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Journal articles on the topic 'Sequences (Mathematics) Summability theory. Transformations (Mathematics)'

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Published: 4 June 2021

Last updated: 3 February 2022

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1

SAVAS, EKREM. "ALMOST CONVERGENCE AND ALMOST SUMMABILITY." Tamkang Journal of Mathematics 21, no. 4 (1990): 327–32. http://dx.doi.org/10.5556/j.tkjm.21.1990.4676.

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2

Patterson, Richard F. "Four dimensional characterization of bounded double sequences." Tamkang Journal of Mathematics 35, no. 2 (2004): 129–34. http://dx.doi.org/10.5556/j.tkjm.35.2004.214.

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In 1945 Brudno presented the following important theorem: If $A$ and $B$ are regular summability matrix methods such that every bounded sequence summed by $A$ is also summed by $B$, then it is summed by $B$ to the same value. R. G. Cooke suggested that a simpler proof would be desirable. Petersen presented such a proof. The goal of the paper is to present an accessible multidimensional analog of Brudno theorem for double sequences using four dimensional matrix transformations.

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Patterson, Richard, and Ekrem Savaş. "Uniformly summable double sequences." Studia Scientiarum Mathematicarum Hungarica 44, no. 1 (2007): 147–58. http://dx.doi.org/10.1556/sscmath.2006.1009.

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In 1945 Brudno presented the following important theorem: If A and B are regular summability matrix methods such that every bounded sequence summed by A is also summed by B , then it is summed by B to the same value. In 1960 Petersen extended Brudno’s theorem by using uniformly summable methods. The goal of this paper is to extend Petersen’s theorem to double sequences by using four dimensional matrix transformations and notion of uniformly summable methods for double sequences. In addition to this extension we shall also present an accessible analogue of this theorem.

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Selvaraj, Chikkanna, and Suguna Selvaraj. "Matrix Transformations Based on Dirichlet Convolution." Canadian Mathematical Bulletin 40, no. 4 (1997): 498–508. http://dx.doi.org/10.4153/cmb-1997-059-6.

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AbstractThis paper is a study of summability methods that are based on Dirichlet convolution. If f(n) is a function on positive integers and x is a sequence such that then x is said to be Af-summable to L. The necessary and sufficient condition for the matrix Af to preserve bounded variation of sequences is established. Also, the matrix Af is investigated as ℓ − ℓ and G − G mappings. The strength of the Af-matrix is also discussed.

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5

Yildiz, Sebnem. "An absolute matrix summability of infinite series and Fourier series." Boletim da Sociedade Paranaense de Matemática 38, no. 7 (2019): 49–58. http://dx.doi.org/10.5269/bspm.v38i7.46594.

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The aim of this paper is to generalize a main theorem concerning weighted mean summability to absolute matrix summability which plays a vital role in summability theory and applications to the other sciences by using quasi-$f$-power sequences.

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Parida, P., S. K. Paikray, Hemen Dutta, B. B. Jena, and M. Dash. "Tauberian theorems for Cesàro summability of nth sequences." Filomat 32, no. 11 (2018): 3993–4004. http://dx.doi.org/10.2298/fil1811993p.

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Tauberian theorem provides a criterion for the convergence of non convergent (summable) sequences. In this paper, we established a Tauberian theorem for nth real sequences via Ces?ro summability by using de la Vall?e Poussin mean and slow oscillation. The discussion and findings are capable to unify several useful concepts in the literature, and should also provide nontrivial extension of several results. Some examples are incorporated in support of our definitions and results. The findings are further expected to be helpful in designing and study several other interesting problems in summabil

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JACQUES, MATTHEW, and IAN SHORT. "Repeated compositions of Möbius transformations." Ergodic Theory and Dynamical Systems 40, no. 2 (2018): 437–52. http://dx.doi.org/10.1017/etds.2018.43.

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We consider a class of dynamical systems generated by finite sets of Möbius transformations acting on the unit disc. Compositions of such Möbius transformations give rise to sequences of transformations that are used in the theory of continued fractions. In that theory, the distinction between sequences of limit-point type and sequences of limit-disc type is of central importance. We prove that sequences of limit-disc type only arise in exceptional circumstances, and we give necessary and sufficient conditions for a sequence to be of limit-disc type. We also calculate the Hausdorff dimension o

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8

Fricke, G. H., and J. A. Fridy. "Matrix Summability of Geometrically Dominated Series." Canadian Journal of Mathematics 39, no. 3 (1987): 568–82. http://dx.doi.org/10.4153/cjm-1987-026-9.

