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Journal articles on the topic 'Formula One'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 March 2023

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1

James, T. "Winning formula [Formular One design success]." Engineering & Technology 1, no. 1 (April 1, 2006): 28–32. http://dx.doi.org/10.1049/et:20060101.

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2

Bush, Andrew, and Adnan Custovic. "Formula one: best is no formula." European Respiratory Journal 49, no. 5 (May 2017): 1700105. http://dx.doi.org/10.1183/13993003.00105-2017.

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3

ORIOL, MARY DAVID. "One Agencyʼs Formula." Home Healthcare Nurse: The Journal for the Home Care and Hospice Professional 15, no. 7 (July 1997): 505–8. http://dx.doi.org/10.1097/00004045-199707000-00010.

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4

Venables, M. "SportsTech: Formula One." Engineering & Technology 8, no. 3 (April 1, 2013): 84–85. http://dx.doi.org/10.1049/et.2013.0313.

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5

Perucca, Antonella. "Reductions of one-dimensional tori." International Journal of Number Theory 13, no. 06 (December 5, 2016): 1473–89. http://dx.doi.org/10.1142/s1793042117500828.

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Consider a non-split one-dimensional torus defined over a number field [Formula: see text]. For a finitely generated group [Formula: see text] of rational points and for a prime number [Formula: see text], we investigate for how many primes [Formula: see text] of [Formula: see text] the size of the reduction of [Formula: see text] modulo [Formula: see text] is coprime to [Formula: see text]. We provide closed formulas for the corresponding Dirichlet density in terms of finitely many computable parameters. To achieve this, we determine in general which torsion fields and Kummer extensions contain the splitting field.
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6

Beswick, Leslie. "One More Writing Formula." English Journal 90, no. 3 (January 2001): 13. http://dx.doi.org/10.2307/821295.

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7

Laursen, Lucas. "Electrifying formula one [News]." IEEE Spectrum 50, no. 11 (November 2013): 9–10. http://dx.doi.org/10.1109/mspec.2013.6655822.

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8

Goh, Amanda. "Lessons from Formula One." Nature 456, no. 7218 (November 2008): 138. http://dx.doi.org/10.1038/nj7218-138c.

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9

Kovtun, A. S., and O. O. Demianenko. "The story of one formula." Mathematics in Modern Technical University 2020, no. 1 (December 13, 2020): 33–45. http://dx.doi.org/10.20535/mmtu-2020.1-033.

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This article aims to represent the diversity of approaches applicable to a certain mathematical problem – Stirling’s approximation was chosen here to achieve the mentioned goal. The first section of the work gives a sight of how the formula appeared, from the derivation of an idea to a publication of the strict results. Further, we provide readers with six different proofs of the approximation. Two of them use methods from calculus and mathematical analysis such that properties of logarithmic function and definite integral as well as representing functions as power series. The other two apply the Gamma function due to its connection with the notion of the factorial, namely Γ(n) = n!, n ∈ N. The last two have a probabilistic idea in their core: both of them combine Poisson distributed random variables with Central Limit Theorem to yield the desired formula. Some of the given proofs are not mathematically rigorous but rather give a sketch of a strict proof. Having all the results we assert that this story can be a good example of the variety of methods that can be used to solve one mathematical problem, even though all the listed proofs use only basic knowledge from several mathematical courses. Keywords: Stirling’s formula; factorial; Taylor series
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10

Rosenthal, Jeffrey S. "Statistics using just one formula." Teaching Statistics 40, no. 1 (September 29, 2017): 7–11. http://dx.doi.org/10.1111/test.12142.

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11

Plaschinsky, P. "ONE FUNCTIONAL OPERATOR INVERSION FORMULA." Mathematical Modelling and Analysis 6, no. 1 (June 30, 2001): 138–46. http://dx.doi.org/10.3846/13926292.2001.9637153.

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Some results about inversion formula of functional operator with generalized dilation are given. By means of commutative Banach algebra theory the explicit form of inversion operator is expressed. Some commutative Banach algebras with countable generator systems are constructed, their maximal ideal spaces are investigated.
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12

Celik, Onur Burak. "Survival of Formula One Drivers." Social Science Quarterly 101, no. 4 (June 13, 2020): 1271–81. http://dx.doi.org/10.1111/ssqu.12819.

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13

Thane, Phil, and Paul Russell. "Formula One electronic gearbox control." Electronics Education 1997, no. 2 (1997): 21–24. http://dx.doi.org/10.1049/ee.1997.0041.

