Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Yeredor, A.; Nielsen, Jan
Bryan: Conference Management Services, 2008, s. 3321-3324. ISBN 978-1-4244-1483-3; ISBN 1-4244-1484-9. [ICASSP 2008, IEEE International Conference on Acoustics, Speech adn Signal Processing. Las Vegas (US), 30.03.2008-04.04.2008] R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : approximate joint diagonalization * blind source separation * autoregressive processes Subject RIV: BB - Applied Statistics, Operational Research
On Computation of Approximate Joint Block-Diagonalization Using Ordinary AJD
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Yeredor, A.; Koldovský, Zbyněk
Heidelberg: Springer, 2012 - (Theis, F.), s. 163-171. (Lecture Notes on Computer Science . 7191). ISBN 978-3-642-28550-9. [Latent Variable Analysis and Signal Separation,10th International Conference, LVA/ICA 2012. Tel Aviv (IL), 12.03.2012-15.03.2012] R&D Projects: GA MŠk 1M0572; GA ČR GA102/09/1278 Institutional support: RVO:67985556 Keywords : joint block diagonalization * independent subspace analysis Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2012/SI/tichavsky-on computation of approximate joint block-diagonalization using ordinary ajd.pdf
On the diagonal approximation of full matrices
Lioen, W.M.
1996-01-01
In this paper the construction of diagonal matrices, in some sense approximating the inverse of a given square matrix, is described. The matrices are constructed using the well-known computer algebra system Maple. The techniques we show are applicable to square matrices in general. Results are given for use in Parallel diagonal-implicit Runge-Kutta (PDIRK) methods. For an s-stage Radau IIA corrector we conjecture $s!$ possibilities for the diagonal matrices.
Diagonal Pade approximations for initial value problems
International Nuclear Information System (INIS)
Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab
Diagonal Pade approximations for initial value problems
Energy Technology Data Exchange (ETDEWEB)
Reusch, M.F.; Ratzan, L.; Pomphrey, N.; Park, W.
1987-06-01
Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab.
A New Algorithm for Complex Non Orthogonal Joint Diagonalization Based on Shear and Givens Rotations
Mesloub, Ammar; Abed-Meraim, Karim; Belouchrani, Adel
2014-01-01
This paper introduces a new algorithm to approximate non-orthogonal joint diagonalization (NOJD) of a set of complex matrices. This algorithm is based on the Frobenius norm formulation of the joint diagonalization (JD) problem and takes advantage from combining Givens and Shear rotations to attempt the approximate JD. It represents a non-trivial generalization of the JDi (Joint Diagonalization) algorithm (Souloumiac2009) to the complex case. The JDi is ﬁrst slightly modiﬁed then generalized t...
Noise Reduction in the Time Domain using Joint Diagonalization
DEFF Research Database (Denmark)
Nørholm, Sidsel Marie; Benesty, Jacob; Jensen, Jesper Rindom; Christensen, Mads Græsbøll
A new filter design based on joint diagonalization of the clean speech and noise covariance matrices is proposed. First, an estimate of the noise is found by filtering the observed signal. The filter for this is generated by a weighted sum of the eigenvectors from the joint diagonalization. Second...
A New Algorithm for Complex Non-Orthogonal Joint Diagonalization Based on Shear and Givens Rotations
Mesloub, Ammar; Abed-Meraim, Karim; Belouchrani, Adel
2014-04-01
This paper introduces a new algorithm to approximate non orthogonal joint diagonalization (NOJD) of a set of complex matrices. This algorithm is based on the Frobenius norm formulation of the JD problem and takes advantage from combining Givens and Shear rotations to attempt the approximate joint diagonalization (JD). It represents a non trivial generalization of the JDi (Joint Diagonalization) algorithm (Souloumiac 2009) to the complex case. The JDi is first slightly modified then generalized to the CJDi (i.e. Complex JDi) using complex to real matrix transformation. Also, since several methods exist already in the literature, we propose herein a brief overview of existing NOJD algorithms then we provide an extensive comparative study to illustrate the effectiveness and stability of the CJDi w.r.t. various system parameters and application contexts.
Comparative performance analysis of nonorthogonal joint diagonalization algorithms
Ammar, Mesloub; Abed-Meraim, Karim; Belouchrani, Adel
2013-01-01
Recently, many non orthogonal joint diagonalization (NOJD) algorithms have been developed and applied in several applications including blind source separation (BSS) problems. The aim of this paper is to provide an overview of major complex NOJD (CNOJD) algorithm and to study and compare their performance analysis reveals many interesting features that help the non expert user to select the CNOJD method depending on the application conditions.
GÜRAY, Arif; Murat KILIÇ; Ajlan ÖZYURT
2002-01-01
In this work, the diagonal tensile strength of furniture edge joints such as wooden dowel, minifix, and alyan screw was investigated in panel-constructed boards for Suntalam and MDF Lam. For this purpose, a diagonal tensile strength test was applied to the 72 samples. According to the results, the maximum diagonal tensile strength was found to be in MDF Lam boards that jointed with alyan screw.
Directory of Open Access Journals (Sweden)
Arif GÜRAY
2002-01-01
Full Text Available In this work, the diagonal tensile strength of furniture edge joints such as wooden dowel, minifix, and alyan screw was investigated in panel-constructed boards for Suntalam and MDF Lam. For this purpose, a diagonal tensile strength test was applied to the 72 samples. According to the results, the maximum diagonal tensile strength was found to be in MDF Lam boards that jointed with alyan screw.
The Hamiltonian of SU(2) lattice gauge theory in approximate tri-diagonal form
International Nuclear Information System (INIS)
Employing Hamiltonian moments of SU(2) lattice gauge theory, with respect to the strong coupling vacuum, the matrix elements of the Lanczos tri-diagonal form are written down from the palquette expansion to order 1/N2p in the number of plaquettes, Np. The consequences of this approximate tri-diagonal form are studied by computing the vacuum energy density and the specific heat in the infinite lattice limit, for strong to weak coupling. The results at this order appear to reach beyond the strong to weak transition point at g1/2c ∼ 2.0, as indicated by the peaking behaviour of the specific heat. The results demonstrate that the plaquette expansion method to the order considered here is able to describe the physics of the vacuum at the strong to weak transition and just beyond. Whilst the accuracy of the results presented here are not quite of the caliber of the t-expansion or Monte-Carlo calculations, the method used here is simpler and, since it is semi-analytic and not dependent on extrapolation, is to a large extent cleaner. In principle, the results can be improved by increasing the plaquette expansion order and/or choosing a better trial state. Furthermore, unlike a variational approach, this framework allows for the calculation of excited states and so physically interesting quantities such as glueball masses and the string tension, could be calculated by diagonalizing the plaquette expansion in the relevant sector. 17 refs., 3 figs
Directory of Open Access Journals (Sweden)
Musa Atar
2010-02-01
Full Text Available The goal of this study was to determine the effects of different joint angles and adhesives on diagonal tension performances of the box-type furniture made from solid wood and medium density fiberboard (MDF. After drilling joints of 75º, 78º, 81º, 84º, and 87º degrees on Oriental beech, European oak, Scotch pine, and MDF samples, a diagonal tensile test was applied on corners glued with polyvinyl acetate (PVAc and polyurethane (D-VTKA = Desmodur-Vinyl Trieketonol Acetate according to ASTM D 1037 standard. With reference to the obtained results, the highest tensile strength was obtained in European oak with PVAc glue and joint angle of 84º, while the lowest value was obtained in MDF with D-VTKA glue and joint angle of 75º. Considering the interaction of wood, adhesive, and joint angle, the highest tensile strength was obtained in European oak with joint angle of 81º and D-VTKA glue (1.089 N.mm-2, whereas the lowest tensile strength was determined in MDF with joint angle of 75º and PVAc glue (0.163 N.mm-2. Therefore, PVAc as glue and 81º as joint angle could be suggested to obtain some advantageous on the dovetail joint process for box-type furniture made from both solid wood and MDF.
Directory of Open Access Journals (Sweden)
You-Gen Xu
2012-03-01
Full Text Available Joint estimation of direction-of-arrival (DOA and polarization with electromagnetic vector-sensors (EMVS is considered in the framework of complex-valued non-orthogonal joint diagonalization (CNJD. Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme. Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation. Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods.
DIAGONAL TENSILE STRENGTH OF AN ORIENTED STRAND-BOARD (OSB FRAME WITH DOVETAIL CORNER JOINT
Directory of Open Access Journals (Sweden)
Kadir Ozkaya
2010-11-01
Full Text Available It was aimed in this study to determine the effect of the number of joints in frames produced from Oriented Strand Board (OSB and of the type of adhesive on the diagonal tensile strength (DTS of the frame. With this objective, a total of 152 specimens were prepared from OSB in accordance with the principles in the EN 2470 test standard. The diagonal tensile test was applied to the specimens in the universal test equipment in accordance with ASTM-D 1037. According to the statistical analysis of the data obtained from the tests, the number of dovetail joints and the type of adhesive had significant effects on the DTS. The highest DTS (0.117 N/mm2 was obtained in the specimens with a single dovetail joint and bonded with the PVAc adhesive. This alternative was followed by the specimens with a double dovetail joint bonded with the PVAc adhesive (0.078 N/mm2 and the specimens with a single dovetail joint bonded with the PU adhesive (0.073 N/mm2. The lowest DTS occurred in the specimens with single and double joints without adhesive. According to these results, adhesive should definitely be used in the corner joining of the dovetail joints, and the single dovetail joint joining type bonded with PVAc adhesive is preferred.
A New Newton's Method with Diagonal Jacobian Approximation for Systems of Nonlinear Equations
Directory of Open Access Journals (Sweden)
M. Y. Waziri
2010-01-01
Full Text Available Problem statement: The major weaknesses of Newton method for nonlinear equations entail computation of Jacobian matrix and solving systems of n linear equations in each of the iterations. Approach: In some extent function derivatives are quit costly and Jacobian is computationally expensive which requires evaluation (storage of n×n matrix in every iteration. Results: This storage requirement became unrealistic when n becomes large. We proposed a new method that approximates Jacobian into diagonal matrix which aims at reducing the storage requirement, computational cost and CPU time, as well as avoiding solving n linear equations in each iterations. Conclusion/Recommendations: The proposed method is significantly cheaper than Newtons method and very much faster than fixed Newtons method also suitable for small, medium and large scale nonlinear systems with dense or sparse Jacobian. Numerical experiments were carried out which shows that, the proposed method is very encouraging.
Carré, Jérôme
2011-01-01
The inspiral of two compact objects in gravitational wave astronomy is described by a post-Newtonian expansion in powers of $(v/c)$. In most cases, it is believed that the post-Newtonian expansion is asymptotically divergent. A standard technique for accelerating the convergence of a power series is to re-sum the series by means of a rational polynomial called a Pad\\'e approximation. If we liken this approximation to a matrix, the best convergence is achieved by staying close to a diagonal Pad\\'e approximation. This broadly presents two subsets of the approximation : a super-diagonal approximation $P^M_N$ and a sub-diagonal approximation $P_M^N$, where $M = N+\\epsilon$, and $\\epsilon$ takes the values of 0 or 1. Left as rational polynomials, the coefficients in both the numerator and denominator need to be re-calculated as the order of the initial power series approximation is increased. However, the sub-diagonal Pad\\'e approximant is computationally advantageous as it can be expressed in terms of a Gauss-lik...
A combined joint diagonalization-MUSIC algorithm for subsurface targets localization
Wang, Yinlin; Sigman, John B.; Barrowes, Benjamin E.; O'Neill, Kevin; Shubitidze, Fridon
2014-06-01
This paper presents a combined joint diagonalization (JD) and multiple signal classification (MUSIC) algorithm for estimating subsurface objects locations from electromagnetic induction (EMI) sensor data, without solving ill-posed inverse-scattering problems. JD is a numerical technique that finds the common eigenvectors that diagonalize a set of multistatic response (MSR) matrices measured by a time-domain EMI sensor. Eigenvalues from targets of interest (TOI) can be then distinguished automatically from noise-related eigenvalues. Filtering is also carried out in JD to improve the signal-to-noise ratio (SNR) of the data. The MUSIC algorithm utilizes the orthogonality between the signal and noise subspaces in the MSR matrix, which can be separated with information provided by JD. An array of theoreticallycalculated Green's functions are then projected onto the noise subspace, and the location of the target is estimated by the minimum of the projection owing to the orthogonality. This combined method is applied to data from the Time-Domain Electromagnetic Multisensor Towed Array Detection System (TEMTADS). Examples of TEMTADS test stand data and field data collected at Spencer Range, Tennessee are analyzed and presented. Results indicate that due to its noniterative mechanism, the method can be executed fast enough to provide real-time estimation of objects' locations in the field.
Single-channel noise reduction using unified joint diagonalization and optimal filtering
Nørholm, Sidsel Marie; Benesty, Jacob; Jensen, Jesper Rindom; Christensen, Mads Græsbøll
2014-12-01
In this paper, the important problem of single-channel noise reduction is treated from a new perspective. The problem is posed as a filtering problem based on joint diagonalization of the covariance matrices of the desired and noise signals. More specifically, the eigenvectors from the joint diagonalization corresponding to the least significant eigenvalues are used to form a filter, which effectively estimates the noise when applied to the observed signal. This estimate is then subtracted from the observed signal to form an estimate of the desired signal, i.e., the speech signal. In doing this, we consider two cases, where, respectively, no distortion and distortion are incurred on the desired signal. The former can be achieved when the covariance matrix of the desired signal is rank deficient, which is the case, for example, for voiced speech. In the latter case, the covariance matrix of the desired signal is full rank, as is the case, for example, in unvoiced speech. Here, the amount of distortion incurred is controlled via a simple, integer parameter, and the more distortion allowed, the higher the output signal-to-noise ratio (SNR). Simulations demonstrate the properties of the two solutions. In the distortionless case, the proposed filter achieves only a slightly worse output SNR, compared to the Wiener filter, along with no signal distortion. Moreover, when distortion is allowed, it is possible to achieve higher output SNRs compared to the Wiener filter. Alternatively, when a lower output SNR is accepted, a filter with less signal distortion than the Wiener filter can be constructed.
Beyond the Tamm-Dancoff approximation for extended systems using exact diagonalization
Sander, Tobias; Maggio, Emanuele; Kresse, Georg
2015-07-01
Linear optical properties can be accurately calculated using the Bethe-Salpeter equation. After introducing a suitable product basis for the electron-hole pairs, the Bethe-Salpeter equation is usually recast into a complex non-Hermitian eigenvalue problem that is difficult to solve using standard eigenvalue solvers. In solid-state physics, it is therefore common practice to neglect the problematic coupling between the positive- and negative-frequency branches, reducing the problem to a Hermitian eigenvalue problem [Tamm-Dancoff approximation (TDA)]. We use time-inversion symmetry to recast the full problem into a quadratic Hermitian eigenvalue problem, which can be solved routinely using standard eigenvalue solvers even at a finite wave vector q . This allows us to access the importance of the coupling between the positive- and negative-frequency branch for prototypical solids. As a starting point for the Bethe-Salpeter calculations, we use self-consistent Green's-function methods (GW ), making the present scheme entirely ab initio. We calculate the optical spectra of carbon (C), silicon (Si), lithium fluoride (LiF), and the cyclic dimer Li2F2 and discuss why the differences between the TDA and the full solution are tiny. However, at finite momentum transfer q , significant differences between the TDA and our exact treatment are found. The origin of these differences is explained.
Institute of Scientific and Technical Information of China (English)
XIA TieQi; WAN Qun; WANG XueGang; ZHENG Yi
2008-01-01
A novel joint diagonalization fractional lower-order spatio-temporal (ST) moments DOA matrix method is proposed to estimate the 2-D DOAs of uncorrelated narrowband signals in the presence of impulsive noise.The new method retains the advantage of the original ST-DOA matrix method which can estimate 2-D DOAs with neither peak searching nor pair matching.Moreover,it can handle sources with common 1-D angles.Simulation results show that the proposed method yields to better performance to restrain the strong impulsive noise than ST-DOA matrix method,especially for low signal-to-noise ratio case.
Single-Channel Noise Reduction using Unified Joint Diagonalization and Optimal Filtering
DEFF Research Database (Denmark)
Nørholm, Sidsel Marie; Benesty, Jacob; Jensen, Jesper Rindom;
2014-01-01
diagonalization corresponding to the least significant eigenvalues are used to form a filter, which effectively estimates the noise when applied to the observed signal. This estimate is then subtracted from the observed signal to form an estimate of the desired signal, i.e., the speech signal. In doing this, we...... consider two cases, where, respectively, no distortion and distortion are incurred on the desired signal. The former can be achieved when the covariance matrix of the desired signal is rank deficient, which is the case, for example, for voiced speech. In the latter case, the covariance matrix of the...... desired signal is full rank, as is the case, for example, in unvoiced speech. Here, the amount of distortion incurred is controlled via a simple, integer parameter, and the more distortion allowed, the higher the output signal-to-noise ratio (SNR). Simulations demonstrate the properties of the two...
Interpolation function for approximating knee joint behavior in human gait
Toth-Taşcǎu, Mirela; Pater, Flavius; Stoia, Dan Ioan
2013-10-01
Starting from the importance of analyzing the kinematic data of the lower limb in gait movement, especially the angular variation of the knee joint, the paper propose an approximation function that can be used for processing the correlation among a multitude of knee cycles. The approximation of the raw knee data was done by Lagrange polynomial interpolation on a signal acquired using Zebris Gait Analysis System. The signal used in approximation belongs to a typical subject extracted from a lot of ten investigated subjects, but the function domain of definition belongs to the entire group. The study of the knee joint kinematics plays an important role in understanding the kinematics of the gait, this articulation having the largest range of motion in whole joints, in gait. The study does not propose to find an approximation function for the adduction-abduction movement of the knee, this being considered a residual movement comparing to the flexion-extension.
Congedo, Marco; Gouy-Pailler, Cedric; Jutten, Christian
2008-01-01
Over the last ten years blind source separation (BSS) has become a prominent processing tool in the study of human electroencephalography (EEG). Without relying on head modeling BSS aims at estimating both the waveform and the scalp spatial pattern of the intracranial dipolar current responsible of the observed EEG. In this review we begin by placing the BSS linear instantaneous model of EEG within the framework of brain volume conduction theory. We then review the concept and current practic...
Chaotic diagonal recurrent neural network
Institute of Scientific and Technical Information of China (English)
Wang Xing-Yuan; Zhang Yi
2012-01-01
We propose a novel neural network based on a diagonal recurrent neural network and chaos,and its structure andlearning algorithm are designed.The multilayer feedforward neural network,diagonal recurrent neural network,and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map.The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks.
Chaotic diagonal recurrent neural network
International Nuclear Information System (INIS)
We propose a novel neural network based on a diagonal recurrent neural network and chaos, and its structure and learning algorithm are designed. The multilayer feedforward neural network, diagonal recurrent neural network, and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map. The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks. (interdisciplinary physics and related areas of science and technology)
Joint Approximation of Information and Distributed Link-Scheduling Decisions in Wireless Networks
Jeon, Sung-eok
2012-01-01
For a large multi-hop wireless network, nodes are preferable to make distributed and localized link-scheduling decisions with only interactions among a small number of neighbors. However, for a slowly decaying channel and densely populated interferers, a small size neighborhood often results in nontrivial link outages and is thus insufficient for making optimal scheduling decisions. A question arises how to deal with the information outside a neighborhood in distributed link-scheduling. In this work, we develop joint approximation of information and distributed link scheduling. We first apply machine learning approaches to model distributed link-scheduling with complete information. We then characterize the information outside a neighborhood in form of residual interference as a random loss variable. The loss variable is further characterized by either a Mean Field approximation or a normal distribution based on the Lyapunov central limit theorem. The approximated information outside a neighborhood is incorpo...
Nonlinear approximation with dictionaries,.. II: Inverse estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...
Huang, Jianping; Wang, Lihui; Chu, Chunyu; Zhang, Yanli; Liu, Wanyu; Zhu, Yuemin
2016-04-29
Diffusion tensor magnetic resonance (DTMR) imaging and diffusion tensor imaging (DTI) have been widely used to probe noninvasively biological tissue structures. However, DTI suffers from long acquisition times, which limit its practical and clinical applications. This paper proposes a new Compressed Sensing (CS) reconstruction method that employs joint sparsity and rank deficiency to reconstruct cardiac DTMR images from undersampled k-space data. Diffusion-weighted images acquired in different diffusion directions were firstly stacked as columns to form the matrix. The matrix was row sparse in the transform domain and had a low rank. These two properties were then incorporated into the CS reconstruction framework. The underlying constrained optimization problem was finally solved by the first-order fast method. Experiments were carried out on both simulation and real human cardiac DTMR images. The results demonstrated that the proposed approach had lower reconstruction errors for DTI indices, including fractional anisotropy (FA) and mean diffusivities (MD), compared to the existing CS-DTMR image reconstruction techniques. PMID:27163322
Efficient quantum circuits for diagonal unitaries without ancillas
International Nuclear Information System (INIS)
The accurate evaluation of diagonal unitary operators is often the most resource-intensive element of quantum algorithms such as real-space quantum simulation and Grover search. Efficient circuits have been demonstrated in some cases but generally require ancilla registers, which can dominate the qubit resources. In this paper, we give a simple way to construct efficient circuits for diagonal unitaries without ancillas, using a correspondence between Walsh functions and a basis for diagonal operators. This correspondence reduces the problem of constructing the minimal-depth circuit within a given error tolerance, for an arbitrary diagonal unitary eif(x-^) in the |x〉 basis, to that of finding the minimal-length Walsh-series approximation to the function f(x). We apply this approach to the quantum simulation of the classical Eckart barrier problem of quantum chemistry, demonstrating that high-fidelity quantum simulations can be achieved with few qubits and low depth
Additivity properties of topological diagonalizations
Bartoszynski, Tomek; SHELAH, Saharon; Tsaban, Boaz
2001-01-01
We answer a question of Just, Miller, Scheepers and Szeptycki whether certain diagonalization properties for sequences of open covers are provably closed under taking finite or countable unions. This is a very concise paper. For a self-contained, complete, and extended treatment of the topic see math.GN/0604451
The diagonal infinity problems of multiple scales
Hubey, HM
1998-01-01
Contains information on topics such as: Cantor Theorem/Paradox, Diagonal of Diagonalization, Hilbert's First Problem, Algebra of Scaling, Multivalued Logics, Chaos in Logic, Knife-edge and Bang-Bang Logics, Liar Paradox and many more.
Spectral diagonal ensemble Kalman filters
Kasanický, Ivan; Vejmelka, Martin
2015-01-01
A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields, which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT) and discrete wavelet transform (DWT) are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles.
Spectral diagonal ensemble Kalman filters
Directory of Open Access Journals (Sweden)
I. Kasanický
2015-01-01
Full Text Available A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT and discrete wavelet transform (DWT are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles.
Study on crack propagation in tubular joints under compressive fatigue loadings
Acevedo, Claire; NUSSBAUMER, Alain
2009-01-01
Large scale tubular truss beams, approximately of 9 m long and 2 m high, were tested under constant amplitude fatigue loading. The beams were made out of circular hollow sections of steel S355, welded to form a uni-planar truss with K-joints, in a shape common to bridge construction. The main goal of these tests was to focus on the fatigue behavior of the joints loaded in compression that is with chord in compression, one diagonal in compression and the remaining diagonal in tension. The test...
A progressive diagonalization scheme for the Rabi Hamiltonian
International Nuclear Information System (INIS)
A diagonalization scheme for the Rabi Hamiltonian, which describes a qubit interacting with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the Rabi Hamiltonian can be solved almost exactly using a progressive scheme that involves a finite set of one variable polynomial equations. The scheme is especially efficient for the lower part of the spectrum. Some low-lying energy levels of the model with several sets of parameters are calculated and compared to those provided by the recently proposed generalized rotating-wave approximation and a full matrix diagonalization.
Two-sided diagonalization of order-three tensors
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Phan, A. H.; Cichocki, A.
Piscataway : IEEE Computer Society, 2015, s. 998-1002. ISBN 978-0-9928626-4-0. ISSN 2076-1465. [23rd European Signal Processing Conference (EUSIPCO). Nice (FR), 31.08.2015-04.09.2015] R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : Multilinear models * parallel factor analysis * joint matrix diagonalization Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2015/SI/tichavsky-0447021.pdf
Block-diagonalized rigidity matrices of symmetric frameworks and applications
Schulze, Bernd
2009-01-01
In this paper, we give a complete self-contained proof that the rigidity matrix of a symmetric bar and joint framework (as well as its transpose) can be transformed into a block-diagonalized form using techniques from group representation theory. This theorem is basic to a number of useful and interesting results concerning the rigidity and flexibility of symmetric frameworks. As an example, we use this theorem to prove a generalization of the Fowler-Guest symmetry extension of Maxwell's rule...
Quantum Diagonalization of Hermitean Matrices
Weigert, S.
2000-01-01
To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource: Hermitean (N ×N) matrices can be diagonalized, in principle, by performing appropriate quantum mechanical measurements. To do so, one considers the given matrix as an observable of a single spin with appropriate length s which can be measured using a generalized Stern-Gerlach apparatus. Th...
Hyperplane Arrangements and Diagonal Harmonics
Armstrong, Drew
2010-01-01
In 2003, Haglund's {\\sf bounce} statistic gave the first combinatorial interpretation of the $q,t$-Catalan numbers and the Hilbert series of diagonal harmonics. In this paper we propose a new combinatorial interpretation in terms of the affine Weyl group of type $A$. In particular, we define two statistics on affine permutations; one in terms of the Shi hyperplane arrangement, and one in terms of a new arrangement - which we call the Ish arrangement. We prove that our statistics are equivalent to the {\\sf area'} and {\\sf bounce} statistics of Haglund and Loehr. In this setting, we observe that {\\sf bounce} is naturally expressed as a statistic on the root lattice. We extend our statistics in two directions: to "extended" Shi arrangements and to the bounded chambers of these arrangements. This leads to a (conjectural) combinatorial interpretation for all integral powers of the Bergeron-Garsia nabla operator applied to the elementary symmetric functions.
Quantum diagonalization of Hermitean matrices
Energy Technology Data Exchange (ETDEWEB)
Weigert, Stefan [Institut de Physique, Universite de Neuchatel, Neuchatel (Switzerland); Department of Mathematics, University of Hull, Hull (United Kingdom)]. E-mail: stefan.weigert@unine.ch
2001-07-13
To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource: Hermitean (NxN) matrices can be diagonalized, in principle, by performing appropriate quantum mechanical measurements. To do so, one considers the given matrix as an observable of a single spin with appropriate length s which can be measured using a generalized Stern-Gerlach apparatus. Then, each run provides one eigenvalue of the observable. As the underlying working principle is the 'collapse of the wavefunction' associated with a measurement, the procedure is neither a digital nor an analogue calculation - it defines thus a new example of a quantum mechanical method of computation. (author)
Quantum diagonalization of Hermitean matrices
International Nuclear Information System (INIS)
To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource: Hermitean (NxN) matrices can be diagonalized, in principle, by performing appropriate quantum mechanical measurements. To do so, one considers the given matrix as an observable of a single spin with appropriate length s which can be measured using a generalized Stern-Gerlach apparatus. Then, each run provides one eigenvalue of the observable. As the underlying working principle is the 'collapse of the wavefunction' associated with a measurement, the procedure is neither a digital nor an analogue calculation - it defines thus a new example of a quantum mechanical method of computation. (author)
Quantum Diagonalization of Hermitean Matrices
Weigert, S
2000-01-01
To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource. It allows one, in principle, to diagonalize hermitean (N by N) matrices by quantum mechanical measurements only. To do so, one considers the given matrix as an observable of a single spin with appropriate length s=(N-1)/2, which can be measured using a generalized Stern-Gerlach apparatus. Then, each run provides one eigenvalue of the observable. As it is based on the `collapse of the wave function' associated with a measurement, the procedure is neither a digital nor an analog calculation---it defines thus a new quantum mechanical method of computation.
Simultaneous diagonalization of two quaternion matrices
Institute of Scientific and Technical Information of China (English)
ZhouJianhua
2003-01-01
The simultaneous diagonalization by congruence of pairs of Hermitian quatemion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quatemion matrix. It is proved that any two semi-positive definite Hermitian quatemion matrices can be simultaneously diagonalized by congruence.
Diagonalizing hermitian matrices of continuous functions
Cyr, Justin; Ekstrand, Jason; Meyers, Nathan; Peoples, Crystal; Peters, Justin R.
2012-01-01
The problem of diagonalizing hermitian matrices of continuous fiunctions was studied by Grove and Pederson in 1984. While diagonalization is not possible in general, in the presence of differentiability conditions we are able to obtain positive results in the case of $2\\times 2$ matrices. It remains open whether our results can be extended to $n\\times n$ matrices.
Diagonally implicit Runge-Kutta methods for 3D shallow water applications
Houwen, van der, P.J.; Sommeijer, Ben
1999-01-01
We construct A-stable and L-stable diagonally implicit Runge-Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge-Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such iterated Runge-Kutta methods are suitable methods for integrating shallow water problems in the sense that the stability boundary is relatively large and that the usually quite fine vertical resolution of the discre...
N-variable rational approximants
International Nuclear Information System (INIS)
''Desirable properties'' of a two-variable generalization of Pade approximants are laid down. The ''Chisholm approximants'' are defined and are shown to obey nearly all of these properties; the alternative ways of completing a unique definition are discussed, and the ''prong structure'' of the defining equations is elucidated. Several generalizations and variants of Chisholm approximants are described: N-variable diagonal, 2-variable simple off-diagonal, N-variable simple and general off-diagonal, and rotationally covariant 2-variable approximants. All of the 2-variable approximants are capable of representing singularities of functions of two variables, and of analytically continuing beyond the polycylinder of convergence of the double series. 8 figures
On triangular algebras with noncommutative diagonals
Institute of Scientific and Technical Information of China (English)
2008-01-01
We construct a triangular algebra whose diagonals form a noncommutative algebra and its lattice of invariant projections contains only two nontrivial projections. Moreover we prove that our triangular algebra is maximal.
Energy patterns in coupled α-helix protein chains with diagonal and off-diagonal couplings
Tabi, C. B.; Ondoua, R. Y.; Ekobena Fouda, H. P.; Kofané, T. C.
2016-07-01
We introduce off-diagonal effects in the three-stranded model of α-helix chains, which bring about additional nonlinear terms to enhance the way energy spreads among the coupled spines. This is analyzed through the modulational instability theory. The linear stability analysis of plane wave solutions is performed and the competitive effects of diagonal and off-diagonal interactions are studied, followed by direct numerical simulations. Some features of the obtained solitonic structures are discussed.
Yang, X H; Chu Yao Quan; Fang, L Z; Yang, Xiao-Hu; Feng, Long-Long; Chu, Yao-Quan; Fang, Li-Zhi
2001-01-01
The power spectrum estimator based on the discrete wavelet transform (DWT) for 3-dimensional samples has been studied. The DWT estimator for multi-dimensional samples provides two types of spectra with respect to diagonal and off-diagonal modes, which are very flexible to deal with configuration-related problems in the power spectrum detection. With simulation samples and mock catalogues of the Las Campanas redshift survey (LCRS), we show (1) the slice-like geometry of the LCRS doesn't affect the off-diagonal power spectrum with ``slice-like'' mode; (2) the Poisson sampling with the LCRS selection function doesn't cause more than 1-$\\sigma$ error in the DWT power spectrum; and (3) the powers of peculiar velocity fluctuations, which cause the redshift distortion, are approximately scale-independent. These results insure that the uncertainties of the power spectrum measurement are under control. The scatter of the DWT power spectra of the six strips of the LCRS survey is found to be rather small. It is less tha...
Matrix-Free Approximate Equilibration
Bradley, Andrew M.; Murray, Walter
2011-01-01
The condition number of a diagonally scaled matrix, for appropriately chosen scaling matrices, is often less than that of the original. Equilibration scales a matrix so that the scaled matrix's row and column norms are equal. Scaling can be approximate. We develop approximate equilibration algorithms for nonsymmetric and symmetric matrices having signed elements that access a matrix only by matrix-vector products.
Benchmarking GW against exact diagonalization for semiempirical models
DEFF Research Database (Denmark)
Kaasbjerg, Kristen; Thygesen, Kristian Sommer
2010-01-01
We calculate ground-state total energies and single-particle excitation energies of seven pi-conjugated molecules described with the semiempirical Pariser-Parr-Pople model using self-consistent many-body perturbation theory at the GW level and exact diagonalization. For the total energies GW...... screening and improve the low-lying excitation energies. The effect of the GW self-energy on the molecular excitation energies is shown to be similar to the inclusion of final-state relaxations in Hartree-Fock theory. We discuss the breakdown of the GW approximation in systems with short-range interactions...
Dual Diagonalization of Reactive Transport Equations
Yeh, G.; Tsai, C.
2013-12-01
One solves a system of species transport equations in the primitive approach to reactive transport modeling. This approach is not able to decouple equilibrium reaction rates from species concentrations. This problem has been overcome with the approach to diagonalizing the reaction matrix since mid 1990's, which yields the same number of transport equations for reaction-extents. In the diagonalization approach, first, a subset of reaction- extent transport equations is solved for concentrations of components and kinetic-variables. Then, the component, kinetic-variable, and mass action equations are solved for all species concentrations. Finally, the equilibrium reaction rates are posterior computed. The difficulty in this approach is that the solution of species concentrations in the second step is a stiff problem when the concentrations of master species are small compared to those of equilibrium species. To overcome the problem of stiffness, we propose a dual diagonalization approach. Here, a second diagonalization is performed on the decomposed unit matrix to yield species concentrations, each as a linear function of reaction extents. In this dual diagonalization approach, four steps are needed to complete the modeling. First, component and kinetic-variable transport equations are solved for the concentrations of components (a subset of reaction-extents) and kinetic-variables (another subset of reaction-extents). Second, the set of mass action equations written in terms of reaction extents are solved for equilibrium-variables (yet another subset of reaction-extents). Third, species concentrations are posterior obtained by solving the set of linear equations defining reaction-extents. Fourth, equilibrium rates are posterior calculated with transport equations for equilibrium-variables. Several example problems will be used to demonstrate the efficiency of this approach. Keywords: Reactive Transport, Reaction-Extent, Component, Kinetic-Variable, Equilibrium
GIT-equivalence and diagonal actions
Kotenkova, Polina Yu.
2010-01-01
We describe the GIT-equivalence classes of linearized ample line bundles for the diagonal actions of the linear algebraic groups $SL(V)$ and $SO(V)$ on ${\\mathbb{P}(V)^{m_1}\\times \\mathbb{P}(V^*)^{m_2}}$ and $\\mathbb{P}(V)^m$ respectively.
F-invariants of diagonal hypersurfaces
Hernández, Daniel J.
