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Journal articles on the topic 'Transformations (Mathematics) Z transformation'

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Published: 4 June 2021

Last updated: 6 February 2022

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1

Green, Edward Lee. "Unified Field Theory From Enlarged Transformation Group. The Covariant Derivative for Conservative Coordinate Transformations and Local Frame Transformations." International Journal of Theoretical Physics 48, no. 2 (July 22, 2008): 323–36. http://dx.doi.org/10.1007/s10773-008-9805-z.

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2

Jaros, Rene, Radek Martinek, and Lukas Danys. "Comparison of Different Electrocardiography with Vectorcardiography Transformations." Sensors 19, no. 14 (July 11, 2019): 3072. http://dx.doi.org/10.3390/s19143072.

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This paper deals with transformations from electrocardiographic (ECG) to vectorcardiographic (VCG) leads. VCG provides better sensitivity, for example for the detection of myocardial infarction, ischemia, and hypertrophy. However, in clinical practice, measurement of VCG is not usually used because it requires additional electrodes placed on the patient’s body. Instead, mathematical transformations are used for deriving VCG from 12-leads ECG. In this work, Kors quasi-orthogonal transformation, inverse Dower transformation, Kors regression transformation, and linear regression-based transformations for deriving P wave (PLSV) and QRS complex (QLSV) are implemented and compared. These transformation methods were not yet compared before, so we have selected them for this paper. Transformation methods were compared for the data from the Physikalisch-Technische Bundesanstalt (PTB) database and their accuracy was evaluated using a mean squared error (MSE) and a correlation coefficient (R) between the derived and directly measured Frank’s leads. Based on the statistical analysis, Kors regression transformation was significantly more accurate for the derivation of the X and Y leads than the others. For the Z lead, there were no statistically significant differences in the medians between Kors regression transformation and the PLSV and QLSV methods. This paper thoroughly compared multiple VCG transformation methods to conventional VCG Frank’s orthogonal lead system, used in clinical practice.

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3

Kemprasit, Yupaporn, and Thawhat Changphas. "Regular order-preserving transformation semigroups." Bulletin of the Australian Mathematical Society 62, no. 3 (December 2000): 511–24. http://dx.doi.org/10.1017/s000497270001902x.

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The semigroup OT (X) of all order-preserving total transformations of a finite chain X is known to be regular. We extend this result to subchains of Z; and we characterise when OT (X) is regular for an interval X in R. We also consider the corresponding idea for partial transformations of arbitrary chains and posets.

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4

Flatto, Leopold, Jeffrey C. Lagarias, and Bjorn Poonen. "The zeta function of the beta transformation." Ergodic Theory and Dynamical Systems 14, no. 2 (June 1994): 237–66. http://dx.doi.org/10.1017/s0143385700007860.

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AbstractThe β-transformation ƒβ(x) = βx(mod 1), for β > 1, has a symbolic dynamics generalizing radix expansions to an integer base. Two important invariants of ƒβ are the (Artin-Mazur) zeta functionwhere Pk counts the number of fixed points of , and the lap-counting function where Lk counts the number of monotonic pieces of the kth iterate . For β-transformations these functions are related by ζβ(z) = (1 − z)Lβ(z). The function ζβ(z) is meromorphic in the unit disk, is holomorphic in {z: |z| < 1/β}, has a simple pole at z = 1/β, and has no other singularities with |z| = 1/β. Let M(β) denote the minimum modulus of any pole of ζβ(z) in |z| < 1 other than z = 1/β, and set M(β) = 1 if no other pole exists with |z| < 1. Then Pk = βk + O((M(β)−1+ε)k) for any ε > 0. This paper shows that M(β) is a continuous function, that ( for all β, and that An asymptotic formula is derived for M(β) as β → 1+, which implies that M(β) < 1 for all β in an interval (1, 1 + c0). The set is shown to have properties analogous to the set of Pisot numbers. It is closed, totally disconnected, has smallest element ≥ 1 + C0 and contains infinitely many β falling in each interval [n, n + 1) for n ∈ ℤ+. All known members of are algebraic integers which are either Pisot or Salem numbers.

