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Journal articles on the topic 'Analytic Calculus'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Rota, Gian-Carlo. "Analytic functional calculus." Advances in Mathematics 55, no. 2 (1985): 209. http://dx.doi.org/10.1016/0001-8708(85)90023-4.

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2

Brook, J. W., and Howard Anton. "Calculus with Analytic Geometry." Mathematical Gazette 73, no. 464 (1989): 154. http://dx.doi.org/10.2307/3619693.

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3

Lord, Nick, A. Mizrahi, and M. Sullivan. "Calculus and Analytic Geometry." Mathematical Gazette 75, no. 472 (1991): 237. http://dx.doi.org/10.2307/3620294.

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4

Suffield, M., G. B. Thomas, and R. L. Finney. "Calculus and Analytic Geometry." Mathematical Gazette 69, no. 447 (1985): 59. http://dx.doi.org/10.2307/3616468.

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5

Dudley, Underwood, and George F. Simmons. "Calculus with Analytic Geometry." American Mathematical Monthly 95, no. 9 (1988): 888. http://dx.doi.org/10.2307/2322923.

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6

Ungar, Peter, Al Shenk, M. A. Munem, D. J. Foulis, and Howard Anton. "Calculus and Analytic Geometry." American Mathematical Monthly 93, no. 3 (1986): 221. http://dx.doi.org/10.2307/2323355.

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7

Goodwillie, Thomas G. "Calculus II: Analytic functors." K-Theory 5, no. 4 (1991): 295–332. http://dx.doi.org/10.1007/bf00535644.

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8

Bains, R. "Calculus and analytic geometry." Advances in Engineering Software and Workstations 13, no. 1 (1991): 53. http://dx.doi.org/10.1016/0961-3552(91)90052-6.

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9

Xu, Dongpo, Cyrus Jahanchahi, Clive C. Took, and Danilo P. Mandic. "Enabling quaternion derivatives: the generalized HR calculus." Royal Society Open Science 2, no. 8 (2015): 150255. http://dx.doi.org/10.1098/rsos.150255.

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Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutati

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10

Brook, J. W., and Louis Leithold. "The Calculus with Analytic Geometry." Mathematical Gazette 71, no. 456 (1987): 162. http://dx.doi.org/10.2307/3616522.

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11

Kalia, R. N. "Fractional calculus and analytic functions." Integral Transforms and Special Functions 4, no. 1-2 (1996): 203–10. http://dx.doi.org/10.1080/10652469608819106.

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12

Le Merdy, Christian. "Two Results About H∞ Functional Calculus on Analytic umd Banach Spaces." Journal of the Australian Mathematical Society 74, no. 3 (2003): 351–78. http://dx.doi.org/10.1017/s1446788700003360.

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AbstractLet X be a Banach space with the analytic UMD property, and let A and B be two commuting sectorial operators on X which admit bounded H∞ functional calculi with respect to angles θ1 and θ2 satisfying θ1 + θ2 > π. It was proved by Kalton and Weis that in this case, A + B is closed. The first result of this paper is that under the same conditions, A + B actually admits a bounded H∞ functional calculus. Our second result is that given a Banach space X and a number 1 ≦ p < ∞, the derivation operator on the vector valued Hardy space Hp (R; X) admits a bounded H∞ functional calculus if

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13

Ungar, Peter. "Calculus and Analytic Geometry. By AI Shenk,Calculus with Analytic Geometry. By M.A. Munem and D. J. Foulis,Calculus with Analytic Geometry. By Howard Anton." American Mathematical Monthly 93, no. 3 (1986): 221–30. http://dx.doi.org/10.1080/00029890.1986.11971793.

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14

Privault, Nicolas. "An analytic approach to stochastic calculus." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 326, no. 3 (1998): 353–58. http://dx.doi.org/10.1016/s0764-4442(97)82994-1.

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15

Djordjević, Dragan S. "Fréchet Derivative and Analytic Functional Calculus." Bulletin of the Malaysian Mathematical Sciences Society 43, no. 2 (2019): 1205–12. http://dx.doi.org/10.1007/s40840-019-00736-6.

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16

Zach, Richard. "Non-Analytic Tableaux for Chellas's Conditional Logic CK and Lewis's Logic of Counterfactuals VC." Australasian Journal of Logic 15, no. 3 (2018): 609. http://dx.doi.org/10.26686/ajl.v15i3.4780.

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Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.

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17

Siddiqi, Jamil A., and Most{éfa Ider. "A symbolic calculus for analytic Carleman classes." Proceedings of the American Mathematical Society 99, no. 2 (1987): 347. http://dx.doi.org/10.1090/s0002-9939-1987-0870798-0.

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18

Squillante, Massimo, and Aldo G. S. Ventre. "On the analytic setting of C-calculus." Journal of Mathematical Analysis and Applications 165, no. 2 (1992): 539–49. http://dx.doi.org/10.1016/0022-247x(92)90057-k.

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19

Fernandez, Arran, Mehmet Ali Özarslan, and Dumitru Baleanu. "On fractional calculus with general analytic kernels." Applied Mathematics and Computation 354 (August 2019): 248–65. http://dx.doi.org/10.1016/j.amc.2019.02.045.

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20

Breaz, Nicoleta, Daniel Breaz, and Shigeyoshi Owa. "Fractional Calculus of Analytic Functions Concerned with Möbius Transformations." Journal of Function Spaces 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/6086409.

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LetAbe the class of functionsf(z)in the open unit diskUwithf(0)=0andf′(0)=1. Also, letw(ζ)be a Möbius transformation inUfor somez∈U. Applying the Möbius transformations, we consider some properties of fractional calculus (fractional derivatives and fractional integrals) off(z)∈A. Also, some interesting examples for fractional calculus are given.

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21

Saliu, Afis, Khalida Inayat Noor, Saqib Hussain, and Maslina Darus. "On Quantum Differential Subordination Related with Certain Family of Analytic Functions." Journal of Mathematics 2020 (November 10, 2020): 1–13. http://dx.doi.org/10.1155/2020/6675732.

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Recently, there is a rapid increase of research in the area of Quantum calculus (known as q -calculus) due to its widespread applications in many areas of study, such as geometric functions theory. To this end, using the concept of q -conic domains of Janowski type as well as q - calculus, new subclasses of analytic functions are introduced. This family of functions extends the notion of α -convex and quasi-convex functions. Furthermore, a coefficient inequality, sufficiency criteria, and covering results for these novel classes are derived. Besides, some remarkable consequences of our investi

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22

Patra, M. I., and S. V. Sharyn. "Operator calculus on the class of Sato’s hyperfunctions." Carpathian Mathematical Publications 5, no. 1 (2013): 114–20. http://dx.doi.org/10.15330/cmp.5.1.114-120.

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We construct a functional calculus for generators of analytic semigroups of operators on a Banach space. The symbol class of the calculus consists of hyperfunctions with a compact support in $[0,\infty)$. Domain of constructed calculus is dense in the Banach space.

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23

Dudley, Underwood. "Calculus with Analytic Geometry. By George F. Simmons." American Mathematical Monthly 95, no. 9 (1988): 888–92. http://dx.doi.org/10.1080/00029890.1988.11972109.

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24

Curto, Raúl E. "Book Review: Analytic functional calculus and spectral decompositions." Bulletin of the American Mathematical Society 14, no. 1 (1986): 136–46. http://dx.doi.org/10.1090/s0273-0979-1986-15421-2.

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25

Fernandez, Arran, and Ceren Ustaoğlu. "On some analytic properties of tempered fractional calculus." Journal of Computational and Applied Mathematics 366 (March 2020): 112400. http://dx.doi.org/10.1016/j.cam.2019.112400.

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26

Srivastava, H. M., Shigeyoshi Owa, and Tadayuki Sekine. "Analytic function theory, fractional calculus and their applications." Applied Mathematics and Computation 187, no. 1 (2007): 1–2. http://dx.doi.org/10.1016/j.amc.2006.08.095.

