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Journal articles on the topic 'Pappus' theorem'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Coghetto, Roland. "Pascal’s Theorem in Real Projective Plane." Formalized Mathematics 25, no. 2 (July 1, 2017): 107–19. http://dx.doi.org/10.1515/forma-2017-0011.

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Summary In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines. For proving Pascal’s theorem, we use the techniques developed in the section “Projective Proofs of Pappus’ Theorem” in the chapter “Pappus’ Theorem: Nine proofs and three variations” [11]. We also follow some ideas from Harrison’s work. With HOL Light, he has the proof of Pascal’s theorem2. For a lemma, we use PROVER93 and OTT2MIZ by Josef Urban4 [12, 6, 7]. We note, that we don’t use Skolem/Herbrand functions (see “Skolemization” in [1]).

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2

Fritsch, Rudolf. "Remarks on orthocenters, Pappus’ theorem and Butterfly theorems." Journal of Geometry 107, no. 2 (December 11, 2015): 305–16. http://dx.doi.org/10.1007/s00022-015-0304-0.

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3

Adams, Cole, Stephen Lovett, and Matthew McMillan. "Generalizations of Pappus’ centroid theorem via Stokes’ theorem." Involve, a Journal of Mathematics 8, no. 5 (September 28, 2015): 771–85. http://dx.doi.org/10.2140/involve.2015.8.771.

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4

Hawrylycz, M. "A geometric identity for Pappus' theorem." Proceedings of the National Academy of Sciences 91, no. 8 (April 12, 1994): 2909. http://dx.doi.org/10.1073/pnas.91.8.2909.

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5

Barbot, Thierry, Gye-Seon Lee, and Viviane Pardini Valério. "Pappus Theorem, Schwartz Representations and Anosov Representations." Annales de l'Institut Fourier 68, no. 6 (2018): 2697–741. http://dx.doi.org/10.5802/aif.3221.

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6

Hooper, W. Patrick. "From Pappus’ Theorem to the Twisted Cubic." Geometriae Dedicata 110, no. 1 (February 2005): 103–34. http://dx.doi.org/10.1007/s10711-004-0543-y.

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7

Thas, C. "An Easy Proof for Some Classical Theorems in Plane Geometry." Canadian Mathematical Bulletin 35, no. 4 (December 1, 1992): 560–68. http://dx.doi.org/10.4153/cmb-1992-073-8.

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AbstractThe main result of this paper is a theorem about three conies in the complex or the real complexified projective plane. Is this theorem new? We have never seen it anywhere before. But since the golden age of projective geometry so much has been published about conies that it is unlikely that no one noticed this result. On the other hand, why does it not appear in the literature? Anyway, it seems interesting to "repeat" this property, because several theorems in connection with straight lines and (or) conies in projective, affine or euclidean planes are in fact special cases of this theorem. We give a few classical examples: the theorems of Pappus-Pascal, Desargues, Pascal (or its converse), the Brocard points, the point of Miquel. Finally, we have never seen in the literature a proof of these theorems using the same short method see the proof of the main theorem).

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8

Jaroma, John H. "89.79 Proof without words: Pappus’ generalisation of Pythagoras’ theorem." Mathematical Gazette 89, no. 516 (November 2005): 493. http://dx.doi.org/10.1017/s0025557200178520.

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9

Braun, Gabriel, and Julien Narboux. "A Synthetic Proof of Pappus’ Theorem in Tarski’s Geometry." Journal of Automated Reasoning 58, no. 2 (April 29, 2016): 209–30. http://dx.doi.org/10.1007/s10817-016-9374-4.

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10

Marchisotto, Elena Anne. "The Theorem of Pappus: A Bridge between Algebra and Geometry." American Mathematical Monthly 109, no. 6 (June 2002): 497. http://dx.doi.org/10.2307/2695440.

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11

Marchisotto, Elena Anne. "The Theorem of Pappus: A Bridge Between Algebra and Geometry." American Mathematical Monthly 109, no. 6 (June 2002): 497–516. http://dx.doi.org/10.1080/00029890.2002.11919880.

