Relevant bibliographies by topics / Mathematics, formulae

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Mathematics, formulae'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Mathematics, formulae"

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Emel’yanov, Dmitry. "Algebras of Binary Isolating Formulas for Tensor Product Theories." Bulletin of Irkutsk State University. Series Mathematics 41 (2022): 131–39. http://dx.doi.org/10.26516/1997-7670.2022.41.131.

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Algebras of distributions of binary isolating and semi-isolating formulae are derived objects for a given theory and reflect binary formula relations between 1-type realizations. These algebras are related to the following natural classification questions: 1) for a given class of theories, determine which algebras correspond to theories from that class, and classify those algebras; 2) classify theories from the class according to the isolating and semi-isolating formulae algebras defined by those theories. The description of a finite algebra of binary isolating formulas unambiguously implies the description of an algebra of binary semi-isolating formulas, which makes it possible to trace the behavior of all binary formula relations of a given theory. The paper describes algebras of binary formulas for tensor products. The Cayley tables are given for the obtained algebras. Based on these tables, theorems are formulated describing all algebras of binary formulae distributions for tensor multiplication theory of regular polygons on an edge. It is shown that they are completely described by two algebras
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Chen, J. T., J. W. Lee, S. K. Kao, and Y. T. Chou. "Construction of a curve by using the state equation of Frenet formula." Journal of Mechanics 37 (2021): 454–65. http://dx.doi.org/10.1093/jom/ufab014.

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Abstract In this paper, the available formulae for the curvature of plane curve are reviewed not only for the time-like but also for the space-like parameter curve. Two ways to describe the curve are proposed. One is the straight way to obtain the Frenet formula according to the given curve of parameter form. The other is that we can construct the curve by solving the state equation of Frenet formula subject to the initial position, the initial tangent, normal and binormal vectors, and the given radius of curvature and torsion constant. The remainder theorem of the matrix and the Cayley–Hamilton theorem are both employed to solve the Frenet equation. We review the available formulae of the radius of curvature and examine their equivalence. Through the Frenet formula, the relation among different expressions for the radius of curvature formulae can be linked. Therefore, we can integrate the formulae in the engineering mathematics, calculus, mechanics of materials and dynamics. Besides, biproduct of two new and simpler formulae and the available four formulae in the textbook of the radius of curvature yield the same radius of curvature for the plane curve. Linkage of centrifugal force and radius of curvature is also addressed. A demonstrative example of the cycloid is given. Finally, we use the two new formulae to obtain the radius of curvature for four curves, namely a circle. The equivalence is also proved. Animation for 2D and 3D curves is also provided by using the Mathematica software to demonstrate the validity of the present approach.
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Fazly, Mostafa, and Juncheng Wei. "On stable solutions of the fractional Hénon–Lane–Emden equation." Communications in Contemporary Mathematics 18, no. 05 (July 18, 2016): 1650005. http://dx.doi.org/10.1142/s021919971650005x.

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We derive monotonicity formulae for solutions of the fractional Hénon–Lane–Emden equation [Formula: see text] when [Formula: see text], [Formula: see text] and [Formula: see text]. Then, we apply these formulae to classify stable solutions of the above equation.
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Emel’yanov, D. Yu. "Algebras of Binary Isolating Formulas for Theories of Root Products of Graphs." Bulletin of Irkutsk State University. Series Mathematics 37 (2021): 93–103. http://dx.doi.org/10.26516/1997-7670.2021.37.93.