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One of the common uses of summability theory is found in its applications to power series. A partial listing such as [l]-[5], [13], and [15]-[17] might serve to remind us of the many instances of summability theory applied to power series. In some studies, the summability transformation is applied to the sequence of partial sums of the power series, while in others it is applied to the general term akzk as a series-to-series transformation. In [2] and [5] the transformation is applied to the coefficient sequence of the Taylor series. In the present study we investigate matrix transformations t

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Buntinas, Martin, and Naza Tanović-Miller. "Strong Boundedness and Strong Convergence in Sequence Spaces." Canadian Journal of Mathematics 43, no. 5 (1991): 960–74. http://dx.doi.org/10.4153/cjm-1991-053-8.

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AbstractStrong convergence has been investigated in summability theory and Fourier analysis. This paper extends strong convergence to a topological property of sequence spaces E. The more general property of strong boundedness is also defined and examined. One of the main results shows that for an FK-space E which contains all finite sequences, strong convergence is equivalent to the invariance property E = ℓ ν0. E with respect to coordinatewise multiplication by sequences in the space ℓν0 defined in the paper. Similarly, strong boundedness is equivalent to another invariance E = ℓν.E. The res

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10

Gökçe, Fadime, та Mehmet Ali Sarigöl. "Extension of Maddox’s space l(μ) with Nörlund means". Asian-European Journal of Mathematics 12, № 06 (2019): 2040005. http://dx.doi.org/10.1142/s1793557120400057.

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In this paper, we introduce a new series space [Formula: see text] as the set of all series summable by the absolute Nörlund summability method, which includes the spaces [Formula: see text] and [Formula: see text] of Maddox [Spaces of strongly summable sequences, Quart. J. Math. 18(1) (1967) 345–355], Sarıgöl [Spaces of series summable by absolute Cesàro and matrix operators, Comm. Math Appl. 7(1) (2016) 11–22], Hazar and Sarıgöl [On absolute Nörlund spaces and matrix operators, Acta Math. Sinica, (English Ser.) 34(5) (2018) 812–826], respectively. Also, we study its some algebraic and topolo

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11

Soltani, A. R., and Z. Shishebor. "Weakly Periodic Sequences of Bounded Linear Transformations: A Spectral Characterization." gmj 6, no. 1 (1999): 91–98. http://dx.doi.org/10.1515/gmj.1999.91.

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Abstract Let X and Y be two Hilbert spaces, and the space of bounded linear transformations from X into Y. Let {An } ⊂ be a weakly periodic sequence of period T. Spectral theory of weakly periodic sequences in a Hilbert space is studied by H. L. Hurd and V. Mandrekar (Spectral theory of periodically and quasi-periodically stationary SαS sequences, University of North Carolina, Chapel Hill, 1991). In this work we proceed further to characterize {An } by a positive measure μ and a number T of -valued functions a 0, . . . , a T–1; in the spectral form , where and Φ is an -valued Borel set functio

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12

KATOK, SVETLANA, and ILIE UGARCOVICI. "Applications of (a,b)-continued fraction transformations." Ergodic Theory and Dynamical Systems 32, no. 2 (2011): 739–61. http://dx.doi.org/10.1017/s0143385711000460.

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AbstractWe describe a general method of arithmetic coding of geodesics on the modular surface based on the study of one-dimensional Gauss-like maps associated to a two-parameter family of continued fractions introduced in [Katok and Ugarcovici. Structure of attractors for (a,b)-continued fraction transformations.J. Modern Dynamics4(2010), 637–691]. The finite rectangular structure of the attractors of the natural extension maps and the corresponding ‘reduction theory’ play an essential role. In special cases, when an (a,b)-expansion admits a so-called ‘dual’, the coding sequences are obtained

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13

Şevli̇, H., and L. Leindler. "On the absolute summability factors of infinite series involving quasi-power-increasing sequences." Computers & Mathematics with Applications 57, no. 5 (2009): 702–9. http://dx.doi.org/10.1016/j.camwa.2008.11.007.

