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Journal articles on the topic 'Projection operator'

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Author: Grafiati

Published: 4 June 2021

Last updated: 28 January 2023

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1

KhaIiI Ibrahim Kadhim. "Principal Components Analysis as enhancement Operator and Compression factor." journal of the college of basic education 17, no. 72 (June 17, 2019): 25–33. http://dx.doi.org/10.35950/cbej.v17i72.4495.

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Principal components analysis (PCA) is effective at compressing information in multivariate data sets by computing orthogonal projections that maximize the amount of data variance. Unfortunately, information content in hyper spectral images does not always coincide with such projections. We propose an application of projection pursuit (pp), which seeks to find a set of projections that are "interesting" in the sense that they deviate from the Gaussian distribution assumption. Once these projections are obtained, they can be used for image compression, segmentation, or enhancement for visual analysis. To find these projections, a two –step iterative process is followed where we first search for a projection that maximizes a projection index based on the information divergence of the projections estimated probability distribution from the Gaussian distribution and then reduce the rank by projections the data on to the subspace orthogonal to the previous projection . To calculate each projections, we use a simplified approach to maximizing the projection index, which does not require optimization algorithm. It searches for a solution by obtaining a set of candidate projections from the data and choosing the one with the highest projection index. The effectiveness of the method is demonstrated through simulated examples as well as data from the hyper spectral digital imagery collection experiment and the spatially enhanced broadband and array spectrograph system.

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2

Orr, John Lindsay, and David R. Pitts. "Factorization of triangular operators and ideals through the diagonal." Proceedings of the Edinburgh Mathematical Society 40, no. 2 (June 1997): 227–41. http://dx.doi.org/10.1017/s0013091500023671.

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We give a necessary and sufficient condition to determine when an operator in the nest algebra of doubly infinite block upper triangular operators factors through a diagonal projection. An example shows that this condition does not extend to more general nest algebras, but a similar criterion yields a description of the ideals of nest algebras generated by diagonal projections.

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3

LIU, GAO-FU, HONG-LING LIU, and GUANG-JIE GUO. "ON DEFORMED BOSON ALGEBRA AND VACUUM PROJECTION OPERATOR ON NONCOMMUTATIVE PLANE." International Journal of Modern Physics A 28, no. 07 (March 14, 2013): 1350020. http://dx.doi.org/10.1142/s0217751x13500206.

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In the noncommutative phase space, a new mapping is proposed to express the noncommutative coordinate and momentum operators in terms of the ordinary coordinate and momentum operators under the case of large noncommutativity parameters (μν>1). Using this mapping matrix, the deformed boson operators can be expressed in terms of the ordinary boson operators. Thus, the normal ordering expansion form of vacuum projection operator is obtained. As an application, the completeness relation of the two-mode deformed coherent states is verified by using the vacuum projection operator.

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4

BOYLAN, MATTHEW. "ARITHMETIC PROPERTIES OF CERTAIN LEVEL ONE MOCK MODULAR FORMS." International Journal of Number Theory 06, no. 01 (February 2010): 185–202. http://dx.doi.org/10.1142/s1793042110002855.

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In a recent work, Bringmann and Ono [4] show that Ramanujan's f(q) mock theta function is the holomorphic projection of a harmonic weak Maass form of weight 1/2. In this paper, we extend the work of Ono in [13]. In particular, we study holomorphic projections of certain integer weight harmonic weak Maass forms on SL 2(ℤ) using Hecke operators and the differential theta-operator.

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5

Surasinghe, Sudam, and Erik M. Bollt. "Randomized Projection Learning Method for Dynamic Mode Decomposition." Mathematics 9, no. 21 (November 4, 2021): 2803. http://dx.doi.org/10.3390/math9212803.