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14

Araújo, André L. Meireles, José Alberto Maia, and Fernando Xavier. "Surfaces of ℙ3 containing one conic and one line." International Journal of Algebra and Computation 29, no. 01 (February 2019): 9–21. http://dx.doi.org/10.1142/s0218196718500601.

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We know from a result due to Noether–Lefschetz that a very general surface of degree at least 4 in [Formula: see text] contains only curves which are complete intersections with other surfaces. The main goal of this paper is to construct an explicit and smooth compactification of a parameter space for surfaces in [Formula: see text] of degree [Formula: see text] for all sufficiently large [Formula: see text], containing one conic and one line. The construction also applies to surfaces in [Formula: see text] containing one plane curve and one line. As an application, we compute the degree of the locus of surfaces of degree [Formula: see text] containing one conic and one line.
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15

Khanna, Nikhil, Juan H. Arredondo, Leena Kathuria, and S. K. Kaushik. "An Improved One Point Quadrature Formula." Numerical Functional Analysis and Optimization 42, no. 2 (January 25, 2021): 123–31. http://dx.doi.org/10.1080/01630563.2020.1870133.

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16

Evans, Nick. "Lessons in speed from Formula One." Nursing Children and Young People 28, no. 5 (June 8, 2016): 9. http://dx.doi.org/10.7748/ncyp.28.5.9.s9.

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17

Roberts, I. "Formula One and global road safety." Journal of the Royal Society of Medicine 100, no. 8 (August 1, 2007): 360–62. http://dx.doi.org/10.1258/jrsm.100.8.360.

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18

Young, J. "Formula One motorsport – racing with materials." Interdisciplinary Science Reviews 24, no. 1 (January 1999): 58–63. http://dx.doi.org/10.1179/030801899678632.

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19

TANAKA, Hiromasa. "Safety Technology in Formula One Racing." Journal of the Society of Mechanical Engineers 109, no. 1048 (2006): 148–49. http://dx.doi.org/10.1299/jsmemag.109.1048_148.

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20

Warden, J. "UK adheres to Formula One exemption." BMJ 315, no. 7120 (November 29, 1997): 1397–402. http://dx.doi.org/10.1136/bmj.315.7120.1397.

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21

Waldo, J. "Embedded computing and Formula One racing." IEEE Pervasive Computing 4, no. 3 (July 2005): 18–21. http://dx.doi.org/10.1109/mprv.2005.56.

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22

Roberts, Ian. "Formula One and global road safety." Journal of the Royal Society of Medicine 100, no. 8 (August 2007): 360–62. http://dx.doi.org/10.1177/014107680710000810.

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23

Korbelář, Miroslav. "Divisibility and groups in one-generated semirings." Journal of Algebra and Its Applications 17, no. 04 (April 2018): 1850071. http://dx.doi.org/10.1142/s0219498818500718.

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Let [Formula: see text] be a semiring generated by one element. Let us denote this element by [Formula: see text] and let [Formula: see text] be a polynomial. It has been proved that if [Formula: see text] contains at least two different monomials, then the elements of the form [Formula: see text] may possibly be contained in any countable commutative semigroup. In particular, divisibility of such elements does not imply their torsion. Let, on the other hand, [Formula: see text] consist of a single monomial (i.e. [Formula: see text], where [Formula: see text]). We show that in this case, the divisibility of [Formula: see text] by infinitely many primes implies that [Formula: see text] generates a group within [Formula: see text]. Further, an element [Formula: see text] is called an [Formula: see text]-fraction of an element [Formula: see text] if [Formula: see text] and [Formula: see text]. We prove that “almost every” [Formula: see text]-fraction of [Formula: see text] can be expressed as [Formula: see text] for some polynomial [Formula: see text] of degree at most [Formula: see text].
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24

Corrales, Hugo, and Carlos E. Valencia. "Arithmetical structures on graphs with connectivity one." Journal of Algebra and Its Applications 17, no. 08 (July 8, 2018): 1850147. http://dx.doi.org/10.1142/s0219498818501475.