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12

Harminc, Matúš, and Lucia Janičková. "Discrete version of the Pythagorean theorem." Mathematical Gazette 102, no. 553 (February 8, 2018): 77–88. http://dx.doi.org/10.1017/mag.2018.9.

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The following observations are motivated by the facts that the area of a planar figure displayed on a screen can be expressed by a certain number of pixels; and if the figure is drawn by a plotter, then its area can be characterised by the total length of a line which fills it in.The generalisations of the Pythagorean theorem are of three kinds. Firstly, the squares on the sides of the right triangle are substituted by other geometrically similar planar figures (Euclid's Elements Book VI, Proposition 31 [1]). Secondly, the assumption of the right angle is omitted (the law of cosines), or both of these generalizations occur simultaneously (Pappus’ area theorem [2], see also H. W. Eves [3]). Thirdly, mathematical spaces other than the plane are considered (for example, de Gua-Faulhaber theorem about trirectangular tetrahedra [3], further generalised by Tinseau [4], Euclideann-spaces, Banach spaces [5], see also [6]).

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13

Tecklenburg, Helga. "A proof of the theorem of Pappus in finite Desarguesian affine planes." Journal of Geometry 30, no. 2 (December 1987): 172–81. http://dx.doi.org/10.1007/bf01227815.

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14

Barrera, W., A. Cano, and J. P. Navarrete. "Pappus’ theorem and a construction of complex Kleinian groups with rich dynamics." Bulletin of the Brazilian Mathematical Society, New Series 45, no. 1 (March 2014): 25–52. http://dx.doi.org/10.1007/s00574-014-0039-9.

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15

Knorr, Wilbur R. "When circles don't look like circles: An optical theorem in Euclid and Pappus." Archive for History of Exact Sciences 44, no. 4 (1992): 287–329. http://dx.doi.org/10.1007/bf00374758.

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16

Lampa-Baczyńska, Magdalena, and Justyna Szpond. "From Pappus Theorem to parameter spaces of some extremal line point configurations and applications." Geometriae Dedicata 188, no. 1 (November 14, 2016): 103–21. http://dx.doi.org/10.1007/s10711-016-0207-8.

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17

Soltani, Mahmoud, Mahmoud Omid, and Reza Alimardani. "Egg volume prediction using machine vision technique based on pappus theorem and artificial neural network." Journal of Food Science and Technology 52, no. 5 (April 10, 2014): 3065–71. http://dx.doi.org/10.1007/s13197-014-1350-6.

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18

Donati, Giorgio. "Pappus' configuration in non commutative projective geometry with application to a theorem of A. Schleiermacher." Rendiconti del Circolo Matematico di Palermo 50, no. 2 (May 2001): 325–28. http://dx.doi.org/10.1007/bf02844987.

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19

Glynn, David G. "A note on Nk configurations and theorems in projective space." Bulletin of the Australian Mathematical Society 76, no. 1 (August 2007): 15–31. http://dx.doi.org/10.1017/s0004972700039435.

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A method of embedding nk configurations into projective space of k–1 dimensions is given. It breaks into the easy problem of finding a rooted spanning tree of the associated Levi graph. Also it is shown how to obtain a “complementary” “theorem” about projective space (over a field or skew-field F) from any nk theorem over F. Some elementary matroid theory is used, but with an explanation suitable for most people. Various examples are mentioned, including the planar configurations: Fano 73, Pappus 93, Desargues 103 (also in 3d-space), Möbius 84 (in 3d-space), and the resulting 74 in 3d-space, 96 in 5d-space, and 107 in 6d-space. (The Möbius configuration is self-complementary.) There are some nk configurations that are not embeddable in certain projective spaces, and these will be taken to similarly not embeddable configurations by complementation. Finally, there is a list of open questions.

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20

Zamudio, Aldo C., Oscar A. Candia, Chi Wing Kong, Brian Wu, and Rosana Gerometta. "Surface change of the mammalian lens during accommodation." American Journal of Physiology-Cell Physiology 294, no. 6 (June 2008): C1430—C1435. http://dx.doi.org/10.1152/ajpcell.90623.2007.