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5

DIXIT, ATUL, RAJAT GUPTA, RAHUL KUMAR, and BIBEKANANDA MAJI. "GENERALIZED LAMBERT SERIES, RAABE’S COSINE TRANSFORM AND A GENERALIZATION OF RAMANUJAN’S FORMULA FOR." Nagoya Mathematical Journal 239 (October 4, 2018): 232–93. http://dx.doi.org/10.1017/nmj.2018.38.

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A comprehensive study of the generalized Lambert series $\sum _{n=1}^{\infty }\frac{n^{N-2h}\text{exp}(-an^{N}x)}{1-\text{exp}(-n^{N}x)},0<a\leqslant 1,~x>0$, $N\in \mathbb{N}$ and $h\in \mathbb{Z}$, is undertaken. Several new transformations of this series are derived using a deep result on Raabe’s cosine transform that we obtain here. Three of these transformations lead to two-parameter generalizations of Ramanujan’s famous formula for $\unicode[STIX]{x1D701}(2m+1)$ for $m>0$, the transformation formula for the logarithm of the Dedekind eta function and Wigert’s formula for $\unicode[STIX]{x1D701}(1/N),N$ even. Numerous important special cases of our transformations are derived, for example, a result generalizing the modular relation between the Eisenstein series $E_{2}(z)$ and $E_{2}(-1/z)$. An identity relating $\unicode[STIX]{x1D701}(2N+1),\unicode[STIX]{x1D701}(4N+1),\ldots ,\unicode[STIX]{x1D701}(2Nm+1)$ is obtained for $N$ odd and $m\in \mathbb{N}$. In particular, this gives a beautiful relation between $\unicode[STIX]{x1D701}(3),\unicode[STIX]{x1D701}(5),\unicode[STIX]{x1D701}(7),\unicode[STIX]{x1D701}(9)$ and $\unicode[STIX]{x1D701}(11)$. New results involving infinite series of hyperbolic functions with $n^{2}$ in their arguments, which are analogous to those of Ramanujan and Klusch, are obtained.

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6

Dixit, Atul, and Bibekananda Maji. "Generalized Lambert series and arithmetic nature of odd zeta values." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 2 (January 24, 2019): 741–69. http://dx.doi.org/10.1017/prm.2018.146.

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AbstractIt is pointed out that the generalized Lambert series $\sum\nolimits_{n = 1}^\infty {[(n^{N-2h})/(e^{n^Nx}-1)]} $ studied by Kanemitsu, Tanigawa and Yoshimoto can be found on page 332 of Ramanujan's Lost Notebook in a slightly more general form. We extend an important transformation of this series obtained by Kanemitsu, Tanigawa and Yoshimoto by removing restrictions on the parameters N and h that they impose. From our extension we deduce a beautiful new generalization of Ramanujan's famous formula for odd zeta values which, for N odd and m > 0, gives a relation between ζ(2m + 1) and ζ(2Nm + 1). A result complementary to the aforementioned generalization is obtained for any even N and m ∈ ℤ. It generalizes a transformation of Wigert and can be regarded as a formula for ζ(2m + 1 − 1/N). Applications of these transformations include a generalization of the transformation for the logarithm of Dedekind eta-function η(z), Zudilin- and Rivoal-type results on transcendence of certain values, and a transcendence criterion for Euler's constant γ.

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7

CHOO, Y. "Computing Transformation Matrix for Bilinear S-Z Transformation." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E90-A, no. 4 (April 1, 2007): 872–74. http://dx.doi.org/10.1093/ietfec/e90-a.4.872.

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8

Gowda, M. Seetharama, and Jiyuan Tao. "Z-transformations on proper and symmetric cones." Mathematical Programming 117, no. 1-2 (July 18, 2007): 195–221. http://dx.doi.org/10.1007/s10107-007-0159-8.

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9

Lin, Huaxin. "Furstenberg Transformations and Approximate Conjugacy." Canadian Journal of Mathematics 60, no. 1 (February 1, 2008): 189–207. http://dx.doi.org/10.4153/cjm-2008-008-2.

