Relevant bibliographies by topics / Biorthogonal system

Contents

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

Academic literature on the topic 'Biorthogonal system'

Author: Grafiati
Published: 4 June 2021
Last updated: 8 February 2022

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Journal articles on the topic "Biorthogonal system"

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Moiseev, Evgeny I. "On certain biorthogonal system." Integral Transforms and Special Functions 2, no. 1 (June 1994): 37–50. http://dx.doi.org/10.1080/10652469408819036.

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Sarsenbi, A. M., and P. A. Terekhin. "Riesz Basicity for General Systems of Functions." Journal of Function Spaces 2014 (2014): 1–3. http://dx.doi.org/10.1155/2014/860279.

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In this paper we find the general conditions for a complete biorthogonal conjugate system to form a Riesz basis. We show that if a complete biorthogonal conjugate system is uniformly bounded and its coefficient space is solid, then the system forms a Riesz basis. We also construct affine Riesz bases as an application to the main result.
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Chen, Yueyun, and Zhenhui Tan. "A General Algorithm for Biorthogonal Functions and Performance Analysis of Biorthogonal Scramble Modulation System." Wireless Sensor Network 02, no. 03 (2010): 199–205. http://dx.doi.org/10.4236/wsn.2010.23026.

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YABLONSKY, EUGENE. "CHARACTERIZATION OF OPERATORS ON A KONDRATIEV SPACE IN THE NON-GAUSSIAN SETTING: BIORTHOGONAL APPROACH." Infinite Dimensional Analysis, Quantum Probability and Related Topics 08, no. 03 (September 2005): 439–52. http://dx.doi.org/10.1142/s0219025705002050.

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A linear bounded operator on a test space of white noise functionals can be characterized in terms of growth conditions imposed on the operator's symbol. This paper extends such characterization to operators on the Kondratiev's test space [Formula: see text] of random variables over a general non-Gaussian probability space. We follow the biorthogonal approach of Yu. Daletsky and his colleagues. In particular, the test space under consideration is generated by the system of multivariate Appell polynomials defined on the underlying infinite dimensional co-nuclear probability space. We further extend this biorthogonal approach to operators by providing a biorthogonal chaos decomposition for operators and by giving a biorthogonal construction for an operator's symbol.
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Garling, D. J. H., and N. Tomczak-Jaegermann. "RUC-systems and Besselian systems in Banach spaces." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 1 (July 1989): 163–68. http://dx.doi.org/10.1017/s0305004100068055.

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Let (rj) be a Rademacher sequence of random variables – that is, a sequence of independent random variables, with , for each j. A biorthogonal system in a Banach space X is called an RUC-system[l] if for every x in [ej] (the closed linear span of the vectors ej), the seriesconverges for almost every ω. A basis which, together with its coefficient functionals, forms an RUC-system is called an RUC-basis. A biorthogonal system is an RLTC-svstem if and only if there exists 1 ≤ K < ∞ such thatfor each x in [ej]: the RUC-constant of the system is the smallest constant K satisfying (1) (see [1], proposition 1.1).
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Shen, L., and Q. Sun. "Biorthogonal Wavelet System for High-Resolution Image Reconstruction." IEEE Transactions on Signal Processing 52, no. 7 (July 2004): 1997–2011. http://dx.doi.org/10.1109/tsp.2004.828939.

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Tumin, Anatoli. "Biorthogonal Eigenfunction System in the Triple-Deck Limit." Studies in Applied Mathematics 117, no. 2 (August 2006): 165–90. http://dx.doi.org/10.1111/j.1467-9590.2006.00351.x.

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Golub, A. P. "A system of biorthogonal polynomials and its applications." Ukrainian Mathematical Journal 41, no. 7 (July 1989): 821–23. http://dx.doi.org/10.1007/bf01060701.

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Bityukov, Yuri, Yuri Deniskin, Galina Deniskina, and Irina Pocebneva. "Application of wavelets and conformal reflections to finding optimal scheme of fiber placement at 3d printing constructions from composition materials." E3S Web of Conferences 244 (2021): 05004. http://dx.doi.org/10.1051/e3sconf/202124405004.