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Classical theories suggest that the surface area of the crystalline lens changes during accommodation while the lens volume remains constant. Our recent work challenged this view by showing that the lens volume decreases as the lens flattens during unaccommodation. In this paper we investigate 1) the magnitude of changes in the surface of the in vitro isolated cow lens during simulated accommodation, as well as that of human lens models, determined from lateral photographs and the application of the first theorem of Pappus; and 2) the velocity of the equatorial diameter recovery of prestretched cow and rabbit lenses by using a custom-built software-controlled stretching apparatus synchronized to a digital camera. Our results showed that the in vitro cow lens surface changed in an unexpected manner during accommodation depending on how much tension was applied to flatten the lens. In this case, the anterior surface initially collapsed with a reduction in surface followed by an increase in surface, when the stretching was applied. In the human lens model, the surface increased when the lens unaccommodated. The lens volume always decreases as the lens flattens. An explanation for the unexpected surface change is presented and discussed. Furthermore, we determined that the changes in lens volume, as reflected by the speed of the equatorial diameter recovery in in vitro cow and rabbit lenses during simulated accommodation, occurred within a physiologically relevant time frame (200 ms), implying a rapid movement of fluid to and from the lens during accommodation.

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21

Pakdemirli, M., and G. Sarı. "A comprehensive perturbation theorem for estimating magnitudes of roots of polynomials." LMS Journal of Computation and Mathematics 16 (2013): 1–8. http://dx.doi.org/10.1112/s1461157012001192.

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AbstractA comprehensive new perturbation theorem is posed and proven to estimate the magnitudes of roots of polynomials. The theorem successfully determines the magnitudes of roots for arbitrary degree of polynomial equations with no restrictions on the coefficients. In the previous papers ‘Pakdemirli and Elmas, Appl. Math. Comput. 216 (2010) 1645–1651’ and ‘Pakdemirli and Yurtsever, Appl. Math. Comput. 188 (2007) 2025–2028’, the given theorems were valid only for some restricted coefficients. The given theorem in this work is a generalization and unification of the past theorems and valid for arbitrary coefficients. Numerical applications of the theorem are presented as examples. It is shown that the theorem produces good estimates for the magnitudes of roots of polynomial equations of arbitrary order and unrestricted coefficients.

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22

Rao, C. Radhakrishna, and D. N. Shanbhag. "Recent results on characterization of probability distributions: a unified approach through extensions of Deny&s theorem." Advances in Applied Probability 18, no. 03 (September 1986): 660–78. http://dx.doi.org/10.1017/s0001867800016013.

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The problem of identifying solutions of general convolution equations relative to a group has been studied in two classical papers by Choquet and Deny (1960) and Deny (1961). Recently, Lau and Rao (1982) have considered the analogous problem relative to a certain semigroup of the real line, which extends the results of Marsaglia and Tubilla (1975) and a lemma of Shanbhag (1977). The extended versions of Deny&s theorem contained in the papers by Lau and Rao, and Shanbhag (which we refer to as LRS theorems) yield as special cases improved versions of several characterizations of exponential, Weibull, stable, Pareto, geometric, Poisson and negative binomial distributions obtained by various authors during the last few years. In this paper we review some of the recent contributions to characterization of probability distributions (whose authors do not seem to be aware of LRS theorems or special cases existing earlier) and show how improved versions of these results follow as immediate corollaries to LRS theorems. We also give a short proof of Lau–Rao theorem based on Deny&s theorem and thus establish a direct link between the results of Deny (1961) and those of Lau and Rao (1982). A variant of Lau–Rao theorem is proved and applied to some characterization problems.

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23

Rao, C. Radhakrishna, and D. N. Shanbhag. "Recent results on characterization of probability distributions: a unified approach through extensions of Deny&s theorem." Advances in Applied Probability 18, no. 3 (September 1986): 660–78. http://dx.doi.org/10.2307/1427182.