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A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on a projected space. In the spirit of Johnson–Lindenstrauss lemma, we will use a random projection to estimate the DMD modes in a reduced dimensional space. In practical applications, snapshots are in a high-dimensional observable space and the DMD operator matrix is massive. Hence, computing DMD with the full spectrum is expensive, so our main computational goal is to estimate the eigenvalue and eigenvectors of the DMD operator in a projected domain. We generalize the current algorithm to estimate a projected DMD operator. We focus on a powerful and simple random projection algorithm that will reduce the computational and storage costs. While, clearly, a random projection simplifies the algorithmic complexity of a detailed optimal projection, as we will show, the results can generally be excellent, nonetheless, and the quality could be understood through a well-developed theory of random projections. We will demonstrate that modes could be calculated for a low cost by the projected data with sufficient dimension.

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6

Yamaev, A. V., M. V. Chukalina, D. P. Nikolaev, L. G. Kochiev, and A. I. Chulichkov. "Neural network regularization in the problem of few-view computed tomography." Computer Optics 46, no. 3 (June 2022): 422–28. http://dx.doi.org/10.18287/2412-6179-co-1035.

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The computed tomography allows to reconstruct the inner morphological structure of an object without physical destructing. The accuracy of digital image reconstruction directly depends on the measurement conditions of tomographic projections, in particular, on the number of recorded projections. In medicine, to reduce the dose of the patient load there try to reduce the number of measured projections. However, in a few-view computed tomography, when we have a small number of projections, using standard reconstruction algorithms leads to the reconstructed images degradation. The main feature of our approach for few-view tomography is that algebraic reconstruction is being finalized by a neural network with keeping measured projection data because the additive result is in zero space of the forward projection operator. The final reconstruction presents the sum of the additive calculated with the neural network and the algebraic reconstruction. First is an element of zero space of the forward projection operator. The second is an element of orthogonal addition to the zero space. Last is the result of applying the algebraic reconstruction method to a few-angle sinogram. The dependency model between elements of zero space of forward projection operator and algebraic reconstruction is built with neural networks. It demonstrated that realization of the suggested approach allows achieving better reconstruction accuracy and better computation time than state-of-the-art approaches on test data from the Low Dose CT Challenge dataset without increasing reprojection error.

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7

Bögli, Sabine, and Marco Marletta. "Essential numerical ranges for linear operator pencils." IMA Journal of Numerical Analysis 40, no. 4 (November 22, 2019): 2256–308. http://dx.doi.org/10.1093/imanum/drz049.

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Abstract We introduce concepts of essential numerical range for the linear operator pencil $\lambda \mapsto A-\lambda B$. In contrast to the operator essential numerical range, the pencil essential numerical ranges are, in general, neither convex nor even connected. The new concepts allow us to describe the set of spectral pollution when approximating the operator pencil by projection and truncation methods. Moreover, by transforming the operator eigenvalue problem $Tx=\lambda x$ into the pencil problem $BTx=\lambda Bx$ for suitable choices of $B$, we can obtain nonconvex spectral enclosures for $T$ and, in the study of truncation and projection methods, confine spectral pollution to smaller sets than with hitherto known concepts. We apply the results to various block operator matrices. In particular, Theorem 4.12 presents substantial improvements over previously known results for Dirac operators while Theorem 4.5 excludes spectral pollution for a class of nonselfadjoint Schrödinger operators which has not been possible to treat with existing methods.

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8

Macdonald, Gordon W. "Distance From Projections to Nilpotents." Canadian Journal of Mathematics 47, no. 4 (August 1, 1995): 841–51. http://dx.doi.org/10.4153/cjm-1995-043-3.

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AbstractThe distance from an arbitrary rank-one projection to the set of nilpotent operators, in the space of k × k matrices with the usual operator norm, is shown to be sec(π/(k:+2))/2. This gives improved bounds for the distance between the set of all non-zero projections and the set of nilpotents in the space of k × k matrices. Another result of note is that the shortest distance between the set of non-zero projections and the set of nilpotents in the space of k × k matrices is .

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9

Semin, Vitalii, and Francesco Petruccione. "Projection operator based expansion of the evolution operator." Journal of Physics A: Mathematical and Theoretical 49, no. 42 (September 23, 2016): 425301. http://dx.doi.org/10.1088/1751-8113/49/42/425301.

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10

Davidsen, Cedric, Kirsten Bolstad, Kristian Ytre-Hauge, Andreas Tefre Samnøy, Kjell Vikenes, and Vegard Tuseth. "Effect of an optimized X-ray blanket design on operator radiation dose in cardiac catheterization based on real-world angiography." PLOS ONE 17, no. 11 (November 10, 2022): e0277436. http://dx.doi.org/10.1371/journal.pone.0277436.

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Background There is increasing concern and focus in the interventional cardiology community on potential long term health issues related to radiation exposure and heavy wearable protection. Optimized shielding measures may reduce operator dose to levels where lighter radioprotective garments can safely be used, or even omitted. X-ray blankets (XRB) are commercially available but suffer from small size and lack of stability. A larger XRB may reduce operator dose but could hamper vascular access and visualization. The aim of this study is to assess shielding effect of an optimized XRB during cardiac catheterization and estimate the potential reduction in annual operator dose based on DICOM Radiation Dose Structured Report (RDSR) data reflecting everyday clinical practice. Methods Data accumulated from 7681 procedures over three years in our RDSR repository was used to identify projection angles and radiation doses during cardiac catheterization. Using an anthropomorphic phantom and a scatter radiation detector, radiation dose to the operator (mSv) and patient (dose area product—DAP) was measured for each angiographic projection for three different shielding setups. Relative operator dose (mSv/DAP) was calculated and multiplied by DAP per projection to estimate effect on operator dose. Results Adding an optimized XRB to a standard shielding setup comprising a table- and ceiling-mounted shield resulted in a 94.9% reduction in estimated operator dose. The largest shielding effect was observed in left and cranial projections where the ceiling-mounted shield offered less protection. Conclusions An optimized XRB is a simple shielding measure that has the potential to reduce operator dose.

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11

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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12

Cai, Z., M. S. deQueiroz, and D. M. Dawson. "A Sufficiently Smooth Projection Operator." IEEE Transactions on Automatic Control 51, no. 1 (January 2006): 135–39. http://dx.doi.org/10.1109/tac.2005.861704.

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13

Maurischat, Kathrin. "Sturm’s operator for scalar weight in arbitrary genus." International Journal of Number Theory 13, no. 10 (October 16, 2017): 2677–86. http://dx.doi.org/10.1142/s1793042117501482.

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In contrast to the well-known cases of large weights, Sturm’s operator does not realize the holomorphic projection operator for lower weights. We prove its failure for arbitrary Siegel modular forms of genus [Formula: see text] and scalar weight [Formula: see text]. This generalizes a result for genus two in [K. Maurischat and R. Weissauer, Phantom holomorphic projections arising from Sturm’s formula, preprint (2016)].

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14

Sanghi, Anupam, Shadab Ahmed, and Jayant R. Haritsa. "Projection-compliant database generation." Proceedings of the VLDB Endowment 15, no. 5 (January 2022): 998–1010. http://dx.doi.org/10.14778/3510397.3510398.

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Synthesizing data using declarative formalisms has been persuasively advocated in contemporary data generation frameworks. In particular, they specify operator output volumes through row-cardinality constraints. However, thus far, adherence to these volumetric constraints has been limited to the Filter and Join operators. A critical deficiency is the lack of support for the Projection operator, which is at the core of basic SQL constructs such as Distinct, Union and Group By. The technical challenge here is that cardinality unions in multi-dimensional space, and not mere summations, need to be captured in the generation process. Further, dependencies across different data subspaces need to be taken into account. We address the above lacuna by presenting PiGen , a dynamic data generator that incorporates Projection cardinality constraints in its ambit. The design is based on a projection subspace division strategy that supports the expression of constraints using optimized linear programming formulations. Further, techniques of symmetric refinement and workload decomposition are introduced to handle constraints across different projection subspaces. Finally, PiGen supports dynamic generation, where data is generated on-demand during query processing, making it amenable to Big Data environments. A detailed evaluation on workloads derived from real-world and synthetic benchmarks demonstrates that PiGen can accurately and efficiently model Projection outcomes, representing an essential step forward in customized database generation.