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Algebras of distributions of binary isolating and semi-isolating formulas are derived objects for given theory and reflect binary formula relations between realizations of 1-types. These algebras are associated with the following natural classification questions: 1) for a given class of theories, determine which algebras correspond to the theories from this class and classify these algebras; 2) to classify theories from a given class depending on the algebras defined by these theories of isolating and semi-isolating formulas. Here the description of a finite algebra of binary isolating formulas unambiguously entails a description of the algebra of binary semi-isolating formulas, which makes it possible to track the behavior of all binary formula relations of a given theory. The paper describes algebras of binary formulae for root products. The Cayley tables are given for the obtained algebras. Based on these tables, theorems describing all algebras of binary formulae distributions for the root multiplication theory of regular polygons on an edge are formulated. It is shown that they are completely described by two algebras.
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Netz, Reviel. "Linguistic formulae as cognitive tools." Pragmatics and Cognition 7, no. 1 (1999): 147–76. http://dx.doi.org/10.1075/pc.7.1.07net.

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Ancient Greek mathematics developed the original feature of being deductive mathematics. This article attempts to give a (partial) explanation f or this achievement. The focus is on the use of a fixed system of linguistic formulae (expressions used repetitively) in Greek mathematical texts. It is shown that (a) the structure of this system was especially adapted for the easy computation of operations of substitution on such formulae, that is, of replacing one element in a fixed formula by another, and it is further argued that (b) such operations of substitution were the main logical tool required by Greek mathematical deduction. The conclusion explains why, assuming the validity of the description above, this historical level (as against the universal cognitive level) is the best explanatory level for the phenomenon of Greek mathematical deduction.
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Bouzeffour, Fethi, and Mubariz Garayev. "Multiple big q-Jacobi polynomials." Bulletin of Mathematical Sciences 10, no. 02 (May 19, 2020): 2050013. http://dx.doi.org/10.1142/s1664360720500137.

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Here, we investigate type II multiple big [Formula: see text]-Jacobi orthogonal polynomials. We provide their explicit formulae in terms of basic hypergeometric series, raising and lowering operators, Rodrigues formulae, third-order [Formula: see text]-difference equation, and we obtain recurrence relations.
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Markhabatov, N. D., and S. V. Sudoplatov. "Pseudofinite Formulae." Lobachevskii Journal of Mathematics 43, no. 12 (December 2022): 3583–90. http://dx.doi.org/10.1134/s1995080222150215.

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Franjic, I., and J. Pecaric. "On corrected Bullen-Simpson's $3/8$ inequality." Tamkang Journal of Mathematics 37, no. 2 (June 30, 2006): 135–48. http://dx.doi.org/10.5556/j.tkjm.37.2006.158.

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The aim of this paper is to derive corrected Bullen-Simpson's 3/8 inequality, starting from corrected Simpson's 3/8 and corrected Maclaurin's formula. By corrected we mean formulae that approximate the integral not only with the values of the function in certain points but also with the value of the first derivative in end points of the interval. These formulae will have a higher degree of exactness than formulae derived in [3].
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Borwein, Jonathan M., David Borwein, and William F. Galway. "Finding and Excluding b-ary Machin-Type Individual Digit Formulae." Canadian Journal of Mathematics 56, no. 5 (October 1, 2004): 897–925. http://dx.doi.org/10.4153/cjm-2004-041-2.

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AbstractConstants with formulae of the form treated by D. Bailey, P. Borwein, and S. Plouffe (BBP formulae to a given base b) have interesting computational properties, such as allowing single digits in their base b expansion to be independently computed, and there are hints that they should be normal numbers, i.e., that their base b digits are randomly distributed. We study a formally limited subset of BBP formulae, which we call Machin-type BBP formulae, for which it is relatively easy to determine whether or not a given constant κ has a Machin-type BBP formula. In particular, given b ∈ ℕ, b > 2, b not a proper power, a b-ary Machin-type BBP arctangent formula for κ is a formula of the form κ = Σmam arctan(–b–m), am ∈ ℚ, while when b = 2, we also allow terms of the form am arctan(1/(1 – 2m)). Of particular interest, we show that π has no Machin-type BBP arctangent formula when b ≠ 2. To the best of our knowledge, when there is no Machin-type BBP formula for a constant then no BBP formula of any form is known for that constant.
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Dedić, Lj, M. Matić, and Josip Pečarić. "Euler-Maclaurin formulae." Mathematical Inequalities & Applications, no. 2 (2003): 247–75. http://dx.doi.org/10.7153/mia-06-24.