2011-01-01
In this note, we derive a formula for the F-pure threshold of diagonal hypersurfaces over a perfect field of prime characteristic. We also calculate the associated test ideal at the F-pure threshold, and give formulas for higher jumping numbers of Fermat hypersurfaces.
Special function of nestin+ neurons in the medial septum-diagonal band of Broca in adult rats
Zhao, Yuhong; Guo, Kaihua; Li, Dongpei; Yuan, Qunfang; Yao, Zhibin
2014-01-01
Nestin+ neurons have been shown to express choline acetyltransferase (ChAT) in the medial septum-diagonal band of Broca in adult rats. This study explored the projection of nestin+ neurons to the olfactory bulb and the time course of nestin+ neurons in the medial septum-diagonal band of Broca in adult rats during injury recovery after olfactory nerve transection. This study observed that all nestin+ neurons were double-labeled with ChAT in the medial septum-diagonal band of Broca. Approximate...
New Criteria for Judging Generalized Strictly Diagonally Dominant Matrix
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-song
2015-01-01
Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc. But it is diﬃcult to judge a matrix is or not generalized strictly diagonally dominant matrix. In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.
Diagonal multisoliton matrix elements in finite volume
Pálmai, T.; Takács, G.
2013-02-01
We consider diagonal matrix elements of local operators between multisoliton states in finite volume in the sine-Gordon model and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Takács which were only valid for diagonal scattering. In order to test the conjecture, we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.
Diagonal-transition quantum cascade detector
Reininger, Peter; Schwarz, Benedikt; Detz, Hermann; MacFarland, Don; Zederbauer, Tobias; Andrews, Aaron Maxwell; Schrenk, Werner; Baumgartner, Oskar; Kosina, Hans; Strasser, Gottfried
2014-09-01
We demonstrate the concept of diagonal transitions for quantum cascade detectors (QCD). Different to standard, vertical QCDs, here the active transition takes place between two energy levels in adjacent wells. Such a scheme has versatile advantages. Diagonal transitions generally yield a higher extraction efficiency and a higher resistance than vertical transitions. This leads to an improved overall performance, although the absorption strength of the active transition is smaller. Since the extraction is not based on resonant tunneling, the design is more robust, with respect to deviations from the nominal structure. In a first approach, a peak responsivity of 16.9 mA/W could be achieved, which is an improvement to the highest shown responsivity of a QCD for a wavelength of 8 μm at room-temperature by almost an order of magnitude.
Alcohol dimers - how much diagonal OH anharmonicity?
Kollipost, Franz; Papendorf, Kim; Lee, Yu-Fang; Lee, Yuan-Pern; Suhm, Martin A
2014-01-01
The OH bond of methanol, ethanol and t-butyl alcohol becomes more anharmonic upon hydrogen bonding and the infrared intensity ratio between the overtone and the fundamental transition of the bridging OH stretching mode decreases drastically. FTIR spectroscopy of supersonic slit jet expansions allows to quantify these effects for isolated alcohol dimers, enabling a direct comparison to anharmonic vibrational predictions. The diagonal anharmonicity increase amounts to 15-18%, growing with incre...
Spectral Diagonal Covariance in Ensemble Kalman Filter
Czech Academy of Sciences Publication Activity Database
Kasanický, Ivan; Eben, Kryštof; Mandel, Jan; Vejmelka, Martin
Munich: Ludwig Maximilians University, 2014. s. 10-10. [ISDA 2014. International Conference on Intelligent Systems Design and Applications. 24.02.2014-28.02.2014, Munich] R&D Projects: GA ČR GA13-34856S Grant ostatní: NSF DMS -1216481 Institutional support: RVO:67985807 Keywords : data assimilation * ensemble Kalman filter * diagonal covariance Subject RIV: DG - Athmosphere Sciences, Meteorology http://www.isda2014.physik.uni-muenchen.de/index.html
The quantum way to diagonalize hermitean matrices
Weigert, Stefan
2003-01-01
An entirely quantum mechanical approach to diagonalize hermitean matrices has been presented recently. Here, the genuinely quantum mechanical approach is considered in detail for (2x2) matrices. The method is based on the measurement of quantum mechanical observables which provides the computational resource. In brief, quantum mechanics is able to directly address and output eigenvalues of hermitean matrices. The simple low-dimensional case allows one to illustrate the conceptual features of ...
Ideals generated by diagonal 2-minors
Ene, Viviana
2011-01-01
With a simple graph $G$ on $[n]$, we associate a binomial ideal $P_G$ generated by diagonal minors of an $n \\times n$ matrix $X=(x_{ij})$ of variables. We show that for any graph $G$, $P_G$ is a prime complete intersection ideal and determine the divisor class group of $K[X]/ P_G$. By using these ideals, one may find a normal domain with free divisor class group of any given rank.
Spectral Diagonal Covariance in Ensemble Kalman Filter
Czech Academy of Sciences Publication Activity Database
Kasanický, Ivan; Eben, Kryštof; Mandel, Jan; Vejmelka, Martin
Munich : Ludwig Maximilians University, 2014. s. 10-10. [ISDA 2014. International Conference on Intelligent Systems Design and Applications. 24.02.2014-28.02.2014, Munich] R&D Projects: GA ČR GA13-34856S Grant ostatní: NSF DMS-1216481 Institutional support: RVO:67985807 Keywords : data assimilation * ensemble Kalman filter * diagonal covariance Subject RIV: DG - Athmosphere Sciences, Meteorology http://www.isda2014.physik.uni-muenchen.de/index.html
On diagonalization in map(M,G)
International Nuclear Information System (INIS)
Motivated by some questions in the path integral approach to (topological) gauge theories, we are led to address the following question: given a smooth map from a manifold M to a compact group G, is it possible to smoothly ''diagonalize'' it, i.e. conjugate it into a map to a maximal torus T of G? We analyze the local and global obstructions and give a complete solution to the problem for regular maps. We establish that these can always be smoothly diagonalized locally and that the obstructions to doing this globally are non-trivial Weyl group and torus bundles on M. We explain the relation of the obstructions to winding numbers of maps into G/T and restrictions of the structure group of a principal G bundle to T and examine the behaviour of gauge fields under this diagonalization. We also discuss the complications that arise in the presence of non-trivial G-bundles and for non-regular maps. We use these results to justify a Weyl integral formula for functional integrals which, as a novel feature not seen in the finite-dimensional case, contains a summation over all those topological T-sectors which arise as restrictions of a trivial principal G bundle and which was used previously to solve completely Yang-Mills theory and the G/ G model in two dimensions. (orig.)
Measurement of off-diagonal transport coefficients in two-phase flow in porous media.
Ramakrishnan, T S; Goode, P A
2015-07-01
The prevalent description of low capillary number two-phase flow in porous media relies on the independence of phase transport. An extended Darcy's law with a saturation dependent effective permeability is used for each phase. The driving force for each phase is given by its pressure gradient and the body force. This diagonally dominant form neglects momentum transfer from one phase to the other. Numerical and analytical modeling in regular geometries have however shown that while this approximation is simple and acceptable in some cases, many practical problems require inclusion of momentum transfer across the interface. Its inclusion leads to a generalized form of extended Darcy's law in which both the diagonal relative permeabilities and the off-diagonal terms depend not only on saturation but also on the viscosity ratio. Analogous to application of thermodynamics to dynamical systems, any of the extended forms of Darcy's law assumes quasi-static interfaces of fluids for describing displacement problems. Despite the importance of the permeability coefficients in oil recovery, soil moisture transport, contaminant removal, etc., direct measurements to infer the magnitude of the off-diagonal coefficients have been lacking. The published data based on cocurrent and countercurrent displacement experiments are necessarily indirect. In this paper, we propose a null experiment to measure the off-diagonal term directly. For a given non-wetting phase pressure-gradient, the null method is based on measuring a counter pressure drop in the wetting phase required to maintain a zero flux. The ratio of the off-diagonal coefficient to the wetting phase diagonal coefficient (relative permeability) may then be determined. The apparatus is described in detail, along with the results obtained. We demonstrate the validity of the experimental results and conclude the paper by comparing experimental data to numerical simulation. PMID:25748636
Generalized Coordinate Bethe Ansatz for open spin chains with non-diagonal boundaries
International Nuclear Information System (INIS)
We introduce a generalization of the original Coordinate Bethe Ansatz that allows to treat the case of open spin chains with non-diagonal boundary matrices. We illustrate it on two cases: the XXX and XXZ chains. Short review on a joint work with N. Crampe (L2C) and D. Simon (LPMA), see arXiv:1009.4119, arXiv:1105.4119 and arXiv:1106.3264.
186 K Operation of Terahertz Quantum-Cascade Lasers Based on a Diagonal Design
Kumar, Sushil; Hu, Qing; Reno, John L.
2009-01-01
Resonant-phonon terahertz quantum-cascade lasers operating up to a heat-sink temperature of 186 K are demonstrated. This record temperature performance is achieved based on a diagonal design, with the objective to increase the upper-state lifetime and therefore the gain at elevated temperatures. The increased diagonality also lowers the operating current densities by limiting the flow of parasitic leakage current. Quantitatively, the diagonality is characterized by a radiative oscillator strength that is smaller by a factor of two from the least of any previously published designs. At the lasing frequency of 3.9 THz, 63 mW of peak optical power was measured at 5 K, and approximately 5 mW could still be detected at 180 K.
Approximate factorization with source terms
Shih, T. I.-P.; Chyu, W. J.
1991-01-01
A comparative evaluation is made of three methodologies with a view to that which offers the best approximate factorization error. While two of these methods are found to lead to more efficient algorithms in cases where factors which do not contain source terms can be diagonalized, the third method used generates the lowest approximate factorization error. This method may be preferred when the norms of source terms are large, and transient solutions are of interest.
The quantum way to diagonalize hermitean matrices
Weigert, S
2003-01-01
An entirely quantum mechanical approach to diagonalize hermitean matrices has been presented recently. Here, the genuinely quantum mechanical approach is considered in detail for (2x2) matrices. The method is based on the measurement of quantum mechanical observables which provides the computational resource. In brief, quantum mechanics is able to directly address and output eigenvalues of hermitean matrices. The simple low-dimensional case allows one to illustrate the conceptual features of the general method which applies to (NxN) hermitean matrices.
Diophantine approximations on fractals
Einsiedler, Manfred; Shapira, Uri
2009-01-01
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure) contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0,1]^2, possessing some symmetry, almost any point is not Dirichlet improvable (hence is well approximable) and has property C (after Cassels). We then settle by similar methods a conjecture of M. Boshernitzan saying that there are no irrational numbers x in the unit interval such that the continued fraction expansions of {nx mod1 : n is a natural number} are uniformly eventually bounded.
An Ancient Egyptian Diagonal Star Table in Mallawi, Egypt
Symons, Sarah; Cockcroft, Robert
2013-11-01
A coffin belonging to an Egyptian Middle Kingdom official Hor-em-hetepu, on public display in the Mallawi Monuments Museum, Egypt, contains a previously-unpublished diagonal star table (or "diagonal star clock"). This table adds to the other twenty-four examples of this type of astronomical record or calendar from around 2100 B.C. The table displays a regular diagonal pattern of decan (star or asterism) names, with some interesting points of content, epigraphy, and typology.
Diagonal lattices and rootless $EE_8$ pairs
Griess, Robert L; Lam, Ching Hung
2011-01-01
Let E be an integral lattice. We first discuss some general properties of an SDC lattice, i.e., a sum of two diagonal copies of E in E \\bot E. In particular, we show that its group of isometries contains a wreath product. We then specialize this study to the case of E = E_8 and provide a new and fairly natural model for those rootless lattices which are sums of a pair of EE_8-lattices. This family of lattices was classified in [7]. We prove that this set of isometry types is in bijection with the set of conjugacy classes of rootless elements in the isometry group O(E_8), i.e., those h \\in O(E_8) such that the sublattice (h - 1)E_8 contains no roots. Finally, our model gives new embeddings of several of these lattices in the Leech lattice.
Wang Feng; Sun Deshu
2015-01-01
The theory of Schur complement plays an important role in many fields, such as matrix theory and control theory. In this paper, applying the properties of Schur complement, some new estimates of diagonally dominant degree on the Schur complement of I(II)-block strictly diagonally dominant matrices and I(II)-block strictly doubly diagonally dominant matrices are obtained, which improve some relative results in Liu [Linear Algebra Appl. 435(2011) 3085-3100]. As an application, we pr...
Special function of nestin+neurons in the medial septum-diagonal band of Broca in adult rats
Institute of Scientific and Technical Information of China (English)
Yuhong Zhao; Kaihua Guo; Dongpei Li; Qunfang Yuan; Zhibin Yao
2014-01-01
Nestin+neurons have been shown to express choline acetyltransferase (ChAT) in the medial septum-diagonal band of Broca in adult rats. This study explored the projection of nestin+neu-rons to the olfactory bulb and the time course of nestin+neurons in the medial septum-diagonal band of Broca in adult rats during injury recovery after olfactory nerve transection. This study observed that all nestin+neurons were double-labeled with ChAT in the medial septum-diagonal band of Broca. Approximately 53.6%of nestin+neurons were projected to the olfactory bulb and co-labeled with fast blue. A large number of nestin+neurons were not present in each region of the medial septum-diagonal band of Broca. Nestin+neurons in the medial septum and vertical limb of the diagonal band of Broca showed obvious compensatory function. The number of nestin+neurons decreased to a minimum later than nestin-/ChAT+neurons in the medial sep-tum-diagonal band of Broca. The results suggest that nestin+cholinergic neurons may have a closer connection to olfactory bulb neurons. Nestin+cholinergic neurons may have a stronger tolerance to injury than Nestin-/ChAT+neurons. The difference between nestin+and nestin-/ChAT+neurons during the recovery process requires further investigations.
Anisotropic localization behavior of graphene in the presence of diagonal and off-diagonal disorders
International Nuclear Information System (INIS)
Anisotropic localization of Dirac fermions in graphene along both the x and y axes was studied using the transfer-matrix method. The two-parameter scaled behavior around the Dirac points was observed along the x axis with off-diagonal disorder. In contrast, the electronic state along the y axis with armchair edges was delocalized, which can be described well by single parameter scaling theory. This implies that the breakdown of the single-parameter scaling is related to the zigzag edge along the x axis. Furthermore, dimerization induced by the substrate suppresses the two-parameter scaling behavior along the x axis and preserves the delocalized state along the y axis. Our results also demonstrate anisotropic localization in graphene with diagonal disorder that can be tuned by dimerization. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays
Directory of Open Access Journals (Sweden)
T. S. Doan
2012-01-01
Full Text Available We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.
Quantum Monte Carlo diagonalization method as a variational calculation
Energy Technology Data Exchange (ETDEWEB)
Mizusaki, Takahiro; Otsuka, Takaharu [Tokyo Univ. (Japan). Dept. of Physics; Honma, Michio
1997-05-01
A stochastic method for performing large-scale shell model calculations is presented, which utilizes the auxiliary field Monte Carlo technique and diagonalization method. This method overcomes the limitation of the conventional shell model diagonalization and can extremely widen the feasibility of shell model calculations with realistic interactions for spectroscopic study of nuclear structure. (author)
Iterative diagonalization for orbital optimization in natural orbital functional theory.
Piris, M; Ugalde, J M
2009-10-01
A challenging task in natural orbital functional theory is to find an efficient procedure for doing orbital optimization. Procedures based on diagonalization techniques have confirmed its practical value since the resulting orbitals are automatically orthogonal. In this work, a new procedure is introduced, which yields the natural orbitals by iterative diagonalization of a Hermitian matrix F. The off-diagonal elements of the latter are determined explicitly from the hermiticity of the matrix of the Lagrange multipliers. An expression for diagonal elements is absent so a generalized Fockian is undefined in the conventional sense, nevertheless, they may be determined from an aufbau principle. Thus, the diagonal elements are obtained iteratively considering as starting values those coming from a single diagonalization of the matrix of the Lagrange multipliers calculated with the Hartree-Fock orbitals after the occupation numbers have been optimized. The method has been tested on the G2/97 set of molecules for the Piris natural orbital functional. To help the convergence, we have implemented a variable scaling factor which avoids large values of the off-diagonal elements of F. The elapsed times of the computations required by the proposed procedure are compared with a full sequential quadratic programming optimization, so that the efficiency of the method presented here is demonstrated. PMID:19219918
Teleportation of an arbitrary mixture of diagonal states of multiqudit
International Nuclear Information System (INIS)
This paper proposes a scheme to teleport an arbitrary mixture of diagonal states of multiqutrit via classical correlation and classical communication. To teleport an arbitrary mixture of diagonal states of N qutrits, N classically correlated pairs of two qutrits are used as channel. The sender (Alice) makes Fourier transform and conditional gate (i.e., XOR(3) gate) on her qutrits and does measurement in appropriate computation bases. Then she sends N ctrits to the receiver (Bob). Based on the received information, Bob performs the corresponding unitary transformation on his qutrits and obtains the teleported state. Teleportation of an arbitrary mixture of diagonal states of multiqudit is also discussed
Teleportation of an arbitrary mixture of diagonal states of multiqudit
Du, Qian-Hua; Lin, Xiu-Min; Chen, Zhi-Hua; Lin, Gong-Wei; Chen, Li-Bo; Gu, Yong-Jian
2008-03-01
This paper proposes a scheme to teleport an arbitrary mixture of diagonal states of multiqutrit via classical correlation and classical communication. To teleport an arbitrary mixture of diagonal states of N qutrits, N classically correlated pairs of two qutrits are used as channel. The sender (Alice) makes Fourier transform and conditional gate (i.e., XOR(3) gate) on her qutrits and does measurement in appropriate computation bases. Then she sends N ctrits to the receiver (Bob). Based on the received information, Bob performs the corresponding unitary transformation on his qutrits and obtains the teleported state. Teleportation of an arbitrary mixture of diagonal states of multiqudit is also discussed.
NONLINEAR BENDING THEORY OF DIAGONAL SQUARE PYRAMID RETICULATED SHALLOW SHELLS
Institute of Scientific and Technical Information of China (English)
肖潭; 刘人怀
2001-01-01
Double-deck reticulated shells are a main form of large space structures. One of the shells is the diagonal square pyramid reticulated shallow shell, whose its upper and lower faces bear most of the load but its core is comparatively flexible. According to its geometrical and mechanical characteristics, the diagonal square pyramid reticulated shallow shell is treated as a shallow sandwich shell on the basis of three basic assumptions. Its constitutive relations are analyzed from the point of view of energy and internal force equivalence. Basic equations of the geometrically nonlinear bending theory of the diagonal square pyramid reticulated shallow shell are established by means of the virtual work principle .
Diagonal representation for a generic matrix valued quantum Hamiltonian
International Nuclear Information System (INIS)
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a running variable are introduced. This method leads to a formal compact expression for the diagonal Hamiltonian which can be expanded in a power series of the Planck constant. In particular, we provide an explicit expression for the diagonal representation of a generic Hamiltonian to the second order in the Planck constant. This result is applied, as a physical illustration, to Dirac electrons and neutrinos in external fields. (orig.)
A study on the diagonal beam quality of a fiber laser pumped source
International Nuclear Information System (INIS)
Improving diode laser fiber coupling efficiency is the key to improving the efficiency of fiber lasers. We have demonstrated a new expression for the diagonal beam quality of a rectangular spot beam of a diode laser, which reflects the actual value approached. By considering the application of fiber coupling and the astigmatism characteristics of the diode laser, we have introduced an astigmatism factor, using the extreme value and the approximation of the overall divergence angle in the offset direction. From this we have obtained a new universal expression for the diagonal beam parameters of the diode laser. The degree of matching between the theoretical value and the experimentally measured value was greater than 99.7%. (paper)
Classical limit of diagonal form factors and HHL correlators
Bajnok, Zoltan
2016-01-01
We propose an expression for the classical limit of diagonal form factors in which we integrate the corresponding observable over the moduli space of classical solutions. In infinite volume the integral has to be regularized by proper subtractions and we present the one, which corresponds to the classical limit of the connected diagonal form factors. In finite volume the integral is finite and can be expressed in terms of the classical infinite volume diagonal form factors and subvolumes of the moduli space. We analyze carefully the periodicity properties of the finite volume moduli space and found a classical analogue of the Bethe-Yang equations. By applying the results to the heavy-heavy-light three point functions we can express their strong coupling limit in terms of the classical limit of the sine-Gordon diagonal form factors.
EXTREME POINTS IN DIAGONAL-DISJOINT IDEALS OF NEST ALGEBRAS
Institute of Scientific and Technical Information of China (English)
董浙; 鲁世杰
2002-01-01
In this paper, the extreme points of the unit ball of diagonal-disjoint ideals in nest algebras are characterized completely; Furthermore, it is shown that every extreme point of the unit ball of 2 has essential-norm one.
Diagonal flips in outer-triangulations on closed surfaces
Cortés Parejo, María del Carmen; Grima Ruiz, Clara Isabel; Márquez Pérez, Alberto; Nakamoto, Atsuhiro
2002-01-01
We show that any two outer-triangulations on the same closed surface can be transformed into each other by a sequence of diagonal flips, up to isotopy, if they have a sufficiently large and equal number of vertices.
Reflexivity and the diagonal argument in proofs of limitative theorems
Młynarski, Kajetan
2011-01-01
This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\\"odel's theorem). The fact, that a formal system contains a sentence, which introduces reflexitivity, does not imply, that the same system does not contain a sentence or a proof procedure which solves this problem. Second basic method of proof - diagonal argument (i.e. showing non-eqiunumerosity o...
Chatterjee, Arghya; Nayak, Tapan K; Sahoo, Nihar Ranjan
2016-01-01
Susceptibilities of conserved quantities, such as baryon number, strangeness and electric charge are sensitive to the onset of quantum chromodynamics (QCD) phase transition and are expected to provide information on the matter produced in heavy-ion collision experiments. A comprehensive study of the second-order diagonal susceptibilities and cross correlations has been made within a thermal model approach of the hadron resonance gas (HRG) model as well as with a hadronic transport model, UrQMD. We perform a detailed analysis of the effect of detector acceptances and choice of particle species in the experimental measurements of the susceptibilities for heavy-ion collisions corresponding to \\sNN = 4 GeV to 200 GeV. The transverse momentum cutoff dependence of suitably normalised susceptibilities are proposed as useful observables to probe the properties of the medium at freezeout.
Directory of Open Access Journals (Sweden)
Yurisman
2010-11-01
Full Text Available This paper presents results of numerical and experimental study of shear link behavior, utilizing diagonal stiffener on web of steel profile to increase shear link performance in an eccentric braced frame (EBF of a steel structure system. The specimen is to examine the behavior of shear link by using diagonal stiffener on web part under static monotonic and cyclic load. The cyclic loading pattern conducted in the experiment is adjusted according to AISC loading standards 2005. Analysis was carried out using non-linear finite element method using MSC/NASTRAN software. Link was modeled as CQUAD shell element. Along the boundary of the loading area the nodal are constraint to produce only one direction loading. The length of the link in this analysis is 400mm of the steel profile of WF 200.100. Important parameters considered to effect significantly to the performance of shear link have been analyzed, namely flange and web thicknesses, , thickness and length of web stiffener, thickness of diagonal stiffener and geometric of diagonal stiffener. The behavior of shear link with diagonal web stiffener was compared with the behavior of standard link designed based on AISC 2005 criteria. Analysis results show that diagonal web stiffener is capable to increase shear link performance in terms of stiffness, strength and energy dissipation in supporting lateral load. However, differences in displacement ductility’s between shear links with diagonal stiffener and shear links based on AISC standards have not shown to be significant. Analysis results also show thickness of diagonal stiffener and geometric model of stiffener to have a significant influence on the performance of shear links. To perform validation of the numerical study, the research is followed by experimental work conducted in Structural Mechanic Laboratory Center for Industrial Engineering ITB. The Structures and Mechanics Lab rotary PAU-ITB. The experiments were carried out using three test
Diagonality of weak neutral current and mixing amplitudes of neutral mesons
International Nuclear Information System (INIS)
A possibility to mix K deg - like systems into their antisystems is investigated in terms of multiquark models. The principle of neutral current diagonality is greatly employed. The scheme with two sets of quarks: four quarks with the charge -1/3 (''down''-quarks) and four quarks with the charge 2/3 (''up''-quarks) is considered. Six systems (antisystems), neutral in charge but ''charged'' in other quantum numbers are found, being referred to as ''down'' and ''up'' systems neutral in charge. The Feynman diagrams contribute into the mixing amplitudes of the indicated systems and into the corresponding antisystems in the fourth order of perturbation theory. The diagonality principle of neutral current signifies that the matrix 0 is a unitary one. Due to the diagonality principle of neutral current the divergences in the mixing amplitude are cancelled. The same result holds for the integral J2 containing the divergence of the approximately lsub(nt) type. All the hadrons with the exotic quantum numbers ''temperament'', ''beauty'', ''charm'', ''strangeness'' are shown to decay into stable hadronic states constructed of coventional quarks p and n
Auditory spatial resolution in horizontal, vertical, and diagonal planes
Grantham, D. Wesley; Hornsby, Benjamin W. Y.; Erpenbeck, Eric A.
2003-08-01
Minimum audible angle (MAA) and minimum audible movement angle (MAMA) thresholds were measured for stimuli in horizontal, vertical, and diagonal (60°) planes. A pseudovirtual technique was employed in which signals were recorded through KEMAR's ears and played back to subjects through insert earphones. Thresholds were obtained for wideband, high-pass, and low-pass noises. Only 6 of 20 subjects obtained wideband vertical-plane MAAs less than 10°, and only these 6 subjects were retained for the complete study. For all three filter conditions thresholds were lowest in the horizontal plane, slightly (but significantly) higher in the diagonal plane, and highest for the vertical plane. These results were similar in magnitude and pattern to those reported by Perrott and Saberi [J. Acoust. Soc. Am. 87, 1728-1731 (1990)] and Saberi and Perrott [J. Acoust. Soc. Am. 88, 2639-2644 (1990)], except that these investigators generally found that thresholds for diagonal planes were as good as those for the horizontal plane. The present results are consistent with the hypothesis that diagonal-plane performance is based on independent contributions from a horizontal-plane system (sensitive to interaural differences) and a vertical-plane system (sensitive to pinna-based spectral changes). Measurements of the stimuli recorded through KEMAR indicated that sources presented from diagonal planes can produce larger interaural level differences (ILDs) in certain frequency regions than would be expected based on the horizontal projection of the trajectory. Such frequency-specific ILD cues may underlie the very good performance reported in previous studies for diagonal spatial resolution. Subjects in the present study could apparently not take advantage of these cues in the diagonal-plane condition, possibly because they did not externalize the images to their appropriate positions in space or possibly because of the absence of a patterned visual field.
Spectral Diagonal Covariance in EnKF
Czech Academy of Sciences Publication Activity Database
Mandel, J.; Kasanický, Ivan; Vejmelka, Martin
Ostrava: Ústav geoniky AV ČR, 2014 - (Blaheta, R.; Starý, J.; Sysalová, D.). s. 64-64 ISBN 978-80-86407-47-0. [Modelling 2014. 02.06.2014-06.06.2014, Rožnov pod Radhoštěm] R&D Projects: GA ČR GA13-34856S Grant ostatní: NSF DMS -1216481 Institutional support: RVO:67985807 Keywords : ensemble Kalman filter * high-dimensional covariance * spectral approximations Subject RIV: BB - Applied Statistics, Operational Research
Spectral Diagonal Covariance in EnKF
Czech Academy of Sciences Publication Activity Database
Mandel, J.; Kasanický, Ivan; Vejmelka, Martin
Ostrava : Ústav geoniky AV ČR, 2014 - (Blaheta, R.; Starý, J.; Sysalová, D.). s. 64-64 ISBN 978-80-86407-47-0. [Modelling 2014. 02.06.2014-06.06.2014, Rožnov pod Radhoštěm] R&D Projects: GA ČR GA13-34856S Grant ostatní: NSF DMS-1216481 Institutional support: RVO:67985807 Keywords : ensemble Kalman filter * high-dimensional covariance * spectral approximations Subject RIV: BB - Applied Statistics, Operational Research
Diagonally loaded SMI algorithm based on inverse matrix recursion
Institute of Scientific and Technical Information of China (English)
Cao Jianshu; Wang Xuegang
2007-01-01
The derivation of a diagonally loaded sample-matrix inversion (LSMI) algorithm on the busis of inverse matrix recursion (i.e. LSMI-IMR algorithm) is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, acorresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings.Simulations show that the LSMI-IMR algorithm is valid.
The Optimal Preconditioner of Strictly Diagonally Dominant Z-matrix
Institute of Scientific and Technical Information of China (English)
Ji-cheng Li; Wei Li
2008-01-01
In this paper, we present a series of new preconditioners with parameters of strictly diagonally dominant Z-matrix, which contain properly two kinds of known preconditioners as special cases. Moreover,we prove the monotonicity of spectral radiuses of iterative matrices with respect to the parameters and some comparison theorems. The results obtained show that the bigger the parameter k is(i.e., we select the more upper right diagonal elements to be the preconditioner), the leas the spectral radius of iterative matrix is. A numerical example generated randomly is provided to illustrate the theoretical results.
Diagonal invariant ideals of Toeplitz algebras on discrete groups
Institute of Scientific and Technical Information of China (English)
许庆祥
2002-01-01
Diagonal invariant ideals of Toeplitz algebras defined on discrete groups are introduced and studied. In terms of isometric representations of Toeplitz algebras associated with quasi-ordered groups, a character of a discrete group to be amenable is clarified. It is proved that when G is Abelian, a closed two-sided non-trivial ideal of the Toeplitz algebra defined on a discrete Abelian ordered group is diagonal invariant if and only if it is invariant in the sense of Adji and Murphy, thus a new proof of their result is given.
Penguins and Pandas: A Note on Teaching Cantor's Diagonal Argument
Rauff, James V.
2008-01-01
Cantor's diagonal proof that the set of real numbers is uncountable is one of the most famous arguments in modern mathematics. Mathematics students usually see this proof somewhere in their undergraduate experience, but it is rarely a part of the mathematical curriculum of students of the fine arts or humanities. This note describes contexts that…
Off-diagonal magnetoimpedance in stress-annealed amorphous ribbons
Czech Academy of Sciences Publication Activity Database
Kraus, Luděk
2008-01-01
Roč. 320, č. 20 (2008), e746-e749. ISSN 0304-8853 Institutional research plan: CEZ:AV0Z10100520 Keywords : amorphous ribbon * giant magnetoimpedance * off-diagonal magnetoimpedance * stress annealing * magnetic anisotropy Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.283, year: 2008
MINRES Residual Norms of Diagonally Translated linear Systems
Czech Academy of Sciences Publication Activity Database
Duintjer Tebbens, Jurjen
Poznan : Adam Mickiewicz University, 2005 - (Markiewicz, A.; Wolynski, W.). s. 37-38 [MAT-TRIAD 2005. Three days full of matrices. 03.03.2005-05.03.2005, Bedlewo] Institutional research plan: CEZ:AV0Z10300504 Keywords : MINRES * convergence of Krylov subspace methods * diagonal translation Subject RIV: BA - General Mathematics
The Oblique Corrections from the Diagonal ETC Interaction
Yoshikawa, Tadashi
1995-01-01
We study the effect of the diagonal extended technicolor(ETC) gauge boson on the oblique correction parameters. It is shown that in the $T$ parameter is unacceptably large when the $Zbb$ vertex correction and $S$ parameter are consistent with the experiments in the ETC model.
Structure Constants of Diagonal Reduction Algebras of gl Type
Sergei Khoroshkin; Oleg Ogievetsky
2011-01-01
We describe, in terms of generators and relations, the reduction algebra, related to the diagonal embedding of the Lie algebra $\\gl_n$ into $\\gl_n\\oplus\\gl_n$. Its representation theory is related to the theory of decompositions of tensor products of $\\gl_n$-modules.
Sang, Huiyan
2011-12-01
This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate models. Our method allows for a nonseparable and nonstationary cross-covariance structure. We also present a covariance approximation approach to facilitate the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approximation consists of two parts: a reduced-rank part to capture the large-scale spatial dependence, and a sparse covariance matrix to correct the small-scale dependence error induced by the reduced rank approximation. We pay special attention to the case that the second part of the approximation has a block-diagonal structure. Simulation results of model fitting and prediction show substantial improvement of the proposed approximation over the predictive process approximation and the independent blocks analysis. We then apply our computational approach to the joint statistical modeling of multiple climate model errors. © 2012 Institute of Mathematical Statistics.
Dynamical Vertex Approximation for Nanoscopic Systems
International Nuclear Information System (INIS)
Full text: We present model calculations for nanoscopic systems including Hubbard-like Coulomb repulsion and double exchange interactions with localized, classical spins. We compare the results of the recently introduced nanoscopic version of the dynamical vertex approximation at dynamical mean field level against exact diagonalization for a Benzene-like ring, where the latter is doable. This comparison allows us to investigate the reliability of the approximation. It shows that, already at the simplest approximation level (i.e. including only local correlations) the results are very accurate in a rather wide range of parameters. Since the computational effort is highly reduced, it is suitable for studying more complex systems. (author)
EFFECT OF ADHESIVE TYPE ON THE BENDING MOMENT CAPACITY OF MITER FRAME CORNER JOINTS
Directory of Open Access Journals (Sweden)
Suat Altun
2010-05-01
Full Text Available The bending moment capacity was studied under the diagonal tensile and compression loadings of miter corner joints with dovetail fitting in frames made with medium density fiberboard (MDF. The influence of the type of adhesive in the joints with dovetail fitting on bending moment capacity under diagonal tensile and compression loading were considered, and the joints without adhesive were compared. A total of 80 each miter frame corner joint specimens with dovetail fitting were made. Polyvinyl acetate (PVAc, polyurethane (PU, and cyanoacrylate (CA adhesives were used, and 20 specimens were prepared without adhesive (WA with dovetail fitting. MDF was used as a frame material, as in normal practice. The specimens were subjected to diagonal tensile and compression loadings in accordance with ASTM-D 143-94. The data were analyzed statistically. The highest bending moment capacity under diagonal tensile loading (46.09 Nm was obtained in the specimens bonded with CA adhesive and the highest bending moment capacity under diagonal compression loading (72.04 Nm was obtained in the specimens glued with PVAc adhesive. Other than this, since there is no difference between these and the unbonded joints, the PU adhesive was not effective in increasing the bending moment capacity under diagonal tensile loading, and the PU and CA adhesives were not effective in increasing the bending moment capacity under diagonal compression loadings.