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The article is devoted to finding the optimal schemes of fiber placement at the production of constructions, reinforced with continuous fibers by 3D printing method. As the optimization of the objective function one of the criteria for the destruction of the composite was chosen. For the process acceleration of multiple solution of the system of partial differential equations describing the stress-strain state of the structure, a computational algorithm based on wavelets built through subdivision schemes is proposed. To set the local coordinate system, it is proposed to use analytical functions, which will be constructed using the well-known Dini and Cisotti formulas, just by specifying the direction of laying the fiber at the product boundary. The article also presents a lifting scheme (lifting scheme) allowing to construct biorthogonal wavelet systems with specified properties using some initial biorthogonal wavelet systems with filters.
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HAWKINS, STUART C., KE CHEN, and PAUL J. HARRIS. "AN OPERATOR SPLITTING PRECONDITIONER FOR MATRICES ARISING FROM A WAVELET BOUNDARY ELEMENT METHOD FOR THE HELMHOLTZ EQUATION." International Journal of Wavelets, Multiresolution and Information Processing 03, no. 04 (December 2005): 601–20. http://dx.doi.org/10.1142/s0219691305001044.

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An operator splitting type preconditioner is presented for fast solution of linear systems obtained by Galerkin discretization of the Burton and Miller formulation for the Helmholtz equation. Our approach differs from usual boundary element treatments of the three-dimensional scattering problem because we use a basis of biorthogonal wavelets. Such wavelets result in a sparse linear system and that facilitates preconditioning and makes matrix vector products cheap to form. In this Part I of our work, we implement a biorthogonal wavelet transform on a closed surface in three dimensions. Numerical results demonstrate the gains in efficiency that are already achievable with this convenient but non-optimal implementation.
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Dissertations / Theses on the topic "Biorthogonal system"

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Webb, Grayson. "Biorthogonal Polynomials." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-140733.

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In this thesis we present some fundamental results regarding orthogonal polynomials and biorthogonal polynomials, the latter defined as in the article "Cauchy Biorthogonal Polynomials", authored by Bertola, Gekhtman, and Szmigielski. We show that total positivity of the kernel can be weakened and how this implies that interlacement for biorthogonal polynomials holds in general. A counterexample is provided showing that in general there does not exist a four-term recurrence relation such as the one found for the Cauchy kernel. As a direct consequence we show that biorthogonal polynomial sequences cannot be considered orthogonal polynomial sequences by an appropriate choice of orthogonality measure. Furthermore, we motivate a conjecture stating that the more general form of interlacement that exists for orthogonal polynomials also exists for biorthogonal polynomials. We end with suggesting some further work that could be of interest.
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Brech, Christina. "Construções genéricas de espaços de Asplund C(K)." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-06062008-112930/.

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Neste trabalho consideramos um método de construções genéricas de espaços compactos e dispersos não-metrizáveis, desenvolvido por Baumgartner, Shelah, Rabus, Juhasz e Soukup. Introduzimos novas técnicas e obtemos novas aplicações relevantes tanto para a topologia dos espaços compactos quanto para a geometria dos espaços de Banach de funções contínuas. As novas técnicas dizem respeito a novas amalgamações de condições do forcing que adiciona os espaços dispersos, bem como a generalizações dos argumentos dos autores acima citados de pontos de um espaço compacto K para medidas de Radon sobre K. Como aplicações, obtemos dois novos espaços compactos e dispersos K_1 e K_2, com as propriedades abaixo. K_1 é um espaço hereditariamente separável de peso aleph_1 tal que C(K_1) possui a propriedade (C) de Corson e não possui a propriedade (E) de Efremov. K_2 é o primeiro exemplo de um espaço compacto disperso, hereditariamente separável, de altura omega_2. Segue que o grau de Lindelöf hereditário de K_2 é aleph_2, mostrando a consistência de que hL(K) é estritamente maior que o sucessor de hd(K) para espaços compactos K. C(K_2) é o primeiro exemplo consistente de um espaço de densidade aleph_2 que não possui um sistema biortogonal não-enumerável.
In this work we consider a method of generic constructions of compact scattered non-metrizable spaces developed by Baumgartner, Shelah, Rabus, Juhasz and Soukup. We introduce new techniques and obtain new applications both relevant to topology of compact spaces and the geometry of Banach spaces of continuous functions. The new techniques concern new amalgamations of conditions of forcing which add the dispersed spaces as well as the generalizations of arguments of the above-mentioned authors from points of a compact space K to Radon measures on K. As applications we obtain two compact scattered spaces K_1 and K_2 with the properties below. K_1 is a hereditarily separable space of weight aleph_1 such that C(K_1) has property (C) of Corson and does not have property (E) of Efremov. K_2 is the first (consistent) example of a compact scattered space which is hereditarily separable and whose height is omega_2. It follows that its hereditary Lindelöf degree is aleph_2, showing the consistency of hL(K) can me strictly greater than the successor of hd(K) for compact spaces K. C(K_2) is the first consistent example of a Banach space of density aleph_2 without uncountable biorthogonal systems.
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Yablonsky, Eugene. "Characterization of operators in non-gaussian infinite dimensional analysis." The Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1054787409.