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Dissertations / Theses on the topic "Mathematics, formulae"

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Witt, Ingo. "Green formulae for cone differential operators." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2663/.

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Green formulae for elliptic cone differential operators are established. This is achieved by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint; thereby utilizing the concept of a discrete asymptotic type. From this description, the singular coefficients replacing the boundary traces in classical Green formulas are deduced.
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Gorokhovsky, Alexander. "Explicit formulae for characteristic classes in Noncommutative Geometry /." The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488191124570879.

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Small, Anthony James. "A twistorial interpretation of the Weierstrass representation formulae." Thesis, University of Warwick, 1988. http://wrap.warwick.ac.uk/34811/.

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The theory of minimal surfaces represents an important chapter in the study of global analysis and remains a testing ground for our understanding of the non-linear partial differential equations of geometry. Perhaps its greatest charm lies in its mercurial avoidance of isolation. Today we see profound applications to such diverse fields as 3-manifold topology and non-abelian gauge theory, to name two ; see [En] for a recent survey and extensive bibliography. (Very recently there have been exciting new applications of the theory of periodic minimal surfaces in 30 to crystallography, see [T&A&H&H].) Consequently, the principal aim of this thesis, which is to establish the groundwork for the investigation of new interactions between minimal surface theory in V, algebraic geometry and soliton theory, see §4.F, is very much in the traditional spirit of the subject.
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Deka, Rabin. "Formulae and multiprocessor algorithms for digital signal microprocessors." Thesis, University of Bradford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.304030.

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Sharp, Richard John. "Asymptotic formulae for closed orbits of hyperbolic flows." Thesis, University of Warwick, 1990. http://wrap.warwick.ac.uk/107982/.

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This thesis consists of three chapters and an appendix each with its own notation and references. Chapter 0 is an introduction which sets out the definitions and results needed in the main part of the thesis. In Chapter 1 we prove an analogue of Mertens' theorem of prime number theory for the closed orbits of an Axiom A flow (restricted to a non-trivial basic set). A similar result is established for the geodesic flow on a non-compact, finite area surface of constant negative curvature. Applying this result to the modular suface yields some asymptotic formulae concerning quadratic forms. In Chapter 2 we give a new proof of an asymptotic formula for the number of closed orbits of a weak-mixing Axiom A flow subject to certain constaints due to S. Lalley. We extend this result to cover the case of finite group extensions and, for transitive Anosov flows, give an application to homology. We also discuss asymptotics for closed orbits in a fixed homology class, extending a result of A. Katsuda and T. Sunada. The appendix, which is included for completeness, is an account of the proof of a technical result of A. Katsuda and T. Sunada which is used extensively in Chapter 2.
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Dehkordi, Massoud Hadian. "Asymptotic formulae for some arithmetic functions in number theory." Thesis, Loughborough University, 1998. https://dspace.lboro.ac.uk/2134/12177.

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This thesis gives some asymptotic formulae associated with some non-negative multiplicative functions, and introduce a new method for proof of some classical formulae in number theory using the Laplace transform.
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Andersson, Johan. "Summation formulae and zeta functions." Doctoral thesis, Stockholm : Department of Mathematics, Stockholm University, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-1074.

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Hostetter, Michael. "Analogical representation in temporal, spatial, and mnemonic reasoning." Thesis, This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-03242009-040545/.

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Abdulla, Thuraya J. A. M. "Modified extended backward differentiation formulae for differential-algebraic equations with applications to time dependent PDEs." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369071.

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Murr, Rüdiger. "Reciprocal classes of Markov processes : an approach with duality formulae." Phd thesis, Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6209/.