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Given a graph [Formula: see text], an arithmetical structure on [Formula: see text] is a pair of positive integer vectors [Formula: see text] such that [Formula: see text] and [Formula: see text] where [Formula: see text] is the adjacency matrix of [Formula: see text]. We describe the arithmetical structures on graph [Formula: see text] with a cut vertex [Formula: see text] in terms of the arithmetical structures on their blocks. More precisely, if [Formula: see text] are the induced subgraphs of [Formula: see text] obtained from each of the connected components of [Formula: see text] by adding the vertex [Formula: see text] and their incident edges, then the arithmetical structures on [Formula: see text] are in one to one correspondence with the [Formula: see text]-rational arithmetical structures on the [Formula: see text]’s. A rational arithmetical structure corresponds to an arithmetical structure where some of the integrality conditions are relaxed.
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25

Khushtova, F. G. "Differentiation formulas and the autotransformation formula for one particular case of the Fox function." REPORTS ADYGE (CIRCASSIAN) INTERNATIONAL ACADEMY OF SCIENCES 20, no. 4 (2020): 15–18. http://dx.doi.org/10.47928/1726-9946-2020-20-4-15-18.

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26

BISWAS, INDRANIL, JACQUES HURTUBISE, and A. K. RAINA. "RANK ONE CONNECTIONS ON ABELIAN VARIETIES." International Journal of Mathematics 22, no. 11 (November 2011): 1529–43. http://dx.doi.org/10.1142/s0129167x11007318.

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Let A be a complex abelian variety. The moduli space [Formula: see text] of rank one algebraic connections on A is a principal bundle over the dual abelian variety A∨ = Pic 0(A) for the group [Formula: see text]. Take any line bundle L on A∨; let [Formula: see text] be the algebraic principal [Formula: see text]-bundle over A∨ given by the sheaf of connections on L. The line bundle L produces a homomorphism [Formula: see text]. We prove that [Formula: see text] is isomorphic to the principal [Formula: see text]-bundle obtained by extending the structure group of the principal [Formula: see text]-bundle [Formula: see text] using this homomorphism given by L. We compute the ring of algebraic functions on [Formula: see text]. As an application of the above result, we show that [Formula: see text] does not admit any nonconstant algebraic function, despite the fact that it is biholomorphic to (ℂ*)2 dim A implying that it has many nonconstant holomorphic functions.
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27

CHEN, YUFEI, MEIFENG DAI, XIAOQIAN WANG, YU SUN, and WEIYI SU. "MULTIFRACTAL ANALYSIS OF ONE-DIMENSIONAL BIASED WALKS." Fractals 26, no. 03 (June 2018): 1850030. http://dx.doi.org/10.1142/s0218348x18500305.

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For an infinite sequence [Formula: see text] of [Formula: see text] and [Formula: see text] with probability [Formula: see text] and [Formula: see text], we mainly study the multifractal analysis of one-dimensional biased walks. Let [Formula: see text] and [Formula: see text]. The Hausdorff and packing dimensions of the sets [Formula: see text] are [Formula: see text], which is the development of the theorem of Besicovitch [On the sum of digits of real numbers represented in the dyadic system, Math. Ann. 110 (1934) 321–330] on random walk, saying that: For any [Formula: see text], the set [Formula: see text] has Hausdorff dimension [Formula: see text].
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28

Kozakevich, V. K., M. Ye Fesenko, L. S. Ziuzina, O. B. Kozakevich, and O. I. Melashchenko. "NEW GENERATION ADAPTED MILK FORMULAS PRODUCED BY UKRAINIAN MANUFACTURERS FOR FEEDING INFANTS UNDER ONE YEAR." Актуальні проблеми сучасної медицини: Вісник Української медичної стоматологічної академії 21, no. 3 (November 16, 2021): 16–20. http://dx.doi.org/10.31718/2077-1096.21.3.16.

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Breastfeeding is known as the only one form of human feeding that formed during the biological evolution. However, when breastfeeding is impossible, the only solution is to use modern adapted milk formulas to nourish infants. One of the most challenging issues is the adaptation of the formula protein quantity and quality to those in breast milk. Reducing the protein content in the adapted formula "Malutka Premium" prevents protein overload of the immature metabolic system of the child. Fats also play an important role in the nutrition of children as they perform two main functions in the body: they serve as structural components of biological cell membranes and energy material. The fatty component of "Malutka Premium" adapted formula is represented by 50% vegetable oils, which provides the required level of polyunsaturated fatty acids. The carbohydrate component of the adapted formula "Malutka Premium1" is represented by lactose; the adapted formula "Malutka Premium 2" also contains dextrinmaltose (30%). Prebiotics oligosaccharides and five most important nucleotides are added to the composition of "Malutka Premium" that enables to normalize the composition of the intestinal microflora and to intensify the digestive processes. Clinical observations of children receiving formulas with oligosaccharides and nucleotides have shown their high efficacy. Children gained weight better and were found as less likely to have functional digestive disorders. Introducing "Malutka premium with the addition of cereals" formulas to the child's diet enables to choose the most appropriate formula taking into account the peculiarities of the child's digestion. Feeding infants with domestic milk formula ensures the balanced intake of all necessary substances required in accordance with the age and allows to parents and paediatricians solve many problems in the nutrition of both healthy children and children with special nutritional needs.
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29