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The problem of identifying solutions of general convolution equations relative to a group has been studied in two classical papers by Choquet and Deny (1960) and Deny (1961). Recently, Lau and Rao (1982) have considered the analogous problem relative to a certain semigroup of the real line, which extends the results of Marsaglia and Tubilla (1975) and a lemma of Shanbhag (1977). The extended versions of Deny&s theorem contained in the papers by Lau and Rao, and Shanbhag (which we refer to as LRS theorems) yield as special cases improved versions of several characterizations of exponential, Weibull, stable, Pareto, geometric, Poisson and negative binomial distributions obtained by various authors during the last few years. In this paper we review some of the recent contributions to characterization of probability distributions (whose authors do not seem to be aware of LRS theorems or special cases existing earlier) and show how improved versions of these results follow as immediate corollaries to LRS theorems. We also give a short proof of Lau–Rao theorem based on Deny&s theorem and thus establish a direct link between the results of Deny (1961) and those of Lau and Rao (1982). A variant of Lau–Rao theorem is proved and applied to some characterization problems.

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24

He, Qun, and Daxiao Zheng. "Some rigidity theorems of harmonic maps between Finsler manifolds." International Journal of Mathematics 25, no. 05 (May 2014): 1450043. http://dx.doi.org/10.1142/s0129167x14500438.

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This paper is to study further properties of harmonic maps between Finsler manifolds. It is proved that any conformal harmonic map from an n(>2)-dimensional Finsler manifold to a Finsler manifold must be homothetic and some rigidity theorems for harmonic maps between Finsler manifolds are given, which improve some results in earlier papers and generalize Eells–Sampson's theorem and Sealey's theorem in Riemannian Geometry.

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25

Asmar, Nakhlé, Earl Berkson, and T. A. Gillespie. "Convolution Estimates and Generalized de Leeuw Theorems for Multipliers of Weak Type (1,1)." Canadian Journal of Mathematics 47, no. 2 (April 1, 1995): 225–45. http://dx.doi.org/10.4153/cjm-1995-011-x.

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AbstractIn the context of a locally compact abelian group, we establish maximal theorem counterparts for weak type (1,1) multipliers of the classical de Leeuw theorems for individual strong multipliers. Special methods are developed to handle the weak type (1,1) estimates involved since standard linearization methods such as Lorentz space duality do not apply to this case. In particular, our central result is a maximal theorem for convolutions with weak type (1,1) multipliers which opens avenues of approximation. These results complete a recent series of papers by the authors which extend the de Leeuw theorems to a full range of strong type and weak type maximal multiplier estimates in the abstract setting.

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26

Moore, Calvin C. "Ergodic theorem, ergodic theory, and statistical mechanics." Proceedings of the National Academy of Sciences 112, no. 7 (February 17, 2015): 1907–11. http://dx.doi.org/10.1073/pnas.1421798112.

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This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics.

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27

Kiesel, R., and U. Stadtmüller. "Tauberian theorems for general power series methods." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 3 (November 1991): 483–90. http://dx.doi.org/10.1017/s0305004100070560.

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Let us assume throughout that (pn) denotes a sequence of reals which satisfiesFor real sequences (sn) with increments an = sn – sn−1 for n ≥ 0,(where s−1 = 0), we consider the power seriesmethod of summability (P), where we sayThe power series methods (P) containthe so-called (Jp)-methods (R = 1)and the Borel-type methods (Bp)(R = ∞). We consider only regular (P)-methods, i.e. sn → s implies sn → s(P). By theorem 5 in [5], p.49, we have regularity if and only ifHere we are interested in the converse conclusion, namely sn → s(P) implies sn → s, which can only be validiffurther conditions, so-called Tauberian conditions are satisfied by (sn). These so-called Tauberian theorems for power series methods have a long history; see e.g. the books [5, 14, 23], and they found new attentionrecently in the papers [6, 18, 19, 20] and [8, 9, 10, 11, 12]. The latter papers contain certain o- Tauberian theorems for all power series methods in question and O-Tauberian theorems, if the weight sequence (pn) can be interpolated by alogarithmico-exponential function g(·)(see e.g. [4]), i.e.

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28

Pfister, W., and H. Stumpf. "Exchange Forces of Composite Particles in Quantum Field Theory." Zeitschrift für Naturforschung A 46, no. 5 (May 1, 1991): 389–400. http://dx.doi.org/10.1515/zna-1991-0503.