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27

Pashaev, Oktay K. "Quantum calculus of Fibonacci divisors and infinite hierarchy of Bosonic–Fermionic Golden quantum oscillators." International Journal of Geometric Methods in Modern Physics 18, no. 05 (2021): 2150075. http://dx.doi.org/10.1142/s0219887821500754.

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Starting from divisibility problem for Fibonacci numbers, we introduce Fibonacci divisors, related hierarchy of Golden derivatives in powers of the Golden Ratio and develop corresponding quantum calculus. By this calculus, the infinite hierarchy of Golden quantum oscillators with integer spectrum determined by Fibonacci divisors, the hierarchy of Golden coherent states and related Fock–Bargman representations in space of complex analytic functions are derived. It is shown that Fibonacci divisors with even and odd [Formula: see text] describe Golden deformed bosonic and fermionic quantum oscill

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28

Ezeafulukwe, Uzoamaka A., and Maslina Darus. "A Note on q–Calculus." Fasciculi Mathematici 55, no. 1 (2015): 53–63. http://dx.doi.org/10.1515/fascmath-2015-0014.

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Abstract In this article, we let PCq denote the class of q-convex functions. Certain analytic properties of the class PCq are studied. The maximum of the absolute value of the Fekete-Szegö functional is briey determined.

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29

Sekine, Tadayuki. "Generalization of certain subclasses of analytic functions." International Journal of Mathematics and Mathematical Sciences 10, no. 4 (1987): 725–32. http://dx.doi.org/10.1155/s0161171287000826.

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We introduce the subclassTj(n,m,α)of analytic functions with negative coefficients by the operatorDn. Coefficient inequalities and distortion theorems of functions inTj(n,m,α)are determind. Further, distortion theorems for fractional calculus of functions inTj(n,m,α)are obtained.

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30

Hill, Brian, and Francesca Poggiolesi. "An Analytic Calculus for the Intuitionistic Logic of Proofs." Notre Dame Journal of Formal Logic 60, no. 3 (2019): 353–93. http://dx.doi.org/10.1215/00294527-2019-0008.

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31

Addad, Boussad, Saïd Amari, and Jean-Jacques Lesage. "Analytic Calculus of Response Time in Networked Automation Systems." IEEE Transactions on Automation Science and Engineering 7, no. 4 (2010): 858–69. http://dx.doi.org/10.1109/tase.2010.2047499.

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32

Uiterdijk, Marc. "A functional calculus for analytic generators ofC 0-groups." Integral Equations and Operator Theory 36, no. 3 (2000): 349–69. http://dx.doi.org/10.1007/bf01213928.

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33

Ma, Ji, Mehmet A. Orgun, and Kamel Adi. "An analytic tableau calculus for a temporalised belief logic." Journal of Applied Logic 9, no. 4 (2011): 289–304. http://dx.doi.org/10.1016/j.jal.2011.08.003.

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34

Sekine, Tadayuki, Shigeyoshi Owa, and Kazuyuki Tsurumi. "Integral means of certain analytic functions for fractional calculus." Applied Mathematics and Computation 187, no. 1 (2007): 425–32. http://dx.doi.org/10.1016/j.amc.2006.08.142.

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35

Fernandez, Arran, and Iftikhar Husain. "Modified Mittag-Leffler Functions with Applications in Complex Formulae for Fractional Calculus." Fractal and Fractional 4, no. 3 (2020): 45. http://dx.doi.org/10.3390/fractalfract4030045.

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Mittag-Leffler functions and their variations are a popular topic of study at the present time, mostly due to their applications in fractional calculus and fractional differential equations. Here we propose a modification of the usual Mittag-Leffler functions of one, two, or three parameters, which is ideally suited for extending certain fractional-calculus operators into the complex plane. Complex analysis has been underused in combination with fractional calculus, especially with newly developed operators like those with Mittag-Leffler kernels. Here we show the natural analytic continuations

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36

Noor, Khalida. "On Analytic Functions Involving the q-Ruscheweyeh Derivative." Fractal and Fractional 3, no. 1 (2019): 10. http://dx.doi.org/10.3390/fractalfract3010010.