Niven, Ivan
2008-01-01
This self-contained treatment originated as a series of lectures delivered to the Mathematical Association of America. It covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both the fractional and integral parts.The author refrains from the use of continuous fractions and includes basic results in the complex case, a feature often neglected in favor of the real number discuss
Tunneling splitting in double-proton transfer: Direct diagonalization results for porphycene
International Nuclear Information System (INIS)
Zero-point and excited level splittings due to double-proton tunneling are calculated for porphycene and the results are compared with experiment. The calculation makes use of a multidimensional imaginary-mode Hamiltonian, diagonalized directly by an effective reduction of its dimensionality. Porphycene has a complex potential energy surface with nine stationary configurations that allow a variety of tunneling paths, many of which include classically accessible regions. A symmetry-based approach is used to show that the zero-point level, although located above the cis minimum, corresponds to concerted tunneling along a direct trans − trans path; a corresponding cis − cis path is predicted at higher energy. This supports the conclusion of a previous paper [Z. Smedarchina, W. Siebrand, and A. Fernández-Ramos, J. Chem. Phys. 127, 174513 (2007)] based on the instanton approach to a model Hamiltonian of correlated double-proton transfer. A multidimensional tunneling Hamiltonian is then generated, based on a double-minimum potential along the coordinate of concerted proton motion, which is newly evaluated at the RI-CC2/cc-pVTZ level of theory. To make it suitable for diagonalization, its dimensionality is reduced by treating fast weakly coupled modes in the adiabatic approximation. This results in a coordinate-dependent mass of tunneling, which is included in a unique Hermitian form into the kinetic energy operator. The reduced Hamiltonian contains three symmetric and one antisymmetric mode coupled to the tunneling mode and is diagonalized by a modified Jacobi-Davidson algorithm implemented in the Jadamilu software for sparse matrices. The results are in satisfactory agreement with the observed splitting of the zero-point level and several vibrational fundamentals after a partial reassignment, imposed by recently derived selection rules. They also agree well with instanton calculations based on the same Hamiltonian
Algebraic methods for diagonalization of a quaternion matrix in quaternionic quantum theory
International Nuclear Information System (INIS)
By means of complex representation and real representation of a quaternion matrix, this paper studies the problem of diagonalization of a quaternion matrix, gives two algebraic methods for diagonalization of quaternion matrices in quaternionic quantum theory
International Nuclear Information System (INIS)
We have developed here a self-consistent coherent potential approximation generalized to take into account effect of clusters. Off-diagonal disorder and short-range order are taken into account. A graphical method married to the recursion technique, enables us to work on realistic three-dimensional lattices. Calculations are shown for a binary alloy on a diamond lattice. (author)
Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures
Dunajski, Maciej
2016-01-01
Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in the basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possibilities. In particular we construct new examples of neutral signature non--diagonal Bianchi type VIII Einstein metrics with self--dual Weyl tensor.
Dynamical response of a disordered ferromagnetic chain: alloy transfer matrix approximation
International Nuclear Information System (INIS)
The alloy transfer matrix approximation is used to study the uniform dynamic susceptibility of a disordered ferromagnetic chain. The approximation allows for a consistent treatment of diagonal and off- diagonal disorder. The results, in the limit of low concentrations, are in agreement with the exact single impurity ones. Intensities and lineshapes for infrared absorption are calculated for finite impurity concentrations and different values of the relative anisotropy parameter of a model alloy. (Author)
Block-bordered diagonalization and parallel iterative solvers
Energy Technology Data Exchange (ETDEWEB)
Alvarado, F.; Dag, H.; Bruggencate, M. ten [Univ. of Wisconsin, Madison, WI (United States)
1994-12-31
One of the most common techniques for enhancing parallelism in direct sparse matrix methods is the reorganization of a matrix into a blocked-bordered structure. Incomplete LDU factorization is a very good preconditioner for PCG in serial environments. However, the inherent sequential nature of the preconditioning step makes it less desirable in parallel environments. This paper explores the use of BBD (Blocked Bordered Diagonalization) in connection with ILU preconditioners. The paper shows that BBD-based ILU preconditioners are quite amenable to parallel processing. Neglecting entries from the entire border can result in a blocked diagonal matrix. The result is a great increase in parallelism at the expense of additional iterations. Experiments on the Sequent Symmetry shared memory machine using (mostly) power system that matrices indicate that the method is generally better than conventional ILU preconditioners and in many cases even better than partitioned inverse preconditioners, without the initial setup disadvantages of partitioned inverse preconditioners.
Diagonal multi-soliton matrix elements in finite volume
Pálmai, T
2012-01-01
We consider diagonal matrix elements of local operators between multi-soliton states in finite volume in the sine-Gordon model, and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Tak\\'acs which were only valid for diagonal scattering. In order to test the conjecture we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.
Off-diagonal Jacobian support for Nodal BCs
Energy Technology Data Exchange (ETDEWEB)
Peterson, John W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Andrs, David [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gaston, Derek R. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Permann, Cody J. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Slaughter, Andrew E. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-01-01
In this brief note, we describe the implementation of o-diagonal Jacobian computations for nodal boundary conditions in the Multiphysics Object Oriented Simulation Environment (MOOSE) [1] framework. There are presently a number of applications [2{5] based on the MOOSE framework that solve complicated physical systems of partial dierential equations whose boundary conditions are often highly nonlinear. Accurately computing the on- and o-diagonal Jacobian and preconditioner entries associated to these constraints is crucial for enabling ecient numerical solvers in these applications. Two key ingredients are required for properly specifying the Jacobian contributions of nonlinear nodal boundary conditions in MOOSE and nite element codes in general: 1. The ability to zero out entire Jacobian matrix rows after \
Natures of Rotating Stall Cell in a Diagonal Flow Fan
Institute of Scientific and Technical Information of China (English)
N. SHIOMI; K. KANEKO; T. SETOGUCHI
2005-01-01
In order to clarify the natures of a rotating stall cell, the experimental investigation was carried out in a high specific-speed diagonal flow fan. The pressure field on the casing wall and the velocity fields at the rotor inlet and outlet were measured under rotating stall condition with a fast response pressure transducer and a single slant hot-wire probe, respectively. The data were processed using the "Double Phase-Locked Averaging (DPLA)"technique, which enabled to obtain the unsteady flow field with a rotating stall cell in the relative co-ordinate system fixed to the rotor. As a result, the structure and behavior of the rotating stall cell in a high specific-speed diagonal flow fan were shown.
A CLT on the SNR of Diagonally Loaded MVDR Filters
Rubio, Francisco; Mestre, Xavier; Hachem, Walid
2012-08-01
This paper studies the fluctuations of the signal-to-noise ratio (SNR) of minimum variance distorsionless response (MVDR) filters implementing diagonal loading in the estimation of the covariance matrix. Previous results in the signal processing literature are generalized and extended by considering both spatially as well as temporarily correlated samples. Specifically, a central limit theorem (CLT) is established for the fluctuations of the SNR of the diagonally loaded MVDR filter, under both supervised and unsupervised training settings in adaptive filtering applications. Our second-order analysis is based on the Nash-Poincar\\'e inequality and the integration by parts formula for Gaussian functionals, as well as classical tools from statistical asymptotic theory. Numerical evaluations validating the accuracy of the CLT confirm the asymptotic Gaussianity of the fluctuations of the SNR of the MVDR filter.
Off-diagonal Bethe ansatz for exactly solvable models
International Nuclear Information System (INIS)
This book serves as an introduction of the off-diagonal Bethe Ansatz method, an analytic theory for the eigenvalue problem of quantum integrable models. It also presents some fundamental knowledge about quantum integrability and the algebraic Bethe Ansatz method. Based on the intrinsic properties of R-matrix and K-matrices, the book introduces a systematic method to construct operator identities of transfer matrix. These identities allow one to establish the inhomogeneous T-Q relation formalism to obtain Bethe Ansatz equations and to retrieve corresponding eigenstates. Several longstanding models can thus be solved via this method since the lack of obvious reference states is made up. Both the exact results and the off-diagonal Bethe Ansatz method itself may have important applications in the fields of quantum field theory, low-dimensional condensed matter physics, statistical physics and cold atom systems.
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher; Russell, Alexander
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities i...
Swelling of a joint ... Joint swelling may occur along with joint pain . The swelling may cause the joint to appear larger or abnormally shaped. Joint swelling can cause pain or stiffness. After an ...
Staircase polygons: moments of diagonal lengths and column heights
International Nuclear Information System (INIS)
We consider staircase polygons, counted by perimeter and sums of k-th powers of their diagonal lengths, k being a positive integer. We derive limit distributions for these parameters in the limit of large perimeter and compare the results to Monte-Carlo simulations of self-avoiding polygons. We also analyse staircase polygons, counted by width and sums of powers of their column heights, and we apply our methods to related models of directed walks
Bott-Kitaev Periodic Table and the Diagonal Map
R. Kennedy; Zirnbauer, M. R.
2014-01-01
Building on the 10-way symmetry classification of disordered fermions, the authors have recently given a homotopy-theoretic proof of Kitaev's "Periodic Table" for topological insulators and superconductors. The present paper offers an introduction to the physical setting and the mathematical model used. Basic to the proof is the so-called Diagonal Map, a natural transformation akin to the Bott map of algebraic topology, which increases by one unit both the momentum-space dimension and the sym...
Modular Analysis of Almost Block Diagonal Systems of Equations
El-Mistikawy, Tarek M. A.
2013-01-01
Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of the methods on the basis of their operation counts, storage needs, and admissibility of partial pivoting. It unveils a robust partial pivoting strategy- local pivoting. Extension of modular analysis to bordered systems is also included.
Covariant diagonalization of the perfect fluid stress-energy tensor
Garat, Alcides
2012-01-01
We introduce new tetrads that manifestly and covariantly diagonalize the stress-energy tensor for a perfect fluid with vorticity at every spacetime point. We discuss the origin of inertia in this special case from the standpoint of our new local tetrads. We believe that this new tetrad might bring about simplification in the analysis of astrophysical relativistic problems where vorticity is present, for instance through the Carter-Lichnerowicz equation.
Strong Linear Correlation Between Eigenvalues and Diagonal Matrix Elements
Shen, J J; Zhao, Y M; Yoshinaga, N
2008-01-01
We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the smaller values to larger ones. By using this linear correlation we are able to predict reasonably all eigenvalues of given shell model Hamiltonian without complicated iterations.
The sl(2|1)(2) Gaudin magnet with diagonal boundary terms
International Nuclear Information System (INIS)
This work is concerned with the quasi-classical limit of the boundary quantum inverse scattering method for the twisted sl(2|1)(2) vertex model with diagonal K-matrices. In this limit Gaudin's Hamiltonians with diagonal boundary terms are presented and diagonalized
Diagonal dominance for the multivariable Nyquist array using function minimization
Leininger, G. G.
1977-01-01
A new technique for the design of multivariable control systems using the multivariable Nyquist array method was developed. A conjugate direction function minimization algorithm is utilized to achieve a diagonal dominant condition over the extended frequency range of the control system. The minimization is performed on the ratio of the moduli of the off-diagonal terms to the moduli of the diagonal terms of either the inverse or direct open loop transfer function matrix. Several new feedback design concepts were also developed, including: (1) dominance control parameters for each control loop; (2) compensator normalization to evaluate open loop conditions for alternative design configurations; and (3) an interaction index to determine the degree and type of system interaction when all feedback loops are closed simultaneously. This new design capability was implemented on an IBM 360/75 in a batch mode but can be easily adapted to an interactive computer facility. The method was applied to the Pratt and Whitney F100 turbofan engine.
Shrinkage-based diagonal Hotelling’s tests for high-dimensional small sample size data
Dong, Kai
2015-09-16
DNA sequencing techniques bring novel tools and also statistical challenges to genetic research. In addition to detecting differentially expressed genes, testing the significance of gene sets or pathway analysis has been recognized as an equally important problem. Owing to the “large pp small nn” paradigm, the traditional Hotelling’s T2T2 test suffers from the singularity problem and therefore is not valid in this setting. In this paper, we propose a shrinkage-based diagonal Hotelling’s test for both one-sample and two-sample cases. We also suggest several different ways to derive the approximate null distribution under different scenarios of pp and nn for our proposed shrinkage-based test. Simulation studies show that the proposed method performs comparably to existing competitors when nn is moderate or large, but it is better when nn is small. In addition, we analyze four gene expression data sets and they demonstrate the advantage of our proposed shrinkage-based diagonal Hotelling’s test.
Institute of Scientific and Technical Information of China (English)
XIEBing_Hao; ZHANGHong－Biao; 等
2002-01-01
An algebraic diagonalization method is proposed.As two examples,the Hamiltonians of BCS ground state under mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized by using SU(2),SU(1,1) Lie algebraic method,respectively.Meanwhile,the eignenstates of the above two models are revealed to be SU(2),SU(1,1) coherent states,respectively,The relation between the usual Bogoliubov-Valatin transformation and the algebraic method in a special case is also discussed.
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
Schmidt, Wolfgang M
1980-01-01
"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)
Static correlation beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian Sommer
2014-01-01
derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly...... for intermediate binding distances. A Hubbard model for the dimer allows us to obtain exact analytical results for the various approximations, which is readily compared with the exact diagonalization of the model. Moreover, the model is shown to reproduce all the qualitative results from the ab initio...
Topological Rice-Mele model in an emergent lattice: Exact diagonalization approach
Biedroń, Krzysztof; Dutta, Omjyoti; Zakrzewski, Jakub
2016-03-01
Using exact diagonalization methods we study possible phases in a one-dimensional model of two differently populated fermionic species in a periodically driven optical lattice. The shaking amplitude and frequency are chosen to resonantly drive s -p transition while minimizing the standard intraband tunnelings. We verify numerically the presence of an emergent density wave configuration of composites for appropriate filling fraction and minimized intraband tunnelings. The majority fermions moving in such a lattice mimic the celebrated Rice-Mele model. Far away from that region, the structure changes to a clustered phase, with the intermediate phase abundantly populated by defects of the density wave. These defects lead to localized modes carrying fractional particle charge. The results obtained are compared with earlier approximate predictions.
Preferential diagonal penetration of vortices into square superconducting networks
International Nuclear Information System (INIS)
We have observed vortex penetration into Nb thin films with square arrays of square holes with variable sizes and lattice constants. We find that when the lattice spacing is large and the width of superconducting line is narrow, vortices penetrate diagonally rather than parallel to the nearest neighbor direction. This phenomenon is also confirmed in NbTiN samples with the same geometry. We also confirm that the direction of edge relative to that of hole array is not relevant. Possible origin of such a preferential penetration is proposed.
Thermodynamics of Rh nuclear spins calculated by exact diagonalization
DEFF Research Database (Denmark)
Lefmann, K.; Ipsen, J.; Rasmussen, F.B.
We have employed the method of exact diagonalization to obtain the full-energy spectrum of a cluster of 16 Rh nuclear spins, having dipolar and RK interactions between first and second nearest neighbours only. We have used this to calculate the nuclear spin entropy, and our results at both positive...... and negative temperatures follow the second-order high-temperature series expansions for \\T\\ > 3 nK. Our findings do not agree with the measurements of the former Rh experiment in Helsinki, where a deviation is seen at much higher temperatures. (C) 2000 Elsevier Science B.V. All rights reserved....
Thermodynamics of Rh nuclear spins calculated by exact diagonalization
DEFF Research Database (Denmark)
Lefmann, K.; Ipsen, J.; Rasmussen, F.B.; Rasmussen, Finn Berg
We have employed the method of exact diagonalization to obtain the full-energy spectrum of a cluster of 16 Rh nuclear spins, having dipolar and RK interactions between first and second nearest neighbours only. We have used this to calculate the nuclear spin entropy, and our results at both positive...... and negative temperatures follow the second-order high-temperature series expansions for |T| > 3 nK. Our findings do not agree with the measurements of the former Rh experiment in Helsinki, where a deviation is seen at much higher temperatures. © 2000 Elsevier Science B.V. All rights reserved....
Performance Theory of Diagonal Conducting Wall MHD Accelerators
Litchford, R. J.
2003-01-01
The theoretical performance of diagonal conducting wall crossed field accelerators is examined on the basis of an infinite segmentation assumption using a cross-plane averaged generalized Ohm's law for a partially ionized gas, including ion slip. The desired accelerator performance relationships are derived from the cross-plane averaged Ohm's law by imposing appropriate configuration and loading constraints. A current dependent effective voltage drop model is also incorporated to account for cold-wall boundary layer effects including gasdynamic variations, discharge constriction, and electrode falls. Definition of dimensionless electric fields and current densities lead to the construction of graphical performance diagrams, which further illuminate the rudimentary behavior of crossed field accelerator operation.
Diagonal Cracking and Shear Strength of Reinforced Concrete Beams
DEFF Research Database (Denmark)
Zhang, Jin-Ping
1997-01-01
found by the usual plastic theory, a physical explanation is given for this phenomenon and a way to estimate the shear capacity of reinforced concrete beams, based on the theory of plasticity, is described. The theoretical calculations are shown to be in fairly good agreement with test results from a......The shear failure of non-shear-reinforced concrete beams with normal shear span ratios is observed to be governed in general by the formation of a critical diagonal crack. Under the hypothesis that the cracking of concrete introduces potential yield lines which may be more dangerous than the ones...
Iterative diagonalization of symmetric matrices in mixed precision
Tsuchida, Eiji
2011-01-01
Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while keeping 64-bit accuracy. Moreover, most of the computationally expensive operations are performed by level-3 BLAS/LAPACK routines in our implementation, thus leading to optimal performance on most platforms. Further improvement can be made by using problem-specific preconditioners which take into account nondiagonal elements.
The Diagonal Compression Field Method using Circular Fans
DEFF Research Database (Denmark)
Hansen, Thomas
2005-01-01
This paper presents a new design method, which is a modification of the diagonal compression field method, the modification consisting of the introduction of circular fan stress fields. The traditional method does not allow changes of the concrete compression direction throughout a given beam if...... if the -value for a given beam could be set to a low value in regions with high shear stresses and thereafter increased in regions with low shear stresses. Thus the shear reinforcement would be reduced and the concrete strength would be utilized in a better way. In the paper it is shown how circular...
On the performance of diagonal lattice space-time codes
Abediseid, Walid
2013-11-01
There has been tremendous work done on designing space-time codes for the quasi-static multiple-input multiple output (MIMO) channel. All the coding design up-to-date focuses on either high-performance, high rates, low complexity encoding and decoding, or targeting a combination of these criteria [1]-[9]. In this paper, we analyze in details the performance limits of diagonal lattice space-time codes under lattice decoding. We present both lower and upper bounds on the average decoding error probability. We first derive a new closed-form expression for the lower bound using the so-called sphere lower bound. This bound presents the ultimate performance limit a diagonal lattice space-time code can achieve at any signal-to-noise ratio (SNR). The upper bound is then derived using the union-bound which demonstrates how the average error probability can be minimized by maximizing the minimum product distance of the code. Combining both the lower and the upper bounds on the average error probability yields a simple upper bound on the the minimum product distance that any (complex) lattice code can achieve. At high-SNR regime, we discuss the outage performance of such codes and provide the achievable diversity-multiplexing tradeoff under lattice decoding. © 2013 IEEE.
End effects in diagonal type nonequilibrium plasma MHD generators
International Nuclear Information System (INIS)
The authors investigate the influence of the attenuation of magnetic induction on the current distribution etc. in the end regions of the diagonal type nonequilibrium plasma MHD generator by a two-dimensional analysis. The numerical calculations are made for an example of the cesium-seeded helium. As a result, a suitable attenuation of the magnetic induction can make the current distribution very uniform near the end region of generator duct and has little influence on the current distribution in the central part of generator, and the output electrodes can be used without large ballast resistors. Also the internal resistance of the end region and the current concentration at the output electrode edges decrease with the attenuation of magnetic flux density. By the author's investigation, it is made clear that the output electrodes of the diagonal type nonequilibrium plasma MHD generator should be arranged in the attenuation region of the magnetic induction, since arranging them in the attenuation region of magnetic flux density can become useful for the improvement of the electrical characteristics of generator. (auth.)
The Chern-Simons state for the non-diagonal Bianchi IX model
Paternoga, Robert; Graham, Robert
1998-01-01
The Bianchi IX mixmaster model is quantized in its non-diagonal form, imposing spatial diffeomorphism, time reparametrization and Lorentz invariance as constraints on physical state vectors before gauge-fixing. The result turns out to be different from quantizing the diagonal model obtained by gauge-fixing already on the classical level. For the non-diagonal model a generalized 9-dimensional Fourier transformation over a suitably chosen manifold connects the representations in metric variable...
Diagonal complexes and the integral homology of the automorphism group of a free product
Griffin, James
2010-01-01
We calculate the integral (co)homology of the group of symmetric automorphisms of a free product. We proceed by constructing a moduli space of cactus products and to describe this space a theory of diagonal complexes is introduced. In doing so we offer a generalisation of the theory of right-angled Artin groups in that each diagonal complex defines what we call a diagonal right-angled Artin group (DRAAG).
Efficiency of actions in attack of diagonal players in female volleyball
Yevgeniya Strelnykova; Tamara Liakhova
2016-01-01
Strelnikova Ye., Lyakhova T. Purpose: to define efficiency of technical and tactical actions of the diagonal player in the attacking actions of a team depending on schemes of a defensive play of the rival. Material & Methods: the competitive process with participation of 10 players of the role –the diagonal forward of qualification and the adult category was investigated in the pedagogical supervision. The efficiency of actions in attack of diagonal players of women's teams of Student's ...
Flatness characteristics for diagonal scans from Varian and Siemens linear accelerators
International Nuclear Information System (INIS)
The advent of 3D treatment planning systems whose algorithms utilize diagonal scan data to perform dose calculations has made the collection of diagonal profile data essential. Manufacturers' specifications (MS) on beam flatness and symmetry apply to both the radial and transverse axes of all square field sizes from 10 x 10 cm2 to the largest field available. Beam profile measurements were obtained for both diagonal axes over a range of field sizes and depths for two units, a Varian 2100C and a Siemens KD. In this note the International Electrotechnical Commission (IEC) flatness definition was used to characterize the diagonal flatness of each beam
Coordinate Bethe ANSÄTZE for Non-Diagonal Boundaries
Ragoucy, Eric
2013-11-01
Bethe ansatz goes back to 1931, when H. Bethe invented it to solve some one-dimensional models, such as XXX spin chain, proposed by W. Heisenberg in 1928. Although it is a very powerful method to compute eigenvalues and eigenvectors of the corresponding Hamiltonian, it can be applied only for very specific boundary conditions: periodic boundary ones, and so-called open-diagonal boundary ones. After reviewing this method, we will present a generalization of it that applies also to open-triangular boundary conditions. This short note presents only the basic ideas of the technique, and does not attend to give a general overview of the subject. Interested readers should refer to the original papers and references therein.
On solution-free sets for simultaneous diagonal polynomials
Smith, Matthew L
2010-01-01
We consider a translation and dilation invariant system consisting of k diagonal equations of degrees 1,2,...,k with integer coefficients in s variables, where s is sufficiently large in terms of k. We show via the Hardy-Littlewood circle method that if a subset A of the natural numbers restricted to the interval [1,N] satisfies Gowers' definition of uniformity of degree k, then it furnishes roughly the expected number of simultaneous solutions to the given equations. If A furnishes no non-trivial solutions to the given system, then we show that the number of elements of A in [1,N] grows no faster than a constant multiple of N/(log log N)^{-c} as N grows to infinity, where c>0 is a constant dependent only on k. In particular, we show that the density of A in [1,N] tends to 0 as N tends to infinity.
Diagnosis of Interaction-driven Topological Phase via Exact Diagonalization
Wu, Han-Qing; He, Yuan-Yao; Fang, Chen; Meng, Zi Yang; Lu, Zhong-Yi
2016-08-01
We propose a general scheme for diagnosing interaction-driven topological phases in the weak interaction regime using exact diagonalization (ED). The scheme comprises the analysis of eigenvalues of the point-group operators for the many-body eigenstates and the correlation functions for physical observables to extract the symmetries of the order parameters and the topological numbers of the underlying ground states at the thermodynamic limit from a relatively small size system afforded by ED. As a concrete example, we investigate the interaction effects on the half-filled spinless fermions on the checkerboard lattice with a quadratic band crossing point. Numerical results support the existence of a spontaneous quantum anomalous Hall phase purely driven by a nearest-neighbor weak repulsive interaction, separated from a nematic Mott insulator phase at strong repulsive interaction by a first-order phase transition.
Performance Theory of Diagonal Conducting Wall Magnetohydrodynamic Accelerators
Litchford, R. J.
2004-01-01
The theoretical performance of diagonal conducting wall crossed-field accelerators is examined on the basis of an infinite segmentation assumption using a cross-plane averaged generalized Ohm s law for a partially ionized gas, including ion slip. The desired accelerator performance relationships are derived from the cross-plane averaged Ohm s law by imposing appropriate configuration and loading constraints. A current-dependent effective voltage drop model is also incorporated to account for cold-wall boundary layer effects, including gasdynamic variations, discharge constriction, and electrode falls. Definition of dimensionless electric fields and current densities leads to the construction of graphical performance diagrams, which further illuminate the rudimentary behavior of crossed-field accelerator operation.
Diagonalization of the XXZ Hamiltonian by Vertex Operators
Davies, B; Jimbo, M; Miwa, T; Nakayashiki, A; Davies, Brian; Foda, Omar; Jimbo, Michio; Miwa, Tetsuji; Nakayashiki, Atsushi
1993-01-01
We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of affine U_q( sl(2) ). Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors. We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limit --- the $su(2)$-invariant Thirring model.
Batista, Milan
2008-01-01
The article presents the theoretical background of the algorithms for solving cyclic block tridiagonal and cyclic block penta-diagonal systems of linear algebraic equations present in [1] and [2]. The theory is based on the Woodbury formula.
Agarwalla, Sanjib Kumar; Saha, Debashis; Takeuchi, Tatsu
2015-01-01
In this article we unravel the role of matter effect in neutrino oscillation in the presence of lepton-flavor-conserving, non-universal non-standard interactions (NSI's) of the neutrino. Employing the Jacobi method, we derive approximate analytical expressions for the effective mass-squared differences and mixing angles in matter. It is shown that, within the effective mixing matrix, the Standard Model (SM) W-exchange interaction only affects $\\theta_{12}$ and $\\theta_{13}$, while the flavor-diagonal NSI's only affect $\\theta_{23}$. The CP-violating phase $\\delta$ remains unaffected. Using our simple and compact analytical approximation, we study the impact of the flavor-diagonal NSI's on the neutrino oscillation probabilities for various appearance and disappearance channels. At higher energies and longer baselines, it is found that the impact of the NSI's can be significant in the numu to numu channel, which can probed in future atmospheric neutrino experiments, if the NSI's are of the order of their curren...
Agarwalla, Sanjib Kumar; Kao, Yee; Saha, Debashis; Takeuchi, Tatsu
2015-11-01
In this article we unravel the role of matter effect in neutrino oscillation in the presence of lepton-flavor-conserving, non-universal non-standard interactions (NSI's) of the neutrino. Employing the Jacobi method, we derive approximate analytical expressions for the effective mass-squared differences and mixing angles in matter. It is shown that, within the effective mixing matrix, the Standard Model (SM) W -exchange interaction only affects θ 12 and θ 13, while the flavor-diagonal NSI's only affect θ 23. The CP-violating phase δ remains unaffected. Using our simple and compact analytical approximation, we study the impact of the flavor-diagonal NSI's on the neutrino oscillation probabilities for various appearance and disappearance channels. At higher energies and longer baselines, it is found that the impact of the NSI's can be significant in the ν μ → ν μ channel, which can probed in future atmospheric neutrino experiments, if the NSI's are of the order of their current upper bounds. Our analysis also enables us to explore the possible degeneracy between the octant of θ 23 and the sign of the NSI parameter for a given choice of mass hierarchy in a simple manner.
Efficiency of actions in attack of diagonal players in female volleyball
Directory of Open Access Journals (Sweden)
Yevgeniya Strelnykova
2016-04-01
Full Text Available Purpose: to define efficiency of technical and tactical actions of the diagonal player in the attacking actions of a team depending on schemes of a defensive play of the rival. Material & Methods: the competitive process with participation of 10 players of the role –the diagonal forward of qualification and the adult category was investigated in the pedagogical supervision. The efficiency of actions in attack of diagonal players of women's teams of Student's volleyball league of Kharkov was defined by mathematical processing of the obtained data. Results: we carried out the analysis of references on a condition of a problem of training of the diagonal player, defined tactical combinations in attack in which the diagonal player and efficiency of game actions of the diagonal player take part in the attacking actions of women's teams of Student's volleyball league of Kharkov defining indicators of efficiency of technical and tactical actions of the diagonal player in the attacking actions of women's teams of Student's league of Kharkov against various schemes of a defensive play of teams of the rival. Conclusions: the offered methodical approach based on a quantitative assessment of the competitive activity will allow to rationalize the structure and distribution of means of trainings and to increase the efficiency of the whole educational and training process of training of diagonal players for a game in attack against teams which build a defensive play according to various schemes.
Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
Cao, Junpeng; Shi, Kangjie; Wang, Yupeng
2013-01-01
With the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the $XXX$ spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated $T-Q$ relation and the Bethe ansatz equations are derived.
Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions
International Nuclear Information System (INIS)
Employing the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the XXX spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated T–Q relation and the Bethe ansatz equations are derived
Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions
Cao, Junpeng; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng
2013-10-01
Employing the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the XXX spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated T-Q relation and the Bethe ansatz equations are derived.
Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
Gombor, Tamas
2015-01-01
The finite volume problem of O(2N) sigma models with integrable diagonal boundaries on a finite interval is investigated. The double row transfer matrix is diagonalized by Algebraic Bethe Ansatz. The boundary Bethe Yang equations for the particle rapidities and the accompanying Bethe Ansatz equations are derived.
The Chern-Simons state for the non-diagonal Bianchi IX model
Paternoga, R; Paternoga, Robert; Graham, Robert
1998-01-01
The Bianchi IX mixmaster model is quantized in its non-diagonal form, imposing spatial diffeomorphism, time reparametrization and Lorentz invariance as constraints on physical state vectors before gauge-fixing. The result turns out to be different from quantizing the diagonal model obtained by gauge-fixing already on the classical level. For the non-diagonal model a generalized 9-dimensional Fourier transformation over a suitably chosen manifold connects the representations in metric variables and in Ashtekar variables. A space of five states in the metric representation is generated from the single physical Chern-Simons state in Ashtekar variables by choosing five different integration manifolds, which cannot be deformed into each other. For the case of a positive cosmological constant $\\Lambda$ we extend our previous study of these five states for the diagonal Bianchi IX model to the non-diagonal case. It is shown that additional discrete (permutation) symmetries of physical states arise in the quantization...
Microscopic diagonal entropy and its connection to basic thermodynamic relations
International Nuclear Information System (INIS)
We define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as Sd=-Σnρnnlnρnn with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the conventional von Neumann entropy Sn = -Trρ ln ρ. However, in contrast to Sn, the d-entropy is not conserved in time in closed Hamiltonian systems. If the system is initially in stationary state then in accord with the second law of thermodynamics the d-entropy can only increase or stay the same. We also show that the d-entropy can be expressed through the energy distribution function and thus it is measurable, at least in principle. Under very generic assumptions of the locality of the Hamiltonian and non-integrability the d-entropy becomes a unique function of the average energy in large systems and automatically satisfies the fundamental thermodynamic relation. This relation reduces to the first law of thermodynamics for quasi-static processes. The d-entropy is also automatically conserved for adiabatic processes. We illustrate our results with explicit examples and show that Sd behaves consistently with expectations from thermodynamics.
A diagonal approach for the catalytic transformation of carbon dioxide
International Nuclear Information System (INIS)
Emissions of carbon dioxide are growing with the massive utilization of hydrocarbons for the production of energy and chemicals, resulting in a threatening global warming. The development of a more sustainable economy is urging to reduce the fingerprint of our current way of life. In this perspective, the organic chemistry industry will face important challenges in the next decades to replace hydrocarbons as a feedstock and use carbon-free energy sources. To tackle this challenge, new catalytic processes have been designed to convert CO2 to high energy and value-added chemicals (formamides, N-heterocycles and methanol), using a novel diagonal approach. The energy efficiency of the new transformations is ensured by the utilization of mild reductants such as hydro-silanes and hydro-boranes. Importantly the reactions are promoted by organic catalysts, which circumvent the problems of cost, abundance and toxicity usually encountered with metal complexes. Based on theoretical and experimental studies, the understanding of the mechanisms involved in these reactions allowed the rational optimization of the catalysts as well as the reaction conditions, in order to match the requirements of sustainable chemistry. (author)
Variance approximation under balanced sampling
Deville, Jean-Claude; Tillé, Yves
2016-01-01
A balanced sampling design has the interesting property that Horvitz–Thompson estimators of totals for a set of balancing variables are equal to the totals we want to estimate, therefore the variance of Horvitz–Thompson estimators of variables of interest are reduced in function of their correlations with the balancing variables. Since it is hard to derive an analytic expression for the joint inclusion probabilities, we derive a general approximation of variance based on a residual technique....
Massively parallel exact diagonalization of strongly correlated systems
Dolfen, Andreas
2011-01-01
The physics of strongly correlated materials poses one of the most challenging problems in condensed-matter sciences. Standard approximations applicable to wide classes of materials such as the local density approximation fail, due to the importance of the Coulomb repulsion between localized electrons. Instead, we resort to non-perturbative many-body methods. The calculations are, however, only feasible for rather small model systems. The full Hamiltonian of a real material is approximated by...
Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections
Meek, Garrett A.; Levine, Benjamin G.
2016-05-01
We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.
Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.
Meek, Garrett A; Levine, Benjamin G
2016-05-14
We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation. PMID:27179473
Rosta, Edina; Warshel, Arieh
2012-01-01
Understanding the relationship between the adiabatic free energy profiles of chemical reactions and the underlining diabatic states is central to the description of chemical reactivity. The diabatic states form the theoretical basis of Linear Free Energy Relationships (LFERs) and thus play a major role in physical organic chemistry and related fields. However, the theoretical justification for some of the implicit LFER assumptions has not been fully established by quantum mechanical studies. This study follows our earlier works1,2 and uses the ab initio frozen density functional theory (FDFT) method3 to evaluate both the diabatic and adiabatic free energy surfaces and to determine the corresponding off-diagonal coupling matrix elements for a series of SN2 reactions. It is found that the off-diagonal coupling matrix elements are almost the same regardless of the nucleophile and the leaving group but change upon changing the central group. Furthermore, it is also found that the off diagonal elements are basically the same in gas phase and in solution, even when the solvent is explicitly included in the ab initio calculations. Furthermore, our study establishes that the FDFT diabatic profiles are parabolic to a good approximation thus providing a first principle support to the origin of LFER. These findings further support the basic approximation of the EVB treatment. PMID:23329895
Rosta, Edina; Warshel, Arieh
2012-01-01
Understanding the relationship between the adiabatic free energy profiles of chemical reactions and the underlining diabatic states is central to the description of chemical reactivity. The diabatic states form the theoretical basis of Linear Free Energy Relationships (LFERs) and thus play a major role in physical organic chemistry and related fields. However, the theoretical justification for some of the implicit LFER assumptions has not been fully established by quantum mechanical studies. This study follows our earlier works(1,2) and uses the ab initio frozen density functional theory (FDFT) method(3) to evaluate both the diabatic and adiabatic free energy surfaces and to determine the corresponding off-diagonal coupling matrix elements for a series of S(N)2 reactions. It is found that the off-diagonal coupling matrix elements are almost the same regardless of the nucleophile and the leaving group but change upon changing the central group. Furthermore, it is also found that the off diagonal elements are basically the same in gas phase and in solution, even when the solvent is explicitly included in the ab initio calculations. Furthermore, our study establishes that the FDFT diabatic profiles are parabolic to a good approximation thus providing a first principle support to the origin of LFER. These findings further support the basic approximation of the EVB treatment. PMID:23329895
Diagonal complexes and the integral homology of the automorphism group of a free product
Griffin, James
2010-01-01
The main goal of this paper is a calculation of the integral (co)homology of the group of symmetric automorphisms of a free product. We proceed by giving a geometric interpretation of symmetric automorphisms via a moduli space of certain diagrams, which we name cactus products. To describe this moduli space a theory of diagonal complexes is introduced. This offers a generalisation of the theory of right-angled Artin groups in that each diagonal complex defines what we call a diagonal right-an...
Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
International Nuclear Information System (INIS)
We consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable transformations independent of the spectral parameter. When the boundary parameters satisfy certain constraints we are able to formulate the diagonalization of the associated double-row transfer matrix by means of the quantum inverse scattering method. This allows us to derive explicit expressions for the eigenvalues and the corresponding Bethe ansatz equations. We also present evidences that the eigenvectors can be build up in terms of multiparticle states for arbitrary S
Directory of Open Access Journals (Sweden)
Norimasa Shiomi
2003-01-01
Full Text Available We carried out investigations for the purpose of clarifying the rotor outlet flow fields with rotating stall cell in a diagonal-flow fan. The test fan was a high–specific-speed (ns=1620 type of diagonal-flow fan that had 6 rotor blades and 11 stator blades. It has been shown that the number of the stall cell is 1, and its propagating speed is approximately 80% of its rotor speed, although little has been known about the behavior of the stall cell because a flow field with a rotating stall cell is essentially unsteady. In order to capture the behavior of the stall cell at the rotor outlet flow fields, hot-wire surveys were performed using a single-slant hotwire probe. The data obtained by these surveys were processed by means of a double phase-locked averaging technique, which enabled us to capture the flow field with the rotating stall cell in the reference coordinate system fixed to the rotor. As a result, time-dependent ensemble averages of the three-dimensional velocity components at the rotor outlet flow fields were obtained. The behavior of the stall cell was shown for each velocity component, and the flow patterns on the meridional planes were illustrated.
Directory of Open Access Journals (Sweden)
Maria Malejki
2007-01-01
Full Text Available We investigate the problem of approximation of eigenvalues of some self-adjoint operator in the Hilbert space \\(l^2(\\mathbb{N}\\ by eigenvalues of suitably chosen principal finite submatrices of an infinite Jacobi matrix that defines the operator considered. We assume the Jacobi operator is bounded from below with compact resolvent. In our research we estimate the asymptotics (with \\(n\\to \\infty\\ of the joint error of approximation for the first \\(n\\ eigenvalues and eigenvectors of the operator by the eigenvalues and eigenvectors of the finite submatrix of order \\(n \\times n\\. The method applied in our research is based on the Rayleigh-Ritz method and Volkmer's results included in [H. Volkmer, Error Estimates for Rayleigh-Ritz Approximations of Eigenvalues and Eigenfunctions of the Mathieu and Spheroidal Wave Equation, Constr. Approx. 20 (2004, 39-54]. We extend the method to cover a class of infinite symmetric Jacobi matrices with three diagonals satisfying some polynomial growth estimates.
DEFF Research Database (Denmark)
Sørensen, Karsten Engsig
Afhandlingen analysere de konkurrenceretlige og selskabsretlige regler som er bestemmende for hvordan et joint venture samarbejde er struktureret......Afhandlingen analysere de konkurrenceretlige og selskabsretlige regler som er bestemmende for hvordan et joint venture samarbejde er struktureret...
QUASI-DIAGONALIZATION FOR A SINGULARLY PERTURBED DIFFERENTIAL SYSTEM WITH TWO PARAMETERS
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
By two successive linear transformations,a singularly perturbed differential system with two parameters is quasi-diagonalized. The method of variation of constants and the principle of contraction map are used to prove the existence of the transformations.
Diagonal recurrence relations for the Stirling numbers of the first kind
Qi, Feng
2013-01-01
In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for special values of the Bell polynomials of the second kind.
A Summary of Design Formulas for Beams Having Thin Webs in Diagonal Tension
Kuhn, Paul
1933-01-01
This report presents an explanation of the fundamental principles and a summary of the essential formulas for the design of diagonal-tension field beams, i.e. beams with very thin webs, as developed by Professor Wagner of Germany.
Diagonal and local environmental effect in magnetic properties of disordered alloys
International Nuclear Information System (INIS)
The most simple cases of studies in the magnetic properties like the diagonal and local environmental effects are studied for a simple and general model of cluster configuration having elements of binary alloys
A joint is where two or more bones come together, like the knee, hip, elbow, or shoulder. Joints can be damaged by many types of injuries or diseases, including Arthritis - inflammation of a joint. It causes pain, stiffness, and swelling. Over time, ...
International Nuclear Information System (INIS)
The coracoclvicular joint, a rear abnormality which may be the cause of pain in the shoulder and limitation of motion of the shoulder joint, is discussed. A case of coracoclvicular joint with shoulder pain was observed in 65 yrs old Korean male
A Method for Solving Cyclic Block Penta-diagonal Systems of Linear Equations
Batista, Milan
2008-01-01
The method for solving cyclic block three-diagonal systems of equations is generalized for solving a block cyclic penta-diagonal system of equations. Introducing a special form of two new variables the original system is split into three block pentagonal systems, which can be solved by the known methods. As such method belongs to class of direct methods without pivoting. Implementation of the algorithm is discussed in some details and the numerical examples are present.
A Method for Solving Cyclic Block Penta-diagonal Systems of Linear Equations
Batista, Milan
2008-01-01
A method for solving cyclic block three-diagonal systems of equations is generalized for solving a block cyclic penta-diagonal system of equations. Introducing a special form of two new variables the original system is split into three block pentagonal systems, which can be solved by the known methods. As such method belongs to class of direct methods without pivoting. Implementation of the algorithm is discussed in some details and the numerical examples are present.
Superposition rule and entanglement in diagonal and probability representations of density states
Man'ko, Vladimir I.; Marmo, Giuseppe; Sudarshan, E C George
2009-01-01
The quasidistributions corresponding to the diagonal representation of quantum states are discussed within the framework of operator-symbol construction. The tomographic-probability distribution describing the quantum state in the probability representation of quantum mechanics is reviewed. The connection of the diagonal and probability representations is discussed. The superposition rule is considered in terms of the density-operator symbols. The separability and entanglement properties of m...
Taking correlations in GPS least squares adjustments into account with a diagonal covariance matrix
Kermarrec, Gaël; Schön, Steffen
2016-05-01
Based on the results of Luati and Proietti (Ann Inst Stat Math 63:673-686, 2011) on an equivalence for a certain class of polynomial regressions between the diagonally weighted least squares (DWLS) and the generalized least squares (GLS) estimator, an alternative way to take correlations into account thanks to a diagonal covariance matrix is presented. The equivalent covariance matrix is much easier to compute than a diagonalization of the covariance matrix via eigenvalue decomposition which also implies a change of the least squares equations. This condensed matrix, for use in the least squares adjustment, can be seen as a diagonal or reduced version of the original matrix, its elements being simply the sums of the rows elements of the weighting matrix. The least squares results obtained with the equivalent diagonal matrices and those given by the fully populated covariance matrix are mathematically strictly equivalent for the mean estimator in terms of estimate and its a priori cofactor matrix. It is shown that this equivalence can be empirically extended to further classes of design matrices such as those used in GPS positioning (single point positioning, precise point positioning or relative positioning with double differences). Applying this new model to simulated time series of correlated observations, a significant reduction of the coordinate differences compared with the solutions computed with the commonly used diagonal elevation-dependent model was reached for the GPS relative positioning with double differences, single point positioning as well as precise point positioning cases. The estimate differences between the equivalent and classical model with fully populated covariance matrix were below the mm for all simulated GPS cases and below the sub-mm for the relative positioning with double differences. These results were confirmed by analyzing real data. Consequently, the equivalent diagonal covariance matrices, compared with the often used elevation
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
Diagonal Loading of Robust General-Rank Beamformer for Direction of Arrival Mismatch
Directory of Open Access Journals (Sweden)
Z.U. Khan
2013-05-01
Full Text Available This study presents a technique which utilizes the movement of the peak of the main beam towards the presumed signal direction with negative diagonal loading for robust general-rank beamformer. The main beam symmetry along presumed signal direction is improved by this movement. When desired signal is contained in the data snapshots, the conventional beamformers face the problem of performance degradation even if there is a small mismatch between the presumed and the actual signal direction. Diagonal loading is a popular technique to mitigate this problem. There is no definite criterion to find diagonal loading level. A new diagonal loading method has been proposed in the literature which utilizes the movement of the peak of main beam towards the presumed signal direction with positive diagonal loading. The proposed technique works iteratively for the selection of negative diagonal loading level to move the main beam at a position to get the beam symmetry at desired level and hence the desired robustness. The mismatched signal will not be cancelled as long as it is within the half of the width of the main beam. But there is the tradeoff between this robustness and interference cancelling capability.
Transformation on non-diagonal mass matrix to a canonical form
Energy Technology Data Exchange (ETDEWEB)
Kaul, M.K.; Panahi, K.K. [GE Nuclear Energy, San Jose, CA (United States)
1996-12-01
Some dynamics phenomena, such as fluid-structure interaction, should be represented by a non-diagonal mass matrix. The inclusion of frequency-independent fluid-structure interaction effects in the dynamic analysis of structures can generally be done by expanding the mass matrix to include non-diagonal added mass terms.Few finite element codes, however, have the capability of handling a non-diagonal mass matrix in a dynamic analysis. This limitation of these type of computer codes can be overcome by expanding the original structural system with added inertial degrees of freedom such that the requirement of the diagonal mass matrix is not violated and at the same time the response of the expanded system is, for all practical purposes, the same as of the original system. This paper demonstrates how this expanded system can be constructed. It also establishes the conditions that must be fulfilled by the new structural system with diagonal mass matrix in order for it to be equivalent to the original system with a non-diagonal mass matrix.
International Nuclear Information System (INIS)
A transition joint is disclosed for joining together tubular pieces formed respectively from a low alloy or carbon steel and a high temperature alloy composition having substantially different characteristics such as coefficient of thermal expansion, the transition joint including a plurality of tubular parts interconnected with each other by means of friction weld joints formed at an angle of 900 to the axis of the transition joint, the tubular parts at opposite ends of the transition joint being selected to facilitate in situ welding to the low alloy or carbon steel and high temperature alloy respectively. This friction welded transition joint can be used whenever different tubular pieces need to be joined together so that the joint can withstand high temperatures, for instance in heat exchangers and the such like. (Auth.)
International Nuclear Information System (INIS)
The procedure adopted in a previous paper to construct a two-body effective interaction by the diagonalization of a bare Hamiltonian within a large space which allows for RPA or TDA core excitations to fully interact with the two valence particles is revised according to some new prescriptions in order to obtain a linked interaction. A rather detailed perturbative analysis which displays the different properties of the interactions evaluated with the previous and the revised method is made. It is argued that the previous interaction was partially linked, which partly explains why, when uniquely defined, it comes out to be close to the present linked interaction. A comparison of the linked interaction with its lowest order perturbative approximations shows that the series representing the RPA interaction is likely to converge more slowly than the TDA series. (Auth.)
International Nuclear Information System (INIS)
The so-called change of picture for operators that arise in approximate two- and one-component relativistic theories is investigated in the framework of the phenomenological and supersymmetry-based quantum-defect approaches. Using the Su transformation that brings the radial wave equations of the Dirac-Coulomb problem into a form nearly identical to those of Schroedinger and Klein-Gordon like equations, we derive the Dirac representative of the nonrelativistic position operator r. A new transition operator that accounts for initial and final states of the active electron is proposed. The recurrence relations obtained previously and applied efficiently to compute diagonal and off-diagonal matrix elements are rederived accordingly. Numerical results for matrix elements of rq between states of the one-electron alkali-like atomic systems exhibit the general trends related to the picture change correction to atomic characteristics. (author)
Sakumichi, Naoyuki; Kawakami, Norio; Ueda, Masahito
2011-01-01
The quantum-statistical cluster expansion method of Lee and Yang is extended to investigate off-diagonal long-range order (ODLRO) in one- and multi-component mixtures of bosons or fermions. Our formulation is applicable to both a uniform system and a trapped system without local-density approximation and allows systematic expansions of one- and multi-particle reduced density matrices in terms of cluster functions which are defined for the same system with Boltzmann statistics. Each term in th...
TMB: Automatic differentiation and laplace approximation
DEFF Research Database (Denmark)
Kristensen, Kasper; Nielsen, Anders; Berg, Casper Willestofte;
2016-01-01
TMB is an open source R package that enables quick implementation of complex nonlinear random effects (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, http://admb-project.org/; Fournier et al. 2011). In addition, it offers easy access to parallel...... computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects are...... automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (approximate to 10(6)) and parameters (approximate to 10...
On the inclusion of the diagonal Born-Oppenheimer correction in surface hopping methods
Gherib, Rami; Ye, Liyuan; Ryabinkin, Ilya G.; Izmaylov, Artur F.
2016-04-01
The diagonal Born-Oppenheimer correction (DBOC) stems from the diagonal second derivative coupling term in the adiabatic representation, and it can have an arbitrary large magnitude when a gap between neighbouring Born-Oppenheimer (BO) potential energy surfaces (PESs) is closing. Nevertheless, DBOC is typically neglected in mixed quantum-classical methods of simulating nonadiabatic dynamics (e.g., fewest-switch surface hopping (FSSH) method). A straightforward addition of DBOC to BO PESs in the FSSH method, FSSH+D, has been shown to lead to numerically much inferior results for models containing conical intersections. More sophisticated variation of the DBOC inclusion, phase-space surface-hopping (PSSH) was more successful than FSSH+D but on model problems without conical intersections. This work comprehensively assesses the role of DBOC in nonadiabatic dynamics of two electronic state problems and the performance of FSSH, FSSH+D, and PSSH methods in variety of one- and two-dimensional models. Our results show that the inclusion of DBOC can enhance the accuracy of surface hopping simulations when two conditions are simultaneously satisfied: (1) nuclei have kinetic energy lower than DBOC and (2) PESs are not strongly nonadiabatically coupled. The inclusion of DBOC is detrimental in situations where its energy scale becomes very high or even diverges, because in these regions PESs are also very strongly coupled. In this case, the true quantum formalism heavily relies on an interplay between diagonal and off-diagonal nonadiabatic couplings while surface hopping approaches treat diagonal terms as PESs and off-diagonal ones stochastically.
International Nuclear Information System (INIS)
In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics
Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
Li, Guang-Liang; Hao, Kun; Yang, Wen-Li; Shi, Kangjie
2016-01-01
The nested off-diagonal Bethe Ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T-Q relations and Bethe Ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the $SU_q(n)$ algebra.
On the Reduction of a Complex Matrix to Triangular or Diagonal by Consimilarity
Institute of Scientific and Technical Information of China (English)
Tongsong Jiang; Musheng Wei
2006-01-01
Two n × n complex matrices A and B are said to be consimilar if S-1 AS = B for some nonsingular n × n complex matrix S. This paper, by means of real representation of a complex matrix, studies problems of reducing a given n × n complex matrix A to triangular or diagonal form by consimilarity, not only gives necessary and sufficient conditions for contriangularization and condiagonalization of a complex matrix, but also derives an algebraic technique of reducing a matrix to triangular or diagonal form by consimilarity.
Boundary energy of the open XXX chain with a non-diagonal boundary term
Nepomechie, Rafael I.; Wang, Chunguang
2014-01-01
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots split evenly into two sets: those that remain finite, and those that become infinite. We argue that the former satisfy conventional Bethe equations, while the latter satisfy a generalization of the Richardson-Gaudin equations. We derive an expression for the leading correction to the boundary energy in terms of the boundary parameters.
Boundary energy of the open XXX chain with a non-diagonal boundary term
International Nuclear Information System (INIS)
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots split evenly into two sets: those that remain finite, and those that become infinite. We argue that the former satisfy conventional Bethe equations, while the latter satisfy a generalization of the Richardson–Gaudin equations. We derive an expression for the leading correction to the boundary energy in terms of the boundary parameters. (fast track communications)
Boundary energy of the open XXX chain with a non-diagonal boundary term
Nepomechie, Rafael I
2013-01-01
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots split evenly into two sets: those that remain finite, and those that become infinite. We argue that the former satisfy conventional Bethe equations, while the latter satisfy a generalization of the Richardson-Gaudin equations. We derive an expression for the leading correction to the boundary energy in terms of the boundary parameters.
Jiang, Tongsong; Jiang, Ziwu; Zhang, Zhaozhong
2015-08-01
In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics.
Energy Technology Data Exchange (ETDEWEB)
Jiang, Tongsong, E-mail: jiangtongsong@sina.com [Department of Mathematics, Linyi University, Linyi, Shandong 276005 (China); Department of Mathematics, Heze University, Heze, Shandong 274015 (China); Jiang, Ziwu; Zhang, Zhaozhong [Department of Mathematics, Linyi University, Linyi, Shandong 276005 (China)
2015-08-15
In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics.
Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
Li, Guang-Liang; Cao, Junpeng; Hao, Kun; Wen, Fakai; Yang, Wen-Li; Shi, Kangjie
2016-09-01
The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the SUq (3)R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T-Q relations and Bethe ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the SUq (n) algebra.
Nonlinear approximation with dictionaries. II. Inverse Estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2006-01-01
In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block...
An Approximate Bayesian Fundamental Frequency Estimator
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt
Joint fundamental frequency and model order estimation is an important problem in several applications such as speech and music processing. In this paper, we develop an approximate estimation algorithm of these quantities using Bayesian inference. The inference about the fundamental frequency and...
Bin Qin
2014-01-01
Relationships between fuzzy relations and fuzzy topologies are deeply researched. The concept of fuzzy approximating spaces is introduced and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained.
Stochastic approximation: invited paper
Lai, Tze Leung
2003-01-01
Stochastic approximation, introduced by Robbins and Monro in 1951, has become an important and vibrant subject in optimization, control and signal processing. This paper reviews Robbins' contributions to stochastic approximation and gives an overview of several related developments.
Rasin, A
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
... or conditions. It may be linked to arthritis , bursitis , and muscle pain . No matter what causes it, ... Autoimmune diseases such as rheumatoid arthritis and lupus Bursitis Chondromalacia patellae Crystals in the joint: gout (especially ...
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Imafuku, Yuji; Abe, Minori; Schmidt, Michael W; Hada, Masahiko
2016-04-01
Methodologies beyond the Born-Oppenheimer (BO) approximation are nowadays important to explain high precision spectroscopic measurements. Most previous evaluations of the BO correction are, however, focused on light-element molecules and based on a nonrelativistic Hamiltonian, so no information about the BO approximation (BOA) breakdown in heavy-element molecules is available. The present work is the first to investigate the BOA breakdown for the entire periodic table, by considering scalar relativistic effects in the Diagonal BO correction (DBOC). In closed shell atoms, the relativistic EDBOC scales as Z(1.25) and the nonrelativistic EDBOC scales as Z(1.17), where Z is the atomic number. Hence, we found that EDBOC becomes larger in heavy element atoms and molecules, and the relativistic EDBOC increases faster than nonrelativistic EDBOC. We have further investigated the DBOC effects on properties such as potential energy curves, spectroscopic parameters, and various energetic properties. The DBOC effects for these properties are mostly affected by the lightest atom in the molecule. Hence, in X2 or XAt molecule (X = H, Li, Na, K, Rb, and Cs) the effect of DBOC systematically decreases when X becomes heavier but in HX molecules, the effect of DBOC seems relatively similar among all the molecules. PMID:27003510
Off-diagonal ekpyrotic scenarios and equivalence of modified, massive and/or Einstein gravity
Vacaru, Sergiu I.
2016-01-01
Using our anholonomic frame deformation method, we show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates and undergoing a phase of ultra-slow contraction can be constructed in massive gravity. In this paper, there are found and studied new classes of locally anisotropic and (in)homogeneous cosmological metrics with open and closed spatial geometries. The late time acceleration is present due to effective cosmological terms induced by nonlinear off-diagonal interactions and graviton mass. The off-diagonal cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaître-Robertson-Walker (FLRW) coordinates. We show that the solutions include matter, graviton mass and other effective sources modeling nonlinear gravitational and matter fields interactions in modified and/or massive gravity, with polarization of physical constants and deformations of metrics, which may explain certain dark energy and dark matter effects. There are stated and analyzed the conditions when such configurations mimic interesting solutions in general relativity and modifications and recast the general Painlevé-Gullstrand and FLRW metrics. Finally, we elaborate on a reconstruction procedure for a subclass of off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes, with an emphasis on open issues and observable signatures.
Some Effects of Row, Diagonal, and Column Screen Formats on Search Time and Strategy.
Emurian, Henry H.; Seborg, Brian H.
1990-01-01
Describes a study of undergraduates that examined differences in computer screen formats and their effects on search time and strategy. Row, diagonal, and column information formats are compared, as well as tightly packed and loosely packed displays, and results of regression and residual analyses are discussed. (38 references) (LRW)
Bethe ansatz solution of the open XX spin chain with non-diagonal boundary terms
International Nuclear Information System (INIS)
We consider the integrable open XX quantum spin chain with non-diagonal boundary terms. We derive an exact inversion identity, by which we obtain the eigenvalues of the transfer matrix and the Bethe ansatz equations. For generic values of the boundary parameters, the Bethe ansatz solution is formulated in terms of the Jacobian elliptic functions. (author)
A diagonalization algorithm revisited and applied to the nuclear shell model
Bianco, D; Andreozzi, F; Lo Iudice, N.; Porrino, A.; Knapp, F
2011-01-01
Abstract An importance sampling iterative algorithm for diagonalizing large matrices is upgraded and adopted for large scale nuclear shell model calculations using a spin uncoupled basis. Its numerical implementation shows that the iterative procedure converges rapidly to the exact eigensolutions achieving an effective drastic cut of the sizes of the Hamiltonian matrix.
Diagonally implicit symplectic Runge-Kutta methods with high algebraic and dispersion order.
Cong, Y H; Jiang, C X
2014-01-01
The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods. PMID:24977178
Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order
Cong, Y. H.; Jiang, C. X.
2014-01-01
The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods.
Block-diagonal semidefinite programming hierarchies for 0/1 programming
Gvozdenovic, N.; Laurent, M.; Vallentin, F.
2009-01-01
Lovasz and Schrijver, and later Lasserre, proposed hierarchies of semidefinite programming relaxations for general 0/1 linear programming problems. In this paper these two constructions are revisited and a new, block-diagonal hierarchy is proposed. It has the advantage of being computationally less
Correlation between eigenvalues and sorted diagonal matrix elements of a large dimensional matrix
International Nuclear Information System (INIS)
Functional dependences of eigenvalues as functions of sorted diagonal elements are given for realistic nuclear shell model (NSM) hamiltonian, the uniform distribution hamiltonian and the GOE hamiltonian. In the NSM case, the dependence is found to be linear. We discuss extrapolation methods for more accurate predictions for low-lying states. (author)
Off-diagonal ekpyrotic scenarios and equivalence of modified, massive and/or Einstein gravity
Directory of Open Access Journals (Sweden)
Sergiu I. Vacaru
2016-01-01
Full Text Available Using our anholonomic frame deformation method, we show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates and undergoing a phase of ultra-slow contraction can be constructed in massive gravity. In this paper, there are found and studied new classes of locally anisotropic and (inhomogeneous cosmological metrics with open and closed spatial geometries. The late time acceleration is present due to effective cosmological terms induced by nonlinear off-diagonal interactions and graviton mass. The off-diagonal cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann–Lamaître–Robertson–Walker (FLRW coordinates. We show that the solutions include matter, graviton mass and other effective sources modeling nonlinear gravitational and matter fields interactions in modified and/or massive gravity, with polarization of physical constants and deformations of metrics, which may explain certain dark energy and dark matter effects. There are stated and analyzed the conditions when such configurations mimic interesting solutions in general relativity and modifications and recast the general Painlevé–Gullstrand and FLRW metrics. Finally, we elaborate on a reconstruction procedure for a subclass of off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes, with an emphasis on open issues and observable signatures.
A Collocation Method for Volterra Integral Equations with Diagonal and Boundary Singularities
Kolk, Marek; Pedas, Arvet; Vainikko, Gennadi
2009-08-01
We propose a smoothing technique associated with piecewise polynomial collocation methods for solving linear weakly singular Volterra integral equations of the second kind with kernels which, in addition to a diagonal singularity, may have a singularity at the initial point of the interval of integration.
Off-diagonal GMI sensor with stress-annealed amorphous ribbon
Czech Academy of Sciences Publication Activity Database
Malátek, M.; Kraus, Luděk
2010-01-01
Roč. 164, 1-2 (2010), 41-45. ISSN 0924-4247 R&D Projects: GA ČR GA102/08/0743 Institutional research plan: CEZ:AV0Z10100520 Keywords : off-diagonal magnetoimpedance * amorphous ribbons * magnetic field sensor Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.933, year: 2010
Approximation of distributed delays
Lu, Hao; Eberard, Damien; Simon, Jean-Pierre
2010-01-01
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and work with the norm defined over the convolution Banach algebra. The class of rational approximates is described, and a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control problem, for which simulations results show the effectiveness of the proposed methodology.
Conditional Density Approximations with Mixtures of Polynomials
DEFF Research Database (Denmark)
Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre;
2015-01-01
Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities is...
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Relativistic quasiparticle random phase approximation in deformed nuclei
Energy Technology Data Exchange (ETDEWEB)
Pena Arteaga, D.
2007-06-25
Covariant density functional theory is used to study the influence of electromagnetic radiation on deformed superfluid nuclei. The relativistic Hartree-Bogolyubov equations and the resulting diagonalization problem of the quasiparticle random phase approximation are solved for axially symmetric systems in a fully self-consistent way by a newly developed parallel code. Three different kinds of high precision energy functionals are investigated and special care is taken for the decoupling of the Goldstone modes. This allows the microscopic investigation of Pygmy and scissor resonances in electric and magnetic dipole fields. Excellent agreement with recent experiments is found and new types of modes are predicted for deformed systems with large neutron excess. (orig.)
Relativistic quasiparticle random phase approximation in deformed nuclei
International Nuclear Information System (INIS)
Covariant density functional theory is used to study the influence of electromagnetic radiation on deformed superfluid nuclei. The relativistic Hartree-Bogolyubov equations and the resulting diagonalization problem of the quasiparticle random phase approximation are solved for axially symmetric systems in a fully self-consistent way by a newly developed parallel code. Three different kinds of high precision energy functionals are investigated and special care is taken for the decoupling of the Goldstone modes. This allows the microscopic investigation of Pygmy and scissor resonances in electric and magnetic dipole fields. Excellent agreement with recent experiments is found and new types of modes are predicted for deformed systems with large neutron excess. (orig.)
Institute of Scientific and Technical Information of China (English)
YueShihong; ZhangKecun
2002-01-01
In a dot product space with the reproducing kernel (r. k. S. ) ,a fuzzy system with the estimation approximation errors is proposed ,which overcomes the defect that the existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach. The structure of the new fuzzy approximator benefits a course got by other means.
Malvina Baica
1985-01-01
The author uses a new modification of Jacobi-Perron Algorithm which holds for complex fields of any degree (abbr. ACF), and defines it as Generalized Euclidean Algorithm (abbr. GEA) to approximate irrationals.This paper deals with approximation of irrationals of degree n=2,3,5. Though approximations of these irrationals in a variety of patterns are known, the results are new and practical, since there is used an algorithmic method.
Expectation Consistent Approximate Inference
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability distributions which are made consistent on a set of moments and encode different features of the original intractable distribution. In this way we are able to use Gaussian approximations for models with ...
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
Merging Belief Propagation and the Mean Field Approximation
DEFF Research Database (Denmark)
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro; Fleury, Bernard Henri
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence) as a....... Our results can be applied, for example, to algorithms that perform joint channel estimation and decoding in iterative receivers. This is demonstrated in a simple example....
Expectation Consistent Approximate Inference
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
International Nuclear Information System (INIS)
Joint imaging is a proven diagnostic procedure which has become indispensable to the detection and treatment of different joint diseases in almost all disciplines. The method is suited for early diagnosis of joint affections both in soft tissue and bone which cannot be detected by X-ray or other procedures. The local activity accumulation depends on the rate of metabolism and is visualized in the scan, which in turn enables the extension and floridity of focal lesions to be evaluated and followed-up. Although joint scans may often give hints to probabilities relevant to differential diagnosis, the method is non-specific and only useful if based on the underlying clinical picture and X-ray finding, if possible. The radiation exposure is very low and does not represent a hazard in cases of adequate assessment of indication. In pregnant women and children the assessment of indication has to be based on very strict principles. The method is suited for out-patient diagnosis and can be applied in all installations equipped with a gamma camera and a technetium generator. (orig.)
Off-Diagonal Ekpyrotic Scenarios and Equivalence of Modified, Massive and/or Einstein Gravity
Vacaru, Sergiu I
2016-01-01
We show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive gravity using the anholonomic frame deformation method. There are found new classes of locally anisotropic and (in) homogeneous cosmological metrics with open and closed spatial geometries. Such solutions describe the late time acceleration due to effective cosmological terms induced by nonlinear off-diagonal interactions and graviton mass. The cosmological metrics and related St\\" uckelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lama\\^{i}tre-Robertson-Walker (FLRW) coordinates. The solutions include matter, graviton mass and other effective sources modelling nonlinear gravitational and matter fields interactions with polarization of physical constants and deformations of metrics, which may explain certain dark energy and dark matter effects. There are stated the conditions when such configurations mimic interesting solu...
Exact solutions in modified massive gravity and off-diagonal wormhole deformations
Energy Technology Data Exchange (ETDEWEB)
Vacaru, Sergiu I. [Alexandru Ioan Cuza University, Rector' s Office, Iasi (Romania); CERN, Theory Division, Geneva 23 (Switzerland)
2014-03-15
We explore off-diagonal deformations of 'prime' metrics in Einstein gravity (for instance, for wormhole configurations) into 'target' exact solutions in f(R,T)-modified and massive/bi-metric gravity theories. The new classes of solutions may, or may not, possess Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions, and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormhole-like objects matching an external black ellipsoid--de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions. (orig.)
Quasilocal charges and the complete GGE for field theories with non-diagonal scattering
Vernier, Eric
2016-01-01
It has recently been shown that some integrable spin chains possess a set of quasilocal conserved charges, with the classic example being the spin-$\\frac{1}{2}$ XXZ Heisenberg chain. These charges have been proven to be essential for properly describing stationary states after a quantum quench, and must be included in the generalized Gibbs ensemble (GGE). We find that similar charges are also necessary for the GGE description of integrable quantum field theories with non-diagonal scattering. A stationary state in a non-diagonal scattering theory is completely specified by fixing the mode-ocuppation density distributions of physical particles, as well auxiliary particles which carry no energy or momentum. We show that the set of conserved charges with integer Lorentz spin, related to the integrability of the model, are unable to fix the distributions of these auxiliary particles, since these charges can only fix kinematical properties of physical particles. The field theory analogs of quasilocal lattice charge...
Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature
Energy Technology Data Exchange (ETDEWEB)
Rajaratnam, Krishan, E-mail: k2rajara@uwaterloo.ca; McLenaghan, Raymond G., E-mail: rgmclenaghan@uwaterloo.ca [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
2014-08-15
We find all orthogonal metrics where the geodesic Hamilton-Jacobi equation separates and the Riemann curvature tensor satisfies a certain equation (called the diagonal curvature condition). All orthogonal metrics of constant curvature satisfy the diagonal curvature condition. The metrics we find either correspond to a Benenti system or are warped product metrics where the induced metric on the base manifold corresponds to a Benenti system. Furthermore, we show that most metrics we find are characterized by concircular tensors; these metrics, called Kalnins-Eisenhart-Miller metrics, have an intrinsic characterization which can be used to obtain them on a given space. In conjunction with other results, we show that the metrics we found constitute all separable metrics for Riemannian spaces of constant curvature and de Sitter space.
Two-dimensional diagonal summing of coincidence spectra for bulk PGNAA applications
Energy Technology Data Exchange (ETDEWEB)
Metwally, W.A.; Gardner, R.P. E-mail: gardner@ncsu.edu; Mayo, C.W
2004-06-11
In the past 10 years, new electronic devices have been developed that allow fast coincidence measurements to be performed that are capable of simultaneously recording the individual spectra as well as the coincidence spectra of multiple detectors. Utilizing these devices with computer software allows multiparameter data acquisition which adds much more flexibility in data analysis. One of the capabilities that is enabled is that of obtaining two-dimensional spectra. In this work, the use of this equipment and the two-dimensional spectra obtained with it are used to allow two-dimensional diagonal summing. The main advantages of this approach are improved peak resolution and very low background (Compton continuum). Possible uses of the two-dimensional diagonal summing are identifying coincidence schemes, performing elemental analysis, and identifying trace elements in bulk samples. The spectra obtained are very promising for these applications.
Two-dimensional diagonal summing of coincidence spectra for bulk PGNAA applications
Metwally, W. A.; Gardner, R. P.; Mayo, C. W.
2004-06-01
In the past 10 years, new electronic devices have been developed that allow fast coincidence measurements to be performed that are capable of simultaneously recording the individual spectra as well as the coincidence spectra of multiple detectors. Utilizing these devices with computer software allows multiparameter data acquisition which adds much more flexibility in data analysis. One of the capabilities that is enabled is that of obtaining two-dimensional spectra. In this work, the use of this equipment and the two-dimensional spectra obtained with it are used to allow two-dimensional diagonal summing. The main advantages of this approach are improved peak resolution and very low background (Compton continuum). Possible uses of the two-dimensional diagonal summing are identifying coincidence schemes, performing elemental analysis, and identifying trace elements in bulk samples. The spectra obtained are very promising for these applications.
Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
Vacaru, Sergiu I
2016-01-01
Geometric methods for constructing exact solutions of motion equations with first order $\\alpha ^{\\prime }$ corrections to the heterotic supergravity action implying a non-trivial Yang-Mills sector and six dimensional, 6-d, almost-K\\"{a}hler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections. In particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The correspond...