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AbstractQuantum fields can be characterized by state functionals and corresponding functional equations. Within this functional representation exchange forces of composite particles are discussed for the case of composite bosons which are bound states of two constituent fermions. The dynamics of these bosons is formulated by means of a weak mapping theorem which establishes a map between the functional equations for the composite boson quantum field and the constituent original fermion quantum field. Evaluation of this theorem leads to expressions which can be identified as quantum field theoretic "direct" forces and exchange forces for or between composite particles. By some theorems the exchange forces are evaluated and an estimate for them is given. The expressions for the direct forces correspond to those which were already derived in previous papers to discuss composite particle dynamics.

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29

Kuleshov, Alexander. "A Remark on the Change of Variable Theorem for the Riemann Integral." Mathematics 9, no. 16 (August 10, 2021): 1899. http://dx.doi.org/10.3390/math9161899.

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In 1961, Kestelman first proved the change in the variable theorem for the Riemann integral in its modern form. In 1970, Preiss and Uher supplemented his result with the inverse statement. Later, in a number of papers (Sarkhel, Výborný, Puoso, Tandra, and Torchinsky), the alternative proofs of these theorems were given within the same formulations. In this note, we show that one of the restrictions (namely, the boundedness of the function f on its entire domain) can be omitted while the change of variable formula still holds.

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30

Gual-Arnau, Ximo, and Vicente Miquel. "Pappus-Guldin theorems for weighted motions." Bulletin of the Belgian Mathematical Society - Simon Stevin 13, no. 1 (March 2006): 123–37. http://dx.doi.org/10.36045/bbms/1148059338.

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31

Saxon, Stephen A., and William H. Ruckle. "Reducing the classical multipliers ℓ∞, C0 and bv0." Proceedings of the Edinburgh Mathematical Society 40, no. 2 (June 1997): 345–52. http://dx.doi.org/10.1017/s0013091500023786.

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For R ∈ {bv0, c0, ℓ∞} a multiplier of FK spaces, the classical sectional convergence theorems permit the reduction of R to any of its dense barrelled subspaces as a simple consequence of the Closed Graph Theorem. (Cf. the Bachelis/Rosenthal reduction of R = ℓ∞ to its dense barrelled subspace m0.) A natural modern setting permits the reduction of R to any of the larger class of dense βφ subspaces. Bennett and Kalton's FK setting remarkably reduced R = ℓ∞ to any of its dense subspaces. This extreme reduction also obtains in the modern βφ setting since, surprisingly, every dense subspace of ℓ∞ is a βφ subspace. Moreover, the standard results, including the Bennett/Kalton reduction, easily follow from their βφ versions and the Closed Graph Theorem. Our two supporting papers find relevant “Non-barrelled dense βφ subspaces” and study “Generalized sectional convergence and multipliers”. Here we specialize the βφ approach to ordinary, particularly unconditional, sectional convergence.

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32

Liu, Haidong, and Fanwei Meng. "Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects." Discrete Dynamics in Nature and Society 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/138984.

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We investigate the existence of periodic solutions for a predator-prey system with Holling function response and mutual interference. Our model is more general than others since it has both Holling type IV function and impulsive effects. With some new analytical tricks and the continuation theorem in coincidence degree theory proposed by Gaines and Mawhin, we obtain a set of sufficient conditions on the existence of positive periodic solutions for such a system. In addition, in the remark, we point out some minor errors which appeared in the proof of theorems in some published papers with relevant predator-prey models. An example is given to illustrate our results.

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33

KELLER, NATHAN. "On the Influences of Variables on Boolean Functions in Product Spaces." Combinatorics, Probability and Computing 20, no. 1 (July 9, 2010): 83–102. http://dx.doi.org/10.1017/s0963548310000234.

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In this paper we consider the influences of variables on Boolean functions in general product spaces. Unlike the case of functions on the discrete cube, where there is a clear definition of influence, in the general case several definitions have been presented in different papers. We propose a family of definitions for the influence that contains all the known definitions, as well as other natural definitions, as special cases. We show that the proofs of the BKKKL theorem and of other results can be adapted to our new definition. The adaptation leads to generalizations of these theorems, which are tight in terms of the definition of influence used in the assertion.

