005.161.1589.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Favre, Charles, and Jan-Li Lin. "Degree growth of rational maps induced from algebraic structures." Conformal Geometry and Dynamics of the American Mathematical Society 21, no. 13 (October 25, 2017): 353–68. http://dx.doi.org/10.1090/ecgd/312.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Ran, Z. "The Degree of the Divisor of Jumping Rational Curves." Quarterly Journal of Mathematics 52, no. 3 (September 1, 2001): 367–83. http://dx.doi.org/10.1093/qjmath/52.3.367.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Prokhorov, V. A. "ON THE DEGREE OF RATIONAL APPROXIMATION OF MEROMORPHIC FUNCTIONS." Russian Academy of Sciences. Sbornik Mathematics 81, no. 1 (February 28, 1995): 1–20. http://dx.doi.org/10.1070/sm1995v081n01abeh003611.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Ferjančič, Karla, Marjeta Krajnc, and Vito Vitrih. "Construction of G 3 rational motion of degree eight." Applied Mathematics and Computation 272 (January 2016): 127–38. http://dx.doi.org/10.1016/j.amc.2015.08.073.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Yu, Dan-sheng, and Song-ping Zhou. "Copositive approximation by rational functions with prescribed numerator degree." Applied Mathematics-A Journal of Chinese Universities 24, no. 4 (December 2009): 411–16. http://dx.doi.org/10.1007/s11766-009-2076-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Dikshit, H. P., A. Ojha, and R. A. Zalik. "Wachspress type rational complex planar splines of degree (3,1)." Advances in Computational Mathematics 2, no. 2 (March 1994): 235–49. http://dx.doi.org/10.1007/bf02521110.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Počkaj, Karla. "Hermite G 1 rational spline motion of degree six." Numerical Algorithms 66, no. 4 (August 18, 2013): 721–39. http://dx.doi.org/10.1007/s11075-013-9756-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Valiunas, Motiejus. "Rational growth and degree of commutativity of graph products." Journal of Algebra 522 (March 2019): 309–31. http://dx.doi.org/10.1016/j.jalgebra.2019.01.001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Rational degree'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles