Journal articles: 'Biorthogonal system'

1

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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Rahman, Mizan. "Some Extensions of Askey-Wilson's Q-Beta Integral and the Corresponding Orthogonal Systems." Canadian Mathematical Bulletin 31, no. 4 (December 1, 1988): 467–76. http://dx.doi.org/10.4153/cmb-1988-068-6.

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AbstractA seven-parameter extension of Askey and Wilson's four parameter q-beta integral is written in a symmetric form as the sum of multiples of two very-well-poised balanced basic hypergeometric 10Φ9 series. Two special cases are considered in which the evaluation of the integral gives single terms by the q-Dixon formula in one case and by a special case of the Verma-Jain formula in the other. An orthogonal polynomial system is obtained in the first case and a system of biorthogonal rational function is obtained in the second. It is also shown that the biorthogonal system represents a generalization of Rogers’ q-ultraspherical polynomials.

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SONI, K., and N. M. TEMME. "On a Biorthogonal System associated with Uniform Asymptotic Expansions." IMA Journal of Applied Mathematics 44, no. 1 (1990): 1–25. http://dx.doi.org/10.1093/imamat/44.1.1.

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Kapustin, N. Yu. "On a spectral problem for a classical biorthogonal system." Differential Equations 52, no. 8 (August 2016): 1088–92. http://dx.doi.org/10.1134/s0012266116080152.

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MI, DONG, HE-SHAN SONG, and YING AN. "A PHYSICAL EXPLANATION FOR THE TILDE SYSTEM IN THERMO FIELD DYNAMICS." Modern Physics Letters A 16, no. 10 (March 28, 2001): 655–61. http://dx.doi.org/10.1142/s0217732301003607.

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For a two-body quantum system, any pure state can be represented by a biorthogonal expression by means of Schmidt decomposition. Using this in the composite system which includes a thermodynamic system and its surroundings, it is found that the tilde system in thermo field dynamics is just the surroundings of the real system.

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Lamichhane, Bishnu P., and Adam McNeilly. "Approximation Properties of a Gradient Recovery Operator Using a Biorthogonal System." Advances in Numerical Analysis 2015 (February 3, 2015): 1–7. http://dx.doi.org/10.1155/2015/187604.

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A gradient recovery operator based on projecting the discrete gradient onto the standard finite element space is considered. We use an oblique projection, where the test and trial spaces are different, and the bases of these two spaces form a biorthogonal system. Biorthogonality allows efficient computation of the recovery operator. We analyze the approximation properties of the gradient recovery operator. Numerical results are presented in the two-dimensional case.

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Jayakumar, K., and S. Thangavel. "Vibration Analysis of Industrial Drive for Broken Bearing Detection Using Probabilistic Wavelet Neural Network." International Journal of Power Electronics and Drive Systems (IJPEDS) 5, no. 4 (April 1, 2015): 541. http://dx.doi.org/10.11591/ijpeds.v5.i4.pp541-551.

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A reliable monitoring of industrial drives plays a vital role to prevent from the performance degradation of machinery. Today’s fault detection system mechanism uses wavelet transform for proper detection of faults, however it required more attention on detecting higher fault rates with lower execution time. Existence of faults on industrial drives leads to higher current flow rate and the broken bearing detected system determined the number of unhealthy bearings but need to develop a faster system with constant frequency domain. Vibration data acquisition was used in our proposed work to detect broken bearing faults in induction machine. To generate an effective fault detection of industrial drives, Biorthogonal Posterior Vibration Signal-Data Probabilistic Wavelet Neural Network (BPPVS-WNN) system was proposed in this paper. This system was focused to reducing the current flow and to identify faults with lesser execution time with harmonic values obtained through fifth derivative. Initially, the construction of Biorthogonal vibration signal-data based wavelet transform in BPPVS-WNN system localizes the time and frequency domain. The Biorthogonal wavelet approximates the broken bearing using double scaling and factor, identifies the transient disturbance due to fault on induction motor through approximate coefficients and detailed coefficient. Posterior Probabilistic Neural Network detects the final level of faults using the detailed coefficient till fifth derivative and the results obtained through it at a faster rate at constant frequency signal on the industrial drive. Experiment through the Simulink tool detects the healthy and unhealthy motor on measuring parametric factors such as fault detection rate based on time, current flow rate and execution time.

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Arati, S., and R. Radha. "Frames, biorthogonal dual and other properties associated with wavelet system on ℝ." International Journal of Wavelets, Multiresolution and Information Processing 17, no. 03 (May 2019): 1950008. http://dx.doi.org/10.1142/s0219691319500085.

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It is well known that the system of translates in [Formula: see text] has been characterized as Bessel sequences, frames and Riesz bases in terms of the Fourier transform. The aim of this paper is to obtain similar types of characterization for the wavelet system emerging out of integer translations and dyadic dilations. The existence of the biorthogonal dual system and nonredundancy properties of the wavelet system are also investigated here.

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Zhao, Haipeng, and Joseph Bentsman. "Biorthogonal Wavelet Based Identification of Fast Linear Time-Varying Systems—Part I: System Representations12." Journal of Dynamic Systems, Measurement, and Control 123, no. 4 (December 27, 2000): 585–92. http://dx.doi.org/10.1115/1.1409549.

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An analytical framework is developed that permits the input-output representations of discrete-time linear time-varying (LTV) systems in terms of biorthogonal bases on compact time intervals. Using these representations, the companion paper, Part II develops computational procedures for rapid identification of fast nonsmooth LTV systems based on short data records. One of the representations proposed is also used in H. Zhao and J. Bentsman, “Block Diagram Reduction of the Interconnected Linear Time-Varying Systems in the Time Frequency Domain,” accepted for publication by Multidimensional Systems and Signal Processing to form system interconnections, or wavelet networks, and develop subsystem connectibility conditions and reduction rules. Under the assumption that the inputs and the outputs of the plants considered in the present work belong to lp spaces, where p=2 or p=∞, their impulse responses are shown to belong to Banach spaces. Further on, by demonstrating that the set of all bounded-input bounded-output (BIBO) stable discrete-time LTV systems is a Banach space, the system representation problem is shown to be reducible to the linear approximation problem in the Banach space setting, with the approximation errors converging to zero as the number of terms in the representation increases. Three types of LTV system representation, based on the input-side, the output-side, and the input-output transformations, are developed and the suitability of each representation for matching a particular type of the LTV system behavior is indicated.

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Abhyankar, Aditya, and Stephanie Schuckers. "A novel biorthogonal wavelet network system for off-angle iris recognition." Pattern Recognition 43, no. 3 (March 2010): 987–1007. http://dx.doi.org/10.1016/j.patcog.2009.08.008.

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Cui, Li-hong, and Zheng-xing Cheng. "A method of construction for biorthogonal multiwavelets system with 2r multiplicity." Applied Mathematics and Computation 167, no. 2 (August 2005): 901–18. http://dx.doi.org/10.1016/j.amc.2004.06.116.

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Berenguer, M. I., D. Gámez, A. I. Garralda-Guillem, and M. C. Serrano Pérez. "Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems." Abstract and Applied Analysis 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/135216.

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We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.

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Veselovska, Ol'ga, and Veronika Dostoina. "A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable." Ukrainian Mathematical Bulletin 17, no. 2 (June 22, 2020): 256–77. http://dx.doi.org/10.37069/1810-3200-2020-17-2-7.

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For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

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Sheng, Ming Wei, Yong Jie Pang, Hai Huang, and Tie Dong Zhang. "A Novel Image Fusion Approach for Underwater Blurred Images." Applied Mechanics and Materials 427-429 (September 2013): 1807–12. http://dx.doi.org/10.4028/www.scientific.net/amm.427-429.1807.

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The main purpose of underwater image fusion is to combine multi-images about the same object into a high-quality image with abundant information. A new underwater image fusion scheme based on Biorthogonal wavelet transform was presented, which is suitable to underwater computer vision system of AUV. Firstly, median filter algorithm was involved for improving the quality and contrast of two source underwater blurred images. Secondly, the different-position-focused underwater images were decomposed by Biorthogonal wavelet and the wavelet coefficients were acquired for reconstructing the fusion image. Finally, the fused image was constructed using the low-frequency and high-frequency domain fusion rules. By adopting a series of experiments for the underwater images fusion, an integrated underwater image with visible outline and distinguishable inner details was obtained.

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Santos, Roberto B. B., and Vinícius R. da Silva. "Non-Hermitian model for asymmetric tunneling." Modern Physics Letters B 28, no. 28 (November 10, 2014): 1450223. http://dx.doi.org/10.1142/s0217984914502236.

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We present a simple non-Hermitian model to describe the phenomenon of asymmetric tunneling between two energy-degenerate sites coupled by a non-reciprocal interaction without dissipation. The system was described using a biorthogonal family of energy eigenvectors, the dynamics of the system was determined by the Schrödinger equation, and unitarity was effectively restored by proper normalization of the state vectors. The results show that the tunneling rates are indeed asymmetrical in this model, leading to an equilibrium that displays unequal occupation of the degenerate systems even in the absence of external interactions.

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Banz, Lothar, Bishnu P. Lamichhane, and Ernst P. Stephan. "Higher Order Mixed FEM for the Obstacle Problem of the p-Laplace Equation Using Biorthogonal Systems." Computational Methods in Applied Mathematics 19, no. 2 (April 1, 2019): 169–88. http://dx.doi.org/10.1515/cmam-2018-0015.

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AbstractWe consider a mixed finite element method for an obstacle problem with the p-Laplace differential operator for {p\in(1,\infty)}, where the obstacle condition is imposed by using a Lagrange multiplier. In the discrete setting the Lagrange multiplier basis forms a biorthogonal system with the standard finite element basis so that the variational inequality can be realized in the point-wise form. We provide a general a posteriori error estimate for adaptivity and prove an a priori error estimate. We present numerical results for the adaptive scheme (mesh-size adaptivity with and without polynomial degree adaptation) for the singular case {p=1.5} and the degenerated case {p=3}. We also present numerical results on the mesh independency and on the polynomial degree scaling of the discrete inf-sup constant when using biorthogonal basis functions for the dual variable defined on the same mesh with the same polynomial degree distribution.

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Ivasyk, Halyna. "The system of powers of conformal mappings and biorthogonal to them systems of the functions." Physico-mathematical modelling and informational technologies, no. 26 (December 30, 2017): 31–44. http://dx.doi.org/10.15407/fmmit2017.26.031.

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In this article we review the methods of power summation of factors. The degree of factors which are arbitrary powers of summation indices are considered. We show that using the Poisson-Abel method only those series can be summarized the order of member increase of which is proportional to the exponent depending on the summation index. At the same time the Gauss-Weierstrass method and other power factors methods can be also applied to the series the terms of which increase in proportion to the exponential dependence of the indices summation.

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YANG, GUOAN, and NANNING ZHENG. "AN OPTIMIZATION ALGORITHM FOR BIORTHOGONAL WAVELET FILTER BANKS DESIGN." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 01 (January 2008): 51–63. http://dx.doi.org/10.1142/s0219691308002215.

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A new approach for designing the Biorthogonal Wavelet Filter Bank (BWFB) for the purpose of image compression is presented in this paper. The approach is broken into two steps. First, an optimal filter bank is designed in the theoretical sense, based on Vaidyanathan's coding gain criterion in the SubBand Coding (SBC) system. Then, the above filter bank is optimized based on the criterion of Peak Signal-to-Noise Ratio (PSNR) in the JPEG2000 image compression system, resulting in a BWFB in practical application sense. With the approach, a series of BWFBs for a specific class of applications related to image compression, such as gray-level images, can be quickly designed. Here, new 7/5 BWFBs are presented based on the above approach for image compression applications. Experiments show that the 7/5 BWFBs not only have excellent compression performance, but also easy computation and are more suitable for VLSI hardware implementations. They perform equally well with respect to 7/5 filters in the JPEG2000 standard.

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Gorenflo, Norbert. "A biorthogonal system for an axialsymmetric disk problem for the Helmholtz equation." Integral Transforms and Special Functions 20, no. 6 (June 2009): 449–57. http://dx.doi.org/10.1080/10652460802645784.

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Benvenuto, Nevio, Franco Chiaraluce, Paolo Falcioni, and Sante Andreoli. "Performance analysis of trellis coded biorthogonal sequences in a variable rate system." European Transactions on Telecommunications 3, no. 3 (May 1992): 231–35. http://dx.doi.org/10.1002/ett.4460030304.

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Wang, Huiqi. "Biorthogonal Frequency Division Multiple Access Cellular System with Angle Division Reuse Scheme." Wireless Personal Communications 70, no. 4 (July 18, 2012): 1553–73. http://dx.doi.org/10.1007/s11277-012-0765-5.

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Agrawal, Ritu, Manisha Sharma, and Bikesh Kumar Singh. "Segmentation of Brain Tumour Based on Clustering Technique: Performance Analysis." Journal of Intelligent Systems 28, no. 2 (April 24, 2019): 291–306. http://dx.doi.org/10.1515/jisys-2017-0027.

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AbstractManual detection and analysis of brain tumours is an exhaustive and time-consuming process. Further, it is subject to intra-observer and inter-observer variabilities. Automated brain tumour segmentation and analysis has thus gained much attention in recent years. However, the existing segmentation techniques do not meet the requirements of real-time use due to limitations posed by poor image quality and image complexity. This article proposes a hybrid approach for image segmentation by combining biorthogonal wavelet transform, skull stripping, fuzzy c-means threshold clustering, Canny edge detection, and morphological operations. Biorthogonal wavelet transform and skull stripping are essential pre-processing steps for analysis of brain images. Initially, biorthogonal wavelet transform is used to remove impulsive noise and skull stripping is employed to eliminate non-cerebral tissue regions from the acquired images, followed by segmentation using fuzzy c-means threshold clustering, Canny edge detection, and morphological processing. The performance of the proposed automated system is tested on standard datasets using performance measures such as Jaccard index, Dice similarity coefficient, execution time, and entropy. The proposed method achieves a Jaccard index and Dice similarity coefficient of 0.886 and 0.935, respectively, which indicate better overlap between the automated segmentation method and manual segmentation method performed by an expert radiologist. The average execution time and average entropy values obtained are 1.001 s and 0.202, respectively. The results obtained are discussed in view of some reported studies in terms of execution time and tumour area. Further work is needed to evaluate the proposed method in routine clinical practice and its effect on radiologists’ performances.

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Mohammad, Mutaz. "Biorthogonal-Wavelet-Based Method for Numerical Solution of Volterra Integral Equations." Entropy 21, no. 11 (November 10, 2019): 1098. http://dx.doi.org/10.3390/e21111098.

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Framelets theory has been well studied in many applications in image processing, data recovery and computational analysis due to the key properties of framelets such as sparse representation and accuracy in coefficients recovery in the area of numerical and computational theory. This work is devoted to shedding some light on the benefits of using such framelets in the area of numerical computations of integral equations. We introduce a new numerical method for solving Volterra integral equations. It is based on pseudo-spline quasi-affine tight framelet systems generated via the oblique extension principles. The resulting system is converted into matrix equations via these generators. We present examples of the generated pseudo-splines quasi-affine tight framelet systems. Some numerical results to validate the proposed method are presented to illustrate the efficiency and accuracy of the method.

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Veselovska, O. V., V. V. Dostoina, and M. I. Klapchuk. "Properties of the second-kind Chebyshev polynomials of complex variable." Researches in Mathematics 28, no. 2 (December 28, 2020): 35. http://dx.doi.org/10.15421/242009.

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We construct a system of functions biorthogonal with Chebyshev polynomials of the second kind on closed contours in the complex plane. Properties of these functions and sufficient conditions of expansion of analytic functions into series in Chebyshev polynomials of the second kind in complex domains are investigated. The examples of such expansions are given. In addition, combinatorial identities of self-interest are obtained.

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Abou-Rjeily, C., N. Daniele, and J. C. Belfiore. "A 2 x 2 antennas ultra-wideband system with biorthogonal pulse position modulation." IEEE Communications Letters 10, no. 5 (May 2006): 366–68. http://dx.doi.org/10.1109/lcomm.2006.1633325.

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Wagner, Marcel, Felix Dangel, Holger Cartarius, Jörg Main, and Günter Wunner. "NUMERICAL CALCULATION OF THE COMPLEX BERRY PHASE IN NON-HERMITIAN SYSTEMS." Acta Polytechnica 57, no. 6 (December 30, 2017): 470. http://dx.doi.org/10.14311/ap.2017.57.0470.

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We numerically investigate topological phases of periodic lattice systems in tight-binding description under the influence of dissipation. The effects of dissipation are effectively described by <em>PT</em>-symmetric potentials. In this framework we develop a general numerical gauge smoothing procedure to calculate complex Berry phases from the biorthogonal basis of the system's non-Hermitian Hamiltonian. Further, we apply this method to a one-dimensional <em>PT</em>-symmetric lattice system and verify our numerical results by an analytical calculation.

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Brown, Jeffrey M., and Miroslav Kolesik. "Properties of Stark Resonant States in Exactly Solvable Systems." Advances in Mathematical Physics 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/125832.

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Properties of Stark resonant states are studied in two exactly solvable systems. These resonances are shown to form a biorthogonal system with respect to a pairing defined by a contour integral that selects states with outgoing wave boundary conditions. Analytic expressions are derived for the pseudonorm, dipole moment, and coupling matrix elements which relate systems with different strengths of the external field. All results are based on explicit calculations made possible by a newly designed integration method for combinations of Airy functions representing resonant eigenstates. Generalizations for one-dimensional systems with short-range potentials are presented, and relations are identified which are likely to hold in systems with three spatial dimensions.

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Zhang, Ming, Zhuo Ma, and Min Xuan Zhang. "FPGA Implementation of Rational Symmetric Biorthogonal 11-9 Wavelet Transform." Applied Mechanics and Materials 182-183 (June 2012): 1791–95. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1791.

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Coefficients of most existing wavelets are irrational, and it costs much hardware resources when implementing on FPGA, which is inefficient especially in embedded system. Some rational wavelets can overcome this deficiency by elaborate design. Motivated by previous works on rational wavelets, we establish a hardware structure for rational 1-D symmetric biorthogonal 11-9 wavelet and implement it on Xilinx FPGA XC3S500E. The experiment reveals that the area in slices of rational 1-D 11-9 wavelet is less than 1/2 of the pipelined 9-7 wavelet when implementing on FPGA.

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Frikha, Tarek, Najmeddine Abdennour, Faten Chaabane, Oussama Ghorbel, Rami Ayedi, Osama R. Shahin, and Omar Cheikhrouhou. "Source Localization of EEG Brainwaves Activities via Mother Wavelets Families for SWT Decomposition." Journal of Healthcare Engineering 2021 (April 28, 2021): 1–11. http://dx.doi.org/10.1155/2021/9938646.

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A Brain-Computer Interface (BCI) is a system used to communicate with an external world through the brain activity. The brain activity is measured by electroencephalography (EEG) signal and then processed by a BCI system. EEG source reconstruction could be a way to improve the accuracy of EEG classification in EEG based brain-computer interface (BCI). The source localization of the human brain activities can be an important resource for the recognition of the cognitive state, medical disorders, and a better understanding of the brain in general. In this study, we have compared 51 mother wavelets taken from 7 different wavelet families, which are applied to a Stationary Wavelet Transform (SWT) decomposition of an EEG signal. This process includes Haar, Symlets, Daubechies, Coiflets, Discrete Meyer, Biorthogonal, and reverse Biorthogonal wavelet families in extracting five different brainwave subbands for source localization. For this process, we used the Independent Component Analysis (ICA) for feature extraction followed by the Boundary Element Model (BEM) and the Equivalent Current Dipole (ECD) for the forward and inverse problem solutions. The evaluation results in investigating the optimal mother wavelet for source localization eventually identified the sym20 mother wavelet as the best choice followed by bior6.8 and coif5.