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34

Zaheer, Neyamat, and Aijaz A. Khan. "Some theorems on generalized polars with arbitrary weight." International Journal of Mathematics and Mathematical Sciences 10, no. 4 (1987): 757–76. http://dx.doi.org/10.1155/s0161171287000851.

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The present paper, which is a continuation of our earlier work in Annali di Mathematica [1] and Journal Math. Seminar [2] (EγEUθPIA), University of Athens, Greece, deals with the problem of determining sufficiency conditions for the nonvanishing of generalized polars (with a vanishing or nonvanishing weight) of the product of abstract homogeneous polynomials in the general case when the factor polynomials have been preassigned independent locations for their respective null-sets. Our main theorems here fully answer this general problem and include in them, as special cases, all the results on the topic known to date and established by Khan, Marden and Zaheer (see Pacific J. Math. 74 (1978), 2, pp. 535-557, and the papers cited above). Besides, one of the main theorems leads to an improved version of Marden's general theorem on critical points of rational functions of the formf1f2…fp/fp+1…fq,fibeing complex-valued polynomials of degreeni.

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35

Domingo-Juan, M. Carmen, and Vicente Miquel. "Pappus type theorems for motions along a submanifold." Differential Geometry and its Applications 21, no. 2 (September 2004): 229–51. http://dx.doi.org/10.1016/j.difgeo.2004.05.005.

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36

Maddux, Roger D. "Identities Generalizing the Theorems of Pappus and Desargues." Symmetry 13, no. 8 (July 29, 2021): 1382. http://dx.doi.org/10.3390/sym13081382.

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The Theorems of Pappus and Desargues (for the projective plane over a field) are generalized here by two identities involving determinants and cross products. These identities are proved to hold in the three-dimensional vector space over a field. They are closely related to the Arguesian identity in lattice theory and to Cayley-Grassmann identities in invariant theory.

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37

Domingo-Juan, M. Carmen, Ximo Gual, and Vicente Miquel. "Pappus type theorems for hypersurfaces in a space form." Israel Journal of Mathematics 128, no. 1 (December 2002): 205–20. http://dx.doi.org/10.1007/bf02785425.

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38

Casasayas, J., J. Llibre, and A. Nunes. "Periodic orbits of transversal maps." Mathematical Proceedings of the Cambridge Philosophical Society 118, no. 1 (July 1995): 161–81. http://dx.doi.org/10.1017/s0305004100073539.

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One of the most useful theorems for proving the existence of fixed points, or more generally, periodic points of a continuous self-map f of a compact manifold, is the Lefschetz fixed point theorem. When studying the periodic points of f it is convenient to use the Lefschetz zeta function Zf(t) of f, which is a generating function for the Lefschetz numbers of all iterates of f. The function Zf(t) is rational in t and can be computed from the homological invariants of f. See Section 2 for a precise definition. Thus there exists a relation, based on the Lefschetz fixed point theorem, between the periodic points of a self-map of a manifold f:M → M and the properties of the induced homomorphism f*i on the homology groups of M. This relation has been used in several papers, namely [F1], [F2], [F3] and [M]. In these papers, sufficient conditions are given for the existence of infinitely many periodic points in the case when all the zeros and poles of the associated Lefschetz zeta function are roots of unit. Here we restrict ourselves to maps defined on manifolds with a certain homology type. For transversal maps f defined on this class of manifolds, it is possible to extend the techniques introduced in [F1], [F3] and [M] in order to obtain information on the set of periods of f. We recover the above mentioned results of J. Franks and T. Matsuoka, and derive new results on the set of periods of f when the associated Lefschetz zeta function has zeros or poles outside the unit circle.

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39

Byszewski, Ludwik. "Existence of a solution of a Fourier nonlocal quasilinear parabolic problem." Journal of Applied Mathematics and Stochastic Analysis 5, no. 1 (January 1, 1992): 43–67. http://dx.doi.org/10.1155/s1048953392000042.

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The aim of this paper is to give a theorem about the existence of a classical solution of a Fourier third nonlocal quasilinear parabolic problem. To prove this theorem, Schauder's theorem is used. The paper is a continuation of papers [1]-[8] and the generalizations of some results from [9]-[11]. The theorem established in this paper can be applied to describe some phenomena in the theories of diffusion and heat conduction with better effects than the analogous classical theorem about the existence of a solution of the Fourier third quasilinear parabolic problem.