Galyautdinov, I. G., and L. I. Galeeva. "GALOIS GROUPS FOR ONE CLASS OF EQUATIONS." Asian-European Journal of Mathematics 04, no. 03 (September 2011): 427–36. http://dx.doi.org/10.1142/s1793557111000344.

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We find recurrent formulas for obtaining minimal polynomials pn(x) ∈ ℤ[x] of numbers of the form [Formula: see text], where n ∈ ℕ. We demonstrate that Galois groups of these polynomials are commutative. By the same token we give examples of equations of arbitrarily high degrees solvable in radicals.
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30

Semenchuk, Vladimir N., and Alexander N. Skiba. "On one generalization of finite 𝔘-critical groups." Journal of Algebra and Its Applications 15, no. 04 (February 19, 2016): 1650063. http://dx.doi.org/10.1142/s0219498816500638.

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A proper subgroup [Formula: see text] of a group [Formula: see text] is said to be: [Formula: see text]-subnormal in [Formula: see text] if there exists a chain of subgroups [Formula: see text] such that [Formula: see text] is a prime for [Formula: see text]; [Formula: see text]-abnormal in [Formula: see text] if for every two subgroups [Formula: see text] of [Formula: see text], where [Formula: see text], [Formula: see text] is not a prime. In this paper we describe finite groups in which every non-identity subgroup is either [Formula: see text]-subnormal or [Formula: see text]-abnormal.
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31

Constantine, David, and Jean-François Lafont. "Marked length rigidity for one-dimensional spaces." Journal of Topology and Analysis 11, no. 03 (September 2019): 585–621. http://dx.doi.org/10.1142/s1793525319500250.

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In a compact geodesic metric space of topological dimension one, the minimal length of a loop in a free homotopy class is well-defined, and provides a function [Formula: see text] (the value [Formula: see text] being assigned to loops which are not freely homotopic to any rectifiable loops). This function is the marked length spectrum. We introduce a subset [Formula: see text], which is the union of all non-constant minimal loops of finite length. We show that if [Formula: see text] is a compact, non-contractible, geodesic space of topological dimension one, then [Formula: see text] deformation retracts to [Formula: see text]. Moreover, [Formula: see text] can be characterized as the minimal subset of [Formula: see text] to which [Formula: see text] deformation retracts. Let [Formula: see text] be a pair of compact, non-contractible, geodesic metric spaces of topological dimension one, and set [Formula: see text]. We prove that any isomorphism [Formula: see text] satisfying [Formula: see text], forces the existence of an isometry [Formula: see text] which induces the map [Formula: see text] on the level of fundamental groups. Thus, for compact, non-contractible, geodesic spaces of topological dimension one, the marked length spectrum completely determines the subset [Formula: see text] up to isometry.
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32

Makowski, Francis T., and Luciano Mariella. "Computer simulation helps improve formula one aerodynamics." ATZautotechnology 2, no. 2 (March 2002): 48–51. http://dx.doi.org/10.1007/bf03246679.

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33

Ericson, Matthew. "Regarding Formula One and global road safety." Journal of the Royal Society of Medicine 101, no. 2 (February 2008): 52. http://dx.doi.org/10.1258/jrsm.2008.070374.

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34

Soprunova, Evgenia. "Exponential Gelfond--Khovanskii formula in dimension one." Proceedings of the American Mathematical Society 136, no. 01 (January 1, 2008): 239–46. http://dx.doi.org/10.1090/s0002-9939-07-09091-0.

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35

Joossens, L. "World: how Formula One swerved round health." Tobacco Control 12, no. 4 (December 1, 2003): 346–48. http://dx.doi.org/10.1136/tc.12.4.346.

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36

Sadler, PA. "Tobacco sponsorship of Formula One motor racing." Lancet 351, no. 9100 (February 1998): 451. http://dx.doi.org/10.1016/s0140-6736(05)78404-x.