The resolution of field identification fixed points in diagonal coset theories
International Nuclear Information System (INIS)
The fixed point resolution problem is solved for diagonal coset theories. The primary fields into which the fixed points are resolved are described by submodules of the branching spaces, obtained as eigenspaces of the automorphisms that implement field identification. To compute the characters and the modular S-matrix we use ''orbit Lie algebras'' and ''twining characters'', which were introduced in a previous paper. The characters of the primary fields are expressed in terms branching functions of twining characters. This allows us to express the modular S-matrix through the S-matrices of the orbit Lie algebras associated to the identification group. Our results can be extended to the larger class of ''generalized diagonal cosets''. (orig.)
Direct current hopping conductance in one-dimensional diagonal disordered systems
Institute of Scientific and Technical Information of China (English)
Ma Song-Shan; Xu Hui; Liu Xiao-Liang; Xiao Jian-Rong
2006-01-01
Based on a tight-binding disordered model describing a single electron band, we establish a direct current (dc) electronic hopping transport conductance model of one-dimensional diagonal disordered systems, and also derive a dc conductance formula. By calculating the dc conductivity, the relationships between electric field and conductivity and between temperature and conductivity are analysed, and the role played by the degree of disorder in electronic transport is studied. The results indicate the conductivity of systems decreasing with the increase of the degree of disorder, characteristics of negative differential dependence of resistance on temperature at low temperatures in diagonal disordered systems, and the conductivity of systems decreasing with the increase of electric field, featuring the non-Ohm's law conductivity.
Ngo, Van A
2013-01-01
We propose a combination between the theory of diagonal entropy representing far-from-equilibrium ensembles and Jarzynski Equality to explore thermalization effects on thermodynamic quantities such as temperature, entropy, mechanical work and free-energy changes. Applying the theory to a quantum harmonic oscillator, we find that diagonal entropy offers a definition of temperature for closed systems far from equilibrium, and a better sampling of reaction pathways than the conventional von Neumann entropy. We also apply the theory to a many-body system of hard-core boson lattice, and discuss the ideas of how to estimate temperature, entropy and measure work distribution functions. The theory suggests a powerful technique to study non-equilibrium dynamics in quantum systems by means of performing work in a series of quenches.
Marušič, Maja; Šket, Primož; Bauer, Lubos; Viglasky, Viktor; Plavec, Janez
2012-01-01
We herein report on the formation and high-resolution NMR solution-state structure determination of a G-quadruplex adopted by d[G3ATG3ACACAG4ACG3] comprised of four G-tracts with the third one consisting of four guanines that are intervened with non-G streches of different lengths. A single intramolecular antiparallel (3+1) G-quadruplex exhibits three stacked G-quartets connected with propeller, diagonal and edgewise loops of different lengths. The propeller and edgewise loops are well structured, whereas the longer diagonal loop is more flexible. To the best of our knowledge, this is the first high-resolution G-quadruplex structure where all of the three main loop types are present. PMID:22532609
Theoretical analysis of three-dimensional bifurcated flow inside a diagonally lid-driven cavity
Feldman, Yuri
2015-08-01
The instability mechanism of fully three-dimensional, highly separated, shear-driven confined flow inside a diagonally lid-driven cavity was investigated. The analysis was conducted on 1003 and 2003 stretched grids by a series of direct numerical simulations utilizing a standard second-order accuracy finite volume code, openFoam. The observed oscillatory instability was found to set in via a subcritical symmetry breaking Hopf bifurcation. Critical values of the Reynolds number Re cr = 2320 and the non-dimensional angular oscillating frequency for the transition from steady to oscillatory flow were accurately determined. An oscillatory regime of the bifurcated flow was analyzed in depth, revealing and characterizing the spontaneous symmetry breaking mechanism. Characteristic spatial patterns of the base flow and the main flow harmonic were determined for the velocity, vorticity and helicity fields. Lagrangian particle tracers were utilized to visualize the mixing phenomenon of the flow from both sides of the diagonal symmetry plane.
Approximations to toroidal harmonics
International Nuclear Information System (INIS)
Toroidal harmonics P/sub n-1/2/1(cosh μ) and Q/sub n-1/2/1(cosh μ) are useful in solutions to Maxwell's equations in toroidal coordinates. In order to speed their computation, a set of approximations has been developed that is valid over the range 0 -10. The simple method used to determine the approximations is described. Relative error curves are also presented, obtained by comparing approximations to the more accurate values computed by direct summation of the hypergeometric series
On avoiding cosmological oscillating behavior for S-brane solutions with diagonal metrics
Ivashchuk, V. D.; Melnikov, V. N.; Singleton, D.
2005-01-01
In certain string inspired higher dimensional cosmological models it has been conjectured that there is generic, chaotic oscillating behavior near the initial singularity -- the Kasner parameters which characterize the asymptotic form of the metric "jump" between different, locally constant values and exhibit a never-ending oscillation as one approaches the singularity. In this paper we investigate a class of cosmological solutions with form fields and diagonal metrics which have a "maximal" ...
Iskandar Shah Mohd Zawawi; Zarina Bibi Ibrahim; Khairil Iskandar Othman
2015-01-01
The diagonally implicit 2-point block backward differentiation formulas (DI2BBDF) of order two, order three, and order four are derived for solving stiff initial value problems (IVPs). The stability properties of the derived methods are investigated. The implementation of the method using Newton iteration is also discussed. The performance of the proposed methods in terms of maximum error and computational time is compared with the fully implicit block backward differentiation formulas (FIBBD...
Self-Calibration of Radio Astronomical Arrays with Non-Diagonal Noise Covariance Matrix
van der Veen, Alle Jan; Wijnholds, Stefan
2015-01-01
The radio astronomy community is currently building a number of phased array telescopes. The calibration of these telescopes is hampered by the fact that covariances of signals from closely spaced antennas are sensitive to noise coupling and to variations in sky brightness on large spatial scales. These effects are difficult and computationally expensive to model. We propose to model them phenomenologically using a non-diagonal noise covariance matrix. The parameters can be estimated using a ...
STUDI PENGARUH SABUK GFRP DIAGONAL TERHADAP KUAT LENTUR BALOK BETON BERTULANG
Duhri, Aswin Perdana
2013-01-01
Some researches have shown that critical phenomena on the use of FRP sheets as external reinforcement is debounding between the FRP sheet and concrete. This research was done to investigate the effect of Diagonal GFRP belt on failure behavior and flexural strength of reinforced concrete beam with additional 1 layer of GFRP sheet. The test was done on reinforced concrete beam specimens with dimension of 150 x 200 x 2500 mm on 2 simple support and were loaded using 2 point conc...
Self-similar solutions with fat tails for a coagulation equation with diagonal kernel
Niethammer, Barbara
2011-01-01
We consider self-similar solutions of Smoluchowski's coagulation equation with a diagonal kernel of homogeneity $\\gamma < 1$. We show that there exists a family of second-kind self-similar solutions with power-law behavior $x^{-(1+\\rho)}$ as $x \\to \\infty$ with $\\rho \\in (\\gamma,1)$. To our knowledge this is the first example of a non-solvable kernel for which the existence of such a family has been established.
Fast and accurate multigrid solution of Poissons equation using diagonally oriented grids
Roberts, A. J.
1999-01-01
We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication between the levels of the multigrid. Numerical experiments solving Poisson's equation in the unit square and unit cube show simple versions of the proposed algorithms are up to twice as fast as correspondingly simple multigrid iterations on a conventional hier...
Diagonal Loading of Robust General-Rank Beamformer for Direction of Arrival Mismatch
Khan, Z. U.; A. Naveed; A. Safeer; F. Zaman
2013-01-01
This study presents a technique which utilizes the movement of the peak of the main beam towards the presumed signal direction with negative diagonal loading for robust general-rank beamformer. The main beam symmetry along presumed signal direction is improved by this movement. When desired signal is contained in the data snapshots, the conventional beamformers face the problem of performance degradation even if there is a small mismatch between the presumed and the actual signal direction. D...
The R-matrix of quantum doubles of Nichols algebras of diagonal type
Energy Technology Data Exchange (ETDEWEB)
Angiono, Iván, E-mail: angiono@famaf.unc.edu.ar [FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba Medina Allende s/n, Ciudad Universitaria (5000) Córdoba (Argentina); Yamane, Hiroyuki, E-mail: hiroyuki@sci.u-toyama.ac.jp [University of Toyama, Faculty of Science, Gofuku 3190, Toyama-shi, Toyama 930-8555 (Japan)
2015-02-15
Let H be the quantum double of a Nichols algebra of diagonal type. We compute the R-matrix of 3-tuples of modules for general finite-dimensional highest weight modules over H. We also calculate a multiplicative formula for the universal R-matrix when H is finite dimensional. We show the unicity of a PBW basis (or a Lusztig-type Poincaré-Birkhoff-Witt basis) with a given convex order.
Doing the twist: diagonal meshes are isomorphic to twisted toroidal Meshes
Pearlmutter, Barak A
1996-01-01
We show that a k x n diagonal mesh is isomorphic to a n+k/2 x n+k/2 - nk/2 twisted toroidal mesh, i.e., a network similar to a standard n+k/2 x n-k/2 toroidal mesh, but with opposite handed twists of n-k/2 in the two directions, which results in a loss of (n-k/2)2 nodes.
Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R
Dimitris Karlis; Ioannis Ntzoufras
2005-01-01
In this paper we present an R package called bivpois for maximum likelihood estimation of the parameters of bivariate and diagonal inflated bivariate Poisson regression models. An Expectation-Maximization (EM) algorithm is implemented. Inflated models allow for modelling both over-dispersion (or under-dispersion) and negative correlation and thus they are appropriate for a wide range of applications. Extensions of the algorithms for several other models are also discussed. Detailed guidance a...
Spin-1/2 XYZ model revisit: General solutions via off-diagonal Bethe ansatz
Energy Technology Data Exchange (ETDEWEB)
Cao, Junpeng [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Collaborative Innovation Center of Quantum Matter, Beijing (China); Cui, Shuai [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Yang, Wen-Li, E-mail: wlyang@nwu.edu.cn [Institute of Modern Physics, Northwest University, Xian 710069 (China); Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048 (China); Shi, Kangjie [Institute of Modern Physics, Northwest University, Xian 710069 (China); Wang, Yupeng, E-mail: yupeng@iphy.ac.cn [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Collaborative Innovation Center of Quantum Matter, Beijing (China)
2014-09-15
The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the inhomogeneous T–Q relations, which allow us to treat both the even N (the number of lattice sites) and odd N cases simultaneously in a unified approach.
Ching, WK; Ng, MK; Wen, YW
2007-01-01
In this paper we consider the solution of Hermitian positive definite block-Toeplitz systems with small size blocks. We propose and study block diagonal and Schur complement preconditioners for such block-Toeplitz matrices. We show that for some block-Toeplitz matrices, the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers where this fixed number depends only on the size of the block. Hence, conjugate gradient type methods, when applied to solv...
Modular Analysis of Sequential Solution Methods for Almost Block Diagonal Systems of Equations
El-Mistikawy, Tarek M. A.
2013-01-01
Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods. It also allows easy assessment of the methods on the basis of their operation counts, storage needs, and admissibility of partial pivoting. The outcome of the analysis and implementation is to discover new methods that outperform a well-known method, a modification of which is, therefore, advocated.
Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
Imbrie, John Z.
2016-07-01
We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a Kolmogorov-Arnold-Moser-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensor-product basis into a complete set of exact many-body eigenfunctions.
A Parallel Algorithm for Solving Block-diagonal Structured Large Linear System
Institute of Scientific and Technical Information of China (English)
SHEN Jie; ZHANG Zhong-lin; CHENG Ji-lin
2001-01-01
A parallel algorithm for solving block-diagonal structured large linear system is presented.This algorithm is based on the "gradient-simplex" method. It partitions a large linear system into several small linear subsystems so that they can be solved in parallel. The algorithm has the merit of high speed and is suitable for the large linear systems with less coupling constrains. The efficiency and applicability of the method is also analyzed.
Diagonalization of multicomponent wave equations with a Born-Oppenheimer example
Weigert, S.; Littlejohn, Robert
1993-01-01
A general method to decouple multicomponent linear wave equations is presented. First, the Weyl calculus is used to transform operator relations into relations between c-number valued matrices. Then it is shown that the symbol representing the wave operator can be diagonalized systematically up to arbitrary order in an appropriate expansion parameter. After transforming the symbols back to operators, the original problem is reduced to solving a set of linear uncoupled scalar wave equations. T...
The decoherence of quantum entanglement and teleportation in Bell-diagonal states
International Nuclear Information System (INIS)
We study the dynamics of entanglement and teleportation in Bell-diagonal states. Using the concepts of concurrence and fidelity, the analytical expressions of the entanglement, the output entanglement and the average fidelity with decoherence are obtained for this model. We discover a class of initial states in which the output entanglement and the average fidelity are destroyed by decoherence. The quality of teleportation depends on the system parameters and time. (authors)
The Distributed Diagonal Force Decomposition Method for Parallelizing Molecular Dynamics Simulations
Boršnik, Urban; Miller, Benjamin T.; Brooks, Bernard R.; Janežič, Dušanka
2011-01-01
Parallelization is an effective way to reduce the computational time needed for molecular dynamics simulations. We describe a new parallelization method, the distributed-diagonal force decomposition method, with which we extend and improve the existing force decomposition methods. Our new method requires less data communication during molecular dynamics simulations than replicated data and current force decomposition methods, increasing the parallel efficiency. It also dynamically load-balanc...
Exact solution for the spin-$s$ XXZ quantum chain with non-diagonal twists
Yung, C. M.; Batchelor, M.T.
1995-01-01
We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon which a Bethe ansatz calculation can be constructed, in contrast to the well-known case of periodic boundary conditions. In this paper we show how the transfer matrix eigenvalue expression for the spin-$s$ XXZ chain twisted by the charge-conjugation matrix ...
Ising n-fold integrals as diagonals of rational functions and integrality of series expansions
International Nuclear Information System (INIS)
We show that the n-fold integrals χ(n) of the magnetic susceptibility of the Ising model, as well as various other n-fold integrals of the ‘Ising class’, or n-fold integrals from enumerative combinatorics, like lattice Green functions, correspond to a distinguished class of functions generalizing algebraic functions: they are actually diagonals of rational functions. As a consequence, the power series expansions of the, analytic at x = 0, solutions of these linear differential equations ‘derived from geometry’ are globally bounded, which means that after just one rescaling of the expansion variable, they can be cast into series expansions with integer coefficients. We also give several results showing that the unique analytical solution of Calabi–Yau ODEs and, more generally, Picard–Fuchs linear ODEs with solutions of maximal weights are always diagonals of rational functions. Besides, in a more enumerative combinatorics context, generating functions whose coefficients are expressed in terms of nested sums of products of binomial terms can also be shown to be diagonals of rational functions. We finally address the question of the relations between the notion of integrality (series with integer coefficients, or, more generally, globally bounded series) and the modularity of ODEs. (paper)
Vacaru, Sergiu I.
2015-04-01
We reinvestigate how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive and -modified gravity using the anholonomic frame deformation method. New classes of locally anisotropic and (in-) homogeneous cosmological metrics are constructed with open and closed spatial geometries. By resorting to such solutions, we show that they describe the late time acceleration due to effective cosmological terms induced by nonlinear off-diagonal interactions, possible modifications of the gravitational action and graviton mass. The cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaître-Robertson-Walker (FLRW) coordinates. The solutions include matter, graviton mass, and other effective sources modeling nonlinear gravitational and matter field interactions with polarization of physical constants and deformations of metrics, which may explain dark energy and dark matter effects. However, we argue that it is not always necessary to modify gravity if we consider the effective generalized Einstein equations with nontrivial vacuum and/or non-minimal coupling with matter. Indeed, we state certain conditions when such configurations mimic interesting solutions in general relativity and modifications, for instance, when we can extract the general Painlevé-Gullstrand and FLRW metrics. In a more general context, we elaborate on a reconstruction procedure for off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes. Finally, open issues and further perspectives are discussed.
Approximations in Inspection Planning
DEFF Research Database (Denmark)
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.; Bloch, Allan
2000-01-01
. One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found by the......Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations...... inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
The Karlqvist approximation revisited
Tannous, C.
2015-01-01
The Karlqvist approximation signaling the historical beginning of magnetic recording head theory is reviewed and compared to various approaches progressing from Green, Fourier, Conformal mapping that obeys the Sommerfeld edge condition at angular points and leads to exact results.
Approximation Behooves Calibration
DEFF Research Database (Denmark)
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Mielke, Steven L; Schwenke, David W; Schatz, George C; Garrett, Bruce C; Peterson, Kirk A
2009-04-23
Multireference configuration interaction (MRCI) calculations of the Born-Oppenheimer diagonal correction (BODC) for H(3) were performed at 1397 symmetry-unique configurations using the Handy-Yamaguchi-Schaefer approach; isotopic substitution leads to 4041 symmetry-unique configurations for the DH(2) mass combination. These results were then fit to a functional form that permits calculation of the BODC for any combination of isotopes. Mean unsigned fitting errors on a test grid of configurations not included in the fitting process were 0.14, 0.12, and 0.65 cm(-1) for the H(3), DH(2), and MuH(2) isotopomers, respectively. This representation can be combined with any Born-Oppenheimer potential energy surface (PES) to yield Born-Huang (BH) PESs; herein, we choose the CCI potential energy surface, the uncertainties of which ( approximately 0.01 kcal/mol) are much smaller than the magnitude of the BODC. Fortran routines to evaluate these BH surfaces are provided. Variational transition state theory calculations are presented comparing thermal rate constants for reactions on the BO and BH surfaces to provide an initial estimate of the significance of the diagonal correction for the dynamics. PMID:19290604
Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei
2015-12-01
In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.
Dutta, Soumitra
1988-01-01
Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.
Institute of Scientific and Technical Information of China (English)
蒋长锦
2002-01-01
A nonlinear system with 3 equations and 3 unknowns was got by using symplectic conditions to reduce the system with 8 equations and 4 unknowns, which the coefficients of 4-stage and 4-order diagonally implicit symplectic Runge-Kutta methods must satisfy. An optimal problem was constructed from the nonlinear system. We investigated on the minimum points of the optimal problem and obtained 9 approximate of them. The 9 computational solutions are obtaind respectively,when Broyden-Flecher-Shanno quasi-Newton methods for solve nonlinear equations was used. These solutions can be regarded as the coefficients of fourth-stage and fourth-order diagonally implicit Runge-Kutta methods respectively.
Applying generalized Pad\\'e approximants in analytic QCD models
Cvetič, Gorazd
2011-01-01
A method of resummation of truncated perturbation series, related to diagonal Pad\\'e approximants but giving results exactly independent of the renormalization scale, was developed more than ten years ago by us with a view of applying it in perturbative QCD. We now apply this method in analytic QCD models, i.e., models where the running coupling has no unphysical singularities, and we show that the method has attractive features such as a rapid convergence. The method can be regarded as a generalization of the scale-setting methods of Stevenson, Grunberg, and Brodsky-Lepage-Mackenzie. The method involves the fixing of various scales and weight coefficients via an auxiliary construction of diagonal Pad\\'e approximant. In low-energy QCD observables, some of these scales become sometimes low at high order, which prevents the method from being effective in perturbative QCD where the coupling has unphysical singularities at low spacelike momenta. There are no such problems in analytic QCD.
DEFF Research Database (Denmark)
Pristed Nielsen, Helene
2013-01-01
Starting from Crenshaw´s point that antiracism often fails to interrogate patriarchy and that feminism often reproduces racist practices (1991: 1252), this paper asks: What are the theoretical reasons for believing that feminism and anti-racism can be regarded as fighting for the joint purpose of...... anti-discrimination in Europe today? And what empirical evidence may be found for such a joint approach? The paper discusses how the contemporary EU context differs from the American context which prompted Crenshaw to raise the point about intersectionality, and it analyses documents and interviews...... from each of the two European umbrella organisations the European Women´s Lobby and the European Network against Racism, as well as a number of their national member organisations from across Europe, both within EU and non-EU member states....
Pietracaprina, Francesca; Ros, Valentina; Scardicchio, Antonello
2016-02-01
In this paper we analyze the predictions of the forward approximation in some models which exhibit an Anderson (single-body) or many-body localized phase. This approximation, which consists of summing over the amplitudes of only the shortest paths in the locator expansion, is known to overestimate the critical value of the disorder which determines the onset of the localized phase. Nevertheless, the results provided by the approximation become more and more accurate as the local coordination (dimensionality) of the graph, defined by the hopping matrix, is made larger. In this sense, the forward approximation can be regarded as a mean-field theory for the Anderson transition in infinite dimensions. The sum can be efficiently computed using transfer matrix techniques, and the results are compared with the most precise exact diagonalization results available. For the Anderson problem, we find a critical value of the disorder which is 0.9 % off the most precise available numerical value already in 5 spatial dimensions, while for the many-body localized phase of the Heisenberg model with random fields the critical disorder hc=4.0 ±0.3 is strikingly close to the most recent results obtained by exact diagonalization. In both cases we obtain a critical exponent ν =1 . In the Anderson case, the latter does not show dependence on the dimensionality, as it is common within mean-field approximations. We discuss the relevance of the correlations between the shortest paths for both the single- and many-body problems, and comment on the connections of our results with the problem of directed polymers in random medium.
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Accuracy of Approximate Eigenstates
Lucha, Wolfgang; Lucha, Wolfgang
2000-01-01
Besides perturbation theory, which requires, of course, the knowledge of the exact unperturbed solution, variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum theory. For a reasonable choice of the employed trial subspace of the domain of H, the lowest eigenvalues of H usually can be located with acceptable precision whereas the trial-subspace vectors corresponding to these eigenvalues approximate, in general, the exact eigenstates of H with much less accuracy. Accordingly, various measures for the accuracy of the approximate eigenstates derived by variational techniques are scrutinized. In particular, the matrix elements of the commutator of the operator H and (suitably chosen) different operators, with respect to degenerate approximate eigenstates of H obtained by some variational method, are proposed here as new criteria for the accuracy of variational eigenstates. These considerations are applied to that Hamiltonian the eig...
Synthesis of approximation errors
Energy Technology Data Exchange (ETDEWEB)
Bareiss, E.H.; Michel, P.
1977-07-01
A method is developed for the synthesis of the error in approximations in the large of regular and irregular functions. The synthesis uses a small class of dimensionless elementary error functions which are weighted by the coefficients of the expansion of the regular part of the function. The question is answered whether a computer can determine the analytical nature of a solution by numerical methods. It is shown that continuous least-squares approximations of irregular functions can be replaced by discrete least-squares approximation and how to select the discrete points. The elementary error functions are used to show how the classical convergence criterions can be markedly improved. There are eight numerical examples included, 30 figures and 74 tables.
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Car, Roberto; E, Weinan
2009-01-01
We propose an algorithm for extracting the diagonal of the inverse matrices arising from electronic structure calculation. The proposed algorithm uses a hierarchical decomposition of the computational domain. It first constructs hierarchical Schur complements of the interior points for the blocks of the domain in a bottom-up pass and then extracts the diagonal entries efficiently in a top-down pass by exploiting the hierarchical local dependence of the inverse matrices. The ...
A New Upper Bound for A-1 of a Strictly α-Diagonally Dominant M-Matrix
Directory of Open Access Journals (Sweden)
Zhanshan Yang
2013-01-01
Full Text Available A new upper bound for A-1 of a real strictly diagonally dominant M-matrix A is present, and a new lower bound of the smallest eigenvalue λminA of A is given, which improved the results in the literature. Furthermore, an upper bound for A-1 of a real strictly α-diagonally dominant M-matrix is shown.
International Nuclear Information System (INIS)
The concept of asymptotic correctability of Bell-diagonal quantum states is generalised to elementary quantum systems of higher dimensions. Based on these results basic properties of quantum state purification protocols are investigated which are capable of purifying tensor products of Bell-diagonal states and which are based on B-steps of the Gottesman-Lo-type with the subsequent application of a Calderbank-Shor-Steane quantum code. Consequences for maximum tolerable error rates of quantum cryptographic protocols are discussed
International Nuclear Information System (INIS)
The concept of asymptotic correctability of Bell-diagonal quantum states is generalized to elementary quantum systems of higher dimensions. Based on these results basic properties of quantum state purification protocols are investigated which are capable of purifying tensor products of Bell-diagonal states and which are based on B-steps of the Gottesman-Lo-type with the subsequent application of a Calderbank-Shor-Steane quantum code. Consequences for maximum tolerable error rates of quantum cryptographic protocols are discussed
Doorway states in the random-phase approximation
Energy Technology Data Exchange (ETDEWEB)
De Pace, A., E-mail: depace@to.infn.it [Istituto Nazionale di Fisica Nucleare, Sezione di Torino, via P.Giuria 1, I-10125 Torino (Italy); Molinari, A. [Dipartimento di Fisica Teorica dell’Università di Torino, via P.Giuria 1, I-10125 Torino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Torino, via P.Giuria 1, I-10125 Torino (Italy); Weidenmüller, H.A. [Max-Planck-Institut für Kernphysik, D-69029 Heidelberg (Germany)
2014-12-15
By coupling a doorway state to a sea of random background states, we develop the theory of doorway states in the framework of the random-phase approximation (RPA). Because of the symmetry of the RPA equations, that theory is radically different from the standard description of doorway states in the shell model. We derive the Pastur equation in the limit of large matrix dimension and show that the results agree with those of matrix diagonalization in large spaces. The complexity of the Pastur equation does not allow for an analytical approach that would approximately describe the doorway state. Our numerical results display unexpected features: The coupling of the doorway state with states of opposite energy leads to strong mutual attraction.
Approximation methods for the partition functions of anharmonic systems
International Nuclear Information System (INIS)
The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations
White, Martin
2014-01-01
This year marks the 100th anniversary of the birth of Yakov Zel'dovich. Amongst his many legacies is the Zel'dovich approximation for the growth of large-scale structure, which remains one of the most successful and insightful analytic models of structure formation. We use the Zel'dovich approximation to compute the two-point function of the matter and biased tracers, and compare to the results of N-body simulations and other Lagrangian perturbation theories. We show that Lagrangian perturbation theories converge well and that the Zel'dovich approximation provides a good fit to the N-body results except for the quadrupole moment of the halo correlation function. We extend the calculation of halo bias to 3rd order and also consider non-local biasing schemes, none of which remove the discrepancy. We argue that a part of the discrepancy owes to an incorrect prediction of inter-halo velocity correlations. We use the Zel'dovich approximation to compute the ingredients of the Gaussian streaming model and show that ...
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
DEFF Research Database (Denmark)
Madsen, Rasmus Elsborg
2005-01-01
The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM that...
Indian Academy of Sciences (India)
Alih Taqi Al-Bayati
2013-02-01
The nuclear structures of 18O and 18F nuclei are studied using particle–particle Tamm–Dancoff approximation (pp TDA) and particle–particle random phase approximation (pp RPA). All possible single-particle states of the allowed angular momenta are considered in the 0p and 1s–0d shells. The Hamiltonian is diagonalized in the presence of Warburton and Brown interactions. The results containing energy-level schemes and transition strength (2) are compared with the available experimental data.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Directory of Open Access Journals (Sweden)
Iskandar Shah Mohd Zawawi
2015-01-01
Full Text Available The diagonally implicit 2-point block backward differentiation formulas (DI2BBDF of order two, order three, and order four are derived for solving stiff initial value problems (IVPs. The stability properties of the derived methods are investigated. The implementation of the method using Newton iteration is also discussed. The performance of the proposed methods in terms of maximum error and computational time is compared with the fully implicit block backward differentiation formulas (FIBBDF and fully implicit block extended backward differentiation formulas (FIBEBDF. The numerical results show that the proposed method outperformed both existing methods.
Anisotropic fluid for a set of non-diagonal tetrads in f(T) gravity
Energy Technology Data Exchange (ETDEWEB)
Hamani Daouda, M., E-mail: daoudah8@yahoo.fr [Universidade Federal do Espirito Santo, Centro de Ciencias Exatas, Departamento de Fisica, Av. Fernando Ferrari s/n, Campus de Goiabeiras, CEP 29075-910, Vitoria, ES (Brazil); Faculte des Sciences et Techniques, Universite Abdou Moumouni de Niamey, BP 10662, Niamey (Niger); Rodrigues, Manuel E., E-mail: esialg@gmail.com [Universidade Federal do Espirito Santo, Centro de Ciencias Exatas, Departamento de Fisica, Av. Fernando Ferrari s/n, Campus de Goiabeiras, CEP 29075-910, Vitoria, ES (Brazil); Houndjo, M.J.S., E-mail: sthoundjo@yahoo.fr [Departamento de Ciencias Naturais, CEUNES, Universidade Federal do Espirito Santo, CEP 29933-415, Sao Mateus, ES (Brazil); Institut de Mathematiques et de Sciences Physiques (IMSP), 01 BP 613 Porto-Novo (Benin)
2012-08-29
We consider f(T) gravity for a Weitzenbock's spherically symmetric and static spacetime, where the metric is projected in the tangent space to the manifold, for a set of non-diagonal tetrads. The matter content is coupled through the energy-momentum tensor of an anisotropic fluid, generating various classes of new black hole and wormhole solutions. One of these classes is that of cold black holes. We also perform the reconstruction scheme of the algebraic function f(T) for two cases where the radial pressure is proportional to f(T) and its first derivative.
Self-Calibration of Radio Astronomical Arrays With Non-Diagonal Noise Covariance Matrix
Wijnholds, Stefan J
2010-01-01
The radio astronomy community is currently building a number of phased array telescopes. The calibration of these telescopes is hampered by the fact that covariances of signals from closely spaced antennas are sensitive to noise coupling and to variations in sky brightness on large spatial scales. These effects are difficult and computationally expensive to model. We propose to model them phenomenologically using a non-diagonal noise covariance matrix. The parameters can be estimated using a weighted alternating least squares (WALS) algorithm iterating between the calibration parameters and the additive nuisance parameters. We demonstrate the effectiveness of our method using data from the low frequency array (LOFAR) prototype station.
Diagonality of weak neutral current and mixing amplitudes of neutral mesons
International Nuclear Information System (INIS)
A possibility to mix neutral systems similar to K0 or D0 into their antisystems in terms of multiquark models is investigated. General formulas for models with 2n number of quarks (n = 3.4 of doublet) for the amplidutes of the indicated mixing and the formulas of mass differences of short- and long-lived states respectively are obtained. All calculations are carried out in unitary gauge for a field propagator of massive vector W boson and in assumption on diagonality of neutral weak current
THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H
Institute of Scientific and Technical Information of China (English)
张灿辉; 冯伟; 黄黔
2002-01-01
The following is proved: 1 ) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular fiexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt 's method. Because of the resulting diagonal fiexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency is improved greatly. The numerical examples show that the method is effective.
CONVERGENCE OF PARALLEL DIAGONAL ITERATION OF RUNGE-KUTTA METHODS FOR DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Xiao-hua Ding; Mingzhu Liu
2004-01-01
Implicit Runge-Kutta method is highly accurate and stable for stiff initial value prob-lem. But the iteration technique used to solve implicit Runge-Kutta method requires lots of computational efforts. In this paper, we extend the Parallel Diagonal Iterated Runge-Kutta(PDIRK) methods to delay differential equations(DDEs). We give the convergence region of PDIRK methods, and analyze the speed of convergence in three parts for the P-stability region of the Runge-Kutta corrector method. Finally, we analysis the speed-up factor through a numerical experiment. The results show that the PDIRK methods to DDEs are efficient.
DEFF Research Database (Denmark)
Völcker, Carsten; Jørgensen, John Bagterp; Thomsen, Per Grove;
2010-01-01
control applied to high order methods for temporal discretization in reservoir simulation. The family of Runge-Kutta methods is presented and in particular the explicit singly diagonally implicit Runge-Kutta (ESDIRK) method with an embedded error estimate is described. A predictive stepsize adjustment...... rule based on error estimates and convergence control of the integrated iterative solver is presented. We try to improve the predictive stepsize control through an extended communication between the convergence rate, the error control and the stepsize. Keywords: Reservoir simulation, implicit Runge-Kutta...
Institute of Scientific and Technical Information of China (English)
Xin-long Luo
2005-01-01
There exists a strong connection between numerical methods for the integration of ordinary differential equations and optimization problems. In this paper, we try to discover further their links. And we transform unconstrained problems to the equivalent ordinary differential equations and construct the LRKOPT method to solve them by combining the second order singly diagonally implicit Runge-Kutta formulas and line search techniques.Moreover we analyze the global convergence and the local convergence of the LRKOPT method. Promising numerical results are also reported.
Diagonal Based Feature Extraction for Handwritten Alphabets Recognition System using Neural Network
Pradeep, J; Himavathi, S; 10.5121/ijcsit.2011.3103
2011-01-01
An off-line handwritten alphabetical character recognition system using multilayer feed forward neural network is described in the paper. A new method, called, diagonal based feature extraction is introduced for extracting the features of the handwritten alphabets. Fifty data sets, each containing 26 alphabets written by various people, are used for training the neural network and 570 different handwritten alphabetical characters are used for testing. The proposed recognition system performs quite well yielding higher levels of recognition accuracy compared to the systems employing the conventional horizontal and vertical methods of feature extraction. This system will be suitable for converting handwritten documents into structural text form and recognizing handwritten names.
Richtárik, Peter
2008-01-01
In this paper we propose and analyze a variant of the level method [4], which is an algorithm for minimizing nonsmooth convex functions. The main work per iteration is spent on 1) minimizing a piecewise-linear model of the objective function and on 2) projecting onto the intersection of the feasible region and a polyhedron arising as a level set of the model. We show that by replacing exact computations in both cases by approximate computations, in relative scale, the theoretical ...
Approximate Bayesian recursive estimation
Czech Academy of Sciences Publication Activity Database
Kárný, Miroslav
2014-01-01
Roč. 285, č. 1 (2014), s. 100-111. ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf
Local approximate inference algorithms
Jung, Kyomin; Shah, Devavrat
2006-01-01
We present a new local approximation algorithm for computing Maximum a Posteriori (MAP) and log-partition function for arbitrary exponential family distribution represented by a finite-valued pair-wise Markov random field (MRF), say $G$. Our algorithm is based on decomposition of $G$ into {\\em appropriately} chosen small components; then computing estimates locally in each of these components and then producing a {\\em good} global solution. We show that if the underlying graph $G$ either excl...