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14

Aebischer, Beat. "The Limiting Behavior of Sequences of Quasiconformal Mappings." Canadian Mathematical Bulletin 33, no. 4 (1990): 494–502. http://dx.doi.org/10.4153/cmb-1990-079-0.

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AbstractThe limiting behavior of sequences of quasiconformal homeomorphisms of the n-sphere Sn is studied using a substitute to the Poincaré extension of Möbius transformations introduced by Tukia. Adapted versions of the limit set and the conical limit set known in the theory of Kleinian groups are utilized. Most of the results also hold for families of homeomorphisms of Sn with the convergence property introduced by Gehring and Martin.

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15

CHU, QING, and NIKOS FRANTZIKINAKIS. "Pointwise convergence for cubic and polynomial multiple ergodic averages of non-commuting transformations." Ergodic Theory and Dynamical Systems 32, no. 3 (2011): 877–97. http://dx.doi.org/10.1017/s014338571100006x.

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AbstractWe study the limiting behavior of multiple ergodic averages involving several, not necessarily commuting, measure-preserving transformations. We work on two types of averages, one that uses iterates along combinatorial parallelepipeds, and another that uses iterates along shifted polynomials. We prove pointwise convergence in both cases, thus answering a question of I. Assani in the former case, and extending the results of B. Host and B. Kra, and A. Leibman in the latter case. Our argument is based on some elementary uniformity estimates of general bounded sequences, decomposition res

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16

Bartoszewicz, Artur, Pratulananda Das, and Szymon Gła̧b. "On matrix summability of spliced sequences and A-density of points." Linear Algebra and its Applications 487 (December 2015): 22–42. http://dx.doi.org/10.1016/j.laa.2015.08.031.

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Talo, Özer, and Feyzi Başar. "Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations." Computers & Mathematics with Applications 58, no. 4 (2009): 717–33. http://dx.doi.org/10.1016/j.camwa.2009.05.002.

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18

Fritzsche, Bernd, Bernd Kirstein та Conrad Mädler. "Transformations of matricial α -Stieltjes non-negative definite sequences". Linear Algebra and its Applications 439, № 12 (2013): 3893–933. http://dx.doi.org/10.1016/j.laa.2013.10.002.

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19

Liu, Lei, Xianwei Zheng, Jingwen Yan, and Xiaodong Niu. "Bessel Sequences and Its F-Scalability." Advances in Applied Mathematics and Mechanics 7, no. 4 (2015): 441–53. http://dx.doi.org/10.4208/aamm.2014.m652.

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AbstractFrame theory, which contains wavelet analysis and Gabor analysis, has become a powerful tool for many applications of mathematics, engineering and quantum mechanics. The study of extension principles of Bessel sequences to frames is important in frame theory. This paper studies transformations on Bessel sequences to generate frames and Riesz bases in terms of operators and scalability. Some characterizations of operators that mapping Bessel sequences to frames and Riesz bases are given. We introduce the definitions of F-scalable and P-scalable Bessel sequences. F-scalability and P-scal

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20

MILENKOVIC, VICTOR, ELISHA SACKS, and STEVEN TRAC. "PLANAR SHAPE MANIPULATION USING APPROXIMATE GEOMETRIC PRIMITIVES." International Journal of Computational Geometry & Applications 23, no. 01 (2013): 1–27. http://dx.doi.org/10.1142/s0218195913500015.

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We present robust algorithms for set operations and affine transformations on curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is O (n log n + k) for an input of size n with k = O (n2) consistency violations. The output is as accurate as the geometric primitives. We validate our algorithms using sequences of six set operations and affine transforms on shapes bounded by algebraic curve segments of degree 1 to 6. We test generic and degenerate inputs.

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21

Kirişci, Murat. "The Hahn Sequence Space Defined by the Cesáro Mean." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/817659.