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15

Nakazi, Takahiko, and Tomoko Osawa. "Finite-rank intermediate Hankel operators on the Bergman space." International Journal of Mathematics and Mathematical Sciences 25, no. 1 (2001): 19–31. http://dx.doi.org/10.1155/s0161171201001971.

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LetL2=L2(D,r dr dθ/π)be the Lebesgue space on the open unit disc and letLa2=L2∩ℋol(D)be the Bergman space. LetPbe the orthogonal projection ofL2ontoLa2and letQbe the orthogonal projection ontoL¯a,02={g∈L2;g¯∈La2, g(0)=0}. ThenI−P≥Q. The big Hankel operator and the small Hankel operator onLa2are defined as: forϕinL∞,Hϕbig(f)=(I−P)(ϕf)andHϕsmall(f)=Q(ϕf)(f∈La2). In this paper, the finite-rank intermediate Hankel operators betweenHϕbigandHϕsmallare studied. We are working on the more general space, that is, the weighted Bergman space.

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16

McDonald, G., and C. Sundberg. "On the Spectra of Unbounded Subnormal Operators." Canadian Journal of Mathematics 38, no. 5 (October 1, 1986): 1135–48. http://dx.doi.org/10.4153/cjm-1986-057-x.

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Putnam showed in [5] that the spectrum of the real part of a bounded subnormal operator on a Hilbert space is precisely the projection of the spectrum of the operator onto the real line. (In fact he proved this more generally for bounded hyponormal operators.) We will show that this result can be extended to the class of unbounded subnormal operators with bounded real parts.Before proceeding we establish some notation. If T is a (not necessarily bounded) operator on a Hilbert space, then D(T) will denote its domain, and σ(T) its spectrum. For K a subspace of D(T), T|K will denote the restriction of T to K. Norms of bounded operators and elements in Hilbert spaces will be indicated by ‖ ‖. All Hilbert space inner products will be written 〈,〉. If W is a set in C, the closure of W will be written clos W, the topological boundary will be written bdy W, and the projection of W onto the real line will be written π(W),

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17

Lamb, Wilson, Ian Murdoch, and John Stewart. "On an operator identity central to projection operator methodology." Physica A: Statistical Mechanics and its Applications 298, no. 1-2 (September 2001): 121–39. http://dx.doi.org/10.1016/s0378-4371(01)00214-x.

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18

Hasebe, Kazuki. "Relativistic Landau models and generation of fuzzy spheres." International Journal of Modern Physics A 31, no. 20n21 (July 27, 2016): 1650117. http://dx.doi.org/10.1142/s0217751x16501177.

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Noncommutative geometry naturally emerges in low energy physics of Landau models as a consequence of level projection. In this work, we proactively utilize the level projection as an effective tool to generate fuzzy geometry. The level projection is specifically applied to the relativistic Landau models. In the first half of the paper, a detail analysis of the relativistic Landau problems on a sphere is presented, where a concise expression of the Dirac–Landau operator eigenstates is obtained based on algebraic methods. We establish [Formula: see text] “gauge” transformation between the relativistic Landau model and the Pauli–Schrödinger nonrelativistic quantum mechanics. After the [Formula: see text] transformation, the Dirac operator and the angular momentum operators are found to satisfy the [Formula: see text] algebra. In the second half, the fuzzy geometries generated from the relativistic Landau levels are elucidated, where unique properties of the relativistic fuzzy geometries are clarified. We consider mass deformation of the relativistic Landau models and demonstrate its geometrical effects to fuzzy geometry. Super fuzzy geometry is also constructed from a supersymmetric quantum mechanics as the square of the Dirac–Landau operator. Finally, we apply the level projection method to real graphene system to generate valley fuzzy spheres.

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19

Wu, Ke-Qing, and Nan-Jing Huang. "The generalised f-projection operator with an application." Bulletin of the Australian Mathematical Society 73, no. 2 (April 2006): 307–17. http://dx.doi.org/10.1017/s0004972700038892.

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In this paper, we introduce a new concept of generalised f-projection operator which extends the generalised projection operator πK : B* → K, where B is a reflexive Banach space with dual space B* and K is a nonempty, closed and convex subset of B. Some properties of the generalised f-projection operator are given. As an application, we study the existence of solution for a class of variational inequalities in Banach spaces.

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20

Мартынов, Олег Михайлович. "Projection constants of the space $l_\infty^{3m}$." Herald of Tver State University. Series: Applied Mathematics, no. 3(66) (December 1, 2022): 76–90. http://dx.doi.org/10.26456/vtpmk642.

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В работе рассматриваются минимальные проекции пространства $l_\infty^{3m}$ на некоторые подпространства коразмерности $m$. Для них найдены относительные проекционные константы, а в случае минимальной проекции с единичной нормой найдено максимальное значение константы сильной единственности. Найденные проекционные константы могут найти применение в вычислительной математике, в частности, для оценки сходимости проекционных методов. The paper considers minimal projections of the space $l_\infty^{3m}$ on some subspace of codimension $m$. Relative projection constants are found for them, and in the case of a minimal projection with a unit norm, the maximum value of the strong uniqueness constant is found. The projection constants found can be used in computational mathematics, in particular, to assess the convergence of projection methods for solving operator equations.

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21

MICULA, SANDA. "On spline collocation and the Hilbert transform." Carpathian Journal of Mathematics 31, no. 1 (2015): 89–95. http://dx.doi.org/10.37193/cjm.2015.01.10.

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In this paper we examine a relationship between the spline collocation projection operator πn and the Hilbert singular integral operator H0. We use Fourier analysis to prove that under certain conditions, a commutator property holds between the two operators. More specifically, we show that for u ∈ Ht, ||(πnH0 − H0πn)u||t ≤ Chλ||u||s (where h = 1/n), for some t, s and λ ∈ R.

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22

FAN, HONG-YI, and GUI-CHUAN YU. "RADON TRANSFORMATION OF THE WIGNER OPERATOR FOR TWO-MODE CORRELATED SYSTEM IN GENERALIZED ENTANGLED STATE REPRESENTATION." Modern Physics Letters A 15, no. 07 (March 7, 2000): 499–507. http://dx.doi.org/10.1142/s0217732300000487.

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We introduce a generalized entangled state |η,λ1,λ2>, which spans a complete and orthonormal representation. Using the technique of integration within an ordered product of operators we prove that the projection operator |η,λ1,λ2><η,λ1,λ2| is just the Radon transformation of the entangled Wigner operator. The inverse Radon transformation is also derived and the tomography theory for two-mode correlated system is established.

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23

Gumenchuk, A., I. Krasikova, and M. Popov. "On linear sections of orthogonally additive operators." Matematychni Studii 58, no. 1 (October 31, 2022): 94–102. http://dx.doi.org/10.30970/ms.58.1.94-102.

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Our first result asserts that, for linear regular operators acting from a Riesz space with the principal projection property to a Banach lattice with an order continuous norm, the $C$-compactness is equivalent to the $AM$-compactness. Next we prove that, under mild assumptions, every linear section of a $C$-compact orthogonally additive operator is $AM$-compact, and every linear section of a narrow orthogonally additive operator is narrow.