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AbstractLet α and β be two Furstenberg transformations on 2-torus associated with irrational numbers θ1, θ2, integers d1, d2 and Lipschitz functions f1 and f2. It is shown that α and β are approximately conjugate in ameasure theoretical sense if (and only if) θ1 ± θ2 = 0 in R/Z. Closely related to the classification of simple amenable C*-algebras, it is shown that α and β are approximately K-conjugate if (and only if) θ1 ± θ2 = 0 in R/Z and |d1| = |d2|. This is also shown to be equivalent to the condition that the associated crossed product C*-algebras are isomorphic.

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10

Wang, Rongdong, and Peng-Yung Woo. "Automatic Computation of Z- & Inverse Z-transformations by Maple." Journal of Symbolic Computation 15, no. 3 (March 1993): 349–63. http://dx.doi.org/10.1006/jsco.1993.1025.

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11

XIAO, Y. "2-D Laplace-Z Transformation." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E89-A, no. 5 (May 1, 2006): 1500–1504. http://dx.doi.org/10.1093/ietfec/e89-a.5.1500.

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12

Shang, Nina, Qinghua Feng, and Huizeng Qin. "Some New Transformation Properties of the Nielsen Generalized Polylogarithm." International Journal of Mathematics and Mathematical Sciences 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/210890.

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Many of the properties of Nielsen generalized polylogarithmSn,p(z), for example, the special value and the transformation formulas, play important roles in the computation of higher order radiative corrections in quantum electrodynamics. In this paper, some transformation formulas ofz→p(z),p(z)=1-z,1/z,1/(1-z),z/(z-1), and(1-z)/zare obtained. In particular, the last three transformation formulas are new results so far in the literature. By use of these transformation formulas presented, new fast algorithms for Nielsen generalized polylogarithmSn,p(z)can be designed. Forsn,p=Sn,p(1), a new recurrence formula is also given. The identities and the calculation ofσn,pandan,pare also investigated.

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13

Strzelecka, Anna, and Piotr Skworcow. "Modelling and Simulation of Utility Service Provision for Sustainable Communities." International Journal of Electronics and Telecommunications 58, no. 4 (December 1, 2012): 389–96. http://dx.doi.org/10.2478/v10177-012-0053-z.

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Abstract Utility service provision is designed to satisfy basic human needs. The main objective of the research is to investigate mathematical methods for evaluating the feasibility of using a more efficient approach for utility services provision, compared to the current diversity of utility products delivered to households. Possibilities for alternative utility service provision that lead to more sustainable solutions include reducing the number of delivered utility products, on-site recycling and use of locally available natural resources. The core of the proposed approach is the simulation system that enables carrying out feasibility study of so-called transformation graph, which describes direct transformations and indirect transformations of the utility products into defined services. The simulation system was implemented in C# and .NET 3.5, while the XML database was implemented using eXist-db. The XML database stores information about all devices, utility products, services and technologies that can be used to define and solve services-provision problems. An example of such problem and its solution is presented in this paper. This research is a part of the All-in-One Project.

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14

Kolmykov, V. A. "Coxeter transformations: Construction of deltoids." Mathematical Notes 79, no. 5-6 (May 2006): 643–48. http://dx.doi.org/10.1007/s11006-006-0073-z.

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15

ETEDADIALIABADI, MAHMOOD. "Generic behavior of a measure-preserving transformation." Ergodic Theory and Dynamical Systems 40, no. 4 (September 25, 2018): 904–22. http://dx.doi.org/10.1017/etds.2018.62.