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Zhu, Weiwei. "The multilevel structures of NURBs and NURBlets on intervals." Diss., St. Louis, Mo. : University of Missouri--St. Louis, 2009. http://etd.umsl.edu/r4262.

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Silva, Juan Carlo da Cruz. "Sobre operadores entre espaços de sequências que atingem a norma." Universidade Federal da Paraí­ba, 2009. http://tede.biblioteca.ufpb.br:8080/handle/tede/7420.

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In this work we present a recent result, due to D. Pellegrino and E. V. Teixeira, that characterizes the continuous linear operators between lpspaces which attain their norms. To this end, we Örstly explore some topics from the Banach space theory, such as Banachís Theorem for basis, Bessaga-Pe ̃czynski Selection Principle and Pittís Theorem.
Neste trabalho apresentaremos um recente resultado, devido a D. Pellegrino e E. V. Teixeira, que caracteriza os operadores lineares contínuos entre espaços lp que atingem a norma. Para tanto, vamos desenvolver alguns tópicos da teoria de bases em espaços de Banach e também mostrar alguns importantes resultados da teoria de espaços de Banach, tais como o Teorema de Banach sobre bases, o Princípio de Seleção de Bessaga- Pe÷czy´nski e o Teorema de Pitt.
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González, Correa Alma Lucía. "Compacta in Banach spaces." Doctoral thesis, Universitat Politècnica de València, 2010. http://hdl.handle.net/10251/8312.

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Capítulo 1. Después de estudiar algunos preliminares sobre familias adecuadas de conjuntos, formulamos y probamos algunas equivalencias, cada una de ellas son una condición suficiente para que la familia defina un conjunto compacto de Gul'ko. Damos una caracterización de conjunto compacto de Gul'ko en términos de emparejamiento con un conjunto $\mathcal{K}$-analítico. Capítulo 2. Estudiamos propiedades de los espacios de Banach débilmente Lindelöf determinados no-separables. Damos una caracterización por medio de la existencia de un generador proyeccional full sobre él. Estudiamos algunos aspectos sobre sistemas biortogonales en espacios de Banach. Usando técnicas de resoluciones proyeccionales de la identidad, probamos una extensión de un resultado de Argyros y Mercourakis. Capítulo 3. En el espacio $(c_0(\Gamma),\|\cdot\|_\infty)$, con $\Gamma\in\mathbb{R}$, damos una norma equivalente estrictamente convexa. Capítulo 4. Consideramos una caracterización de los subespacios de espacios de Banach débilmente compactamente generados, en términos de una propiedad de cubrimiento de la bola unidad por medio de conjuntos $\epsilon$-débilmente compactos. Reemplazamos este concepto por otro más preciso que llamamos $\epsilon$-débilmente auto-compactos, este concepto permite una mejor descripción. Capítulo 5. Damos condiciones intrínsecas, necesarias y suficientes para que un espacio de Banach sea generado por $c_0(\Gamma)$ o $\ell_p(\Gamma)$ para $p\in(1,+\infty)$. Ofrecemos una nueva demostración de un resultado de Rosenthal, sobre operadores de $c_0(\Gamma)$ en un espacio de Banach.
González Correa, AL. (2008). Compacta in Banach spaces [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8312
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Ouaili, Lydia. "Contrôlabilité de quelques systèmes paraboliques." Thesis, Aix-Marseille, 2020. http://theses.univ-amu.fr.lama.univ-amu.fr/200604_OUAILI_351nl894f5gh253lyuyt716uvgkl9_TH.