Fragments of approximate counting
Czech Academy of Sciences Publication Activity Database
Buss, S.R.; Kolodziejczyk, L.. A.; Thapen, Neil
2014-01-01
Roč. 79, č. 2 (2014), s. 496-525. ISSN 0022-4812 R&D Projects: GA AV ČR IAA100190902 Institutional support: RVO:67985840 Keywords : approximate counting * bounded arithmetic * ordering principle Subject RIV: BA - General Mathematics Impact factor: 0.541, year: 2014 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9287274&fileId=S0022481213000376
International Nuclear Information System (INIS)
Highlights: • Development of optimization rules for S2 quadrature sets. • Studying the dependency of optimized S2 quadratures on composition and geometry. • Demonstrating S2 procedures preserving the features of higher approximations. - Abstract: Discrete ordinates method relies on approximating the integral term of the transport equation with the aid of quadrature summation rules. These quadratures are usually based on certain assumptions which assure specific symmetry rules and transport/diffusion limits. Generally, these assumptions are not problem-dependent which results in inaccuracies in some instances. Here, various methods have been developed for more accurate estimation of the independent angle in S2 approximation, as it is tightly related to valid estimation of the diffusion coefficient/length. We proposed and examined a method to reduce a complicated problem that usually is consisting many energy groups and discrete directions (SN) to an equivalent one-group S2 problem while it mostly preserves general features of the original model. Some numerical results are demonstrated to show the accuracy of proposed method
Distributionally Robust Joint Chance Constrained Problem under Moment Uncertainty
Directory of Open Access Journals (Sweden)
Ke-wei Ding
2014-01-01
Full Text Available We discuss and develop the convex approximation for robust joint chance constraints under uncertainty of first- and second-order moments. Robust chance constraints are approximated by Worst-Case CVaR constraints which can be reformulated by a semidefinite programming. Then the chance constrained problem can be presented as semidefinite programming. We also find that the approximation for robust joint chance constraints has an equivalent individual quadratic approximation form.
Energy Technology Data Exchange (ETDEWEB)
Chalasani, P.; Saias, I. [Los Alamos National Lab., NM (United States); Jha, S. [Carnegie Mellon Univ., Pittsburgh, PA (United States)
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
International Nuclear Information System (INIS)
A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points in the...
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Approximations to Euler's constant
International Nuclear Information System (INIS)
We study a problem of finding good approximations to Euler's constant γ=lim→∞ Sn, where Sn = Σk=Ln (1)/k-log(n+1), by linear forms in logarithms and harmonic numbers. In 1995, C. Elsner showed that slow convergence of the sequence Sn can be significantly improved if Sn is replaced by linear combinations of Sn with integer coefficients. In this paper, considering more general linear transformations of the sequence Sn we establish new accelerating convergence formulae for γ. Our estimates sharpen and generalize recent Elsner's, Rivoal's and author's results. (author)
Chen, Dan
2012-01-01
We consider the problem of approximating the majority depth (Liu and Singh, 1993) of a point q with respect to an n-point set, S, by random sampling. At the heart of this problem is a data structures question: How can we preprocess a set of n lines so that we can quickly test whether a randomly selected vertex in the arrangement of these lines is above or below the median level. We describe a Monte-Carlo data structure for this problem that can be constructed in O(nlog n$ time, can answer queries O((log n)^{4/3}) expected time, and answers correctly with high probability.
Diagonalization of coupled scalars and its application to the supersymmetric neutral Higgs sector
International Nuclear Information System (INIS)
We introduce a momentum dependent mixing angle α(p2) which allow us to diagonalize at any external momentum p the one-loop corrected inverse propagator matrix of two coupled scalar fields while keeping the full momentum dependence in the self energies. We compare this method with more traditional techniques applied to the diagonalization of coupled scalars at the one-loop level. This method is applied to the CP-even Higgs sector of the Minimal Supersymmetric Model, defining the momentum dependent mixing angle α(p2), and calculating the two CP-even Higgs masses and the mixing angle at these two scales. We compare the results obtained in this way with alternative techniques. We make explicit the relation between α(p2) and the running mixing angle. We find differences between the mixing angle calculated with our method compared with more traditional methods, and these differences are relevant for Higgs searches at LEP2. (author). 22 refs, 4 figs
On the inclusion of the diagonal Born-Oppenheimer correction in surface hopping methods
Gherib, Rami; Ryabinkin, Ilya G; Izmaylov, Artur F
2016-01-01
The diagonal Born-Oppenheimer correction (DBOC) stems from the diagonal second derivative coupling term in the adiabatic representation, and it can have an arbitrary large magnitude when a gap between neighbouring Born-Oppenheimer (BO) potential energy surfaces (PESs) is closing. Nevertheless, DBOC is typically neglected in mixed quantum-classical methods of simulating nonadiabatic dynamics (e.g., fewest-switch surface hopping (FSSH) method). A straightforward addition of DBOC to BO PESs in the FSSH method, FSSH+D, has been shown to lead to numerically much inferior results for models containing conical intersections. More sophisticated variation of the DBOC inclusion, phase-space surface-hopping (PSSH) was more successful than FSSH+D but on model problems without conical intersections. This work comprehensively assesses the role of DBOC in nonadiabatic dynamics of two electronic state problems and the performance of FSSH, FSSH+D, and PSSH methods in variety of one- and two-dimensional models. Our results sho...
Measuring our peculiar velocity on the CMB with high-multipole off-diagonal correlations
International Nuclear Information System (INIS)
Our peculiar velocity with respect to the CMB rest frame is known to induce a large dipole in the CMB. However, the motion of an observer has also the effect of distorting the anisotropies at all scales, as shown by Challinor and Van Leeuwen (2002), due to aberration and Doppler effects. We propose to measure independently our local motion by using off-diagonal two-point correlation functions for high multipoles. We study the observability of the signal for temperature and polarization anisotropies. We point out that Planck can measure the velocity β with an error of about 30% and the direction with an error of about 20°. This method constitutes a cross-check, which can be useful to verify that our CMB dipole is due mainly to our velocity or to disentangle the velocity from other possible intrinsic sources. Although in this paper we focus on our peculiar velocity, a similar effect would result also from other intrinsic vectorial distortion of the CMB which would induce a dipolar lensing. Measuring the off-diagonal correlation terms is therefore a test for a preferred direction on the CMB sky
Randomly Generating Four Mixed Bell-Diagonal States with a Concurrences Sum to Unity
Institute of Scientific and Technical Information of China (English)
S. P. Toh; Hishamuddin Zainuddin; Kim Eng Foo
2012-01-01
A two-qubit system in quantum information theory is the simplest bipartite quantum system and its concurrence for pure and mixed states is well known. As a subset of two-qubit systems, Bell-diagonal states can be depicted by a very simple geometrical representation of a tetrahedron with sides of length 2√2. Based on this geometric representation, we propose a simple approach to randomly generate four mixed Bell decomposable states in which the sum of their concurrence is equal to one.%A two-qubit system in quantum information theory is the simplest bipartite quantum system and its concurrence for pure and mixed states is well known.As a subset of two-qubit systems,Bell-diagonal states can be depicted by a very simple geometrical representation of a tetrahedron with sides of length 2(√2).Based on this geometric representation,we propose a simple approach to randomly generate four mixed Bell decomposable states in which the sum of their concurrence is equal to one.
Forces and mechanical energy fluctuations during diagonal stride roller skiing; running on wheels?
Kehler, Alyse L; Hajkova, Eliska; Holmberg, Hans-Christer; Kram, Rodger
2014-11-01
Mechanical energy can be conserved during terrestrial locomotion in two ways: the inverted pendulum mechanism for walking and the spring-mass mechanism for running. Here, we investigated whether diagonal stride cross-country roller skiing (DIA) utilizes similar mechanisms. Based on previous studies, we hypothesized that running and DIA would share similar phase relationships and magnitudes of kinetic energy (KE), and gravitational potential energy (GPE) fluctuations, indicating elastic energy storage and return, as if roller skiing is like 'running on wheels'. Experienced skiers (N=9) walked and ran at 1.25 and 3 m s(-1), respectively, and roller skied with DIA at both speeds on a level dual-belt treadmill that recorded perpendicular and parallel forces. We calculated the KE and GPE of the center of mass from the force recordings. As expected, the KE and GPE fluctuated with an out-of-phase pattern during walking and an in-phase pattern during running. Unlike walking, during DIA, the KE and GPE fluctuations were in phase, as they are in running. However, during the glide phase, KE was dissipated as frictional heat and could not be stored elastically in the tendons, as in running. Elastic energy storage and return epitomize running and thus we reject our hypothesis. Diagonal stride cross-country skiing is a biomechanically unique movement that only superficially resembles walking or running. PMID:25189366
On a Criterion for Simultaneous Block-Diagonalization of Normal Matrices
Pastuszak, G.; Kamizawa, T.; Jamiołkowski, A.
2016-03-01
Assume that A1, … , As are complex normal n × n matrices, p is a natural number and S2p is the standard polynomial in 2p non-commutative variables. It follows from classical results of S. Amitsur, J. Levitzki and H. Shapiro that A1, … , As can be simultaneously block-diagonalized by a unitary matrix with blocks of sizes not greater than p if and only if the algebra generated by A1, … , As satisfies the polynomial identity S2p = 0. We call this theorem the ALS-criterion for simultaneous block-diagonalization of normal matrices. In this paper, we present some application of the ALS-criterion in quantum theory. Namely, we give another proof of the renowned Morris-Shore transformation. Moreover, we discuss computable versions of the ALS-criterion. These versions allow one to verify the condition S2p = 0 in a finite number of steps. Such an approach is more useful in practical applications than the original one.
Knee joint replacement is a surgery to replace a knee joint with a man-made joint. The artificial joint is called a prosthesis . ... cartilage and bone are removed from the knee joint. Man-made pieces are then placed in the ...
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Thoft-Christensen, Palle
In this paper the preliminary results obtained by tests on tubular joints are presented. The joints are T-joints and the loading is static. It is the intention in continuation of these tests to perform tests on other types of joints (e.g. Y-joints) and also with dynamic loading. The purpose of th...
The Compact Approximation Property does not imply the Approximation Property
Willis, George A.
1992-01-01
It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.
The behavior of reinforced concrete knee joints under earthquake loads
Angelakos, Bill
The poor performance of knee joint connections during recent earthquakes motivated a number of experimental investigations of knee joint behavior under reversed cyclic loading. In this work the knee joint design problem is studied through a collective evaluation of the available experimental results and analytical modeling. The objective is to identify the critical response variables controlling the mechanics of knee joints under earthquake loads and to quantify the influence they have on the strength and deformation capacity of the joint. A knee joint model is derived from simple mechanical constructs of equilibrium and compatibility. The parametric dependence of knee joint behavior is investigated for critical design parameters such as concrete strength, amounts and yield strengths of horizontal and vertical transverse reinforcement, and bond demand. Three different limiting equations are developed from the model limiting the joint shear resistance according with the three alternative modes of joint shear failure. These are: (i) yielding of horizontal and vertical transverse reinforcement, (ii) and (iii) yielding in either of the two principal reinforcing directions accompanied by crushing of the concrete in compression (here the softening influence of orthogonal tensile deformations is considered). For those test specimens from the experimental database that experienced a joint shear failure, the simple knee joint model predicts their joint shear capacity well. Consistent with observations from interior connections it is shown that anchorage of the main reinforcement in the knee joint region prevails as the determining factor of the response of the joint panel. In addition, the same basic physical model that describes the source of resistance in interior connections also applies to knee joints; truss action, and diagonal strut action. By favorably anchoring the beam and column bars it is possible to develop the joint shear strength which is associated with one
... a Clinical Trial Journal Articles Arthritis July 2014 Joint Replacement Surgery: Health Information Basics for You and Your Family What Is Joint Replacement Surgery? Joint replacement surgery is removing a ...
X-ray - joint; Arthrography; Arthrogram ... x-ray technologist will help you position the joint to be x-rayed on the table. Once in place, pictures are taken. The joint may be moved into other positions for more ...
Joint instability and osteoarthritis.
Blalock, Darryl; Miller, Andrew; Tilley, Michael; Wang, Jinxi
2015-01-01
Joint instability creates a clinical and economic burden in the health care system. Injuries and disorders that directly damage the joint structure or lead to joint instability are highly associated with osteoarthritis (OA). Thus, understanding the physiology of joint stability and the mechanisms of joint instability-induced OA is of clinical significance. The first section of this review discusses the structure and function of major joint tissues, including periarticular muscles, which play a significant role in joint stability. Because the knee, ankle, and shoulder joints demonstrate a high incidence of ligament injury and joint instability, the second section summarizes the mechanisms of ligament injury-associated joint instability of these joints. The final section highlights the recent advances in the understanding of the mechanical and biological mechanisms of joint instability-induced OA. These advances may lead to new opportunities for clinical intervention in the prevention and early treatment of OA. PMID:25741184
Direction-of-Arrival Estimation Based on Joint Sparsity
Zhitao Huang; Yiyu Zhou; Junhua Wang
2011-01-01
We present a DOA estimation algorithm, called Joint-Sparse DOA to address the problem of Direction-of-Arrival (DOA) estimation using sensor arrays. Firstly, DOA estimation is cast as the joint-sparse recovery problem. Then, norm is approximated by an arctan function to represent joint sparsity and DOA estimation can be obtained by minimizing the approximate norm. Finally, the minimization problem is solved by a quasi-Newton method to estimate DOA. Simulation results show that our algorithm ha...
Deng, Luzhen; Mi, Deling; He, Peng; Feng, Peng; Yu, Pengwei; Chen, Mianyi; Li, Zhichao; Wang, Jian; Wei, Biao
2015-01-01
For lack of directivity in Total Variation (TV) which only uses x-coordinate and y-coordinate gradient transform as its sparse representation approach during the iteration process, this paper brought in Adaptive-weighted Diagonal Total Variation (AwDTV) that uses the diagonal direction gradient to constraint reconstructed image and adds associated weights which are expressed as an exponential function and can be adaptively adjusted by the local image-intensity diagonal gradient for the purpose of preserving the edge details, then using the steepest descent method to solve the optimization problem. Finally, we did two sets of numerical simulation and the results show that the proposed algorithm can reconstruct high-quality CT images from few-views projection, which has lower Root Mean Square Error (RMSE) and higher Universal Quality Index (UQI) than Algebraic Reconstruction Technique (ART) and TV-based reconstruction method. PMID:26405935
Spacesuit mobility knee joints
Vykukal, H. C. (Inventor)
1979-01-01
Pressure suit mobility joints are for use in interconnecting adjacent segments of an hermetically sealed spacesuit in which low torques, low leakage and a high degree of reliability are required. Each of the joints is a special purpose joint characterized by substantially constant volume and low torque characteristics and includes linkages which restrain the joint from longitudinal distension and includes a flexible, substantially impermeable diaphragm of tubular configuration spanning the distance between pivotally supported annuli. The diaphragms of selected joints include rolling convolutions for balancing the joints, while various joints include wedge-shaped sections which enhance the range of motion for the joints.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Interacting boson approximation
International Nuclear Information System (INIS)
Lectures notes on the Interacting Boson Approximation are given. Topics include: angular momentum tensors; properties of T/sub i//sup (n)/ matrices; T/sub i//sup (n)/ matrices as Clebsch-Gordan coefficients; construction of higher rank tensors; normalization: trace of products of two s-rank tensors; completeness relation; algebra of U(N); eigenvalue of the quadratic Casimir operator for U(3); general result for U(N); angular momentum content of U(3) representation; p-Boson model; Hamiltonian; quadrupole transitions; S,P Boson model; expectation value of dipole operator; S-D model: U(6); quadratic Casimir operator; an O(5) subgroup; an O(6) subgroup; properties of O(5) representations; quadratic Casimir operator; quadratic Casimir operator for U(6); decomposition via SU(5) chain; a special O(3) decomposition of SU(3); useful identities; a useful property of D/sub αβγ/(α,β,γ = 4-8) as coupling coefficients; explicit construction of T/sub x//sup (2)/ and d/sub αβγ/; D-coefficients; eigenstates of T3; and summary of T = 2 states
International Nuclear Information System (INIS)
The off-diagonal magnetoimpedance in glass-coated Co-based amorphous microwires is studied using a pick-up coil wound around the sample. The first and second harmonics in the pick-up coil voltage were measured as a function of the external magnetic field. It was observed that the first harmonic in the voltage corresponding to the linear off-diagonal magnetoimpedance was very small. This fact is attributed to the existence of the regular bamboo domain structure within a surface layer of the microwire. On the contrary, the second harmonic in the voltage differed from zero, which is related to the domain-walls motion
International Nuclear Information System (INIS)
Evidence of temperature gradient driven particle flux was observed from the sawtooth induced density propagation phenomenon in JT-60. This off-diagonal particle flux was confirmed using the numerical calculation of measured chord integrated electron density. It was shown that the discrepancies between thermal and particle diffusivities estimated from the perturbation method and energy/particle balance analysis can be explained by considering the flux equations with off-diagonal transport terms. These flux equations were compared with the E x B convective fluxes in an electro-static drift wave instability and it was found that the E x B fluxes are consistent with several experimental observations. (author)
International Nuclear Information System (INIS)
This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation. (general)
Non-diagonal boundary conditions for gl(1|1) super spin chains
Energy Technology Data Exchange (ETDEWEB)
Grabinski, Andre M; Frahm, Holger, E-mail: frahm@itp.uni-hannover.d [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstrasse 2, 30167 Hannover (Germany)
2010-01-29
We study a one-dimensional model of free fermions with gl(1|1) supersymmetry and demonstrate how non-diagonal boundary conditions can be incorporated into the framework of the graded quantum inverse scattering method (gQISM) by means of super matrices with entries from a superalgebra. For super Hermitian twists and open boundary conditions subject to a certain constraint, we solve the eigenvalue problem for the super transfermatrix by means of the graded algebraic Bethe ansatz technique (gABA) starting from a fermionic coherent state. For generic boundary conditions the algebraic Bethe ansatz cannot be applied. In this case the spectrum of the super transfermatrix is obtained from a functional relation.
International Nuclear Information System (INIS)
We report the calculation of preliminary potential surfaces necessary to treat dissociative recombination (DR) of electrons with N2H+. We performed multi-reference, configuration interaction calculations with a large active space for N2H+ and N2H, using the GAMESS electronic structure code. Rydberg-valence coupling is strong in N2H, and a systematic procedure is desirable to isolate the appropriate dissociating, autoionizing states. We used the block diagonalization method, which requires only modest additional effort beyond the standard methodology. We treated both linear and bent geometries of the molecules, with N2 fixed at its equilibrium separation. The results indicate that the crossing between the dissociating neutral curve and the initial ion potential is not favorably located, suggesting that the direct mechanism for DR will be small. Dynamics calculations using the multi-configuration, time-dependent Hartree (MCTDH) method confirm this conclusion.
Simulation of a 3 Gb/s SAC-OCDMA Based on Multi-Diagonal Code
Directory of Open Access Journals (Sweden)
Ashwani Tiwari, Dharmendra Singh
2013-12-01
Full Text Available In this paper we've modelled and simulated a 3Gb/s (3×1Gb/s optical system supported spectral amplitude coding writing for the optical code-division multiple-access (SAC-OCDMA theme. So as to cut back the result of multiple-access interference, we've utilized a replacement family of SAC-OCDMA codes known as a multi-diagonal (MD code. The new code family supported the MD code reveals properties of zero cross-correlation code, flexibility in choosing the code parameters and support of a large no of users, combined with high rate. each the numerical and simulation results have to make clear that our optical system supported the MD code will accommodate most numbers of co-occurring users with higher rate transmission and lower bit error rates, compared to the previous SAC-OCDMA codes.
Solving block linear systems with low-rank off-diagonal blocks is easily parallelizable
Energy Technology Data Exchange (ETDEWEB)
Menkov, V. [Indiana Univ., Bloomington, IN (United States)
1996-12-31
An easily and efficiently parallelizable direct method is given for solving a block linear system Bx = y, where B = D + Q is the sum of a non-singular block diagonal matrix D and a matrix Q with low-rank blocks. This implicitly defines a new preconditioning method with an operation count close to the cost of calculating a matrix-vector product Qw for some w, plus at most twice the cost of calculating Qw for some w. When implemented on a parallel machine the processor utilization can be as good as that of those operations. Order estimates are given for the general case, and an implementation is compared to block SSOR preconditioning.
Matrix diagonalization algorithm and its applicability to the nuclear shell model
International Nuclear Information System (INIS)
An importance-sampling iterative algorithm for diagonalizing shell model Hamiltonian matrices is reviewed and implemented in a spin uncoupled basis. Shell model spaces of dimensions up to N 9 are considered. The analysis shows that about 10% of the basis states are enough to bring the eigenvalues to convergence. This fraction of states, however, is insufficient to lead to convergence of the transition strengths, thereby limiting the applicability of the method to not too large spaces. In its domain of validity, the method yields a large number of eigensolutions and can be usefully adopted for rather complete studies of low-energy spectroscopy. This is done here for 132,134Xe isotopes. The calculation yields spectra and electromagnetic responses in fairly good agreement with the available experimental data and unveils the properties of the low-energy states of these isotopes, including their proton-neutron symmetry.
Old and new results in regularity theory for diagonal elliptic systems via blowup techniques
Beck, Lisa; Bulíček, Miroslav; Frehse, Jens
2015-12-01
We consider quasilinear diagonal elliptic systems in bounded domains subject to Dirichlet, Neumann or mixed boundary conditions. The leading elliptic operator is assumed to have only measurable coefficients, and the nonlinearities (Hamiltonians) are allowed to be of quadratic (critical) growth in the gradient variable of the unknown. These systems appear in many applications, in particular in differential geometry and stochastic differential game theory. We impose on the Hamiltonians structural conditions developed between 1972-2002 and also a new condition (sum coerciveness) introduced in recent years (in the context of the pay off functional in stochastic game theory). We establish existence, Hölder continuity, Liouville properties, W 2, q estimates, etc. for solutions, via a unified approach through the blow-up method. The main novelty of the paper is the introduction of a completely new technique, which in particular leads to smoothness of the solution also for dimensions d ≥ 3.
High-precision evaluation of Wigner's d-matrix by exact diagonalization
Feng, X M; Yang, W; Jin, G R
2015-01-01
The precise calculations of the Wigner's d-matrix are important in various research fields. Due to the presence of large numbers, direct calculations of the matrix using the Wigner's formula suffer from loss of precision. We present a simple method to avoid this problem by expanding the d-matrix into a complex Fourier series and calculate the Fourier coefficients by exactly diagonalizing the angular-momentum operator $J_{y}$ in the eigenbasis of $J_{z}$. This method allows us to compute the d-matrix and its various derivatives for spins up to a few thousand. The precision of the d-matrix from our method is about $10^{-14}$ for spins up to $100$.
Energy Technology Data Exchange (ETDEWEB)
Serra, Maria; Husar, Attila; Feroldi, Diego; Riera, Jordi [Institut de Robotica i Informatica Industrial, Universitat Politecnica de Catalunya, Consejo Superior de Investigaciones Cientificas, C. Llorens i Artigas 4, 08028 Barcelona (Spain)
2006-08-25
This work is focused on the selection of operating conditions in polymer electrolyte membrane fuel cells. It analyses efficiency and controllability aspects, which change from one operating point to another. Specifically, several operating points that deliver the same amount of net power are compared, and the comparison is done at different net power levels. The study is based on a complex non-linear model, which has been linearised at the selected operating points. Different linear analysis tools are applied to the linear models and results show important controllability differences between operating points. The performance of diagonal control structures with PI controllers at different operating points is also studied. A method for the tuning of the controllers is proposed and applied. The behaviour of the controlled system is simulated with the non-linear model. Conclusions indicate a possible trade-off between controllability and optimisation of hydrogen consumption. (author)
Exact quantum states for the diagonal Bianchi type IX model with negative cosmological constant
Paternoga, R; Paternoga, Robert; Graham, Robert
1996-01-01
Quantum states of the diagonal Bianchi type IX model with negative cosmological constant \\Lambda are obtained by transforming the Chern-Simons solution in Ashtekar's variables to the metric representation. We apply our method developed earlier for \\Lambda>0 and obtain five linearly independent solutions by using the complete set of topologically inequivalent integration contours in the required generalized Fourier-transformation. A caustic in minisuperspace separates two Euclidean regimes at small and large values of the scale parameter from a single classically interpretable Lorentzian regime in between, corresponding to the fact that classically these model-Universes recollapse. Just one particular solution out of the five we find gives a normalizable probability distribution on both branches of the caustic. However, in contrast to the case of positive cosmological constant, this particular solution neither satisfies the semi-classical no-boundary condition, nor does the special initial condition it picks o...
A new alternating bi-diagonal compact scheme for non-uniform grids
Sengupta, Tapan K.; Sengupta, Aditi
2016-04-01
A new compact scheme has been developed for any non-uniform grid. The compact scheme has been developed for spatial discretization and is analyzed here in conjunction with four-stage, fourth order Runge-Kutta (RK4) scheme for time integration while solving the one-dimensional convection equation. The space-time discretization combination is calibrated by subjecting the system to global spectral analysis (GSA) which was developed by the authors' group. Here, the compact scheme has been obtained by using a combination of two bi-diagonal schemes. The novel aspect of this scheme is its application in the physical plane directly without the necessity of mapping or transformations. Some typical cases for problems in acoustics, as well as fluid mechanics, have been studied here and potential use in large eddy simulations (LES) has been demonstrated by solving Navier-Stokes equation for lid driven cavity.
Phase transitions in the diagonal ensemble of two-band Chern insulators
Wang, Pei; Kehrein, Stefan
2016-05-01
We identify a new class of phase transitions when calculating the Hall conductance of two-band Chern insulators in the long-time limit after a global quench of the Hamiltonian. The Hall conductance is expressed as the integral of the Berry curvature in the diagonal ensemble. Even if the Chern number of the unitarily-evolving wave function is conserved, the Hall conductance as a function of the energy gap in the post-quench Hamiltonian displays a continuous but nonanalytic behavior, that is it has a logarithmically divergent derivative as the gap closes. The coefficient of this logarithmic function is the ratio of the change of the Chern number for the ground state of the post-quench Hamiltonian to the energy gap in the initial state. This nonanalytic behavior is universal in two-band Chern insulators.
Šimunek, Ján; Noga, Jozef
2012-12-01
It is shown that the non-terminating expansions of the wave function within the variational coupled cluster singles (VCCS) can be exactly treated by summing up the one-particle density matrix elements in the occupied block using simple recurrence relation. At the same time, this leads to an extremely simple 'a priori' diagonalization free algorithm for the solution of the Hartree-Fock equations. This treatment corresponds to a non-unitary transformation of orbitals, however, preserving the norm and idempotency of the density matrix. The resulting algorithm enables a Hartree-Fock solution with 'a priori' localized orbitals. Similar approach can be applied within the Kohn-Sham theory. Analysis of the VCCS expansion in terms of the generalized perturbation theory is also presented. Numerical results are presented for model systems N2, F2, H2O, NH3 but also for a larger Uracile molecule and an interaction of four Guanine molecules.
Diagonalization of multicomponent wave equations with a Born-Oppenheimer example
Energy Technology Data Exchange (ETDEWEB)
Weigert, S.; Littlejohn, R.G. (Department of Physics and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (United States))
1993-05-01
A general method to decouple multicomponent linear wave equations is presented. First, the Weyl calculus is used to transform operator relations into relations between [ital c]-number valued matrices. Then it is shown that the symbol representing the wave operator can be diagonalized systematically up to arbitrary order in an appropriate expansion parameter. After transforming the symbols back to operators, the original problem is reduced to solving a set of linear uncoupled [ital scalar] wave equations. The procedure is exemplified for a particle with a Born-Oppenheimer-type Hamiltonian valid through second order in [h bar]. The resulting effective scalar Hamiltonians are seen to contain an additional velocity-dependent potential. This contribution has not been reported in recent studies investigating the adiabatic motion of a neutral particle moving in an inhomogeneous magnetic field. Finally, the relation of the general method to standard quantum-mechanical perturbation theory is discussed.
Diagonal and transition magnetic moments of negative parity heavy baryons in QCD sum rules
Aliev, T M; Barakat, T; Savcı, M
2015-01-01
Diagonal and transition magnetic moments of the negative parity, spin-1/2 heavy baryons are studied in framework of the light cone QCD sum rules. By constructing the sum rules for different Lorentz structures, the unwanted contributions coming from negative (positive) to positive (negative) parity transitions are removed. It is obtained that the magnetic moments of all baryons, except $\\Lambda_b^0$, $\\Sigma_c^+$ and $\\Xi_c^{\\prime +}$, are quite large. It is also found that the transition magnetic moments between neutral negative parity heavy $\\Xi_Q^{\\prime 0}$ and $\\Xi_Q^0$ baryons are very small. Magnetic moments of the $\\Sigma_Q \\to \\Lambda_Q$ and $ \\Xi_Q^{\\prime \\pm} \\to \\Xi_Q^\\pm$ transitions are quite large and can be measured in further experiments.
Superfluidity or supersolidity as a consequence of off-diagonal long-range order
International Nuclear Information System (INIS)
We present a general derivation of Hess-Fairbank effect or nonclassical rotational inertial (NCRI), i.e., the refusal to rotate with its container, as well as the quantization of angular momentum, as consequences of off-diagonal long-range order (ODLRO) in an interacting Bose system. Afterwards, the path integral formulation of superfluid density is rederived without ignoring the centrifugal potential. Finally and in particular, for a class of variational wave functions used for solid helium, treating the constraint of single-valuedness boundary condition carefully, we show that there is no ODLRO and, especially, demonstrate explicitly that NCRI cannot be possessed in absence of defects, even though there exist zero-point motion and exchange effect
The feature extraction of ship radiated noise with Fourth Order Cumulant diagonal slice
Institute of Scientific and Technical Information of China (English)
FAN Yangyu; SUN Jincai; HAO Chongyang; LI Ya'an
2004-01-01
After analyzed Fourth Order Cumulant (FOC) of harmonic signals theoretically, the FOC is divided into three parts. The first is the cubic frequency (phase) coupling components.The second is the double frequency (phase) coupling components (ω1 + ω2 = ω3 + ω4). The last is the rest components. On the basis of the study, the FOC diagonal slice is used to extract the cubic frequency (phase) coupling feature, double frequency (phase) coupling feature and the "sub-band energy" feature of ship-radiated noise. In terms of the fea tures, the three type ships are classified by artificial neural network. The correct classification rates of A, B and C ships are 92.5%, 92.7%, 88.6%, respectively. The results show the method is effective and practical.
On separable Fokker-Planck equations with a constant diagonal diffusion matrix
International Nuclear Information System (INIS)
We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients B1(x-vector),B2(x-vector),B3(x-vector) providing separability of the corresponding Fokker-Planck equations and carry out variable separation in the latter. It is established, in particular, that the necessary condition for the Fokker-Planck equation to be separable is that the drift coefficients B-vector (x-vector) must be linear. We also find the necessary condition for R-separability of the Fokker-Planck equation. Furthermore, exact solutions of the Fokker-Planck equation with separated variables are constructed. (author)
Improved Approximations for Some Polymer Extension Models
Petrosyan, Rafayel
2016-01-01
We propose approximations for force-extension dependencies for the freely jointed chain (FJC) and worm-like chain (WLC) models as well as for extension-force dependence for the WLC model. Proposed expressions show less than 1% relative error in the useful range of the corresponding variables. These results can be applied for fitting force-extension curves obtained in molecular force spectroscopy experiments. Particularly they can be useful for cases where one has geometries of springs in series and/or in parallel where particular combination of expressions should be used for fitting the data. All approximations have been obtained following the same procedure of determining the asymptotes and then reducing the relative error of that expression by adding an appropriate term obtained from fitting its absolute error.
Block-diagonal representations for covariance-based anomalous change detectors
Energy Technology Data Exchange (ETDEWEB)
Matsekh, Anna M [Los Alamos National Laboratory; Theiler, James P [Los Alamos National Laboratory
2010-01-01
We use singular vectors of the whitened cross-covariance matrix of two hyper-spectral images and the Golub-Kahan permutations in order to obtain equivalent tridiagonal representations of the coefficient matrices for a family of covariance-based quadratic Anomalous Change Detection (ACD) algorithms. Due to the nature of the problem these tridiagonal matrices have block-diagonal structure, which we exploit to derive analytical expressions for the eigenvalues of the coefficient matrices in terms of the singular values of the whitened cross-covariance matrix. The block-diagonal structure of the matrices of the RX, Chronochrome, symmetrized Chronochrome, Whitened Total Least Squares, Hyperbolic and Subpixel Hyperbolic Anomalous Change Detectors are revealed by the white singular value decomposition and Golub-Kahan transformations. Similarities and differences in the properties of these change detectors are illuminated by their eigenvalue spectra. We presented a methodology that provides the eigenvalue spectrum for a wide range of quadratic anomalous change detectors. Table I summarizes these results, and Fig. I illustrates them. Although their eigenvalues differ, we find that RX, HACD, Subpixel HACD, symmetrized Chronochrome, and WTLSQ share the same eigenvectors. The eigen vectors for the two variants of Chronochrome defined in (18) are different, and are different from each other, even though they share many (but not all, unless d{sub x} = d{sub y}) eigenvalues. We demonstrated that it is sufficient to compute SVD of the whitened cross covariance matrix of the data in order to almost immediately obtain highly structured sparse matrices (and their eigenvalue spectra) of the coefficient matrices of these ACD algorithms in the white SVD-transformed coordinates. Converting to the original non-white coordinates, these eigenvalues will be modified in magnitude but not in sign. That is, the number of positive, zero-valued, and negative eigenvalues will be conserved.
Puelles, Luis; Morales-Delgado, N; Merchán, P; Castro-Robles, B; Martínez-de-la-Torre, M; Díaz, C; Ferran, J L
2016-07-01
The telencephalic subpallium is the source of various GABAergic interneuron cohorts that invade the pallium via tangential migration. Based on genoarchitectonic studies, the subpallium has been subdivided into four major domains: striatum, pallidum, diagonal area and preoptic area (Puelles et al. 2013; Allen Developing Mouse Brain Atlas), and a larger set of molecularly distinct progenitor areas (Flames et al. 2007). Fate mapping, genetic lineage-tracing studies, and other approaches have suggested that each subpallial subdivision produces specific sorts of inhibitory interneurons, distinguished by differential peptidic content, which are distributed tangentially to pallial and subpallial target territories (e.g., olfactory bulb, isocortex, hippocampus, pallial and subpallial amygdala, striatum, pallidum, septum). In this report, we map descriptively the early differentiation and apparent migratory dispersion of mouse subpallial somatostatin-expressing (Sst) cells from E10.5 onward, comparing their topography with the expression patterns of the genes Dlx5, Gbx2, Lhx7-8, Nkx2.1, Nkx5.1 (Hmx3), and Shh, which variously label parts of the subpallium. Whereas some experimental results suggest that Sst cells are pallidal, our data reveal that many, if not most, telencephalic Sst cells derive from de diagonal area (Dg). Sst-positive cells initially only present at the embryonic Dg selectively populate radially the medial part of the bed nucleus striae terminalis (from paraseptal to amygdaloid regions) and part of the central amygdala; they also invade tangentially the striatum, while eschewing the globus pallidum and the preoptic area, and integrate within most cortical and nuclear pallial areas between E10.5 and E16.5. PMID:26189100
Methods of Approximation Theory in Complex Analysis and Mathematical Physics
Saff, Edward
1993-01-01
The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...