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40

Harmon, Joseph E. "Current Contents of Theoretical Scientific Papers." Journal of Technical Writing and Communication 22, no. 4 (October 1992): 357–75. http://dx.doi.org/10.2190/v051-8uka-w8fj-u54n.

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This article discusses the typical form and content of forty theoretical scientific papers. These papers were chosen from the 400 most-cited papers in the Science Citation Index for the period 1945–1988 (reported by Eugene Garfield in a series of recent essays appearing in Current Contents). It was found that the typical form for these papers is similar to that for experimental and methods papers, but the content differs substantially. In brief, the content follows the logical sequence: problem or need, assumptions made in attempting to solve problem or meet need, theorem derived from those assumptions and additional considerations, proof of theorem by logical reasoning or validation by comparison with what is established or establishable, conclusions from previous discussion, and recommendations on future experimental or theoretical work. Also, compared with experimental and methods papers, these theoretical papers have somewhat fewer figures and tables, but many more references and equations.

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Melham, Tom. "CALL FOR PAPERS Journal of Functional Programming Special Issue on Theorem Provers and Functional Programming." Journal of Functional Programming 7, no. 1 (January 1997): 125–26. http://dx.doi.org/10.1017/s0956796897009350.

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A special issue of the Journal of Functional Programming will be devoted to the use of functional programming in theorem proving. The submission deadline is 31 August 1997.The histories of theorem provers and functional languages have been deeply intertwined since the advent of Lisp. A notable example is the ML family of languages, which are named for the meta language devised for the LCF theorem prover, and which provide both the implementation platform and interaction facilities for numerous later systems (such as Coq, HOL, Isabelle, NuPrl). Other examples include Lisp (as used for ACL2, PVS, Nqthm) and Haskell (as used for Veritas).This special issue is devoted to the theory and practice of using functional languages to implement theorem provers and using theorem provers to reason about functional languages. Topics of interest include, but are not limited to:– architecture of theorem prover implementations– interface design in the functional context– limits of the LCF methodology– impact of host language features– type systems– lazy vs strict languages– imperative (impure) features– performance problems and solutions– problems of scale– special implementation techniques– term representations (e.g. de Bruijn vs name carrying vs BDDs)– limitations of current functional languages– mechanised theories of functional programming

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Flessas, G. P., P. G. L. Leach, and S. Cotsakis. "On Noether's formulation of her theorem." Canadian Journal of Physics 73, no. 7-8 (July 1, 1995): 543. http://dx.doi.org/10.1139/p95-079.

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In some recent papers and comments there has been a difference of opinion as to what a Noetherian integral is. We settle the matter by referring to Noether's paper of 1918 which is a more reliable guide to her work than some textbooks.

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Panek, Emil. "Non-Stationary Gale Economy with Limited Technology and Multilane Turnpike. ”Weak”, ”Strong” and ”Very Strong” Turnpike Theorem." Przegląd Statystyczny 65, no. 4 (January 30, 2019): 373–93. http://dx.doi.org/10.5604/01.3001.0014.0595.

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In the author’s previous papers (2016a, 2016b) the generalized concept of turnpike in the stationary Gale’s economy has been proposed – a single turnpike (single von Neumann’s ray) has been replaced with a compact bundle of turnpikes and it has been called multilane turnpike. It has been proven that the ”weak” turnpike theorem holds in (a) stationary Gale’s economy with fixed (unchangeable in time) production technology and in (b) non-stationary Gale’s economy with technology convergent with time to a limit technology. In this article, in reference to the aforementioned papers, alongside with the ”weak” turnpike theorem, the proof of the ”strong” and ”very strong” turnpike theorem has been presented for the partially modified assumptions in a non-stationary economy with multilane turnpike and with technology convergent with time to a limit technology.

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Gill, Richard David. "Does Geometric Algebra Provide a Loophole to Bell’s Theorem?" Entropy 22, no. 1 (December 31, 2019): 61. http://dx.doi.org/10.3390/e22010061.