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Dans cette thèse, on s’intéresse à la contrôlabilité d’équations paraboliques et à son coût. On étudie dans un premier temps, la contrôlabilité à zéro d’un système de deux équations paraboliques couplés en dimension 1 d’espace, pour lesquelles l’opérateur spacial est de type Sturm-Liouville, avec des conditions au bord de type Dirichlet et un contrôle distribué. Par la méthode des moments on montre l’existence d’un temps minimal de contrôlabilité à zéro sous des conditions géométrique sur le couplage des deux équations. Dans un autre travail, rédigé en collaboration avec González-Burgos, on s’intéresse aux familles biorthogonales aux exponentielles complexes (dont la partie réelle est dominante), sous une condition de gap faible. On montre des estimées inférieures et supérieures de ces familles. Celles ci, sont utilisées pour obtenir le coût du contrôle du système parabolique étudié dans la première partie. Enfin, dans la dernière partie, on utilise les résultats précédents. Ils nous permettent de montrer la contrôlabilité à zéro d’un système parabolique en dimension d’espace supérieure à 1. De plus, on montre la contrôlabilité locale à zéro d’un système parabolique non linéaire de type réaction-diffusion avec un contrôle distribué
In this work we investigate the null controllability of parabolic equations and its cost. We start by studying the null controllability of the one dimensional 2 2 coupled parabolic equations, for which the associated spatial operator is of type Sturm-Liouville, with Dirichlet boundary conditions and internal control. Using the moments method we show the existence of a minimal control time connected to some geometrical conditions on the coupling terms. In an other work, with the collaboration of González-Burgos, we analyze the properties of biorthogonal families to complex exponentials (with dominant real part) under weak gap condition. We prove precise upper and lower bounds for these families. Then, we present an application of these estimates to study the control cost of the parabolic system of the first part. Finally, by using the control cost estimate, we study the null controllability properties of parabolic system, on cylindrical domain with boundary control and local null controllability properties of non linear reaction diffusion system with distributed control
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Anoh, Kelvin O. O., Raed A. Abd-Alhameed, Steven M. R. Jones, James M. Noras, Yousef A. S. Dama, A. M. Altimimi, N. T. Ali, and M. S. Alkhambashi. "Comparison of orthogonal and biorthogonal wavelets for multicarrier systems." 2013. http://hdl.handle.net/10454/9610.

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No
Wavelets are constructed from the basis sets of their parent scaling functions of the two-scale dilation equation (1). Whereas orthogonal wavelets come from one orthogonal basis set, the biorthogonal wavelets project from different basis sets. Each basis set is correspondingly weighted to form filters, either highpass or lowpass, which form the constituents of quadrature mirror filter (QMF) banks. Consequently, these filters can be used to design wavelets, the differently weighted parameters contributing respective wavelet properties which influence the performance of the transforms in applications, for example multicarrier modulation. This study investigated applications for onward multicarrier modulation applications. The results show that the optimum choice of particular wavelet adopted in digital multicarrier communication signal processing may be quite different from choices in other areas of wavelet applications, for example image and video compression.
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Phy, Lyn. "Applications of weak*-basic sequences and biorthogonal systems to question in Banach space theory /." Diss., 2000. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:9982855.

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Tian, Jun. "The mathematical theory and applications of biorthogonal Coifman wavelet systems." Thesis, 1996. http://hdl.handle.net/1911/19113.

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In this thesis, we present a theoretical study of biorthogonal Coifman wavelet systems, a family of biorthogonal wavelet systems with vanishing moments equally distributed between scaling functions and wavelet functions. One key property of these wavelet systems is that they provide nice wavelet sampling approximation with exponential decay. Moreover they are compactly supported, symmetric, have growing smoothness with large degrees, and converge to the sinc wavelet system. Using a time domain design method, the exact formulas of the coefficients of biorthogonal Coifman wavelet systems of all degrees are obtained. An attractive feature behind it is that all the coefficients are dyadic rational, which means that we can implement a very fast multiplication-free discrete wavelet transform, which consists of only addition and shift operations, on digital computers. The transform coding performance of biorthogonal Coifman wavelet systems is quite comparable to other widely used wavelet systems. The orthogonal counterparts, orthogonal Coifman wavelet systems, are also discussed in this thesis. In addition we develop a new wavelet-based embedded image coding algorithm, the Wavelet-Difference-Reduction algorithm. Unlike zerotree type schemes which use spatial orientation tree structures to implicitly locate the significant wavelet transform coefficients, this new algorithm is a direct approach to find the positions of significant coefficients. It combines the discrete wavelet transform, differential coding, binary reduction, ordered bit plane transmission, and adaptive arithmetic coding. The encoding can be stopped at any point, which allows a target rate or distortion metric to be met exactly; the decoder can also terminate the decoding at any point, and produce a corresponding reconstruction image. Our algorithm provides a fully embedded code to successively approximate the original image source; thus it's well suited for progressive image transmission. It is very simple in its form (which will make the encoding and decoding very fast), and has a clear geometric structure, which enables us to process the image data in the compressed wavelet domain. The image coding results of it are quite competitive with almost all previous reported image compression algorithms on standard test images.
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Books on the topic "Biorthogonal system"

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Biorthogonality and its applications to numerical analysis. New York: M. Dekker, 1992.