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Del Junco–Lemańczyk [Generic spectral properties of measure-preserving maps and applications. Proc. Amer. Math. Soc., 115 (3) (1992)] showed that a generic measure-preserving transformation satisfies certain orthogonality conditions. More precisely, there is a dense $G_{\unicode[STIX]{x1D6FF}}$ subset of measure preserving transformations such that, for every $T\in G$ and $k(1),k(2),\ldots ,k(l)\in \mathbb{Z}^{+}$, $k^{\prime }(1),k^{\prime }(2),\ldots ,k^{\prime }(l^{\prime })\in \mathbb{Z}^{+}$, the convolutions $$\begin{eqnarray}\unicode[STIX]{x1D70E}_{T^{k(1)}}\ast \cdots \ast \unicode[STIX]{x1D70E}_{T^{k(l)}}\quad \text{and}\quad \unicode[STIX]{x1D70E}_{T^{k^{\prime }(1)}}\ast \cdots \ast \unicode[STIX]{x1D70E}_{T^{k^{\prime }(l^{\prime })}},\end{eqnarray}$$ where $\unicode[STIX]{x1D70E}_{T^{k}}$ is the maximal spectral type of $T^{k}$, are mutually singular, provided that $(k(1),k(2),\ldots ,k(l))$ is not a rearrangement of $(k^{\prime }(1),k^{\prime }(2),\ldots ,k^{\prime }(l^{\prime }))$. We will introduce analogous orthogonality conditions for continuous unitary representations of the group of all measurable functions with values in the circle, $L^{0}(\unicode[STIX]{x1D707},\mathbb{T})$, which we denote by the DL-condition. We connect the DL-condition with a result of Solecki [Unitary representations of the groups of measurable and continuous functions with values in the circle. J. Funct. Anal., 267 (2014), pp. 3105–3124] which identifies continuous unitary representations of $L^{0}(\unicode[STIX]{x1D707},\mathbb{T})$ with a collection of measures $\{\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D705}}\}$, where $\unicode[STIX]{x1D705}$ runs over all increasing finite sequence of non-zero integers. In particular, we show that the ‘probabilistic’ DL-condition translates to ‘deterministic’ orthogonality conditions on the measures $\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D705}}$. As a corollary, we show that the same orthogonality conditions as in the result by Del Junco–Lemańczyk hold for a generic unitary operator on a separable infinite-dimensional Hilbert space.

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16

Memić, Nacima. "Mahler coefficients of locally scaling transformations on $\mathbb{Z}_{p}$." Colloquium Mathematicum 162, no. 1 (2020): 53–76. http://dx.doi.org/10.4064/cm7810-6-2019.

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17

Moroianu, Andrei, and Liviu Ornea. "Transformations of locally conformally Kähler manifolds." manuscripta mathematica 130, no. 1 (May 30, 2009): 93–100. http://dx.doi.org/10.1007/s00229-009-0278-z.

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18

Nakasho, Kazuhisa, Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. "Rank of Submodule, Linear Transformations and Linearly Independent Subsets of Z-module." Formalized Mathematics 22, no. 3 (September 1, 2014): 189–98. http://dx.doi.org/10.2478/forma-2014-0021.

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Summary In this article, we formalize some basic facts of Z-module. In the first section, we discuss the rank of submodule of Z-module and its properties. Especially, we formally prove that the rank of any Z-module is equal to or more than that of its submodules, and vice versa, and that there exists a submodule with any given rank that satisfies the above condition. In the next section, we mention basic facts of linear transformations between two Z-modules. In this section, we define homomorphism between two Z-modules and deal with kernel and image of homomorphism. In the last section, we formally prove some basic facts about linearly independent subsets and linear combinations. These formalizations are based on [9](p.191-242), [23](p.117-172) and [2](p.17-35).

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19

Flatto, Leopold, and Jeffrey C. Lagarias. "The lap-counting function for linear mod one transformations I: explicit formulas and renormalizability." Ergodic Theory and Dynamical Systems 16, no. 3 (June 1996): 451–91. http://dx.doi.org/10.1017/s0143385700008920.