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The -space of all sequences is given as such that converges and is a null sequence which is called the Hahn sequence space and is denoted by . Hahn (1922) defined the space and gave some general properties. G. Goes and S. Goes (1970) studied the functional analytic properties of this space. The study of Hahn sequence space was initiated by Chandrasekhara Rao (1990) with certain specific purpose in the Banach space theory. In this paper, the matrix domain of the Hahn sequence space determined by the Cesáro mean first order, denoted by , is obtained, and some inclusion relations and some topolog

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22

Morgan-Lang, Connor, Ryan McLaughlin, Zachary Armstrong, Grace Zhang, Kevin Chan, and Steven J. Hallam. "TreeSAPP: the Tree-based Sensitive and Accurate Phylogenetic Profiler." Bioinformatics 36, no. 18 (2020): 4706–13. http://dx.doi.org/10.1093/bioinformatics/btaa588.

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Abstract Motivation Microbial communities drive matter and energy transformations integral to global biogeochemical cycles, yet many taxonomic groups facilitating these processes remain poorly represented in biological sequence databases. Due to this missing information, taxonomic assignment of sequences from environmental genomes remains inaccurate. Results We present the Tree-based Sensitive and Accurate Phylogenetic Profiler (TreeSAPP) software for functionally and taxonomically classifying genes, reactions and pathways from genomes of cultivated and uncultivated microorganisms using refere

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23

PETTOROSSI, ALBERTO, MAURIZIO PROIETTI, and VALERIO SENNI. "Transformations of logic programs on infinite lists." Theory and Practice of Logic Programming 10, no. 4-6 (2010): 383–99. http://dx.doi.org/10.1017/s1471068410000177.

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AbstractWe consider an extension of logic programs, called ω-programs, that can be used to define predicates overinfinite lists. ω-programs allow us to specify properties of the infinite behavior of reactive systems and, in general, properties of infinite sequences of events. The semantics of ω-programs is an extension of the perfect model semantics. We present variants of the familiar unfold/fold rules which can be used for transforming ω-programs. We show that these new rules are correct, that is, their application preserves the perfect model semantics. Then we outline a general methodology

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24

Ustimenko, Vasyl. "Explicit constructions of extremal graphs and new multivariate cryptosystems." Studia Scientiarum Mathematicarum Hungarica 52, no. 2 (2015): 185–204. http://dx.doi.org/10.1556/012.2015.52.2.1312.

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New multivariate cryptosystems are introduced. Sequences f(n) of bijective polynomial transformations of bijective multivariate transformations of affine spaces Kn, n = 2, 3, ... , where K is a finite commutative ring with special properties, are used for the constructions of cryptosystems. On axiomatic level, the concept of a family of multivariate maps with invertible decomposition is proposed. Such decomposition is used as private key in a public key infrastructure. Requirements of polynomiality of degree and density allow to estimate the complexity of encryption procedure for a public user

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25

Visnyai, T. "Convergence fields of regular matrix transformations of sequences of elements of Banach spaces." Miskolc Mathematical Notes 7, no. 1 (2006): 101. http://dx.doi.org/10.18514/mmn.2006.127.

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26

Gallas, Jason A. C. "Equivalence among orbital equations of polynomial maps." International Journal of Modern Physics C 29, no. 09 (2018): 1850082. http://dx.doi.org/10.1142/s0129183118500821.

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This paper shows that orbital equations generated by iteration of polynomial maps do not necessarily have a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear transformations. Five direct and five inverse transformations are established explicitly between a pair of orbits defined by cyclic quintic polynomials with real roots and minimum discriminant. In addition, infinite sequences of transformations generated recursively are introduced and shown to produce unlimited supplies of equivalent orbital equations. Such transform

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27

Orhan, Sevda, Fadime Dirik, and Kamil Demirci. "A Korovkin-type approximation theorem for double sequences of positive linear operators of two variables in statistical $A$-summability sense." Miskolc Mathematical Notes 15, no. 2 (2014): 625. http://dx.doi.org/10.18514/mmn.2014.658.

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28

Melamed, Benjamin. "The empirical TES methodology: modeling empirical time series." Journal of Applied Mathematics and Stochastic Analysis 10, no. 4 (1997): 333–53. http://dx.doi.org/10.1155/s1048953397000403.

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TES (Transform-Expand-Sample) is a versatile class of stochastic sequences defined via an autoregressive scheme with modulo-1 reduction and additional transformations. The scope of TES encompasses a wide variety of sample path behaviors, which in turn give rise to autocorrelation functions with diverse functional forms - monotone, oscillatory, alternating, and others. TES sequences are readily generated on a computer, and their autocorrelation functions can be numerically computed from accurate analytical formulas at a modest computational cost.This paper presents the empirical TES modeling me

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Jagerman, David L., and Benjamin Melamed. "On Markovian traffic with applications to TES processes." Journal of Applied Mathematics and Stochastic Analysis 7, no. 3 (1994): 373–96. http://dx.doi.org/10.1155/s1048953394000316.