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24

Douar, Brahim, Chiraz Latiri, Michel Liquiere, and Yahya Slimani. "A Projection Bias in Frequent Subgraph Mining Can Make a Difference." International Journal on Artificial Intelligence Tools 23, no. 05 (October 2014): 1450005. http://dx.doi.org/10.1142/s0218213014500055.

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The aim of the frequent subgraph mining task is to find frequently occurring subgraphs in a large graph database. However, this task is a thriving challenge, as graph and subgraph isomorphisms play a key role throughout the computations. Since subgraph isomorphism testing is a hard problem, subgraph miners are exponential in runtime. To alleviate the complexity issue, we propose to introduce a bias in the projection operator and instead of using the costly subgraph isomorphism projection, one can use a polynomial projection having a semantically-valid structural interpretation. This paper presents a new projection operator for graphs named AC-projection, which exhibits nice theoretical complexity properties. We study the size of the search space as well as some practical properties of the projection operator. We also introduce a novel breadth-first algorithm for frequent AC-reduced subgraphs mining. Then, we prove experimentally that we can achieve an important performance gain (polynomial complexity projection) without or with non-significant loss of discovered patterns in terms of quality.

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Semenov, Volodymyr, Dmytro Siryk, and Oleh Kharkov. "Adaptive operator extrapolation method." Physico-mathematical modelling and informational technologies, no. 33 (September 5, 2021): 143–47. http://dx.doi.org/10.15407/fmmit2021.33.143.

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This paper is devoted to the study of nоvel algorithm with Bregman projection for solving variational inequalities in Hilbert space. Proposed algorithm is an adaptive version of the operator extrapolation method, where the used rule for updating the step size does not require knowledge of Lipschitz constants and the calculation of operator values at additional points. An attractive feature of the algorithm is only one computation at the iterative step of the Bregman projection onto the feasible set.

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26

Doust, Ian. "A weaker condition for normality." Glasgow Mathematical Journal 36, no. 2 (May 1994): 249–53. http://dx.doi.org/10.1017/s0017089500030792.

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One of the most important results of operator theory is the spectral theorem for normal operators. This states that a normal operator (that is, a Hilbert space operator T such that T*T= TT*), can be represented as an integral with respect to a countably additive spectral measure,Here E is a measure that associates an orthogonal projection with each Borel subset of ℂ. The countable additivity of this measure means that if x Eℋ can be written as a sum of eigenvectors then this sum must converge unconditionally.

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27

Pagitsas, Michael, Ali Nadim, and Howard Brenner. "Projection operator analysis of macrotransport processes." Journal of Chemical Physics 84, no. 5 (March 1986): 2801–7. http://dx.doi.org/10.1063/1.450305.

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28

Uchiyama, Chikako. "Projection Operator Approaches to Complex Susceptibility." Progress of Theoretical Physics Supplement 184 (2010): 476–96. http://dx.doi.org/10.1143/ptps.184.476.

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29

Zhang, Jun. "A cost-effective multigrid projection operator." Journal of Computational and Applied Mathematics 76, no. 1-2 (December 1996): 325–33. http://dx.doi.org/10.1016/s0377-0427(96)00117-3.

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30

Góźdź, A., and M. Dębicki. "Time operator and quantum projection evolution." Physics of Atomic Nuclei 70, no. 3 (March 2007): 529–36. http://dx.doi.org/10.1134/s106377880703012x.

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31

Lee, Stephen. "Projection operator Hueckel method and antiferromagnetism." Journal of the American Chemical Society 112, no. 19 (September 1990): 6777–83. http://dx.doi.org/10.1021/ja00175a006.

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32

Govaerts, Jan. "Projection operator approach to constrained systems." Journal of Physics A: Mathematical and General 30, no. 2 (January 21, 1997): 603–17. http://dx.doi.org/10.1088/0305-4470/30/2/022.