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Weidman, Patrick D., Syahira Mansur, and Anuar Ishak. "Biorthogonal stretching and shearing of an impermeable surface in a uniformly rotating fluid system." Meccanica 52, no. 7 (August 6, 2016): 1515–25. http://dx.doi.org/10.1007/s11012-016-0507-y.

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Hou, GuoLin, GaoWa Qi, YaNan Xu, and Alatancang Chen. "The separable Hamiltonian system and complete biorthogonal expansion method of Mindlin plate bending problems." Science China Physics, Mechanics and Astronomy 56, no. 5 (April 19, 2013): 974–80. http://dx.doi.org/10.1007/s11433-013-5062-0.

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Zhao, Haipeng, and Joseph Bentsman. "Biorthogonal Wavelet Based Identification of Fast Linear Time-Varying Systems—Part II: Algorithms and Performance Analysis12." Journal of Dynamic Systems, Measurement, and Control 123, no. 4 (December 27, 2000): 593–600. http://dx.doi.org/10.1115/1.1409550.

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The present work proposes a new class of algorithms for identification of fast linear time-varying systems on short time intervals, based on the biorthogonal function decomposition. When certain features of the system dynamics are known a priori, the algorithms admit their embedding into the identification procedure through the choice of the matching bases, yielding the rapidly convergent identification laws. The speed-up is attained via utilizing both time and frequency localized bases, permitting identification of fewer coefficients without noticeable loss of accuracy. Simulation shows that the resulting high speed identification algorithms can reject small persistent random disturbances as well as capture the fast changes in system dynamics. The algorithm development is based on the results of Part I where it is shown that the sets of all bounded-input-bounded-output (BIBO) stable or l2-stable linear discrete-time-varying (LTV) systems are Banach spaces, and modeling and identification of these systems are reducible to linear approximation problems in a Banach space setting.

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Huang, Bo, Peng Jiao Sun, and Xiao Man Wang. "The Denoising Method Based on Wavelet Transform in Signal Dynamic Detection." Advanced Materials Research 889-890 (February 2014): 766–69. http://dx.doi.org/10.4028/www.scientific.net/amr.889-890.766.

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In this paper the application of wavelet in data detection of dynamic testing is chiefly researched , i.e. , by applying the method of wavelet denoising to eliminate the non-stationary random noise which produced in data detection of dynamic testing , by analyzing dynamic testing data to define the optimal wavelet as well as the optimal decomposition scale. Based on actual requirements of dynamic testing system, to reconstruct the data accurately by using FIR filter with biorthogonal wavelet, the method has a favorable effect.

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Lamichhane, Bishnu Prasad. "A mixed finite element method based on a biorthogonal system for nearly incompressible elastic problems." ANZIAM Journal 50 (November 17, 2008): 324. http://dx.doi.org/10.21914/anziamj.v50i0.1422.

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Ji, Hong-Keun, Guoming Wang, and Gyung-Suk Kil. "Optimal Detection and Identification of DC Series Arc in Power Distribution System on Shipboards." Energies 13, no. 22 (November 16, 2020): 5973. http://dx.doi.org/10.3390/en13225973.

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In this paper, a series arc was simulated under resistive load and motor load, which are mainly used in small ships, and the arc signal was analyzed using discrete wavelet transform. After calculating the correlation coefficient between the single arc pulse and the wavelet, Biorthogonal (bior) 3.1 was selected as the optimal mother wavelet, and the signal was analyzed using multiresolution analysis. From the results, arc signals were distributed in the detail components D2, D3, D4 and D5, corresponding to a frequency range of 19.5–312.5 kHz, with the optimal arc signal extracted based on these values. In addition, in order to distinguish between arc and normal conditions, signal energy was analyzed. By applying the magnitude and signal energy analysis method, the DC series arc generated in the power distribution system of a shipboard was identified.