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37

Luik, JC. "Tobacco sponsorship of Formula One motor racing." Lancet 351, no. 9100 (February 1998): 451–52. http://dx.doi.org/10.1016/s0140-6736(05)78405-1.

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38

Charlton, Anne, David While, and Sheila Kelly. "Tobacco sponsorship of Formula One motor racing." Lancet 351, no. 9100 (February 1998): 452. http://dx.doi.org/10.1016/s0140-6736(05)78406-3.

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39

Vaidya, Sharad G., and Jayant S. Vaidya. "Tobacco sponsorship of Formula One motor racing." Lancet 351, no. 9100 (February 1998): 452. http://dx.doi.org/10.1016/s0140-6736(05)78407-5.

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40

Dunn, William, and Joseph G. Murphy. "The Patient Handoff: Medicine's Formula One Moment." Chest 134, no. 1 (July 2008): 9–12. http://dx.doi.org/10.1378/chest.08-0998.

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41

Cattaneo, Carla, and Luigi Fontana. "D'Alembert formula on finite one-dimensional networks." Journal of Mathematical Analysis and Applications 284, no. 2 (August 2003): 403–24. http://dx.doi.org/10.1016/s0022-247x(02)00392-x.

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42

Parkash, Anand. "One dimensional local domains and radical formula." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 56, no. 2 (January 22, 2014): 729–33. http://dx.doi.org/10.1007/s13366-014-0189-3.

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43

Schredelseker, Klaus, and Fedja Fidahic. "Stock Market Reactions and Formula One Performance." Journal of Sport Management 25, no. 4 (July 2011): 305–13. http://dx.doi.org/10.1123/jsm.25.4.305.

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Due to the global financial crisis, the investments of car manufacturers are going to be revised as never before; especially this is the case for any kind of commitment in sport sponsoring. In Formula One on the one hand costs are exploding, on the other hand money becomes shortened. That is why it becomes interesting to know to what extent a manufacturer’s involvement in this sport is worth it. We use an event study methodology analyzing the stock market response after race performances from 2005 to 2007. Our main results: McLaren- Mercedes and Fiat-Ferrari generate positive abnormal returns after wins for DaimlerChrysler and Fiat, and significantly weaker abnormal returns after losses. Conversely, returns for Renault change in an opposite way.
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44

Mehta, Aditi, Aashima Lakra, Adnan Godil, Aastik Dudani, and Amaan Shaikh. "APPLICATIONS OF OPERATIONS RESEARCH IN FORMULA ONE." International Journal of Engineering Applied Sciences and Technology 6, no. 6 (October 1, 2021): 270–75. http://dx.doi.org/10.33564/ijeast.2021.v06i06.038.

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Formula one is one of the world's most high-paced sports in which a fraction of seconds can cost a win. From the method of calculating the time spent on a pitstop, when the car should come for the pitstop, fuel consumption, race strategy, aerodynamics, mechanics, engine power is all influenced by operation research. The paper aims at different techniques such as optimization and simulation, further discussing the different types of methods used. It provides brief information about the outcomes, drawbacks, and recommendations given for the efficient use of these techniques in the F1 racing world. It also addresses improvements that can be done by logistics, the necessary factors which need to be considered in the simulation model, and so on. The main objective is to study these techniques and provide an overview and limitations of each method, emphasizing the need for additional research to find solutions.
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45

Mustafayev, Jeyhun. "The impact of formula one in Azerbaijan." Scientific News of Academy of Physical Education and Sport 1, no. 2 (December 23, 2019): 51–53. http://dx.doi.org/10.28942/ssj.v1i2.122.

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Siyasi və ictimai xadimlərin fikrincə, Formula 1 Azərbaycan üçün böyük bir fürsətdir. Onlar bu idman hadisəsinin iqtisadi və təqdimat məsələlərinə təsir etdiyini düşünürlər. Eyni zamanda dünyada bu məşhur idman növü turizm sektoru ilə bağlı fayda gətirəcəkdir Məqalənin məqsədi Azərbaycanda keçirilmiş bu beynəlxalq tədbirin ilkin nəticə- lərini göstərməkdir. Burada Formula 1-in əsas aspektləri və onun perspektivləri tədqiq edilmişdir. Bir tərəfdən bu, daha çox audito- riya cəlb edən məşhur idman müsabiqəsidir. Digər tərəfdən ölkəmizin iqtisadiyyatını zənginləşdirəcəkdir. Bundan başqa, Formula 1-in araşdırılması digər beynəlxalq tədbirlərin təşkilinə də müsbət təsir göstərə bilər.
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46

Marovt, Janko. "One-sided sharp order in rings." Journal of Algebra and Its Applications 15, no. 09 (August 22, 2016): 1650161. http://dx.doi.org/10.1142/s0219498816501619.