Gram stain of joint fluid ... A sample of joint fluid is needed. The fluid sample is sent to a lab where a small drop is placed in a ... on how to prepare for the removal of joint fluid, see joint fluid aspiration .
Operators of Approximations and Approximate Power Set Spaces
Institute of Scientific and Technical Information of China (English)
ZHANG Xian-yong; MO Zhi-wen; SHU Lan
2004-01-01
Boundary inner and outer operators are introduced; and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.
Litofsky, Joshua; Viswanathan, Rama
2015-01-01
Matrix diagonalization, the key technique at the heart of modern computational chemistry for the numerical solution of the Schrödinger equation, can be easily introduced in the physical chemistry curriculum in a pedagogical context using simple Hückel molecular orbital theory for p bonding in molecules. We present details and results of…
Diagonalization of infinite transfer matrix of boundary $U_{q,p}(A_{N-1}^{(1)})$ face model
Kojima, Takeo
2010-01-01
We study infinitely many commuting operators $T_B(z)$, which we call infinite transfer matrix of boundary $U_{q,p}(A_{N-1}^{(1)})$ face model. We diagonalize infinite transfer matrix $T_B(z)$ by using free field realizations of the vertex operators of the elliptic quantum group $U_{q,p}(A_{N-1}^{(1)})$.
Directory of Open Access Journals (Sweden)
Jaime Sepúlveda
2007-01-01
Full Text Available Las intervenciones en salud pública dirigidas a niños en México han ubicado a este país entre los siete países encaminados a cumplir las metas de reducción de la mortalidad infantil para 2015. La información para este estudio se ha tomado de diferentes fuentes: los censos poblacionales; los registros de mortalidad de la Secretaría de Salud y del Instituto Nacional de Estadística, Geografía e Informática; el registro nominal de niños recolectado por el Programa de Vacunación Universal; y las encuestas nacionales de nutrición. Con estos datos se estudió la asociación temporal y la plausibilidad biológica de las diferentes intervenciones en salud pública, para explicar la reducción de las tasas de mortalidad entre niños, infantes y recién nacidos. Las tasas de mortalidad en menores de cinco años han descendido de casi 64 muertes a menos de 23 por cada 1 000 niños nacidos vivos registrados en los últimos 25 años. Se observó una reducción drástica en las tasas de mortalidad por diarrea, junto con la eliminación de polio, difteria y sarampión. El estado nutricional de los niños mejoró de manera significativa en cuanto a bajo peso para la talla, baja talla para la edad y bajo peso para la edad. En los últimos 25 años, se mantuvieron intervenciones altamente costo-efectivas que acercaron los servicios de salud de atención primaria a los hogares, lo que aquí se ha llamado estrategia diagonal. A pesar de que no es posible establecer una relación de causalidad entre la reducción de la mortalidad en menores de cinco años y los factores investigados, se presenta evidencia basada en la asociación temporal y en la plausibilidad biológica que indica que la alta cobertura de las intervenciones de salud pública, los avances en educación de las mujeres, protección social, disponibilidad de agua potable y saneamiento, así como nutrición, impactaron en el resultado observado. Por otro lado, el liderazgo y la continuidad
Seismic Behavor of RC Beam-Column Joint with Additional Bars under Cyclic Loading
Institute of Scientific and Technical Information of China (English)
LU Xilin; Tonny H.URUKAP; LI Sen
2011-01-01
The behavior of Beam-Column Joints in moment resisting frame structures are susceptible to damage caused by seismic effects due to poor performance of the joint. A good number of researches were carried out to understand the complex mechanism of RC joints which are considered in seismic design code practices presently adopted. The traditional construction detailing of transverse reinforcement have shown serious joint failure.This paper introduces a new design philosophy involving the use of additional diagonal bars within the joint particularly suitable for low to medium seismic effects in earthquake zones throughout the world. In lieu to this study, ten (10) full-scale interior beam-column specimens were constructed with various additional reinforcement details and configurations as will be discussed in the later. The experiment provided adequate results to proof the idea of additional bars as suitable approach in reinforced concrete structures where earthquake is eminent. While compared with overall cracking observation during the test, the specimen with additional bars (diagonal and straight) had shown few cracks on the column than the ones without. Furthermore, concrete confinement is certainly an important design method as recommended by certain international codes.
Approximation algorithms and hardness of approximation for knapsack problems
Buhrman, H.; Loff, B.; Torenvliet, L.
2012-01-01
We show various hardness of approximation algorithms for knapsack and related problems; in particular we will show that unless the Exponential-Time Hypothesis is false, then subset-sum cannot be approximated any better than with an FPTAS. We also give a simple new algorithm for approximating knapsac
Approximate nonlinear self-adjointness and approximate conservation laws
International Nuclear Information System (INIS)
In this paper, approximate nonlinear self-adjointness for perturbed PDEs is introduced and its properties are studied. Consequently, approximate conservation laws which cannot be obtained by the approximate Noether theorem are constructed by means of the method. As an application, a class of perturbed nonlinear wave equations is considered to illustrate the effectiveness. (paper)
International Nuclear Information System (INIS)
Exact numerical diagonalization is carried out for the Bohr Hamiltonian with a β-soft, axially stabilized potential. Wave function and observable properties are found to be dominated by strong β-γ coupling effects. The validity of the approximate separation of variables introduced with the X(5) model, extensively applied in recent analyses of axially stabilized transitional nuclei, is examined, and the reasons for its breakdown are analyzed
$\\sigma $ -Approximately Contractible Banach Algebras
Momeni, M; Yazdanpanah, T.; Mardanbeigi, M. R.
2012-01-01
We investigate $\\sigma $ -approximate contractibility and $\\sigma $ -approximate amenability of Banach algebras, which are extensions of usual notions of contractibility and amenability, respectively, where $\\sigma $ is a dense range or an idempotent bounded endomorphism of the corresponding Banach algebra.
Energy Technology Data Exchange (ETDEWEB)
Martovetsky, N N
2007-12-06
ITER Central Solenoid uses butt joints for connecting the pancakes in the CS module. The principles of the butt joining of the CICC were developed by the JAPT during CSMC project. The difference between the CSMC butt joint and the CS butt joint is that the CS butt joint is an in-line joint, while the CSMC is a double joint through a hairpin jumper. The CS butt joint has to carry the hoop load. The straight length of the joint is only 320 mm, and the vacuum chamber around the joint has to have a split in the clamp shell. These requirements are challenging. Fig.1 presents a CSMC joint, and Fig.2 shows a CS butt joint. The butt joint procedure was verified and demonstrated. The tool is capable of achieving all specified parameters. The vacuum in the end was a little higher than the target, which is not critical and readily correctable. We consider, tentatively that the procedure is established. Unexpectedly, we discover significant temperature nonuniformity in the joint cross section, which is not formally a violation of the specs, but is a point of concern. All testing parameters are recorded for QA purposes. We plan to modify the butt joining tool to improve its convenience of operation and provide all features necessary for production of butt joints by qualified personnel.
Approximation by planar elastic curves
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2015-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
Approximate sine-Gordon solitons
Energy Technology Data Exchange (ETDEWEB)
Stratopoulos, G.N. (Dept. of Mathematical Sciences, Durham Univ. (United Kingdom)); Zakrzewski, W.J. (Dept. of Mathematical Sciences, Durham Univ. (United Kingdom))
1993-08-01
We look at the recently proposed scheme of approximating a sine-Gordon soliton by an expression derived from two dimensional instantons. We point out that the scheme of Sutcliffe in which he uses two dimensional instantons can be generalised to higher dimensions and that these generalisations produce even better approximations than the original approximation. We also comment on generalisations to other models. (orig.)
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Behaviour of fibre-reinforced high-performance concrete in exterior beam-column joint
Muthupriya, P.; Boobalan, S. C.; Vishnuram, B. G.
2014-09-01
This paper presents the effect of reinforced high performance concrete (HPC) in exterior beam-column joint with and without fibre under monotonic loading. In this experimental investigation, cross-diagonal bars have been provided at the joint for reducing the congestion of reinforcement in joints, and also M75 grade of concrete with optimum mix proportion of 10 % silica fume and 0.3 % glass fibre was used. Four exterior beam-column joint sub-assemblages were tested. The specimens were divided into two types based on the reinforcement detailing. Type A comprises two joint sub-assemblages with joint detailing as per construction code of practice in India (IS 456-2000), and Type B comprises two joint sub-assemblages with joint detailing as per ductile detailing code of practice in India (IS 13920-1993). In each group there was one specimen of control mix and the remaining one specimen of fibre-reinforced mix. All the test specimens were designed to satisfy the strong column-weak beam concept. The performances of specimens were compared with the control mix and the fibre-reinforced mix. The results show that exterior beam-column joint specimens with silica fume and glass fibre in the HPC mix showed better performance.
Directory of Open Access Journals (Sweden)
Mounir Esslaoui
2013-06-01
Full Text Available The combination of multiuser multiple-input multiple-output (MU-MIMO technology with orthogonal frequency division multiplexing (OFDM is an attractive solution for next generation of wireless local area networks (WLANs, currently standardized within IEEE 802.11ac, and the fourth-generation (4G mobile cellular wireless systems to achieve a very high system throughput while satisfying quality of service (QoS constraints. In particular, Block Diagonalization (BD scheme is a low-complexity precoding technique for MU-MIMO downlink channels, which completely pre-cancels the multiuser interference. The major issue of the BD scheme is that the number of users that can be simultaneously supported is limited by the ratio of the number of base station transmit antennas to the number of user receive antennas. When the number of users is large, a subset of users must be selected, and selection algorithms should be designed to maximize the total system throughput. In this paper, the BD technique is extended to MU-MIMO-OFDM systems and a low complexity user scheduling algorithm is proposed to find the optimal subset of users that should transmit simultaneously, in light of the instantaneous channel state information (CSI, such that the total system sum-rate capacity is maximized. Simulation results show that the proposed scheduling algorithm achieves a good trade-off between sum-rate capacity performance and computational complexity.
Long-range asymptotic expansion of the diagonal Born–Oppenheimer correction
International Nuclear Information System (INIS)
Graphical abstract: We derived formulas for coefficients A6, A8, A10 determining long-range asymptotic behavior of the adiabatic correction to the potential energy. The formulas were used to compute the coefficients for hydrogen molecule and helium dimers. Abstract: Formulas for the coefficients A6, A8, and A10 determining the long-range asymptotic behavior Ead(R)∼-A6R-6-A8R-8-A10R-10 of the diagonal Born–Oppenheimer (adiabatic) correction Ead(R) to the potential energy of a diatomic molecule are derived using two standard definitions of Ead(R). The first one is based on the explicit separation of the center-of-mass and rotational coordinates from the total Hamiltonian of a system, while the second definition uses the Born–Handy expression in a laboratory system of coordinates. Expressions for the asymptotic coefficients resulting from both definitions are proved to be equivalent. The obtained formulas are used to compute the asymptotics of the adiabatic correction for the ground state of the hydrogen molecule and for the helium dimer in the lowest quintet and singlet states. In the latter case basis sets up to 8-tuple zeta quality were used to adequately account for the electron correlation effects.
Comment on "Benchmarking Compressed Sensing, Super-Resolution, and Filter Diagonalization"
Mandelshtam, Vladimir A
2016-01-01
In a recent paper [Int. J. Quant. Chem. (2016) DOI: 10.1002/qua.25144, arXiv:1502.06579] Markovich, Blau, Sanders, and Aspuru-Guzik presented a numerical evaluation and comparison of three methods, Compressed Sensing (CS), Super-Resolution (SR), and Filter Diagonalization (FDM), on their ability of "recovering information" from time signals, concluding that CS and RS outperform FDM. We argue that this comparison is invalid for the following reasons. FDM is a well established method designed for solving the harmonic inversion problem or, similarly, for the problem of spectral estimation, and as such should be applied only to problems of this kind. The authors incorrectly assume that the problem of data fitting is equivalent to the spectral estimation problem, regardless of what parametric form is used, and, consequently, in all five numerical examples FDM is applied to the wrong problem. Moreover, the authors' implementation of FDM turned out to be incorrect, leading to extremely bad results, caused by numeric...
Ahmed, Hassan Yousif; Nisar, K. S.
2013-08-01
Code with ideal in-phase cross correlation (CC) and practical code length to support high number of users are required in spectral amplitude coding-optical code division multiple access (SAC-OCDMA) systems. SAC systems are getting more attractive in the field of OCDMA because of its ability to eliminate the influence of multiple access interference (MAI) and also suppress the effect of phase induced intensity noise (PIIN). In this paper, we have proposed new Diagonal Eigenvalue Unity (DEU) code families with ideal in-phase CC based on Jordan block matrix with simple algebraic ways. Four sets of DEU code families based on the code weight W and number of users N for the combination (even, even), (even, odd), (odd, odd) and (odd, even) are constructed. This combination gives DEU code more flexibility in selection of code weight and number of users. These features made this code a compelling candidate for future optical communication systems. Numerical results show that the proposed DEU system outperforms reported codes. In addition, simulation results taken from a commercial optical systems simulator, Virtual Photonic Instrument (VPI™) shown that, using point to multipoint transmission in passive optical network (PON), DEU has better performance and could support long span with high data rate.
Block-diagonal similarity renormalization group and effective nucleon-nucleon interactions
Szpigel, S.; Timóteo, V. S.; Ruiz Arriola, E.
2016-04-01
We apply the block-diagonal similarity renormalization group to a simple toy-model for the nucleon-nucleon (NN) interaction in the 1 S 0 channel, aiming to analyze the complementarity between the explicit and the implicit renormalization approaches in nuclear physics. By explicit renormalization we mean the methods based on the wilsonian renormalization group in which high-energy modes above a given cutoff scale are integrated out while their effects are replaced by scale dependent effective interactions consistently generated in the process. We call implicit renormalization the usual procedure of cutoff effective theories in which the high-energy modes above the cutoff scale are simply removed and their effects are included through parametrized cutoff dependent counterterms whose strengths are fixed by fitting low-energy data. We compare the effective interactions obtained in both schemes and find a wide range of cutoff scales where they overlap. We further analyze the role played by the one-pion exchange (OPE) considering a δ-shell plus OPE representation for the NN interaction.
Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review
Kennedy, Christopher A.; Carpenter, Mark H.
2016-01-01
A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.
Kam, Chee Zhou; Kueh, Ahmad Beng Hong
2013-01-01
A laminated composite plate element with an interface description is developed using the finite element approach to investigate the bending performance of two-layer cross-ply laminated composite plates in presence of a diagonally perturbed localized interfacial degeneration between laminae. The stiffness of the laminate is expressed through the assembly of the stiffnesses of lamina sub-elements and interface element, the latter of which is formulated adopting the well-defined virtually zero-thickness concept. To account for the extent of both shear and axial weak bonding, a degeneration ratio is introduced in the interface formulation. The model has the advantage of simulating a localized weak bonding at arbitrary locations, with various degeneration areas and intensities, under the influence of numerous boundary conditions since the interfacial description is expressed discretely. Numerical results show that the bending behavior of laminate is significantly affected by the aforementioned parameters, the greatest effect of which is experienced by those with a localized total interface degeneration, representing the case of local delamination. PMID:24319360
Directory of Open Access Journals (Sweden)
Chee Zhou Kam
2013-01-01
Full Text Available A laminated composite plate element with an interface description is developed using the finite element approach to investigate the bending performance of two-layer cross-ply laminated composite plates in presence of a diagonally perturbed localized interfacial degeneration between laminae. The stiffness of the laminate is expressed through the assembly of the stiffnesses of lamina sub-elements and interface element, the latter of which is formulated adopting the well-defined virtually zero-thickness concept. To account for the extent of both shear and axial weak bonding, a degeneration ratio is introduced in the interface formulation. The model has the advantage of simulating a localized weak bonding at arbitrary locations, with various degeneration areas and intensities, under the influence of numerous boundary conditions since the interfacial description is expressed discretely. Numerical results show that the bending behavior of laminate is significantly affected by the aforementioned parameters, the greatest effect of which is experienced by those with a localized total interface degeneration, representing the case of local delamination.
Fixed-complexity vector perturbation with Block diagonalization for MU-MIMO systems
Mohaisen, Manar; Chang, KyungHi; Ji, Seunghwan; Joung, Jinsoup
2009-01-01
Block diagonalization (BD) is an attractive technique that transforms the multi-user multiple-input multiple-output (MU-MIMO) channel into parallel single-user MIMO (SU-MIMO) channels with zero inter-user interference (IUI). In this paper, we combine the BD technique with two deterministic vector perturbation (VP) algorithms that reduce the transmit power in MU-MIMO systems with linear precoding. These techniques are the fixed-complexity sphere encoder (FSE) and the QR-decomposition with M-algorithm encoder (QRDM-E). In contrast to the conventional BD VP technique, which is based on the sphere encoder (SE), the proposed techniques have fixed complexity and a tradeoff between performance and complexity can be achieved by controlling the size of the set of candidates for the perturbation vector. Simulation results and analysis demonstrate the properness of the proposed techniques for the next generation mobile communications systems which are latency and computational complexity limited. In MU-MIMO system with ...
The diagonal spin basis and calculation of processes involving polarized particles
Galynsky, M V
1998-01-01
The review of developed by the authors new techniques for covariant calculation of matrix elements in QED, the so-called formalism of "Diagonal Spin Basis" (DSB), is presented. In DSB spin 4-vectors of in- and out- fermions are expressed just in terms of their 4-momenta. In this approach the little Lorentz group, common for the initial and final states,is realized. This brings the spin operators of in- and out-particles to coincidence. The developed approach is valid both for massive fermions and for massless ones. There occur no problems with accounting for spin flip amplitudes in it. Just 4-momenta of particles participating in reactions are required in it to construct the mathematical apparatus for calculations of matrix elements. We apply this formalism to the next processes: 1) Möller and Bhabha bremsstrahlung ($e^{\\pm}e^- \\to e^{\\pm}e^- \\gamma$) in the ultrarelativistic limit when initial particles and photon are helicity polarized; 2) Compton back-scattering of photons of intensive circularly polarize...
On the relative energy associated with space-times of diagonal metrics
Indian Academy of Sciences (India)
Murat Korunur; Mustafa Salti; Ali havare
2007-05-01
In order to evaluate the energy distribution (due to matter and ﬁelds including gravitation) associated with a space-time model of generalized diagonal metric, we consider the Einstein, Bergmann–Thomson and Landau–Lifshitz energy and/or momentum deﬁnitions both in Einstein's theory of general relativity and the teleparallel gravity (the tetrad theory of gravitation). We ﬁnd same energy distribution using Einstein and Bergmann–Thomson formulations, but we also ﬁnd that the energy–momentum prescription of Landau–Lifshitz disagree in general with these deﬁnitions. We also give eight different well-known space-time models as examples, and considering these models and using our results, we calculate the energy distributions associated with them. Furthermore, we show that for the Bianchi Type-I models all the formulations give the same result. This result agrees with the previous works of Cooperstock–Israelit, Rosen, Johri et al, Banerjee–Sen, Xulu, Vargas and Saltı et al and supports the viewpoints of Albrow and Tryon.
Joint fluid culture ... fungi, or viruses grow. This is called a culture. If these germs are detected, other tests may ... is no special preparation needed for the lab culture. How to prepare for the removal of joint ...
Temporomandibular Joint Dysfunction
The temporomandibular joint (TMJ) connects your jaw to the side of your head. When it works well, it enables you to ... For people with TMJ dysfunction, problems with the joint and muscles around it may cause Pain that ...
Knee joint replacement - slideshow
... this page: //medlineplus.gov/ency/presentations/100088.htm Knee joint replacement - series To use the sharing features ... 4 out of 4 Normal anatomy Overview The knee is a complex joint. It contains the distal ...
... en because of implant loosening, wear, infection, and dislocation. When this occurs, a second joint replacement surgery — called a revision surgery — may be necessary. Is Shoulder Joint Replacement for You? The decision to have ...
The DSUBm approximation scheme for the coupled cluster method and applications to quantum magnets
Directory of Open Access Journals (Sweden)
R.F. Bishop
2009-01-01
Full Text Available A new approximate scheme, DSUBm, is described for the coupled cluster method. We apply it to two well-studied (spin-1/2 Heisenberg antiferromagnet spin-lattice models, namely: the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the sublattice magnetization and the quantum critical point. They are in good agreement with those from such alternative methods as spin-wave theory, series expansions, exact diagonalization techniques, quantum Monte Carlo methods and those from the CCM using the LSUBm scheme.
Scaling for Mixtures of Hard Ions and Dipoles in the Mean Spherical Approximation
Blum, L.
2001-01-01
Using new scaling parameters $\\beta_i$, we derive simple expressions for the excess thermodynamic properties of the Mean Spherical Approximation (MSA) for the ion-dipole mixture. For the MSA and its extensions we have shown that the thermodynamic excess functions are a function of a reduced set of scaling matrices ${\\mathbf\\Gamma}_\\chi$. We show now that for factorizable interactions like the hard ion-dipole mixture there is a further reduction to a diagonal matrices ${\\mathbf\\beta}_\\chi$. Th...
Preconditioning matrices for the pseudospectral approximation of first-order operators
Funaro, D.; Rothman, E.
1989-01-01
The behavior of the eigenvalues of preconditioning matrices for the pseudospectral approximation to the derivative operator has been analyzed in one and two dimensions. The one-dimensional analysis resulted in real and positive eigenvalues for the selected tridiagonal matrices. In the two-dimensional analysis, the eigenvalues of the selected block-diagonal matrices behaved well, but the preconditioner is full and therefore not suitable for applications. The Richardson scheme has been applied in the unpreconditioned as well as the preconditioned version to find the solution of the model problem.
On the relaxation of a two-level system: Beyond the weak-coupling approximation
Reichman, David R.; Silbey, Robert J.
1996-01-01
The model of two nondegenerate quantum levels coupled linearly and off-diagonally to a bath of quantum mechanical harmonic oscillators studied previously by Laird, Budimir, and Skinner is re-examined. Interpretations are made for both the fourth order population relaxation and dephasing processes. Some of the methods used are applied to the standard spin-boson problem. The question of experimental detection of predicted phenomena is discussed. An approximate method, based on a canonical transformation of the original Hamiltonian is proposed to study the problem.
DEFF Research Database (Denmark)
Sørensen, Karsten Engsig
2001-01-01
The article analysis problems connected with corporate joint ventures. Among others the possible conflicts between the joint venture agreement and the statutes of the companies is examined, as well as certain problems connected to the fact that the joint venture partners have created commen control...
Approximate solutions for the skyrmion
Ponciano, J A; Fanchiotti, H; Canal-Garcia, C A
2001-01-01
We reconsider the Euler-Lagrange equation for the Skyrme model in the hedgehog ansatz and study the analytical properties of the solitonic solution. In view of the lack of a closed form solution to the problem, we work on approximate analytical solutions. We show that Pade approximants are well suited to continue analytically the asymptotic representation obtained in terms of a power series expansion near the origin, obtaining explicit approximate solutions for the Skyrme equations. We improve the approximations by applying the 2-point Pade approximant procedure whereby the exact behaviour at spatial infinity is incorporated. An even better convergence to the exact solution is obtained by introducing a modified form for the approximants. The new representations share the same analytical properties with the exact solution at both small and large values of the radial variable r.
The Smoothed Approximate Linear Program
Desai, V V; Moallemi, C C
2009-01-01
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a well studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our program--the `smoothed approximate linear program'--is distinct from such approaches and relaxes the restriction to lower bounding approximations in an appropriate fashion while remaining computationally tractable. Doing so appears to have several advantages: First, we demonstrate substantially superior bounds on the quality of approximation to the optimal cost-to-go function afforded by our approach. Second, experiments with our approach on a challenging problem (the game of Tetris) show that the approach outperforms the existing LP approach (which has previously been shown to be competitive with several AD...
Approximate Grammar for Information Extraction
Sriram, V; Reddy, B. Ravi Sekar; Sangal, R.
2003-01-01
In this paper, we present the concept of Approximate grammar and how it can be used to extract information from a documemt. As the structure of informational strings cannot be defined well in a document, we cannot use the conventional grammar rules to represent the information. Hence, the need arises to design an approximate grammar that can be used effectively to accomplish the task of Information extraction. Approximate grammars are a novel step in this direction. The rules of an approximat...
BDD Minimization for Approximate Computing
Soeken, Mathias; Grosse, Daniel; Chandrasekharan, Arun; Drechsler, Rolf
2016-01-01
We present Approximate BDD Minimization (ABM) as a problem that has application in approximate computing. Given a BDD representation of a multi-output Boolean function, ABM asks whether there exists another function that has a smaller BDD representation but meets a threshold w.r.t. an error metric. We present operators to derive approximated functions and present algorithms to exactly compute the error metrics directly on the BDD representation. An experimental evaluation demonstrates the app...
High Sensitivity Magnetic Sensors Based on Off-diagonal Magnetoimpedance in Amorphous FeCoSiB Wires
Directory of Open Access Journals (Sweden)
N.A. Yudanov
2013-12-01
Full Text Available The magnetoimpedance (MI effect has a potential for the development of high performance magnetic sensors. For sensor applications, off-diagonal configuration is preferable when the MI element is excited by ac current and the output is detected from the coil. In the present work, the off-diagonal sensor design was advanced by utilising a complex waveform excitation produced by a microcontroller and applied to a multiple wire MI element. For optimised excitation with a waveform close to a positive half sine form and characteristic frequency of 8 MHz the field resolution of about 60 mV/Oe was achieved. The pulse excitation does not require an additional bias since it includes controllable low frequency components. The concept of microcontroller driven sensor element could be attractive for the development of intellectual sensors.
Vacaru, Sergiu I
2015-01-01
We re-investigate how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive and f-modified gravity using the anholonomic frame deformation method. There are constructed new classes of locally anisotropic and (in) homogeneous cosmological metrics with open and closed spatial geometries. By resorting such solutions, we show that they describe the late time acceleration due to effective cosmological terms induced by nonlinear off-diagonal interactions, possible modifications of the gravitational action and graviton mass. The cosmological metrics and related St\\" uckelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lama\\^{\\i}tre-Robertson-Walker (FLRW) coordinates. The solutions include matter, graviton mass and other effective sources modelling nonlinear gravitational and matter fields interactions with polarization of physical constants and deformations of metrics, which may explain dark ene...
On the performance of diagonal lattice space-time codes for the quasi-static MIMO channel
Abediseid, Walid
2013-06-01
There has been tremendous work done on designing space-time codes for the quasi-static multiple-input multiple-output (MIMO) channel. All the coding design to date focuses on either high-performance, high rates, low complexity encoding and decoding, or targeting a combination of these criteria. In this paper, we analyze in detail the performance of diagonal lattice space-time codes under lattice decoding. We present both upper and lower bounds on the average error probability. We derive a new closed form expression of the lower bound using the so-called sphere-packing bound. This bound presents the ultimate performance limit a diagonal lattice space-time code can achieve at any signal-to-noise ratio (SNR). The upper bound is simply derived using the union-bound and demonstrates how the average error probability can be minimized by maximizing the minimum product distance of the code. © 2013 IEEE.
Lacroix, D; Bender, M
2008-01-01
Multi-reference calculations along the lines of the Generator Coordinate Method or the restoration of broken symmetries within the nuclear Energy Density Functional (EDF) framework are becoming a standard tool in nuclear structure physics. These calculations rely on the extension of a single-reference energy functional, of the Gogny or the Skyrme types, to non-diagonal energy kernels. There is no rigorous constructive framework for this extension so far. The commonly accepted way proceeds by formal analogy with the expressions obtained when applying the generalized Wick theorem to the non-diagonal matrix element of a Hamilton operator between two product states. It is pointed out that this procedure is ill-defined when extended to EDF calculations as the generalized Wick theorem is taken outside of its range of applicability. In particular, such a procedure is responsible for the appearance of spurious divergences and steps in multi-reference EDF energies, as was recently observed in calculations restoring pa...
Gheorghiu, Tamara; Vacaru, Sergiu I
2014-01-01
We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity, GR, and modified gravity theories when the field equations decouple with respect to certain types of nonholonomic frames of reference. This allows us to construct various classes of exact solutions when the coefficients of fundamental geometric/ physical objects depend on all spacetime coordinates via corresponding classes of generating and integration functions and/or constants. Such (modified) spacetimes can be with Killing and non-Killing symmetries, describe nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants. Our method can be extended to higher dimensions which simplifies some proofs for imbedded and nonholonomically constrained four dimensional configurations. We reproduce the Kerr solution and show how to deform it nonholonomically into new classes of generic off-diagonal solutions depending on 3-8 spacetime coordinates. There are anal...
Simulating Strength Behaviors of Corner Joints of Wood Constructions by Using Finite Element Method
Directory of Open Access Journals (Sweden)
Bulent Kaygin
2016-06-01
Full Text Available Using finite element method (FEM has become wide spread in the field of wood mechanics for analyzing difficult problems instead of conventional methods. The objective of this study is to determine the strength properties of wood corner joints using FEM. For this purpose, diagonal compression and diagonal tension experiments were carried out using dowel, mortise and tenon elements. Corner joints (L-type were prepared with Scotch pine (Pinus sylvestris L. and Beech (Fagus orientalis Lipsky woods. Data obtained experimentally were used in FEM computer modeling to determine structural specifi cations of wood materials. The amount of deformation as a result of compression-tension in the corner joints was determined and then simulated with a computer program using FEM (ANSYS Multiphysics/LS-DYNA. As a result, the amount of deformation obtained from experiments was consistent with the FEM computer modeling with 90 to 97 %. It is suggested that strength properties of joints can be forecast by using FEM computer modeling instead of physical experiments that may cause loss of time, increase of cost and destruction of materials.
Sakumichi, Naoyuki; Kawakami, Norio; Ueda, Masahito
2012-04-01
The quantum-statistical cluster expansion method of Lee and Yang is extended to investigate off-diagonal long-range order (ODLRO) in one-component and multicomponent mixtures of bosons or fermions. Our formulation is applicable to both a uniform system and a trapped system without local-density approximation and allows systematic expansions of one-particle and multiparticle reduced density matrices in terms of cluster functions, which are defined for the same system with Boltzmann statistics. Each term in this expansion can be associated with a Lee-Yang graph. We elucidate a physical meaning of each Lee-Yang graph; in particular, for a mixture of ultracold atoms and bound dimers, an infinite sum of the ladder-type Lee-Yang 0-graphs is shown to lead to Bose-Einstein condensation of dimers below the critical temperature. In the case of Bose statistics, an infinite series of Lee-Yang 1-graphs is shown to converge and gives the criteria of ODLRO at the one-particle level. Applications to a dilute Bose system of hard spheres are also made. In the case of Fermi statistics, an infinite series of Lee-Yang 2-graphs is shown to converge and gives the criteria of ODLRO at the two-particle level. Applications to a two-component Fermi gas in the tightly bound limit are also made.
Mou, Si; Sun, Liangliang; Wojcik, Roza; Dovichi, Norman J.
2013-01-01
Automated diagonal capillary electrophoresis is a two-dimensional separation method that incorporates an immobilized enzyme reactor at the distal end of the first capillary and employs identical electrophoretic separation modes in both dimensions. Components undergo a preliminary separation in the first capillary. Fractions are parked in the reactor where some components undergo transformation. The fractions are then periodically transferred to the second capillary and replaced by the next co...
Liebsch, A.; Ishida, H.; Merino, J.
2008-01-01
The influence of short-range Coulomb correlations on the Mott transition in the single-band Hubbard model at half filling is studied within cellular dynamical mean-field theory for square and triangular lattices. Finite-temperature exact diagonalization is used to investigate correlations within two-, three-, and four-site clusters. Transforming the nonlocal self-energy from a site basis to a molecular-orbital basis, we focus on the interorbital charge transfer between these cluster molecular...
Bracken, Paul
A Hamiltonian which describes the interaction of a single atom with two photon modes is introduced. It is shown that the Hamiltonian can be diagonalized in a particular basis. The energies and an eigenvector basis set are obtained. Some quasi-probability densities are calculated using amplitudes determined with respect to the rotated basis. Some of the physical phenomena which are manifested in the calculations are discussed.
Menousakis, Efstratios; Kaxiras, Efthimios
1989-01-01
We establish the correctness of our exact diagonalization results for the ground state of the effective strong-coupling Hubbard Hamiltonian, and the consistency of their interpretation within the finite-size system studied. We discuss why comparison of our results to calculations by S. Tang and J. E. Hirsch (preceding Comment) is misleading and inconclusive. The possible importance of finite-size effects has already been pointed out.
Institute of Scientific and Technical Information of China (English)
Li Ta-tsien(李大潜); Peng Yue-Jun
2003-01-01
Abstract We prove that the C0 boundedness of solution impliesthe global existence and uniqueness of C1 solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C1 solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity.
Directory of Open Access Journals (Sweden)
Sergio Benavente C.
2013-12-01
Full Text Available Introduction: The Diagonal Earlobe Crease is the first extracardiac sign of Coronary Heart Disease (CHD, associated with generalized atherosclerosis. There is controversy about its validity. Objective: Determine sign’s prevalence in hospitalized population with very-high cardiovascular risk, of a medical center in the southern area of Santiago-Chile, and recognize its association with CHD and Cerebrovascular Disease (CVD. Method: Case and control study. 304 male patients, ≥60 years-old, with personal CHD medical history and hospitalized between May and December of 2012 at El Pino Hospital were included. They were divided in 2 groups, evaluating the presence/absence of DELC by photography. Group 1: submitted to coronarography with significant obstruction (≥50% stenosis in ≥1 coronary artery. Group 2: submitted to simple brain computed tomography with hypodensity of cerebral parenchyma, effacement of sulci, brain edema and/or intraparenchymatous hemorrage. Controls were defined as patients wich result of interventions lack the described injuries. Case-Control ratio of 1:1. The sign’s prevalence was determined. The results where adjusted according to cardiovascular risk factors, by conditional logistic regression. Results: Prevalence of DELC in cases (56.96%, was higher than controls (43.04% (p<0.01. DELC Odds Ratio: CHD = 2.79 [1.14-6.83] (p<0.03, and CVD = 2,55 [1.19–5.48] (p<0.02. Conclusion: This study identified a significative difference between prevalence in both groups, similar with the tendency described in literature. This study, also detected a significant positive association, independent of cardiovascular risk factors, between DELC with CHD and CVD.