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Eleuch, Hichem, and Ingrid Rotter. "Loss, Gain, and Singular Points in Open Quantum Systems." Advances in Mathematical Physics 2018 (September 2, 2018): 1–9. http://dx.doi.org/10.1155/2018/3653851.

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Non-Hermitian quantum physics is used successfully for the description of different puzzling experimental results, which are observed in open quantum systems. Mostly, the influence of exceptional points on the dynamical properties of the system is studied. At these points, two complex eigenvalues Ei≡Ei+iΓi/2 of the non-Hermitian Hamiltonian H coalesce (where Ei is the energy and Γi is the inverse lifetime of the state i). We show that also the eigenfunctions Φi of the two states play an important role, sometimes even the dominant one. Besides exceptional points, other critical points exist in non-Hermitian quantum physics. At these points a=acr in the parameter space, the biorthogonal eigenfunctions of H become orthogonal. For illustration, we show characteristic numerical results.

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Garif’yanov, F. N., and E. V. Strezhneva. "On a system of entire functions of class A which is biorthogonal to a lacunar power system on the ray." Siberian Mathematical Journal 58, no. 1 (January 2017): 63–66. http://dx.doi.org/10.1134/s0037446617010086.

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Lamichhane, Bishnu Prasad, and Michael H. Meylan. "A new MITC finite element method for Reissner--Mindlin plate problem based on a biorthogonal system." ANZIAM Journal 58 (July 16, 2017): 1. http://dx.doi.org/10.21914/anziamj.v58i0.11754.

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Chakib, Houda, Brahim Minaoui, Abderrahim Salhi, and Imad Badi. "Switching of Wavelet Transforms by Neural Network for Image Compression." Journal of Electronic Commerce in Organizations 16, no. 1 (January 2018): 43–56. http://dx.doi.org/10.4018/jeco.2018010104.

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Nowadays, digital images compression requires more and more significant attention of researchers. Even when high data rates are available, image compression is necessary in order to reduce the memory used, as well the transmission cost. An ideal image compression system must yield high-quality compressed image with high compression ratio. In this article, a neural network is implemented for image compression using the feature of wavelet transform. The idea is that a back-propagation neural network can be trained to relate the image contents to its ideal compression method between two different wavelet transforms: orthogonal (Haar) and biorthogonal (bior4.4).

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Goh, Say Song, S. L. Lee, Zuowei Shen, and W. S. Tang. "Construction of Schauder decomposition on banach spaces of periodic functions." Proceedings of the Edinburgh Mathematical Society 41, no. 1 (February 1998): 61–91. http://dx.doi.org/10.1017/s001309150001943x.

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This paper deals with Schauder decompositions of Banach spaces X2π of 2π-periodic functions by projection operators Pk onto the subspaces Vk, k = 0,1,…, which form a multiresolution of X2π,. The results unify the study of wavelet decompositions by orthogonal projections in the Hilbert space on one hand and by interpolatory projections in the Banach space C2π on the other. The approach, using “orthogonal splines”, is constructive and leads to the construction of a Schauder decomposition of X2π and a biorthogonal system for X2π, and its dual X2π. Decomposition and reconstruction algorithms are derived from the construction.

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Zhang, Guang Bin, Yun Jian Ge, and Yong Jiu Liu. "Fault Diagnosis of Gearbox Based on Wavelet Transforms and Neural Networks." Applied Mechanics and Materials 148-149 (December 2011): 919–22. http://dx.doi.org/10.4028/www.scientific.net/amm.148-149.919.

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In this paper, an actual system based on wavelet transform and artificial neural networks was established to diagnose different types of fault in a gearbox. As a key step, biorthogonal wavelet was used to denoise in feature extraction of signals because of its properties of compact support, high vanishing moment and symmetry. Consequently, a multi-layer perceptron network were designed to diagnose the fault status with feature vectors as inputs. In order to improve the network learning speed and stability, Levenberg-Marquardt algorithm was used to train the network. The present classification accuracy indicates the effectiveness of gearbox failure diagnosis.

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Journal articles on the topic 'Biorthogonal system'

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