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33

Tuncer, Necibe, and Anotida Madzvamuse. "Projected Finite Elements for Systems of Reaction-Diffusion Equations on Closed Evolving Spheroidal Surfaces." Communications in Computational Physics 21, no. 3 (February 7, 2017): 718–47. http://dx.doi.org/10.4208/cicp.oa-2016-0029.

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AbstractThe focus of this article is to present the projected finite element method for solving systems of reaction-diffusion equations on evolving closed spheroidal surfaces with applications to pattern formation. The advantages of the projected finite element method are that it is easy to implement and that it provides a conforming finite element discretization which is “logically” rectangular. Furthermore, the surface is not approximated but described exactly through the projection. The surface evolution law is incorporated into the projection operator resulting in a time-dependent operator. The time-dependent projection operator is composed of the radial projection with a Lipschitz continuous mapping. The projection operator is used to generate the surface mesh whose connectivity remains constant during the evolution of the surface. To illustrate the methodology several numerical experiments are exhibited for different surface evolution laws such as uniform isotropic (linear, logistic and exponential), anisotropic, and concentration-driven. This numerical methodology allows us to study new reaction-kinetics that only give rise to patterning in the presence of surface evolution such as theactivator-activatorandshort-range inhibition; long-range activation.

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34

El-Shobaky, Entisarat, Sahar Mohammed Ali, and Wataru Takahashi. "On projection constant problems and the existence of metric projections in normed spaces." Abstract and Applied Analysis 6, no. 7 (2001): 401–11. http://dx.doi.org/10.1155/s1085337501000732.

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We give the sufficient conditions for the existence of a metric projection onto convex closed subsets of normed linear spaces which are reduced conditions than that in the case of reflexive Banach spaces and we find a general formula for the projections onto the maximal proper subspaces of the classical Banach spacesl p,1≤p<∞andc 0. We also give the sufficient and necessary conditions for an infinite matrix to represent a projection operator froml p,1≤p<∞orc 0onto anyone of their maximal proper subspaces.

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35

MA, SHAN-JUN. "RESOLUTION OF THE UNITY OF NORMALLY ORDERED GAUSSIAN OPERATOR FORM FOR CONSTRUCTING NEW QUANTUM MECHANICAL REPRESENTATIONS." Modern Physics Letters B 24, no. 01 (January 10, 2010): 81–87. http://dx.doi.org/10.1142/s0217984910022159.

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A convenient approach for deriving new quantum mechanical representations is presented, that is, constructing the unity of normally ordered Gaussian operator forms and then decomposing it as projection operators. As examples, two two-mode complicated entangled state representations are derived by combining the coordinate eigenvector completeness and the coherent state.

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36

KHAN, SOHAIL A. "PROJECTION OPERATOR TREATMENT FOR SUB-COULOMB WIDTHS." International Journal of Modern Physics E 13, no. 06 (December 2004): 1217–24. http://dx.doi.org/10.1142/s0218301304002624.

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An exact expression using the projection operator method to extract widths and spectroscopic factors is derived. It is applied to sub-Coulomb resonances as they occur in α-decay. A number of α-decaying nuclei are investigated. The widths and spectroscopic factors extracted using the proposed expression are found to be in excellent agreement with those obtained by other methods. Earlier equations of the projection operator for widths and spectroscopic factors would give unrealistic results in this region.

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37

Li, Chi-Kwong, Mikio Nakahara, Yiu-Tung Poon, Nung-Sing Sze, and Hiroyuki Tomita. "Recovery in quantum error correction for general noise without measurement." Quantum Information and Computation 12, no. 1&2 (January 2012): 149–58. http://dx.doi.org/10.26421/qic12.1-2-10.

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It is known that one can do quantum error correction without syndrome measurement, which is often done in operator quantum error correction (OQEC). However, the physical realization could be challenging, especially when the recovery process involves high-rank projection operators and a superoperator. We use operator theory to improve OQEC so that the implementation can always be done by unitary gates followed by a partial trace operation. Examples are given to show that our error correction scheme outperforms the existing ones in various scenarios.