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In this paper, we use concepts of q-calculus to introduce a certain type of q-difference operator, and using it define some subclasses of analytic functions. Inclusion relations, coefficient result, and some other interesting properties of these classes are studied.

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37

Aouf, M. K., та T. M. Seoudy. "Некоторые результаты о подчинении для одного функционального класса, определяемого $q$-разностным оператором типа Салагина". Владикавказский математический журнал, № 4() (22 грудня 2020): 7–15. http://dx.doi.org/10.46698/q5183-3412-9769-d.

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The theory of the basic quantum calculus (that is, the basic q-calculus) plays important roles in many diverse areas of the engineering, physical and mathematical science. Making use of the basic definitions and concept details of the q-calculus, Govindaraj and Sivasubramanian [10] defined the Salagean type q-difference (q-derivative) operator. In this paper, we introduce a certain subclass of analytic functions with complex order in the open unit disk by applying the Salagean type q-derivative operator in conjunction with the familiar principle of subordination between analytic functions. Als

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38

Shi, Lei, Muhammad Ghaffar Khan, and Bakhtiar Ahmad. "Some Geometric Properties of a Family of Analytic Functions Involving a Generalized q-Operator." Symmetry 12, no. 2 (2020): 291. http://dx.doi.org/10.3390/sym12020291.

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In analysis, the introduction of q-calculus has been a revelation. It has a deep impact on various concepts and applications of pure and applied sciences. In this article we investigate certain geometric properties relating to convolution of functions of a newly defined class of analytic functions. The important region of the lemniscate of Bernoulli is considered. Here we utilize concepts of q-calculus which enhances and generalizes the vitality of this research work. In the same context we study the Fekete–Szegö problem.

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39

FISCHER, TORSTEN, and HANS HENRIK RUGH. "Transfer operators for coupled analytic maps." Ergodic Theory and Dynamical Systems 20, no. 1 (2000): 109–43. http://dx.doi.org/10.1017/s0143385700000079.

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We consider analytically coupled circle maps (uniformly expanding and analytic) on the ${\mathbb Z}^d$-lattice with exponentially decaying interaction. We introduce Banach spaces for the infinite-dimensional system that include measures whose finite-dimensional marginals have analytic, exponentially bounded densities. Using residue calculus and ‘cluster expansion’-like techniques we define transfer operators on these Banach spaces. We get a unique (in the considered Banach spaces) probability measure that exhibits exponential decay of correlations.

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40

Chalendar, I., J. Esterle, and J. R. Partington. "Estimates near the origin for functional calculus on analytic semigroups." Journal of Functional Analysis 275, no. 3 (2018): 698–711. http://dx.doi.org/10.1016/j.jfa.2018.03.012.

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41

Matsuzawa, Tadato. "A calculus approach to hyperfunctions III." Nagoya Mathematical Journal 118 (June 1990): 133–53. http://dx.doi.org/10.1017/s0027763000003032.

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In the previous papers, [18] and [19], we have given some basis of a calculus approach to hyperfunctions. We have taken hyperfunctions with the compact support as initial values of the solutions of the heat equation. More precisely, let A′[K] be the space of analytic functionals supported by a compact subset K of Rn and let E(x, t) be the n-dimensional heat kernel given by.

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42

Popescu, Gelu. "!COMMUTANT LIFTING, TENSOR ALGEBRAS, AND FUNCTIONAL CALCULUS." Proceedings of the Edinburgh Mathematical Society 44, no. 2 (2001): 389–406. http://dx.doi.org/10.1017/s0013091598001059.

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AbstractA non-commutative multivariable analogue of Parrott’s generalization of the Sz.-Nagy–Foia\c{s} commutant lifting theorem is obtained. This yields Tomita-type commutant results and interpolation theorems (e.g. Sarason, Nevanlinna–Pick, Carathéodory) for $F_n^\infty\,\bar{\otimes}\,\M$, the weakly-closed algebra generated by the spatial tensor product of the non-commutative analytic Toeplitz algebra $F_n^\infty$ and an arbitrary von Neumann algebra $\M$. In particular, we obtain interpolation theorems for bounded analytic functions from the open unit ball of $\mathbb{C}^n$ into a von Neu

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43

Haciomeroglu, Erhan Selcuk, Leslie Aspinwall, and Norma C. Presmeg. "Connecting Research to Teaching: Visual and Analytic Thinking in Calculus." Mathematics Teacher 103, no. 2 (2009): 140–45. http://dx.doi.org/10.5951/mt.103.2.0140.