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AbstractLinear mod one transformations are the maps of the unit interval given by fβα(x) = βx + α (mod 1), with β > 1 and 0 ≤ α < 1. The lap-counting function is the function where the lap number Ln essentially counts the number of monotonic pieces of the nth iterate . We derive an explicit factorization formula for Lβα(z) which directly shows that Lβα(z) is a function meromorphic in the open unit disk {z: |z| < 1} and analytic in the open disk {z: |z| < 1/β}, with a simple pole at z = 1/β.Comparison with a known formula for the Artin—Mazur—Ruelle zeta function ζβ,α(z) of fβα shows that Lβα(z) and ζβ,α(z) have identical sets of singularities in the disk {z: |z| < 1}. We derive two more factorization formulae for Lβ,α(z) valid for certain parameter ranges of (β, α). When 1 < α + β ≤ 2, there is sometimes a ‘renormalization’ structure of such maps present, which has previously been studied in connection with simplified models for the Lorenz attractor. In the case that fβα is non-trivially renormalizable, we obtain a factorization formula for Lβα(z). For (β, α) in a region contained in 2 < α + β ≤ 3 we obtain a factorization formula which relates Lβα(z) to a ‘rescaled’ lap-counting function from the region 1 < α + β ≤ 2. The various factorizations exhibit certain singularities of Lβα(z) on the circle |z| = 1/β. These singularities are related to topological dynamical properties of fβ,α. In parts II and III we show that these comprise the complete set of such singularities on the circle |z| = 1/β.

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20

Gazizov, R. K., and V. O. Lukashchuk. "Similarity of approximate transformation groups." Siberian Mathematical Journal 51, no. 1 (January 2010): 1–11. http://dx.doi.org/10.1007/s11202-010-0001-z.

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21

Gadella, Manuel, and Fernando Gómez-Cubillo. "Eigenfunction Expansions and Transformation Theory." Acta Applicandae Mathematicae 109, no. 3 (October 22, 2008): 721–42. http://dx.doi.org/10.1007/s10440-008-9342-z.

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22

Dixit, Atul. "Analogues of the general theta transformation formula." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 143, no. 2 (March 18, 2013): 371–99. http://dx.doi.org/10.1017/s0308210511001685.

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A new class of integrals involving the confluent hypergeometric function 1F1(a;c;z) and the Riemann Ξ-function is considered. It generalizes a class containing some integrals of Ramanujan, Hardy and Ferrar and gives, as by-products, transformation formulae of the form F(z, α) = F(iz, β), where αβ = 1. As particular examples, we derive an extended version of the general theta transformation formula and generalizations of certain formulae of Ferrar and Hardy. A one-variable generalization of a well-known identity of Ramanujan is also given. We conclude with a generalization of a conjecture due to Ramanujan, Hardy and Littlewood involving infinite series of the Möbius function.

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23

Yakubovich, Semyon B. "On the Lebedev transformation in Hardy's spaces." International Journal of Mathematics and Mathematical Sciences 2004, no. 66 (2004): 3603–16. http://dx.doi.org/10.1155/s0161171204301365.

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We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy's spaceH2,A,A>0. This gives another version of the Fourier-integral-type theorem for the Lebedev transform. The result is generalized for a weighted Hardy spaceH⌢2,A≡H⌢2((−A,A);|Γ(1+Rez+iτ)|2dτ),0<A<1, of analytic functionsf(z),z=Rez+iτ, in the strip|Rez|≤A. Boundedness and inversion properties of the Lebedev transformation from this space into the spaceL2(ℝ+;x−1dx)are considered. WhenRez=0, we derive the familiar Plancherel theorem for the Kontorovich-Lebedev transform.

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24

Beasley, LeRoy B., Alexander E. Guterman, Sang-Gu Lee, and Seok-Zun Song. "Linear transformations preserving the Grassmannian over Mn(Z+)." Linear Algebra and its Applications 393 (December 2004): 39–46. http://dx.doi.org/10.1016/j.laa.2003.08.018.

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25

Tryhuk, Václav. "On transformations z(t) = y(ϕ(t)) of ordinary differential equations." Czechoslovak Mathematical Journal 50, no. 3 (September 2000): 509–18. http://dx.doi.org/10.1023/a:1022877409091.

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26

Zhang, Heping, Rijun Zha, and Haiyuan Yao. "Z -transformation graphs of maximum matchings of plane bipartite graphs." Discrete Applied Mathematics 134, no. 1-3 (January 2004): 339–50. http://dx.doi.org/10.1016/s0166-218x(03)00305-6.