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In 2007, and in a series of later papers, Joy Christian claimed to refute Bell’s theorem, presenting an alleged local realistic model of the singlet correlations using techniques from geometric algebra (GA). Several authors published papers refuting his claims, and Christian’s ideas did not gain acceptance. However, he recently succeeded in publishing yet more ambitious and complex versions of his theory in fairly mainstream journals. How could this be? The mathematics and logic of Bell’s theorem is simple and transparent and has been intensely studied and debated for over 50 years. Christian claims to have a mathematical counterexample to a purely mathematical theorem. Each new version of Christian’s model used new devices to circumvent Bell’s theorem or depended on a new way to misunderstand Bell’s work. These devices and misinterpretations are in common use by other Bell critics, so it useful to identify and name them. I hope that this paper can serve as a useful resource to those who need to evaluate new “disproofs of Bell’s theorem”. Christian’s fundamental idea is simple and quite original: he gives a probabilistic interpretation of the fundamental GA equation a · b = ( a b + b a ) / 2 . After that, ambiguous notation and technical complexity allows sign errors to be hidden from sight, and new mathematical errors can be introduced.

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L. Yakymiv, Arsen. "Local Limit Theorem for the Multiple Power Series Distributions." Mathematics 8, no. 11 (November 19, 2020): 2067. http://dx.doi.org/10.3390/math8112067.

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We study the behavior of multiple power series distributions at the boundary points of their existence. In previous papers, the necessary and sufficient conditions for the integral limit theorem were obtained. Here, the necessary and sufficient conditions for the corresponding local limit theorem are established. This article is dedicated to the memory of my teacher, professor V.M. Zolotarev.

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Chlebowicz, Agnieszka, Mohamed Abdalla Darwish, and Kishin Sadarangani. "Existence and Asymptotic Stability of Solutions of a Functional Integral Equation via a Consequence of Sadovskii’s Theorem." Journal of Function Spaces 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/324082.

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Using the technique of measures of noncompactness and, in particular, a consequence of Sadovskii’s fixed point theorem, we prove a theorem about the existence and asymptotic stability of solutions of a functional integral equation. Moreover, in order to illustrate our results, we include one example and compare our results with those obtained in other papers appearing in the literature.

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Huang, Yen-Chang. "Generalizations of the Theorems of Pappus-Guldin in the Heisenberg groups." Journal of Geometric Analysis 31, no. 10 (March 18, 2021): 10374–401. http://dx.doi.org/10.1007/s12220-021-00649-6.

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Chen, Lizhen, Anran Li, and Chongqing Wei. "Multiple Solutions for a Class of Fractional Schrödinger-Poisson System." Journal of Function Spaces 2019 (July 31, 2019): 1–8. http://dx.doi.org/10.1155/2019/8981528.

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We investigate a class of fractional Schrödinger-Poisson system via variational methods. By using symmetric mountain pass theorem, we prove the existence of multiple solutions. Moreover, by using dual fountain theorem, we prove the above system has a sequence of negative energy solutions, and the corresponding energy values tend to 0. These results extend some known results in previous papers.

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Macfarlane, A. J. "The Morley tricorn a solid figure constructed from the diagram for Morley's theorem." Mathematical Gazette 95, no. 532 (March 2011): 49–51. http://dx.doi.org/10.1017/s002555720000231x.

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Morley's theorem states that the points of intersection of adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle, known as Morley's triangle. See Figure 1.Concise proofs of the theorem are given in recent papers [1, 2]. A good picture of important previous work can be obtained by looking at [3, p. 1999], and examining references cited there.

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Hao, Zhao-Cai, Jin Liang, and Ti-Jun Xiao. "Singular boundary value problem on infinite time scale." Discrete Dynamics in Nature and Society 2006 (2006): 1–13. http://dx.doi.org/10.1155/ddns/2006/71580.

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This paper deals with a class of singular boundary value problems of differential equations on infinite time scale. An existence theorem of positive solutions is established by using the Schauder fixed point theorem and perturbation and operator approximation method, which resolves the singularity successfully and differs from those of some papers. In the end of the paper, an example is given to illustrate our main result.

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