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This work is concerned with the characterization of certain classes of stochastic processes via duality formulae. In particular we consider reciprocal processes with jumps, a subject up to now neglected in the literature. In the first part we introduce a new formulation of a characterization of processes with independent increments. This characterization is based on a duality formula satisfied by processes with infinitely divisible increments, in particular Lévy processes, which is well known in Malliavin calculus. We obtain two new methods to prove this duality formula, which are not based on the chaos decomposition of the space of square-integrable function- als. One of these methods uses a formula of partial integration that characterizes infinitely divisible random vectors. In this context, our characterization is a generalization of Stein’s lemma for Gaussian random variables and Chen’s lemma for Poisson random variables. The generality of our approach permits us to derive a characterization of infinitely divisible random measures. The second part of this work focuses on the study of the reciprocal classes of Markov processes with and without jumps and their characterization. We start with a resume of already existing results concerning the reciprocal classes of Brownian diffusions as solutions of duality formulae. As a new contribution, we show that the duality formula satisfied by elements of the reciprocal class of a Brownian diffusion has a physical interpretation as a stochastic Newton equation of motion. Thus we are able to connect the results of characterizations via duality formulae with the theory of stochastic mechanics by our interpretation, and to stochastic optimal control theory by the mathematical approach. As an application we are able to prove an invariance property of the reciprocal class of a Brownian diffusion under time reversal. In the context of pure jump processes we derive the following new results. We describe the reciprocal classes of Markov counting processes, also called unit jump processes, and obtain a characterization of the associated reciprocal class via a duality formula. This formula contains as key terms a stochastic derivative, a compensated stochastic integral and an invariant of the reciprocal class. Moreover we present an interpretation of the characterization of a reciprocal class in the context of stochastic optimal control of unit jump processes. As a further application we show that the reciprocal class of a Markov counting process has an invariance property under time reversal. Some of these results are extendable to the setting of pure jump processes, that is, we admit different jump-sizes. In particular, we show that the reciprocal classes of Markov jump processes can be compared using reciprocal invariants. A characterization of the reciprocal class of compound Poisson processes via a duality formula is possible under the assumption that the jump-sizes of the process are incommensurable.
Diese Arbeit befasst sich mit der Charakterisierung von Klassen stochastischer Prozesse durch Dualitätsformeln. Es wird insbesondere der in der Literatur bisher unbehandelte Fall reziproker Klassen stochastischer Prozesse mit Sprungen untersucht. Im ersten Teil stellen wir eine neue Formulierung einer Charakterisierung von Prozessen mit unabhängigen Zuwächsen vor. Diese basiert auf der aus dem Malliavinkalkül bekannten Dualitätsformel für Prozesse mit unendlich oft teilbaren Zuwächsen. Wir präsentieren zusätzlich zwei neue Beweismethoden dieser Dualitätsformel, die nicht auf der Chaoszerlegung des Raumes quadratintegrabler Funktionale beruhen. Eine dieser Methoden basiert auf einer partiellen Integrationsformel fur unendlich oft teilbare Zufallsvektoren. In diesem Rahmen ist unsere Charakterisierung eine Verallgemeinerung des Lemma fur Gaußsche Zufallsvariablen von Stein und des Lemma fur Zufallsvariablen mit Poissonverteilung von Chen. Die Allgemeinheit dieser Methode erlaubt uns durch einen ähnlichen Zugang die Charakterisierung unendlich oft teilbarer Zufallsmaße. Im zweiten Teil der Arbeit konzentrieren wir uns auf die Charakterisierung reziproker Klassen ausgewählter Markovprozesse durch Dualitätsformeln. Wir beginnen mit einer Zusammenfassung bereits existierender Ergebnisse zu den reziproken Klassen Brownscher Bewegungen mit Drift. Es ist uns möglich die Charakterisierung solcher reziproken Klassen durch eine Dualitätsformel physikalisch umzudeuten in eine Newtonsche Gleichung. Damit gelingt uns ein Brückenschlag zwischen derartigen Charakterisierungsergebnissen und der Theorie stochastischer Mechanik durch den Interpretationsansatz, sowie der Theorie stochastischer optimaler Steuerung durch den mathematischen Ansatz. Unter Verwendung der Charakterisierung reziproker Klassen durch Dualitätsformeln beweisen wir weiterhin eine Invarianzeigenschaft der reziproken Klasse Browscher Bewegungen mit Drift unter Zeitumkehrung. Es gelingt uns weiterhin neue Resultate im Rahmen reiner Sprungprozesse zu beweisen. Wir beschreiben reziproke Klassen Markovscher Zählprozesse, d.h. Sprungprozesse mit Sprunghöhe eins, und erhalten eine Charakterisierung der reziproken Klasse vermöge einer Dualitätsformel. Diese beinhaltet als Schlüsselterme eine stochastische Ableitung nach den Sprungzeiten, ein kompensiertes stochastisches Integral und eine Invariante der reziproken Klasse. Wir präsentieren außerdem eine Interpretation der Charakterisierung einer reziproken Klasse im Rahmen der stochastischen Steuerungstheorie. Als weitere Anwendung beweisen wir eine Invarianzeigenschaft der reziproken Klasse Markovscher Zählprozesse unter Zeitumkehrung. Einige dieser Ergebnisse werden fur reine Sprungprozesse mit unterschiedlichen Sprunghöhen verallgemeinert. Insbesondere zeigen wir, dass die reziproken Klassen Markovscher Sprungprozesse vermöge reziproker Invarianten unterschieden werden können. Eine Charakterisierung der reziproken Klasse zusammengesetzter Poissonprozesse durch eine Dualitätsformel gelingt unter der Annahme inkommensurabler Sprunghöhen.
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Books on the topic "Mathematics, formulae"

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Group, Engineering Mathematics. Mathematics Formulae for Engineers and Scientists. Pulau Pinang, Malaysia: Penerbit Universiti Sains Malaysia, 2018.

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R, Spiegel Murray, and Spiegel Murray R, eds. Mathematical handbook of formulas and tables. 2nd ed. New York: McGraw-Hill, 1999.

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Sobolev, S. L. The theory of cubature formulas. Dordrecht: Kluwer, Academic Publishers, 1997.

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Salem, Lionel. The most beautiful mathematical formulas. New York: J. Wiley, 1992.

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Company, Chemical Rubber, ed. CRC standard mathematical tables and formulae. 3rd ed. Boca Raton, FL: CRC Press, 2012.

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1957-, Zwillinger Daniel, and Chemical Rubber Company, eds. CRC standard mathematical tables and formulae. 3rd ed. Boca Raton, Florida: CRC Press, 1996.

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T͡Sypkin, A. G. Mathematical formulas: Algebra, geometry, mathematical analysis. Moscow: Mir Publishers, 1988.

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Sankaracarya, Jayadguru. Vedic mathematics: Or sixteen simple mathematical formulae from the Vedas. 2nd ed. Delhi: Motilal Banarsidass, 1992.

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Hicks, Tyler Gregory. Civil engineering formulas. 2nd ed. New York: McGraw-Hill, 2010.

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Jeffrey, Alan. Handbook of mathematical formulas and integrals. 2nd ed. San Diego: Academic Press, 2000.

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Book chapters on the topic "Mathematics, formulae"

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Stroud, K. A. "Reduction Formulae." In Engineering Mathematics, 516–30. London: Palgrave Macmillan UK, 1987. http://dx.doi.org/10.1007/978-1-349-18708-9_17.

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Bird, John. "Transposing formulae." In Engineering Mathematics, 83–89. 8th edition. | Abingdon, Oxon ; New York, NY : Routledge, 2017.: Routledge, 2017. http://dx.doi.org/10.4324/9781315561851-12.

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Stroud, Ken A. "Reduction Formulae." In Engineering Mathematics, 516–30. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4615-9653-0_17.

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Stroud, K. A. "Reduction Formulae." In Engineering Mathematics, 517–30. London: Macmillan Education UK, 1987. http://dx.doi.org/10.1007/978-1-349-12153-3_17.

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Bird, John. "Transposing formulae." In Basic Engineering Mathematics, 102–10. 7th ed. | Abingdon, Oxon ; New York, NY : Routledge, 2017.: Routledge, 2017. http://dx.doi.org/10.4324/9781315561776-17.

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Penner, Robert. "Kan Formulae." In Lecture Notes in Mathematics, 45–49. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43996-5_9.

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Iohara, Kenji, and Yoshiyuki Koga. "Determinant Formulae." In Springer Monographs in Mathematics, 125–48. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-160-8_4.

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Jajte, Ryszard. "Asymptotic formulae." In Lecture Notes in Mathematics, 37–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0098427.

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Bird, John. "Reduction formulae." In Bird's Higher Engineering Mathematics, 497–505. 9th ed. Ninth edition. | Abingdon, Oxon ; New York : Routledge, 2021.: Routledge, 2021. http://dx.doi.org/10.1201/9781003124221-43.

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Martzloff, Jean-Claude. "Approximation Formulae." In A History of Chinese Mathematics, 325–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-540-33783-6_17.

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Conference papers on the topic "Mathematics, formulae"

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Brackx, Fred, Hennie De Schepper, David Eelbode, and Vladimír Souček. "Explicit Formulae for Monogenic Projections." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991024.

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Milovanović, Gradimir V., Tomislav Igić, and Novica Tončev. "Quadrature formulae for problems in mechanics." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756328.

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Bock, S., and K. Gürlebeck. "On Recurrence Formulae of Solid Spherical Monogenics." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991007.

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Cangul, Ismail Naci, Aysun Yurttas, Muge Togan, and Ahmet Sinan Cevik. "New formulae for Zagreb indices." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992462.

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Brackx, F., H. De Schepper, D. Eelbode, and V. Souček. "Explicit Formulae for the Hermitean Monogenic Projection Operator." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991013.

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Cangul, Ismail Naci, Aysun Yurttas, Muge Togan, and Ahmet Sinan Cevik. "Some formulae for the Zagreb indices of graphs." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756139.

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Lin, Xiaoyan, Liangcai Gao, Xuan Hu, Zhi Tang, Yingnan Xiao, and Xiaozhong Liu. "A mathematics retrieval system for formulae in layout presentations." In SIGIR '14: The 37th International ACM SIGIR Conference on Research and Development in Information Retrieval. New York, NY, USA: ACM, 2014. http://dx.doi.org/10.1145/2600428.2609611.

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Ovseevich, A., and Michail D. Todorov. "Explicit Formulae for Ellipsoids Approximating Reachable Sets." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS' 33: 33rd International Conference. AIP, 2007. http://dx.doi.org/10.1063/1.2806041.

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Bock, Sebastian. "On generalized Kolosov-Muskhelishvili formulae for the finite cylinder." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043902.

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Bock, S., K. Gürlebeck, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "On Hypercomplex Differential and Primitivation Operators with Applications to Representation Formulae of Linear Elastostatics." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790252.

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Reports on the topic "Mathematics, formulae"

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Näslund-Hadley, Emma. IDB Briefly Noted: No. 9 : June, 2011: Less Talk, More Play: Bolstering Math Learning in Argentina. Inter-American Development Bank, June 2011. http://dx.doi.org/10.18235/0008215.

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Argentina and the Inter-American Development Bank (IDB) joined forces to test a new math education model called Mathematics for All (MAT). After just one academic year, learning increased in schools using the model, with particularly dramatic improvements among underperforming students. This brief describes how MAT improved learning by focusing on the development of mathematical thinking rather than on the memorization of formulas.
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Alarcon Lopez, Luis Guillermo. The Impact of Obligations in Spectrum Value. Inter-American Development Bank, July 2017. http://dx.doi.org/10.18235/0007977.