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27

SCARPARO, EDUARDO. "Homology of odometers." Ergodic Theory and Dynamical Systems 40, no. 9 (March 13, 2019): 2541–51. http://dx.doi.org/10.1017/etds.2019.13.

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We compute the homology groups of transformation groupoids associated with odometers and show that certain $(\mathbb{Z}\rtimes \mathbb{Z}_{2})$-odometers give rise to counterexamples to the HK conjecture, which relates the homology of an essentially principal, minimal, ample groupoid $G$ with the K-theory of $C_{r}^{\ast }(G)$. We also show that transformation groupoids of odometers satisfy the AH conjecture.

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28

Johnson, Aimee S. A., and Ayşe A. Şahin. "Isometric Extensions of zero entropy $\mathbb Z^{\lowercase {d}}$ Loosely Bernoulli Transformations." Transactions of the American Mathematical Society 352, no. 3 (October 6, 1999): 1329–43. http://dx.doi.org/10.1090/s0002-9947-99-02500-3.

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29

Gorkavyy, Vasyl, and Olena Nevmerzhytska. "Pseudo-spherical Submanifolds with Degenerate Bianchi Transformation." Results in Mathematics 60, no. 1-4 (June 28, 2011): 103–16. http://dx.doi.org/10.1007/s00025-011-0168-z.

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30

Wang, Haifeng, and Yufeng Zhang. "Residual Symmetries and Bäcklund Transformations of Strongly Coupled Boussinesq–Burgers System." Symmetry 11, no. 11 (November 4, 2019): 1365. http://dx.doi.org/10.3390/sym11111365.

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In this article, we construct a new strongly coupled Boussinesq–Burgers system taking values in a commutative subalgebra Z 2 . A residual symmetry of the strongly coupled Boussinesq–Burgers system is achieved by a given truncated Painlevé expansion. The residue symmetry with respect to the singularity manifold is a nonlocal symmetry. Then, we introduce a suitable enlarged system to localize the nonlocal residual symmetry. In addition, a Bäcklund transformation is obtained with the help of Lie’s first theorem. Further, the linear superposition of multiple residual symmetries is localized to a Lie point symmetry, and a N-th Bäcklund transformation is also obtained.

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31

Weiß, Christian. "Discrepancy properties and conjugacy classes of interval exchange transformations." Monatshefte für Mathematik 196, no. 2 (July 23, 2021): 399–410. http://dx.doi.org/10.1007/s00605-021-01610-z.

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AbstractInterval exchange transformations are typically uniquely ergodic maps and therefore have uniformly distributed orbits. Their degree of uniformity can be measured in terms of the star-discrepancy. Few examples of interval exchange transformations with low-discrepancy orbits are known so far and only for $$n=2,3$$ n = 2 , 3 intervals, there are criteria to completely characterize those interval exchange transformations. In this paper, it is shown that having low-discrepancy orbits is a conjugacy class invariant under composition of maps. To a certain extent, this approach allows us to distinguish interval exchange transformations with low-discrepancy orbits from those without. For $$n=4$$ n = 4 intervals, the classification is almost complete with the only exceptional case having monodromy invariant $$\rho = (4,3,2,1)$$ ρ = ( 4 , 3 , 2 , 1 ) . This particular monodromy invariant is discussed in detail.

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32

Tryhuk, Václav. "Transformations z(t) = L(t)y(ϕ(t)) of ordinary differential equations." Czechoslovak Mathematical Journal 50, no. 3 (September 2000): 519–29. http://dx.doi.org/10.1023/a:1022829525930.

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33

Fu-ji, Zhang, Guo Xiao-feng, and Chen Rong-si. "Z-transformation graphs of perfect matchings of hexagonal systems." Discrete Mathematics 72, no. 1-3 (December 1988): 405–15. http://dx.doi.org/10.1016/0012-365x(88)90233-6.

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34

Zhang, Heping, and Fuji Zhang. "Total Z-transformation graphs of perfect matching of plane bipartite graphs." Electronic Notes in Discrete Mathematics 5 (July 2000): 317–20. http://dx.doi.org/10.1016/s1571-0653(05)80196-9.