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A frequent message in mathematics education focuses on the benefits of multiple representations of mathematical concepts (Aspinwall and Shaw 2002). The National Council of Teachers of Mathematics, for instance, claims that “different representations support different ways of thinking about and manipulating mathematical objects” (NCTM 2000, p. 360). A recommendation conveyed in the ongoing calculus reform movement is that students should use multiple representations and make connections among them so that they can develop deeper and more robust understanding of the concepts.

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44

Raina, R. K., and H. M. Srivastava. "Some subclasses of analytic functions associated with fractional calculus operators." Computers & Mathematics with Applications 37, no. 9 (1999): 73–84. http://dx.doi.org/10.1016/s0898-1221(99)00115-7.

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45

French, Rohan. "A Simple Sequent Calculus for Angell’s Logic of Analytic Containment." Studia Logica 105, no. 5 (2017): 971–94. http://dx.doi.org/10.1007/s11225-017-9719-y.

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46

Popescu, Gelu. "Functional calculus and multi-analytic models on regular Λ-polyballs". Journal of Mathematical Analysis and Applications 491, № 1 (2020): 124312. http://dx.doi.org/10.1016/j.jmaa.2020.124312.

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47

Haciomeroglu, Erhan Selcuk, Leslie Aspinwall, and Norma C. Presmeg. "Connecting Research to Teaching: Visual and Analytic Thinking in Calculus." Mathematics Teacher 103, no. 2 (2009): 140–45. http://dx.doi.org/10.5951/mt.103.2.0140.

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Abstract:

A frequent message in mathematics education focuses on the benefits of multiple representations of mathematical concepts (Aspinwall and Shaw 2002). The National Council of Teachers of Mathematics, for instance, claims that “different representations support different ways of thinking about and manipulating mathematical objects” (NCTM 2000, p. 360). A recommendation conveyed in the ongoing calculus reform movement is that students should use multiple representations and make connections among them so that they can develop deeper and more robust understanding of the concepts.

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48

Oanta, Emil, Eliodor Constantinescu, Alexandra Raicu, and Tiberiu Axinte. "Analytic General Solution Employed to Calculate the Geometrical Characteristics in Structural Problems." Advanced Materials Research 1036 (October 2014): 697–702. http://dx.doi.org/10.4028/www.scientific.net/amr.1036.697.

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The automatic calculus in structural problems was a constant concern of the authors, several models of the phenomena being based on algorithmic generalizations of the analytical methods, where the solutions were either ‘exact’ or numerical. The calculus of the geometrical characteristics is important, being closely related to the calculus of the stresses, of the displacements, of the bucking and in other structural problems. This is why an algorithm designed to compute the geometrical characteristics, must take into account all these aspects. A first general and original solution was to create

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49

Selvakumaran, K. A., Sunil Dutt Purohit, and Aydin Secer. "Majorization for a Class of Analytic Functions Defined byq-Differentiation." Mathematical Problems in Engineering 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/653917.

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We introduce a new class of multivalent analytic functions defined by usingq-differentiation and fractionalq-calculus operators. Further, we investigate majorization properties for functions belonging to this class. Also, we point out some new and known consequences of our main result.

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50

Matsuzawa, Tadato. "A calculus approach to hyperfunctions I." Nagoya Mathematical Journal 108 (December 1987): 53–66. http://dx.doi.org/10.1017/s0027763000002646.

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In this paper, we shall give a new characterization of hyperfunctions without algebraic method and apply to give simpler proofs to problems discussed in [3], Chapter 9. In [3], the spaces of hyperfunctions A′(K) with compact support in K ⊂ Rn (n ≧ 1) is considered as the dual of the space A(K) of functions which are real analytic near K. Each element u of A′(K) is characterized as a density of a double layer potential in Rn × R.

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