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Markov processes are an important ingredient in a variety of stochastic applications. Notable instances include queueing systems and traffic processes offered to them. This paper is concerned with Markovian traffic, i.e., traffic processes whose inter-arrival times (separating the time points of discrete arrivals) form a real-valued Markov chain. As such this paper aims to extend the classical results of renewal traffic, where interarrival times are assumed to be independent, identically distributed. Following traditional renewal theory, three functions are addressed: the probability of the nu

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30

Shi, Jinjing, Ronghua Shi, Xiaoqi Peng, Ying Guo, and Moon Ho Lee. "Quantum relay cooperative communication via space-time transmission." Quantum Information and Computation 15, no. 7&8 (2015): 660–76. http://dx.doi.org/10.26421/qic15.7-8-7.

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Two novel quantum relay cooperative communication schemes $1S2R1D$ and $2S2R2D$ are proposed by applying the wireless communication technique in the quantum system. The orthogonal quantum signals in consecutive quantum sequences are prepared to avoid mutual interference and they are firstly transmitted to the quantum relay node and then to the destination node with space-time transmission. Moreover, quantum operations and transformations are implemented on the relay node and the destination node to maximize the correct information transmission. The fidelity between original and final received

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Kumar, Dr Amresh, and Dr Ram Kishore Singh. "A Role of Hilbert Space in Sampled Data to Reduced Error Accumulation by Over Sampling Then the Computational and Storage Cost Increase Using Signal Processing On 2-Sphere Dimension”." International Journal of Scientific Research and Management 8, no. 05 (2020): 386–96. http://dx.doi.org/10.18535/ijsrm/v8i05.ec02.

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Hilbert Space has wide usefulness in signal processing research. It is pitched at a graduate student level, but relies only on undergraduate background material. The needs and concerns of the researchers In engineering differ from those of the pure science. It is difficult to put the finger on what distinguishes the engineering approach that we have taken. In the end, if a potential use emerges from any result, however abstract, then an engineer would tend to attach greater value to that result. This may serve to distinguish the emphasis given by a mathematician who may be interested in the pr

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32

Yıldız, Şebnem. "A new factor theorem on absolute matrix summability method." Journal of Applied Analysis, September 25, 2021. http://dx.doi.org/10.1515/jaa-2021-2060.

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Abstract In this paper, we have a new matrix generalization with absolute matrix summability factor of an infinite series by using quasi-β-power increasing sequences. That theorem also includes some new and known results dealing with some basic summability methods

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33

Barrios Rolanía, D., and J. C. García-Ardila. "Geronimus transformations for sequences of d-orthogonal polynomials." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 114, no. 1 (2019). http://dx.doi.org/10.1007/s13398-019-00765-7.

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Khan, Vakeel A., and Umme Tuba. "On paranormed Ideal convergent sequence spaces defined by Jordan totient function." Journal of Inequalities and Applications 2021, no. 1 (2021). http://dx.doi.org/10.1186/s13660-021-02634-7.

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AbstractThe study of sequence spaces and summability theory has been an important aspect in defining new notions of convergence for the sequences that do not converge in the usual sense. Paving the way into the applications of law of large numbers and theory of functions, it has proved to be an essential tool. In this paper we generalise the classical Maddox sequence spaces $c_{0}(p)$ c 0 ( p ) , $c(p)$ c ( p ) , $\ell (p)$ ℓ ( p ) and $\ell _{\infty }(p)$ ℓ ∞ ( p ) and define new ideal paranormed sequence spaces $c^{I}_{0}(\Upsilon ^{r}, p)$ c 0 I ( ϒ r , p ) , $c^{I}(\Upsilon ^{r}, p)$ c I (

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35

Zhu, Bao-Xuan, and Hua Sun. "Linear Transformations Preserving the Strong $q$-log-convexity of Polynomials." Electronic Journal of Combinatorics 22, no. 3 (2015). http://dx.doi.org/10.37236/5168.