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35

Fülöp and Vogler. "Tree Series Transformations that Respect Copying." Theory of Computing Systems 36, no. 3 (June 2003): 247–93. http://dx.doi.org/10.1007/s00224-003-1072-z.

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36

San Miguel, A. "Deformable Asymmetric Tops under Similarity Transformations." Journal of Nonlinear Science 13, no. 5 (October 1, 2003): 471–85. http://dx.doi.org/10.1007/s00332-003-0539-z.

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37

de, Malafosse, Ali Fares, and Ali Ayad. "Matrix transformations and application to perturbed problems of some sequence spaces equations with operators." Filomat 32, no. 14 (2018): 5123–30. http://dx.doi.org/10.2298/fil1814123m.

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Given any sequence z = (zn)n?1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y = (yn)n?1 such that y/z = (yn/zn)n?1 ? E; in particular, cz = s(c) z denotes the set of all sequences y such that y/z converges. Starting with the equation Fx = Fb we deal with some perturbed equation of the form ? + Fx = Fb, where ? is a linear space of sequences. In this way we solve the previous equation where ? =(Ea)T and (E,F) ? {(l?,c), (c0,l?), (c0,c), (lp,c), (lp,l?), (w0,l?)} with p ? 1, and T is a triangle.

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38

Pogorelov, Boris A., and Marina A. Pudovkina. "On groups containing the additive group of the residue ring or the vector space." Discrete Mathematics and Applications 28, no. 4 (August 28, 2018): 231–47. http://dx.doi.org/10.1515/dma-2018-0021.

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Abstract Groups which are most frequently used as key addition groups in iterative block ciphers include the regular permutation representation $\begin{array}{} \displaystyle V_{n}^{+} \end{array}$ of the group of vector key addition, the regular permutation representation $\begin{array}{} \displaystyle \mathbb{Z}_{{2^n}}^{+} \end{array}$ of the additive group of the residue ring, and the regular permutation representation $\begin{array}{} \displaystyle \mathbb{Z}_{{2^n} + 1}^ \odot \end{array}$ of the multiplicative group of a prime field (in the case where 2n + 1 is a prime number). In this work we consider the extension of the group Gn generated by $\begin{array}{} \displaystyle V_{n}^{+} \end{array}$ and $\begin{array}{} \displaystyle \mathbb{Z}_{{2^n}}^{+} \end{array}$ by means of transformations and groups which naturally arise in cryptographic applications. Examples of such transformations and groups are the groups $\begin{array}{} \displaystyle \mathbb{Z}_{{2^d}}^{+} \times V_{n - d}^{+} ~\text{and}~ V_{n - d}^{+}\times \mathbb{Z}_{{2^d}}^{+} \end{array}$ and pseudoinversion over the field GF(2n) or over the Galois ring GR(2md, 2m).

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39

SUN, ZHI-HONG. "TRANSFORMATION FORMULAS FOR THE NUMBER OF REPRESENTATIONS OF BY LINEAR COMBINATIONS OF FOUR TRIANGULAR NUMBERS." Bulletin of the Australian Mathematical Society 102, no. 1 (January 8, 2020): 39–49. http://dx.doi.org/10.1017/s0004972719001400.

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Let $\mathbb{Z}$ and $\mathbb{Z}^{+}$ be the set of integers and the set of positive integers, respectively. For $a,b,c,d,n\in \mathbb{Z}^{+}$, let $t(a,b,c,d;n)$ be the number of representations of $n$ by $\frac{1}{2}ax(x+1)+\frac{1}{2}by(y+1)+\frac{1}{2}cz(z+1)+\frac{1}{2}dw(w+1)$ with $x,y,z,w\in \mathbb{Z}$. Using theta function identities we prove 13 transformation formulas for $t(a,b,c,d;n)$ and evaluate $t(2,3,3,8;n)$, $t(1,1,6,24;n)$ and $t(1,1,6,8;n)$.