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Freund, Roland W. Formally biorthogonal polynomials and a look-ahead Levinson algorithm for general Toeplitz systems. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1992.

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Hajek, Petr, Vicente Montesinos Santalucia, and Jon Vanderwerff. Biorthogonal Systems in Banach Spaces. Springer, 2008.

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Biorthogonal Systems in Banach Spaces. New York, NY: Springer New York, 2007. http://dx.doi.org/10.1007/978-0-387-68915-9.

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Hajek, Petr, Vicente Montesinos Santalucia, Jon Vanderwerff, and Vaclav Zizler. Biorthogonal Systems in Banach Spaces. Springer, 2011.

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Biorthogonal Systems in Banach Spaces (CMS Books in Mathematics). Springer, 2007.

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Hajek, Petr, Vicente Montesinos Santalucia, Jon Vanderwerff, and Vaclav Zizler. Biorthogonal Systems in Banach Spaces (CMS Books in Mathematics). Springer New York, 2007.

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Chenoweth, David M. Chemical Tools for Imaging, Manipulating, and Tracking Biological Systems: Diverse Chemical, Optical and Biorthogonal Methods. Elsevier Science & Technology Books, 2020.

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Book chapters on the topic "Biorthogonal system"

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Ciesielski, Zbigniew. "Biorthogonal System of Polynomials on the Standard Simplex." In Multivariate Approximation Theory III, 116–19. Basel: Birkhäuser Basel, 1985. http://dx.doi.org/10.1007/978-3-0348-9321-3_11.

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Kapoor, Gaurav, Vishesh Kumar Mishra, Rabindra Nath Shaw, and Ankush Ghosh. "Fault Detection in Power Transmission System Using Reverse Biorthogonal Wavelet." In Lecture Notes in Electrical Engineering, 381–93. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0749-3_28.

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Wang, Baohong, and Yinchang Kong. "The Traits of Biorthogonal Quarternary Small Function Wraps According to Quantity Matrix Dilation." In Advances in Computer Science, Intelligent System and Environment, 101–6. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23756-0_17.

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Guirao, Antonio J., Vicente Montesinos, and Václav Zizler. "Biorthogonal Systems." In Open Problems in the Geometry and Analysis of Banach Spaces, 51–57. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-33572-8_3.

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Prasad, P. M. K., and G. Umamadhuri. "Biorthogonal Wavelet-based Image Compression." In Advances in Intelligent Systems and Computing, 391–404. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-7868-2_38.

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Valdivia, M. "On Certain Total Biorthogonal Systems in Banach Spaces." In Generalized Functions and Their Applications, 271–80. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4899-1591-7_26.

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Kapoor, Gaurav. "Protection of Nine-Phase Transmission Line Using Biorthogonal-2.2 Wavelet Transform." In Algorithms for Intelligent Systems, 119–31. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-8820-4_12.

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Rajput, Yogesh M., Ramesh R. Manza, Rathod D. Deepali, Manjiri B. Patwari, Manoj Saswade, and Neha Deshpande. "Design New Biorthogonal Wavelet Filter for Extraction of Blood Vessels and Calculate the Statistical Features." In Advances in Intelligent Systems and Computing, 647–55. New Delhi: Springer India, 2016. http://dx.doi.org/10.1007/978-81-322-2755-7_67.

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"Chapter 11: Biorthogonal Systems." In Notes on Forcing Axioms, 113–31. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814571586_0011.

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Maity, Santi P. "Spread Spectrum Watermarking." In Digital Rights Management, 559–88. IGI Global, 2013. http://dx.doi.org/10.4018/978-1-4666-2136-7.ch026.