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In this paper, we give a sufficient condition for the linear transformation preserving the strong $q$-log-convexity. As applications, we get some linear transformations (for instance, Morgan-Voyce transformation, binomial transformation, Narayana transformations of two kinds) preserving the strong $q$-log-convexity. In addition, our results not only extend some known results, but also imply the strong $q$-log-convexities of some sequences of polynomials.

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Köcher, Chris. "Reachability Problems on Reliable and Lossy Queue Automata." Theory of Computing Systems, June 19, 2021. http://dx.doi.org/10.1007/s00224-021-10031-2.

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AbstractWe study the reachability problem for queue automata and lossy queue automata. Concretely, we consider the set of queue contents which are forwards resp. backwards reachable from a given set of queue contents. Here, we prove the preservation of regularity if the queue automaton loops through some special sets of transformation sequences. This is a generalization of the results by Boigelot et al. and Abdulla et al. regarding queue automata looping through a single sequence of transformations. We also prove that our construction is possible in polynomial time.

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Liu, Lily Li, and Ya-Nan Li. "Recurrence Relations for the Linear Transformation Preserving the Strong $q$-Log-Convexity." Electronic Journal of Combinatorics 23, no. 3 (2016). http://dx.doi.org/10.37236/5913.

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Let $[T(n,k)]_{n,k\geqslant0}$ be a triangle of positive numbers satisfying the three-term recurrence relation\[T(n,k)=(a_1n+a_2k+a_3)T(n-1,k)+(b_1n+b_2k+b_3)T(n-1,k-1).\]In this paper, we give a new sufficient condition for linear transformations\[Z_n(q)=\sum_{k=0}^{n}T(n,k)X_k(q)\]that preserves the strong $q$-log-convexity of polynomials sequences. As applications, we show linear transformations, given by matrices of the binomial coefficients, the Stirling numbers of the first kind and second kind, the Whitney numbers of the first kind and second kind, preserving the strong $q$-log-convexit

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38

"Proposed experimental tests of a theory of fine microstructure and the two-well problem." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 338, no. 1650 (1992): 389–450. http://dx.doi.org/10.1098/rsta.1992.0013.

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Predictions are made based on an analysis of a new nonlinear theory of martensitic transformations introduced by the authors. The crystal is modelled as a nonlinear elastic material, with a free-energy function that is invariant with respect to both rigid-body rotations and the appropriate crystallographic symmetries. The predictions concern primarily the two-well problem , that of determining all possible energy-minimizing deformations that can be obtained with two coherent and macroscopically unstressed variants of martensite. The set of possible macroscopic deformations obtained is complete

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39

Zhao, Feng-Zhen. "On Log-concavity of a Class of Generalized Stirling Numbers." Electronic Journal of Combinatorics 19, no. 2 (2012). http://dx.doi.org/10.37236/2228.

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This paper considers the generalized Stirling numbers of the first and second kinds. First, we show that the sequences of the above generalized Stirling numbers are both log-concave under some mild conditions. Then, we show that some polynomials related to the above generalized Stirling numbers are $q$-log-concave or $q$-log-convex under suitable conditions. We further discuss the log-convexity of some linear transformations related to generalized Stirling numbers of the first kind.

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Pontes, Helaine Maria De Souza, Celia FIinck Brandt, and Ana Luiza Ruschel Nunes. "O estado da arte da teoria dos registros de representação semiótica na educação matemática State of the art theory of semiotics representation registers in mathematics education." Educação Matemática Pesquisa : Revista do Programa de Estudos Pós-Graduados em Educação Matemática 19, no. 1 (2017). http://dx.doi.org/10.23925/1983-3156.2017v19i1p297-325.

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O objeto de estudo deste trabalho de investigação consiste em saber como a Teoria dos Registros de Representação Semiótica se evidencia nas pesquisas científicas brasileiras, portanto tem como objetivo revelar o nível de abrangência, objeto matemático, procedimentos metodológicos e aspectos da teoria de Duval mais recorrentes nestas pesquisas. Desta forma, trata-se de uma pesquisa bibliográfica com delineamento do estado da arte. Os resultados apresentados demonstram a predominância da Educação Básica; a variedade dos objetos matemáticos; o destaque tanto das Sequências Didáticas quanto das At

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