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Radiofrequency spectrum is an essential asset for mobile network operators. Governments set its value to organize competitive frequency auctions and define recurrent payments, such as taxes and right of use. This publication sustains that governments should value radio frequency spectrum as a function of the intended frequency use policy and corresponding obligations. A mathematical formula is proposed to articulate, quantitatively, the relationship between spectrum value and regulatory obligations, including promoting new market entrants, conditioning of wholesale obligations, definition of coverage goals, and requirement to support public safety and first respondent services. This paper targets, in general, the telecommunication ministries, national regulatory authorities, and government entities that address the topic of valuing radio frequency spectrum.
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Pinchuk, O. P., V. A. Tkachenko, and O. Yu Burov. AV and VR as Gamification of Cognitive Tasks. CEUR Workshop Proceedings, 2019. http://dx.doi.org/10.33407/lib.naes.718697.

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The paper presents a comparative analysis of the functionality of mobile applications of the augmented reality Da Vinci Machines AR, Electricity AR, Bridges AR, Geometry, the collection of VR models VictoryVR Science Curriculum and the digital collection Mozaik. The possibility of using these tools for educational purposes is explored, in particular, to construct cognitive tasks for students during the study of subjects in the natural and mathematical cycle. The indicated shortcomings are stated, didactic requirements for such educational activities are formulated. Among others, attention is focused on the following indicators: hardware, usability, variability of model parameters, interactivity, interdisciplinary use, and the ability to activate certain cognitive actions of students, degree/form of gamification. The educational potential of using interactive models and video is analyzed for both group and individual work with students. Examples of methodical developments are given.
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Ratmanski, Kiril, and Sergey Vecherin. Resilience in distributed sensor networks. Engineer Research and Development Center (U.S.), October 2022. http://dx.doi.org/10.21079/11681/45680.

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With the advent of cheap and available sensors, there is a need for intelligent sensor selection and placement for various purposes. While previous research was focused on the most efficient sensor networks, we present a new mathematical framework for efficient and resilient sensor network installation. Specifically, in this work we formulate and solve a sensor selection and placement problem when network resilience is also a factor in the optimization problem. Our approach is based on the binary linear programming problem. The generic formulation is probabilistic and applicable to any sensor types, line-of-site and non-line-of-site, and any sensor modality. It also incorporates several realistic constraints including finite sensor supply, cost, energy consumption, as well as specified redundancy in coverage areas that require resilience. While the exact solution is computationally prohibitive, we present a fast algorithm that produces a near-optimal solution that can be used in practice. We show how such formulation works on 2D examples, applied to infrared (IR) sensor networks designed to detect and track human presence and movements in a specified coverage area. Analysis of coverage and comparison of sensor placement with and without resilience considerations is also performed.
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Zaika, Oksana V., Tetiana A. Vakaliuk, Andrii V. Riabko, Roman P. Kukharchuk, Iryna S. Mintii, and Serhiy O. Semerikov. Selection of online tools for creating math tests. [б. в.], 2021. http://dx.doi.org/10.31812/123456789/4594.