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We generalize the notion of the left-sharp and the right-sharp partial orders to [Formula: see text] where [Formula: see text] is a ring with identity and [Formula: see text] the subset of elements in [Formula: see text] which have the group inverse. We connect these orders to well-known sharp and minus partial orders. Properties of one-sided sharp partial orders in [Formula: see text] are studied and some known results are generalized.
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47

Mu, Quanwu. "One Diophantine inequality with unlike powers of prime variables." International Journal of Number Theory 13, no. 06 (December 5, 2016): 1531–45. http://dx.doi.org/10.1142/s1793042117500853.

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Let [Formula: see text] be an integer with [Formula: see text] and [Formula: see text] be any real number. Suppose that [Formula: see text] are nonzero real numbers, not all of the same sign and [Formula: see text] is irrational. It is proved that the inequality [Formula: see text] has infinitely many solutions in prime variables [Formula: see text], where [Formula: see text] for [Formula: see text], and [Formula: see text] for [Formula: see text]. This gives an improvement of the recent result.
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48

Liu, Yan-Jun, and Yang Liu. "Finite groups with exactly one composite character degree." Journal of Algebra and Its Applications 15, no. 07 (July 22, 2016): 1650132. http://dx.doi.org/10.1142/s0219498816501322.

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Motivated by Isaacs and Passman’s characterization of finite groups all of whose nonlinear complex irreducible characters have prime degrees, we investigate finite groups [Formula: see text] with exactly one character degree that is not a prime. We show that either [Formula: see text] is solvable with [Formula: see text] or [Formula: see text] for distinct primes [Formula: see text], or up to an abelian direct factor, [Formula: see text] is isomorphic to the alternating group [Formula: see text].
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49

Guo, Qing-Chao, and Yee-Chung Jin. "Estimating coefficients in one-dimensional depth-averaged sediment transport model." Canadian Journal of Civil Engineering 28, no. 3 (June 1, 2001): 536–40. http://dx.doi.org/10.1139/l00-120.

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Abstract:
Various coefficients in sediment transport models must be accounted for. Models based on depth-averaged equations and sediment carrying capacity formula contain some coefficients: α, k, and m. At the present, no widely acceptable method has been developed for determining the values of these coefficients. The focus of this paper is in the development of semi-theoretical formulas for estimating these coefficients such that, in practical applications, the uncertainty involved in selecting coefficients is minimized. Model verification shows that the coefficients obtained from the proposed formulas give a good simulation of the channel bed deformation. In addition, Rouse's equation for sediment concentration distribution will become solvable because the reference concentration can be determined from the derived expression for α. The simulated concentration profiles obtained by solving the Rouse's equation and α formula agree reasonably well with the measured data.Key words: depth-averaged model, sediment transport, sediment-carrying capacity.
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50

Sedeño-Noda, Antonio. "Ranking One Million Simple Paths in Road Networks." Asia-Pacific Journal of Operational Research 33, no. 05 (October 2016): 1650042. http://dx.doi.org/10.1142/s0217595916500421.

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Abstract:
In this paper, we address the problem of finding the [Formula: see text] best paths connecting a given pair of nodes in a directed graph with arbitrary lengths. We introduce an algorithm to determine the [Formula: see text] best paths in order of length when repeat nodes in the paths are allowed. We obtain an O[Formula: see text] time and O[Formula: see text] space algorithm to implicitly determine the [Formula: see text] shortest paths in a directed graph with [Formula: see text] nodes and [Formula: see text] arcs. Empirical results where the algorithm was used to compute one hundred million paths in USA road networks are reported. A non-trivial modification of the previous algorithm is performed obtaining an O[Formula: see text] time method to compute paths without repeat nodes and to answer the next question: how many paths [Formula: see text] in practice are needed to identify [Formula: see text] simple paths using the previous algorithm? We find that the response is usually O[Formula: see text] based on an experiment computing one million paths in USA road networks. The determination of a theoretical tight bound on [Formula: see text] remains as an open problem.
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