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Spread spectrum (SS) watermarking has proven to be efficient, robust and cryptographically secure. Each bit of watermark information is embedded over wide spectrum of the host signal based on spectrum spreading concept of SS modulation in digital communication and can easily be integrated with many existing data transmission scheme. This has made SS watermarking method more attractive during recent times for many non-conventional applications such as broadcast monitoring, security in communication, authentication and blind assessment of quality of services (QoS) for multimedia signals in mobile radio network. These applications essentially demand development of low cost algorithms so that they can be implemented on real time system through hardware realization. Hardware realization offers advantages over software realization in terms of less area, low execution time, low power, real-time performance, high reliability and also ease of integration with existing consumer electronics devices. This chapter first presents a brief review on hardware implementation of digital watermarking algorithms, followed by development of hardware architecture for spatial domain and fast Walsh transform (FWT) domain SS watermark system design using field programmable gate array (FPGA). A brief sketch on hardware implementation for biorthogonal wavelet based Hilbert transform is also shown that may be extended to design SS watermarking based on the concept of two previous architectures. Few challenges for hardware design of watermarking algorithms are then mentioned with an objective to give an idea how to develop watermarking algorithms so that it can be implemented on hardware. The chapter ends with few open research problems on hardware architecture as scope of future research work.
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Conference papers on the topic "Biorthogonal system"

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BERRIOCHOA, ELÍAS, ALICIA CACHAFEIRO, and JOSÉ GARCÍA-AMOR. "A SYSTEM OF BIORTHOGONAL TRIGONOMETRIC POLYNOMIALS." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770752_0006.

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Tumin, Anatoli. "Biorthogonal Eigenfunction System in the Triple-Deck Limit." In 43rd AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2005. http://dx.doi.org/10.2514/6.2005-524.

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Liu, Zhangyi, and Jiu Hui Wu. "Wavelet Element Method for Computing Band Structures of Phononic Crystals." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-62443.

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In this paper we combine biorthogonal wavelet systems with the philosophy of Spectral Element Method to obtain a biorthogonal wavelet system on fairly general bounded domains. We also extend the boundary adaption of wavelet elements to first order derivatives allowing the construction of basis functions that exactly satisfy boundary conditions. Since this method allows us to take advantage of structural features of phononic crystals and the boundary conditions are satisfied rigorously, a better accuracy and higher efficiency can be obtained.
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Pan, Rijing, and Zhiqing Yao. "Biorthogonal Nonunifrom B-spline Wavelets with Small Supports." In 2nd International Conference on Computer Application and System Modeling. Paris, France: Atlantis Press, 2012. http://dx.doi.org/10.2991/iccasm.2012.363.

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Sun, B. X., L. J. Zhang, and Y. Zang. "Biorthogonal wavelet transformation application in intelligent attitude/heading test system." In IET International Conference on Information Science and Control Engineering 2012 (ICISCE 2012). Institution of Engineering and Technology, 2012. http://dx.doi.org/10.1049/cp.2012.2421.

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Chiquete, Carlos, and Anatoli Tumin. "Biorthogonal Eigenfunction System for Supersonic Inviscid Flow Past a Flat Plate." In 37th AIAA Fluid Dynamics Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-3982.

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Hu, Haiping, Weidong Hou, Hong Liu, and Yu L. Mo. "Construction of compactly supported biorthogonal wavelet based on Human Visual System." In International Symposium on Optical Science and Technology, edited by Mark S. Schmalz. SPIE, 2000. http://dx.doi.org/10.1117/12.409248.

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Jun Lu and Hua Li. "The characteristics of a class of biorthogonal bivariable wavelet packets." In 2009 2nd International Conference on Power Electronics and Intelligent Transportation System (PEITS). IEEE, 2009. http://dx.doi.org/10.1109/peits.2009.5406919.

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Pei, Qiuyu, and Honglin Guo. "Investigation into Characteristics of Biorthogonal Finitely Supported Nonseparable Ternary Wavelet Wraps." In 2011 Third Pacific-Asia Conference on Circuits, Communications and System (PACCS). IEEE, 2011. http://dx.doi.org/10.1109/paccs.2011.5990166.

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Chao, Huang, Huang Li-Li, Jiang Hong-Yan, and Zhong Wei-Jun. "Online Time Series Forecasting Based on Biorthogonal Wavelet Kernel Support Vector Machine." In 2012 International Conference on Computer Science and Service System (CSSS). IEEE, 2012. http://dx.doi.org/10.1109/csss.2012.16.

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