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The article considers online tools for creating tests, which should be used when teaching mathematics in both higher education and general secondary education. Among the variety of online means of creating tests by the method of expert evaluation, three were identified, which allow conducting various tests both in the classroom and remotely, which are free and do not require special conditions for their use and which work on smartphones. The advantages and disadvantages of three online tools for creating tests Kahoot!, Quizizz, Classtime are analyzed, and a comparative description of the selected tools is given. Criteria for the selection of such tools were identified – functional-didactic and organizational. The following indicators belong to the functional-didactic: the presence of different types of questions, including open-ended; use of formulas, both in questions and in answers; use of pictures, both in questions and in answers; no restrictions on the length of questions and answers; instant receipt of results by the teacher, their evaluation and analysis; instant receipt of results by the respondent; to the organizational: the availability of a free version; no need to install the program; ease of use – characterizes the convenience and clarity of the interface for creating tests and their use; possibility of testing in online and offline mode; time limits, both for a single question and the whole test; random order of questions/answer options; instant demonstration of the correct answer to the respondent. With the help of expert evaluation, it was found that according to these criteria, Quizizz is the most appropriate for testing.
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Denys, R. M. L51712 Fracture Behavior of Large-Diameter Girth Welds - Effect of Weld Metal Yield Strength Part II. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), May 1994. http://dx.doi.org/10.55274/r0010121.

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Fitness for purpose girth defect assessments assume the presence of a single defect. This assumption is not always fulfilled. Welds may contain many small defects. These defects, when considered individually and without interaction, are generally innocuous. However, this may be a false conclusion as to the true strength or deformation capacity of the weld because neighbouring imperfections or defects may interact and may be more severe than each individual imperfection. When non-destructive examinations reveal multiple defects, a defect recategorisation procedure has to be applied to determine whether neighbouring defects will interact other under load. The interaction criteria of BS PD6493, ASME Boiler and Pressure Vessel Code Section XI and the Japanese fitness-of-purpose code WES 2805 are based on a combination of linear elastic fracture mechanics calculations and engineering judgement. The PD6493 and ASME XI rules are based on the principle that the increase in the stress intensity magnification caused by interaction of neigbouring defects should be limited to 20% (PD 6493) and 6% (ASME XI), whereas the WES criterion is based on the principle that the stress intensity magnification or CTOD value of the interacting neighbouring defects should be limited to 20% of the shortest defect. As the fracture behaviour of line pipe girth welds differs from linear elastic behaviour, it is expected that the existing rules are not necessarily applicable for elastic-plastic or plastic material behaviours. This consideration suggests that there exist a need for developing criteria which permit plasticity effects to be incorporated. The mathematical treatment of multiple defects under elastic-plastic and or plastic fracture conditions is a complex issue because it is not possible to predict yielding behaviour and make a distinction between local and ligament collapse. Because of this limitation, it is thus necessary to employ large scale tensile tests in which the interaction effects can be reproduced. In persuing this approach, it is further possible: (a) to verify and establish the conservatism built into the existing interaction criteria. (b) to formulate alternative interaction criteria for elastic-plastic or plastic behavior. The goal of this study was to obtain information on the failure behavior of girth welds containing two coplanar fatigue pre-cracked defects. The results were correlated with tests on welds containing a single crack to determine the engineering significance of existing defect interaction rules under elastic-plastic and plastic fracture conditions.
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L51900 Development of User Friendly Models for Design of CP Systems for Buried Pipelines (CP3D). Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), January 2008. http://dx.doi.org/10.55274/r0010911.

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CP3D is a complex and powerful piece of modeling software, and it is very computationally intensive. This document is intended to provide an introductory guide to CP3D. The objective is to develop a model that can be used to calculate the effect of impressed-current and sacrificial anode cathodic protection (CP) of coated and bare pipelines. Conventional anode resistance formulas, developed for bare pipes protected by remote anodes, are not appropriate for calculating the cathodic protection requirements for multiple pipes, pipes with coating holidays, and pipelines protected by different anode systems or with anodes placed in close proximity to the pipe. The mathematical model must be suitable for use by a corrosion engineer. Availability of a model for CP could greatly reduce the amount of fieldwork needed to determine the best method for correcting a problem with cathodically protected pipelines or designing a CP system for new pipelines. The model could be used to determine the maximum size of a holiday that could be protected by a given CP system, to determine the influence of a local variation of soil resistivity on protection, and as a tool for training corrosion engineers on the influence of design changes in CP systems.
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