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40

di Giacomo, Benedito, César Augusto Galvão de Morais, Vagner Augusto de Souza, and Luiz Carlos Neves. "Modeling Errors in Coordinate Measuring Machines and Machine Tools Using Homogeneous Transformation Matrices (HTM)." Advanced Materials Research 1025-1026 (September 2014): 56–59. http://dx.doi.org/10.4028/www.scientific.net/amr.1025-1026.56.

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Coordinate Measuring Machines (CMM's) have attributes to provide results with accuracy and repeatability in measurements, so they are considered equipment with potential for application in industrial environments, specifically in inspection processes. However, as in a machine tools the knowledge of the errors in CMM is needed and allows applying techniques of error compensation. This study aimed to develop a mathematical model of the kinematic errors of a bridge type CMM in "X", "Y" and "Z" directions. Modeling of the errors was accomplished using coordinate transformations applied to the rigid body kinematics; the method of the homogeneous transformation was used for the development of the model. The position and angular errors for the three axes of CMM, in addition to errors related to the absence of orthogonality between them were equated. This study allowed to conclude that modeling of errors applied to CMM allied to calibration is able to evaluate the metrological performance of equipment with displacement on guides, thus is possible to use this technique as error budget analysis in machines.

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Zhang, Heping, Fuji Zhang, and Haiyuan Yao. "Z-transformation graphs of perfect matchings of plane bipartite graphs." Discrete Mathematics 276, no. 1-3 (February 2004): 393–404. http://dx.doi.org/10.1016/s0012-365x(03)00319-4.

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Tsodikov, A., and G. Garibotti. "Profile information matrix for nonlinear transformation models." Lifetime Data Analysis 13, no. 1 (October 5, 2006): 139–59. http://dx.doi.org/10.1007/s10985-006-9023-z.

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Furno, Joanna. "Orbit equivalence of $$p$$ p -adic transformations and their iterates." Monatshefte für Mathematik 175, no. 2 (June 7, 2014): 249–76. http://dx.doi.org/10.1007/s00605-014-0645-z.

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Gökçe, Fadime, and Mehmet Ali Sarigöl. "Series spaces derived from absolute Fibonacci summability and matrix transformations." Bollettino dell'Unione Matematica Italiana 13, no. 1 (May 7, 2019): 29–38. http://dx.doi.org/10.1007/s40574-019-00201-z.

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Fried, Eliot. "Sharp-Interface Nematic-Isotropic Phase Transformations With Flow." Archive for Rational Mechanics and Analysis 190, no. 2 (March 5, 2008): 227–65. http://dx.doi.org/10.1007/s00205-007-0107-z.

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Osswald, Horst. "On Anticipative Girsanov Transformations for Lévy Processes." Journal of Theoretical Probability 22, no. 2 (November 13, 2008): 474–81. http://dx.doi.org/10.1007/s10959-008-0197-z.

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Xu, Xing-Lei, Shi-Min Xu, Yun-Hai Zhang, Hong-Qi Li, and Ji-Suo Wang. "The Transformations from the New Intermediate Entangled State." International Journal of Theoretical Physics 50, no. 10 (May 17, 2011): 3176–85. http://dx.doi.org/10.1007/s10773-011-0821-z.

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Janvresse, Élise, Emmanuel Roy, and Thierry de la Rue. "Invariant measures for Cartesian powers of Chacon infinite transformation." Israel Journal of Mathematics 224, no. 1 (March 6, 2018): 1–37. http://dx.doi.org/10.1007/s11856-018-1634-z.

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Zhang, Heping, Lingbo Zhao, and Haiyuan Yao. "The Z-Transformation graph for an outerplane bipartite graph has a Hamilton path." Applied Mathematics Letters 17, no. 8 (August 2004): 897–901. http://dx.doi.org/10.1016/j.am1.2003.12.002.

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Gaál, M., and G. Nagy. "A Characterization of Unitary-Antiunitary Similarity Transformations via Kubo–Ando Means." Analysis Mathematica 45, no. 2 (August 17, 2018): 311–19. http://dx.doi.org/10.1007/s10476-018-0401-z.

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