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38

Koya, Yoshiharu, Masashige Hori, and Isao Mizoshiri. "Border detection of Echocardiogram using Projection Operator." IEEJ Transactions on Electronics, Information and Systems 120, no. 8-9 (2000): 1236–41. http://dx.doi.org/10.1541/ieejeiss1987.120.8-9_1236.

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39

Nakamura, M., and N. Mishima. "Generalized Projection Operator Method of Constrained Systems." Progress of Theoretical Physics 81, no. 2 (February 1, 1989): 451–61. http://dx.doi.org/10.1143/ptp.81.451.

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40

Dobe, J., S. P. Ivanova, R. V. Jolos, and R. Pedrosa. "Projection operator in the boson expansion techniques." Physical Review C 41, no. 4 (April 1, 1990): 1840–44. http://dx.doi.org/10.1103/physrevc.41.1840.

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41

Seke, J. "Projection-operator method in the interaction picture." Physical Review A 36, no. 12 (December 1, 1987): 5841–43. http://dx.doi.org/10.1103/physreva.36.5841.

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42

Kroó, András, and Allan Pinkus. "On Stability of the Metric Projection Operator." SIAM Journal on Mathematical Analysis 45, no. 2 (January 2013): 639–61. http://dx.doi.org/10.1137/120873534.

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43

Magnus, Wim, Lucien Lemmens, and Fons Brosens. "Quantum canonical ensemble: A projection operator approach." Physica A: Statistical Mechanics and its Applications 482 (September 2017): 1–13. http://dx.doi.org/10.1016/j.physa.2017.04.069.

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44

Zarikian, Vrej. "Alternating-projection algorithms for operator-theoretic calculations." Linear Algebra and its Applications 419, no. 2-3 (December 2006): 710–34. http://dx.doi.org/10.1016/j.laa.2006.06.012.

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45

Batalin, Igor A., Simon L. Lyakhovich, and Robert Marnelius. "Projection operator approach to general constrained systems." Physics Letters B 534, no. 1-4 (May 2002): 201–8. http://dx.doi.org/10.1016/s0370-2693(02)01590-3.

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46

Sanchez, S. d'A, M. A. P. Lima, and M. T. do N. Varella. "Feshbach projection operator approach to positron annihilation." Journal of Physics: Conference Series 194, no. 7 (November 1, 2009): 072008. http://dx.doi.org/10.1088/1742-6596/194/7/072008.

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47

Kohmura, T., M. Maruyama, H. Ohta, and Y. Hashimoto. "Projection Operator Method for Collective Tunneling Transitions." Progress of Theoretical Physics 107, no. 1 (January 1, 2002): 87–116. http://dx.doi.org/10.1143/ptp.107.87.

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48

Ding, Jiu, and Tien Tien Li. "Projection solutions of Frobenius-Perron operator equations." International Journal of Mathematics and Mathematical Sciences 16, no. 3 (1993): 465–84. http://dx.doi.org/10.1155/s0161171293000584.

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We construct in this paper the first order and second order piecewise polynomial finite approximation schemes for the computation of invariant measures of a class of nonsingular measurable transformations on the unit interval of the real axis. These schemes are based on the Galerkin's projection method forL1-spaces and are proved to be convergent for the class of Frobenius-Perron operators.

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49

Capuzzi, F., and C. Mahaux. "Projection Operator Approach to the Self-Energy." Annals of Physics 245, no. 1 (January 1996): 147–208. http://dx.doi.org/10.1006/aphy.1996.0006.

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50

Sauermann, G., W. Just, K. P. Karmann, and Zhang Yu-mei. "Projection operator formulation for second order response." Physica A: Statistical Mechanics and its Applications 140, no. 3 (January 1987): 597–611. http://dx.doi.org/10.1016/0378-4371(87)90083-5.

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