Rotational Angles and Velocities During Down the Line and Diagonal Across Court Volleyball Spikes
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Justin R. Brown
2014-05-01
Full Text Available The volleyball spike is an explosive movement that is frequently used to end a rally and earn a point. High velocity spikes are an important skill for a successful volleyball offense. Although the influence of vertical jump height and arm velocity on spiked ball velocity (SBV have been investigated, little is known about the relationship of shoulder and hip angular kinematics with SBV. Other sport skills, like the baseball pitch share similar movement patterns and suggest trunk rotation is important for such movements. The purpose of this study was to examine the relationship of both shoulder and hip angular kinematics with ball velocity during the volleyball spike. Methods: Fourteen Division I collegiate female volleyball players executed down the line (DL and diagonally across-court (DAC spikes in a laboratory setting to measure shoulder and hip angular kinematics and velocities. Each spike was analyzed using a 10 Camera Raptor-E Digital Real Time Camera System. Results: DL SBV was significantly greater than for DAC, respectively (17.54±2.35 vs. 15.97±2.36 m/s, p<0.05. The Shoulder Hip Separation Angle (S-HSA, Shoulder Angular Velocity (SAV, and Hip Angular Velocity (HAV were all significantly correlated with DAC SBV. S-HSA was the most significant predictor of DAC SBV as determined by regression analysis. Conclusions: This study provides support for a relationship between a greater S-HSA and SBV. Future research should continue to 1 examine the influence of core training exercise and rotational skill drills on SBV and 2 examine trunk angular velocities during various types of spikes during play.
Lim, S. P.; Sheng, D. N.
2016-07-01
A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high-energy densities through a disorder-driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target highly excited states for MBL systems. By studying the one-dimensional Heisenberg spin chain in a random field, we demonstrate the accuracy of the method in obtaining energy eigenstates and the corresponding statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks: one at zero and another one at the quantized entropy S =ln2 with an exponential decay tail on the S >ln2 side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop power-law correlations. The corresponding phase diagram contains an intermediate or crossover regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in this regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.
Nicotine induction of theta frequency oscillations in rodent medial septal diagonal band in vitro
Institute of Scientific and Technical Information of China (English)
Cheng-biao LU; Cheng-zhang LI; Dong-liang LI; Zaineb HENDERSON
2013-01-01
Aim:This study aimed to examine the role of the nicotinic receptor (nAChR) in the generation of theta oscillations (4-12 Hz) in vitro.Methods:Electrophysiological studies were performed on medial septal diagonal band area (MSDB) slices to measure theta oscillation.Immunofluorescence and confocal microscopy studies were carried out to detect α4 nAChR and β2 nAChR subunits in perfused-fixed tissue from VGluT2-GFP and GAD67-GFP transgenic mice.Results:Application of nicotine to MSDB slices produced persistent theta oscillations in which area power increased in a doseresponsive manner.This activity was inhibited by GABAA receptor antagonists and partially by ionotropic glutamate receptor antagonists,indicating the involvement of local GABAergic and glutamatergic neurons in the production of the rhythmic activity.The nicotineinduced theta activity was also inhibited selectively by non-α7*nAChR antagonists,suggesting the presence of these receptor types on GABAergic and glutamatergic neuron populatjons in the MSDB.This was confirmed by immunofluorescence and confocal microscopy studies in transgenic mice in which the GABAergic and glutamatergic neurons express green fluorescent protein (GFP),showing Iocalisation of β2 nAChR and α4 nAChR subunits,the most common constituents of non-α7*nAChRs,in both cell types in the MSDB.Conclusion:Theta activity in the MSDB may be generated by tonic stimulation of non-α7*nAChRs.
Energy Technology Data Exchange (ETDEWEB)
Vacaru, Sergiu I. [University ' ' Al. I. Cuza' ' Iasi, Rector' s Department, Iasi (Romania)
2015-04-01
We reinvestigate how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive and f-modified gravity using the anholonomic frame deformation method. New classes of locally anisotropic and (in-) homogeneous cosmological metrics are constructed with open and closed spatial geometries. By resorting to such solutions, we show that they describe the late time acceleration due to effective cosmological terms induced by nonlinear off-diagonal interactions, possible modifications of the gravitational action and graviton mass. The cosmological metrics and related Stueckelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaitre-Robertson-Walker (FLRW) coordinates. The solutions include matter, graviton mass, and other effective sources modeling nonlinear gravitational and matter field interactions with polarization of physical constants and deformations of metrics, which may explain dark energy and dark matter effects. However, we argue that it is not always necessary to modify gravity if we consider the effective generalized Einstein equations with nontrivial vacuum and/or non-minimal coupling with matter. Indeed, we state certain conditions when such configurations mimic interesting solutions in general relativity and modifications, for instance, when we can extract the general Painleve-Gullstrand and FLRW metrics. In a more general context, we elaborate on a reconstruction procedure for off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes. Finally, open issues and further perspectives are discussed. (orig.)
Karantanis, Nikolaos-Evangelos; Youlatos, Dionisios; Rychlik, Leszek
2015-09-01
Research on primate origins has revolved around arboreality and, more specifically, the adaptations that are linked to safe navigation in the fine-branch niche. To this end, extant non-primate mammals have been used as models to assess the significance of these adaptations. However, the size of these models is larger than that estimated for early primates. In contrast, the feathertail marsupial glider Acrobates pygmaeus, with a body mass of 12 g, a clawless opposable hallux, and terminal branch feeding habits appears more suited to modeling behavioral adaptations to the small branch milieu. Analysis of video recordings of 18 feathertail gliders walking on poles of variable diameter and inclination revealed that they preferentially used diagonal sequence gaits, fast velocities and low duty factors. Diagonal gaits did not correlate to duty factor, but increased as substrate size decreased, and from descending to ascending locomotion. Furthermore, the duty factor index increased in more diagonal gaits and ascending locomotion. Finally, velocities were lower on smaller substrates, and were mainly regulated by stride frequency and, to a lesser degree, stride length. Feathertail glider gaits displayed noteworthy behavioral convergences with primate quadrupedalism, but some of these results need additional investigation. Despite any discrepancies, these features appear to be favorable for quadrupedal progression on small branches, providing a selective advantage for navigating within a fine branch niche and highlighting the importance of small body size in early primate evolution. PMID:26204798
Energy Technology Data Exchange (ETDEWEB)
Gheorghiu, Tamara [University ' ' Al. I. Cuza' ' Iasi, Project IDEI, Iasi (Romania); University of Medicine and Pharmacy ' ' Gr. T. Popa' ' Iasi, Faculty of Medicine, Iasi (Romania); Vacaru, Olivia [National College of Iasi, Iasi (Romania); Vacaru, Sergiu I. [CERN, Theory Division, Geneva 23 (Switzerland); University ' ' Al. I. Cuza' ' Iasi, Rector' s Office, Iasi (Romania)
2014-12-01
We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and modified gravity theories when the field equations decouple with respect to certain types of nonholonomic frames of reference. This allows us to construct various classes of exact solutions when the coefficients of the fundamental geometric/physical objects depend on all spacetime coordinates via corresponding classes of generating and integration functions and/or constants. Such (modified) spacetimes display Killing and non-Killing symmetries, describe nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants. Our method can be extended to higher dimensions which simplifies some proofs for embedded and nonholonomically constrained four-dimensional configurations. We reproduce the Kerr solution and show how to deform it nonholonomically into new classes of generic off-diagonal solutions depending on 3-8 spacetime coordinates. Certain examples of exact solutions are analyzed and they are determined by contributions of a new type of interactions with sources in massive gravity and/or modified f(R,T) gravity. We conclude that by considering generic off-diagonal nonlinear parametric interactions in GR it is possible to mimic various effects in massive and/or modified gravity, or to distinguish certain classes of ''generic'' modified gravity solutions which cannot be encoded in GR. (orig.)
International Nuclear Information System (INIS)
We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and modified gravity theories when the field equations decouple with respect to certain types of nonholonomic frames of reference. This allows us to construct various classes of exact solutions when the coefficients of the fundamental geometric/physical objects depend on all spacetime coordinates via corresponding classes of generating and integration functions and/or constants. Such (modified) spacetimes display Killing and non-Killing symmetries, describe nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants. Our method can be extended to higher dimensions which simplifies some proofs for embedded and nonholonomically constrained four-dimensional configurations. We reproduce the Kerr solution and show how to deform it nonholonomically into new classes of generic off-diagonal solutions depending on 3-8 spacetime coordinates. Certain examples of exact solutions are analyzed and they are determined by contributions of a new type of interactions with sources in massive gravity and/or modified f(R,T) gravity. We conclude that by considering generic off-diagonal nonlinear parametric interactions in GR it is possible to mimic various effects in massive and/or modified gravity, or to distinguish certain classes of ''generic'' modified gravity solutions which cannot be encoded in GR. (orig.)
International Nuclear Information System (INIS)
We reinvestigate how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive and f-modified gravity using the anholonomic frame deformation method. New classes of locally anisotropic and (in-) homogeneous cosmological metrics are constructed with open and closed spatial geometries. By resorting to such solutions, we show that they describe the late time acceleration due to effective cosmological terms induced by nonlinear off-diagonal interactions, possible modifications of the gravitational action and graviton mass. The cosmological metrics and related Stueckelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaitre-Robertson-Walker (FLRW) coordinates. The solutions include matter, graviton mass, and other effective sources modeling nonlinear gravitational and matter field interactions with polarization of physical constants and deformations of metrics, which may explain dark energy and dark matter effects. However, we argue that it is not always necessary to modify gravity if we consider the effective generalized Einstein equations with nontrivial vacuum and/or non-minimal coupling with matter. Indeed, we state certain conditions when such configurations mimic interesting solutions in general relativity and modifications, for instance, when we can extract the general Painleve-Gullstrand and FLRW metrics. In a more general context, we elaborate on a reconstruction procedure for off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes. Finally, open issues and further perspectives are discussed. (orig.)
Gheorghiu, Tamara; Vacaru, Olivia; Vacaru, Sergiu I.
2014-12-01
We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and modified gravity theories when the field equations decouple with respect to certain types of nonholonomic frames of reference. This allows us to construct various classes of exact solutions when the coefficients of the fundamental geometric/physical objects depend on all spacetime coordinates via corresponding classes of generating and integration functions and/or constants. Such (modified) spacetimes display Killing and non-Killing symmetries, describe nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants. Our method can be extended to higher dimensions which simplifies some proofs for embedded and nonholonomically constrained four-dimensional configurations. We reproduce the Kerr solution and show how to deform it nonholonomically into new classes of generic off-diagonal solutions depending on 3-8 spacetime coordinates. Certain examples of exact solutions are analyzed and they are determined by contributions of a new type of interactions with sources in massive gravity and/or modified f(R,T) gravity. We conclude that by considering generic off-diagonal nonlinear parametric interactions in GR it is possible to mimic various effects in massive and/or modified gravity, or to distinguish certain classes of "generic" modified gravity solutions which cannot be encoded in GR.
Gamow-Teller resonances and a separable approximation for Skyrme tensor interactions
Directory of Open Access Journals (Sweden)
Severyukhin A. P.
2012-12-01
Full Text Available A finite rank separable approximation for the quasiparticle random phase approximation (QRPA with Skyrme interactions is applied to study properties of the Gamow-Teller (GT resonances in the neutron-rich Cd isotopes. This approximation enables one to reduce considerably the dimension of matrix that must be diagonalized to perform QRPA calculations in a very large configuration space. Our results from the SGII Skyrme interaction with the tensor interactions and the density-dependent zero-range pairing interaction show that the GT distribution is noticeably modified when the tensor correlations are taken into account. In particular, for 130Cd the dominant peak is moved 3.6 MeV downward and 10% of the GT distribution is shifted to the high excitation energy region near E=50MeV.
International Nuclear Information System (INIS)
A new approach was recently presented to compute correlation energies within the random phase approximation using Lanczos chains and an optimal basis set (Rocca 2014 J. Chem. Phys. 140 18A501). This novel method avoids the explicit calculation of conduction states and represents linear response functions on a compact auxiliary basis set obtained from the diagonalization of an approximate dielectric matrix that contains only the kinetic energy contribution. Here, we extend this formalism, originally implemented for molecular systems, to treat periodic solids. In particular, the approximate dielectric matrix used to build the auxiliary basis set is generalized to avoid unphysical negative gaps, that make the model inefficient. The numerical convergence of the method is discussed and the accuracy is demonstrated considering a set including three covalently bonded (C, Si, and SiC) and three weakly bonded (Ne, Ar, and Kr) solids. (paper)
Beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Chebyshev polynomial approximation to approximate partial differential equations
Caporale, Guglielmo Maria; Cerrato, Mario
2008-01-01
This pa per suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions t...
Directory of Open Access Journals (Sweden)
José Roberto Ortale
2005-06-01
Full Text Available OBJETIVO: O objetivo deste trabalho é a descrição dos ramos lateral, diagonal e ântero-superior, no tecido adiposo epicárdico do ventrículo esquerdo, e a análise da freqüência e do diâmetro destes, conforme o tipo de circulação coronariana. O conhecimento preciso desses ramos tem aplicabilidade na abordagem cirúrgica para a sua revascularização ou durante a injeção de substâncias cardioplégicas nos mesmos. MÉTODO: Dissecados 50 corações obtidos de necropsias de adultos, fixados em solução de formol e o ventrículo esquerdo dividido em três terços: superior, médio e inferior. O ramo lateral originou-se do ramo circunflexo; o ramo diagonal, do ponto de divisão da artéria coronária esquerda e o ramo ântero-superior, do ramo interventricular anterior no terço superior do ventrículo esquerdo. Para cada ramo foram medidos o comprimento no epicárdio e o diâmetro, além disso foi relacionado o fluxo sangüíneo com o tipo de circulação coronariana. RESULTADOS: O diâmetro do ramo lateral, presente em 88% dos casos, variou de 0,6 a 4,5 mm (média 2,1 ± 0,7mm. O diâmetro do ramo diagonal, presente em 50% dos casos, variou de 1,0 a 3,8 mm (média 2,2 ± 0,7 mm. O diâmetro do ramo ântero-superior, presente em 84% dos casos, variou de 1,0 a 4,1 mm (média 2,5 ± 0,8 mm. Foram encontrados: 30/50 (60% casos de dominância da artéria coronária direita, 14/50 (28% casos de tipo balanceado e 6/12 (12% casos de dominância da artéria coronária esquerda. A média do fluxo sangüíneo do ramo ântero-superior apresentou valor decrescente nos tipos: dominância da artéria coronária direita, balanceado e dominância da artéria coronária esquerda. Inversamente, o ramo lateral mostrou valor crescente, enquanto o ramo diagonal apresentou maior fluxo no tipo balanceado. CONCLUSÃO: Os resultados demonstraram a complementaridade entre os ramos lateral, diagonal e ântero-superior, bem como a correlação entre a distribui
The efficiency of Flory approximation
International Nuclear Information System (INIS)
The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)
Approximate Reanalysis in Topology Optimization
DEFF Research Database (Denmark)
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures is...... investigated. The nested optimization problem is re-formulated to accommodate the use of an approximate displacement vector and the design sensitivities are derived accordingly. It is shown that relatively rough approximations are acceptable since the errors are taken into account in the sensitivity analysis...
Emergency Entry with One Control Torque: Non-Axisymmetric Diagonal Inertia Matrix
Llama, Eduardo Garcia
2011-01-01
In another work, a method was presented, primarily conceived as an emergency backup system, that addressed the problem of a space capsule that needed to execute a safe atmospheric entry from an arbitrary initial attitude and angular rate in the absence of nominal control capability. The proposed concept permits the arrest of a tumbling motion, orientation to the heat shield forward position and the attainment of a ballistic roll rate of a rigid spacecraft with the use of control in one axis only. To show the feasibility of such concept, the technique of single input single output (SISO) feedback linearization using the Lie derivative method was employed and the problem was solved for different number of jets and for different configurations of the inertia matrix: the axisymmetric inertia matrix (I(sub xx) > I(sub yy) = I(sub zz)), a partially complete inertia matrix with I(sub xx) > I(sub yy) > I(sub zz), I(sub xz) not = 0 and a realistic complete inertia matrix with I(sub xx) > I(sub yy) > I)sub zz), I(sub ij) not= 0. The closed loop stability of the proposed non-linear control on the total angle of attack, Theta, was analyzed through the zero dynamics of the internal dynamics for the case where the inertia matrix is axisymmetric (I(sub xx) > I(sub yy) = I(sub zz)). This note focuses on the problem of the diagonal non-axisymmetric inertia matrix (I(sub xx) > I(sub yy) > I(sub zz)), which is half way between the axisymmetric and the partially complete inertia matrices. In this note, the control law for this type of inertia matrix will be determined and its closed-loop stability will be analyzed using the same methods that were used in the other work. In particular, it will be proven that the control system is stable in closed-loop when the actuators only provide a roll torque.
Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates
Directory of Open Access Journals (Sweden)
Bui The Anh
2013-02-01
Full Text Available Let X be a metric space with doubling measure and L a one-to-one operator of type ω having a bounded H∞ -functional calculus in L2(X satisfying the reinforced (pL; qL off-diagonal estimates on balls, where pL ∊ [1; 2 and qL ∊ (2;∞]. Let φ : X × [0;∞ → [0;∞ be a function such that φ (x;· is an Orlicz function, φ(·;t ∊ A∞(X (the class of uniformly Muckenhoupt weights, its uniformly critical upper type index l(φ ∊ (0;1] and φ(·; t satisfies the uniformly reverse Hölder inequality of order (qL/l(φ′, where (qL/l(φ′ denotes the conjugate exponent of qL/l(φ. In this paper, the authors introduce a Musielak-Orlicz-Hardy space Hφ;L(X, via the Lusin-area function associated with L, and establish its molecular characterization. In particular, when L is nonnegative self-adjoint and satisfies the Davies-Gaffney estimates, the atomic characterization of Hφ,L(X is also obtained. Furthermore, a sufficient condition for the equivalence between Hφ,L(ℝn and the classical Musielak-Orlicz-Hardy space Hv(ℝn is given. Moreover, for the Musielak-Orlicz-Hardy space Hφ,L(ℝn associated with the second order elliptic operator in divergence form on ℝn or the Schrödinger operator L := −Δ + V with 0 ≤ V ∊ L1loc(ℝn, the authors further obtain its several equivalent characterizations in terms of various non-tangential and radial maximal functions; finally, the authors show that the Riesz transform ∇L−1/2 is bounded from Hφ,L(ℝn to the Musielak-Orlicz space Lφ(ℝn when i(φ ∊ (0; 1], from Hφ,L(ℝn to Hφ(ℝn when i(φ ∊ (; 1], and from Hφ,L(ℝn to the weak Musielak-Orlicz-Hardy space WHφ(ℝn when i(φ=is attainable and φ(·; t ∊ A1(X, where i(φ denotes the uniformly critical lower type index of φ
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Approximate maximizers of intricacy functionals
Buzzi, Jerome
2009-01-01
G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the neural complexity of a family of random variables. This functional is a special case of intricacy, i.e., an average of the mutual information of subsystems whose weights have good mathematical properties. Moreover, its maximum value grows at a definite speed with the size of the system. In this work, we compute exactly this speed of growth by building "approximate maximizers" subject to an entropy condition. These approximate maximizers work simultaneously for all intricacies. We also establish some properties of arbitrary approximate maximizers, in particular the existence of a threshold in the size of subsystems of approximate maximizers: most smaller subsystems are almost equidistributed, most larger subsystems determine the full system. The main ideas are a random construction of almost maximizers with a high statistical symmetry and the consideration of entropy profiles, i.e., the average entropies of sub-systems of a given size. ...
Metrical Diophantine approximation for quaternions
Dodson, Maurice
2011-01-01
The metrical theory of Diophantine approximation for quaternions is developed using recent results in the general theory. In particular, Quaternionic analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch are established.
Metrical Diophantine approximation for quaternions
Dodson, Maurice; Everitt, Brent
2014-11-01
Analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch in the metrical theory of Diophantine approximation are established for quaternions by applying results on the measure of general `lim sup' sets.
Managing Joint Production Motivation
DEFF Research Database (Denmark)
Lindenberg, Siegwart; Foss, Nicolai Juul
2011-01-01
We contribute to the microfoundations of organizational performance by proffering the construct of joint production motivation. Under such motivational conditions individuals see themselves as part of a joint endeavor, each with his or her own roles and responsibilities; generate shared represent......We contribute to the microfoundations of organizational performance by proffering the construct of joint production motivation. Under such motivational conditions individuals see themselves as part of a joint endeavor, each with his or her own roles and responsibilities; generate shared...... representations of actions and tasks; cognitively coordinate cooperation; and choose their own behaviors in terms of joint goals. Using goal-framing theory, we explain how motivation for joint production can be managed by cognitive/symbolic management and organizational design....
Reinforcement Learning via AIXI Approximation
Veness, Joel; Ng, Kee Siong; Hutter, Marcus; Silver, David
2010-01-01
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To deve...
Binary nucleation beyond capillarity approximation
Kalikmanov, V.I.
2010-01-01
Large discrepancies between binary classical nucleation theory (BCNT) and experiments result from adsorption effects and inability of BCNT, based on the phenomenological capillarity approximation, to treat small clusters. We propose a model aimed at eliminating both of these deficiencies. Adsorption is taken into account within Gibbsian approximation. Binary clusters are treated by means of statistical-mechanical considerations: tracing out the molecular degrees of freedom of the more volatil...
Chebyshev approximation for multivariate functions
Sukhorukova, Nadezda; Ugon, Julien; Yost, David
2015-01-01
In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is very elegant. The optimality conditions are based on the notion of alternance (maximal deviation points with alternating deviation signs). It is not very straightforward, however, how to extend the notion of alternance to the case of multivariate functions. There have been several attempts to extend the theory of Cheby...
Analytic Approximations for Spread Options
Carol Alexander; Aanand Venkatramanan
2007-01-01
Even in the simple case that two price processes follow correlated geometric Brownian motions with constant volatility no analytic formula for the price of a standard European spread option has been derived, except when the strike is zero in which case the option becomes an exchange option. This paper expresses the price of a spread option as the price of a compound exchange option and hence derives a new analytic approximation for its price and hedge ratios. This approximation has several ad...
Wavelet Sparse Approximate Inverse Preconditioners
Chan, Tony F.; Tang, W.-P.; Wan, W. L.
1996-01-01
There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.
Shearlets and Optimally Sparse Approximations
Kutyniok, Gitta; Lim, Wang-Q
2011-01-01
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported sh...
Relativistic regular approximations revisited: An infinite-order relativistic approximation
International Nuclear Information System (INIS)
The concept of the regular approximation is presented as the neglect of the energy dependence of the exact Foldy - Wouthuysen transformation of the Dirac Hamiltonian. Expansion of the normalization terms leads immediately to the zeroth-order regular approximation (ZORA) and first-order regular approximation (FORA) Hamiltonians as the zeroth- and first-order terms of the expansion. The expansion may be taken to infinite order by using an un-normalized Foldy - Wouthuysen transformation, which results in the ZORA Hamiltonian and a non-unit metric. This infinite-order regular approximation, IORA, has eigenvalues which differ from the Dirac eigenvalues by order E3/c4 for a hydrogen-like system, which is a considerable improvement over the ZORA eigenvalues, and similar to the non-variational FORA energies. A further perturbation analysis yields a third-order correction to the IORA energies, TIORA. Results are presented for several systems including the neutral U atom. The IORA eigenvalues for all but the 1s spinor of the neutral system are superior even to the scaled ZORA energies, which are exact for the hydrogenic system. The third-order correction reduces the IORA error for the inner orbitals to a very small fraction of the Dirac eigenvalue. copyright 1999 American Institute of Physics
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Concept Approximation between Fuzzy Ontologies
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Fuzzy ontologies are efficient tools to handle fuzzy and uncertain knowledge on the semantic web; but there are heterogeneity problems when gaining interoperability among different fuzzy ontologies. This paper uses concept approximation between fuzzy ontologies based on instances to solve the heterogeneity problems. It firstly proposes an instance selection technology based on instance clustering and weighting to unify the fuzzy interpretation of different ontologies and reduce the number of instances to increase the efficiency. Then the paper resolves the problem of computing the approximations of concepts into the problem of computing the least upper approximations of atom concepts. It optimizes the search strategies by extending atom concept sets and defining the least upper bounds of concepts to reduce the searching space of the problem. An efficient algorithm for searching the least upper bounds of concept is given.
Liebsch, A.; Ishida, H.; Merino, J.
2008-01-01
The influence of short-range Coulomb correlations on the Mott transition in the single-band Hubbard model at half-filling is studied within cellular dynamical mean field theory for square and triangular lattices. Finite-temperature exact diagonalization is used to investigate correlations within two-, three-, and four-site clusters. Transforming the non-local self-energy from a site basis to a molecular orbital basis, we focus on the inter-orbital charge transfer between these cluster molecul...
Exact Bond-Located Spin Ground State in the Hubbard Chain with Off-Diagonal Coulomb Interactions
Itoh, Kazuhito; Nakamura, Masaaki; Muramoto, Norihiro
2001-01-01
We show the existence of an exact ground state in certain parameter regimes of one-dimensional half-filled extended Hubbard model with site-off-diagonal interactions. In this ground state, the bond-located spin correlation exhibits a long-range order. In the case when the spin space is SU(2) symmetric, this ground state degenerates with higher spin states including a fully ferromagnetic state. We also discuss the relation between the exact bond-ordered ground state and the critical bond-spin-...
Directory of Open Access Journals (Sweden)
Tao Zhou
2015-01-01
Full Text Available Recently it was revealed that the whole Fermi surface is fully gapped for several families of underdoped cuprates. The existence of the finite energy gap along the d-wave nodal lines (nodal gap contrasts the common understanding of the d-wave pairing symmetry, which challenges the present theories for the high-Tc superconductors. Here we propose that the incommensurate diagonal spin-density-wave order can account for the above experimental observation. The Fermi surface and the local density of states are also studied. Our results are in good agreement with many important experiments in high-Tc superconductors.
de Leon, J. Ponce
2001-01-01
We consider a version of Kaluza-Klein theory where the cylinder condition is not imposed. The metric is allowed to have explicit dependence on the "extra" coordinate(s). This is the usual scenario in brane-world and space-time-matter theories. We extend the usual discussion by considering five-dimensional metrics with off-diagonal terms. We replace the condition of cylindricity by the requirement that physics in four-dimensional space-time should remain invariant under changes of coordinates ...
Energy Technology Data Exchange (ETDEWEB)
Lucht, P.H.
1977-11-01
The t less than 0 multiperipheral formalism of Ciafaloni, DeTar, Misheloff, Mueller, Muzinich and Yesian is reviewed, extended, and applied to the ordered S-matrix whose ring amplitudes comprise the zeroth level of the topological expansion. Toller M-function notation is used throughout. The bootstrap and cylinder problems are formulated in terms of a well defined helicity pole propagator; a definition of the complete twisted Reggeon loop, which appears in the one-twist term of the cylinder, is given as a helicity pole expansion. Some consideration is given to the following subjects: diagonalization, naturality, threshold behavior, Regge cuts, and complex helicity.
Analysis of MG-SIP algorithm in solving large-scaled nine-diagonal linear equation set
International Nuclear Information System (INIS)
In order to deal with the problem of nine-diagonal linear equation set which was commonly existed in heat conduction in circular cylindrical coordinates, a new algorithm by combining SIP (strong implicit procedure) and MG (MultiGrid) method was studied. The new algorithm was realized with computer code and its features such as the speed and accuracy in solving actual problems were discussed by analyzing the relationship between these features and some related parameters and comparing with some representative algorithms of today. The results show that this algorithm has an advantage in the speed of solving in terms of problems with high mesh density. (authors)
International Nuclear Information System (INIS)
We study the finite-temperature expectation values of exponential fields in the sine-Gordon model. Using finite-volume regularization, we give a low-temperature expansion of such quantities in terms of the connected diagonal matrix elements, for which we provide explicit formulas. For special values of the exponent, computations by other methods are available and used to validate our findings. Our results can also be interpreted as a further support for a previous conjecture about the connection between finite- and infinite-volume form factors valid up to terms exponentially decaying in the volume
Directory of Open Access Journals (Sweden)
Ma Bao-Li
2013-09-01
Full Text Available In this work, we investigate the trajectory tracking and point stabilization problems of asymmetric underactuated surface ships with non-diagonal inertia and damping matrices. By combining the novel state and input transformations, the direct Lyapunov approach, and the nonlinear time-varying tools, the trajectory tracking controller is derived, guaranteeing global κ-exponential convergence of state trajectory to the reference one satisfying mild persistent exciting conditions. By properly designing the reference trajectory, the proposed tracking scheme is also generalized to achieve global uniform asymptotic point stabilization. Simulation examples are given to illustrate the effectiveness of the proposed control schemes.
International Nuclear Information System (INIS)
Recently it was revealed that the whole Fermi surface is fully gapped for several families of underdoped cuprates. The existence of the finite energy gap along the d-wave nodal lines (nodal gap) contrasts the common understanding of the d-wave pairing symmetry, which challenges the present theories for the high-Tc superconductors. Here we propose that the incommensurate diagonal spin-density-wave order can account for the above experimental observation. The Fermi surface and the local density of states are also studied. Our results are in good agreement with many important experiments in high-Tc superconductors
Sacroiliac joint pain - aftercare
The sacroiliac joint (SIJ) is a term used to describe the place where the sacrum and the iliac bones join. The ... The main purpose of the joint is to connect the spine and the pelvis. As a result, there is very little movement at the SIJ. Major reasons ...
International Nuclear Information System (INIS)
The paper presents the progress report of the Joint European Torus (JET) Joint Undertaking, 1986. The report contains a survey of the scientific and technical achievements on JET during 1986; the more important articles referred to in this survey are reproduced as appendices to this Report. The last section discusses developments which might improve the overall performance of the machine. (U.K.)
Appleberry, W. T.
1978-01-01
Modified crowned-spline joint is lightweight, durable, and requires minimum of parts. It does not use rubber cushions to limit play and is useful over wide temperature range. It has inner ball and socket to provide rigid connection with no axial play. Joint can be adapted to form pinned connection between segmented torque tubes.
An Approximation Ratio for Biclustering
Puolamäki, Kai; Hanhijärvi, Sami; Garriga, Gemma C
2007-01-01
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on the rows and on the columns of the input matrix. We show that such a solution yields a worst-case approximation ratio of 1+sqrt(2) under L1-norm for 0-1 valued matrices, and of 2...
An Approximation Ratio for Biclustering
Puolamäki, Kai; Garriga, Gemma C
2007-01-01
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on the rows and on the columns of the input matrix. We show that such a solution yields a worst-case approximation ratio of 1+sqrt(2) under L1-norm for 0-1 valued matrices, and of 2 under L2-norm for real valued matrices.
Shearlets and Optimally Sparse Approximations
DEFF Research Database (Denmark)
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations of...... provide optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an...
MR diagnosis of temporomandibular joint. A study of joint effusion
Energy Technology Data Exchange (ETDEWEB)
Kaneda, Takashi; Yamashiro, Mitsuaki; Ozawa, Kaoru; Suzuki, Hiromi; Okada, Hiroyuki; Yamamoto, Hirotsugu [Nihon Univ., Matsudo, Chiba (Japan). School of Dentistry
1998-03-01
The purposes of this study were to evaluate the relationship between correlation of MR joint effusion of the temporomandibular joint and disk position, to evaluate the relationship between joint effusion and aging, and to assess the frequency of MR joint effusion of bilateral temporomandibular joints. The temporomandibular joints of 192 patients with clinical symptoms of temporomandibular joint disorders were imaged bilaterally using high field, surface-coil MR imaging. Oblique sagittal and coronal proton density-weighted and T2-weighted images were obtained. Imaging findings of joint effusion were correlated with disk position, aging, and bilateral temporomandibular joints. MR showed effusion in 4% of the joints with normal superior disk position, 36% of the joints with disk displacement with reduction, and 45% of the joints with disk displacement without reduction. There were significant differences in the incidence of joint effusion between normal disk position and anterior disk displacement with or without reduction. Younger patients less than 40 years were significant higher the incidence of joint effusion than those of older patients. A significant association was seen between joint effusion and aging. MR showed effusion in 17% of the unilateral temporomandibular joint, 24% of the bilateral temporomandibular joints. There was no significant difference between unilateral and bilateral case. These results indicated that joint effusion using MR imaging was associated with varied temporomandibular joint pathologic states. (author)
MR diagnosis of temporomandibular joint. A study of joint effusion
International Nuclear Information System (INIS)
The purposes of this study were to evaluate the relationship between correlation of MR joint effusion of the temporomandibular joint and disk position, to evaluate the relationship between joint effusion and aging, and to assess the frequency of MR joint effusion of bilateral temporomandibular joints. The temporomandibular joints of 192 patients with clinical symptoms of temporomandibular joint disorders were imaged bilaterally using high field, surface-coil MR imaging. Oblique sagittal and coronal proton density-weighted and T2-weighted images were obtained. Imaging findings of joint effusion were correlated with disk position, aging, and bilateral temporomandibular joints. MR showed effusion in 4% of the joints with normal superior disk position, 36% of the joints with disk displacement with reduction, and 45% of the joints with disk displacement without reduction. There were significant differences in the incidence of joint effusion between normal disk position and anterior disk displacement with or without reduction. Younger patients less than 40 years were significant higher the incidence of joint effusion than those of older patients. A significant association was seen between joint effusion and aging. MR showed effusion in 17% of the unilateral temporomandibular joint, 24% of the bilateral temporomandibular joints. There was no significant difference between unilateral and bilateral case. These results indicated that joint effusion using MR imaging was associated with varied temporomandibular joint pathologic states. (author)
Reconstruction of diagonal elements of density matrix using maximum likelihood estimation
International Nuclear Information System (INIS)
The data of the experiment of Schiller et al., Physic Letters 77(1996), are alternatively evaluated using the maximum likelihood estimation. The given data are fitted better than by the standard deterministic approach. Nevertheless, the data are fitted equally well by a whole family of states. Standard deterministic predictions correspond approximately to the envelope of these maximum likelihood solutions. (author)
Approximation properties of basis functions in variational three-body problem
Vanyashin, V S
2000-01-01
A new variational basis with well-behaved local approximation properties and multiple output is proposed for Coulomb systems. The trial function has proper behaviour at all Coulomb centres. Nonlinear asymptotic parameters are introduced softly: they do not destroy the self-optimized local behaviour of the wave function at vanishing interparticle distances. The diagonalization of the Hamiltonian on a finite Hilbert subspace gives a number of meaningful eigenvalues. Thus together with the ground state some excited states are also reliably approximated. For three-body systems all matrix elements are analytically obtainable up to rational functions of asymptotic parameters. The feasibility of the new basis usage has been proved by a pilot computer algebra calculation. The negative sign of an electron pair local energy at their Coulomb centre has been revealed. PACS number: 31.15.Pf
A Reduced Order, One Dimensional Model of Joint Response
Energy Technology Data Exchange (ETDEWEB)
DOHNER,JEFFREY L.
2000-11-06
As a joint is loaded, the tangent stiffness of the joint reduces due to slip at interfaces. This stiffness reduction continues until the direction of the applied load is reversed or the total interface slips. Total interface slippage in joints is called macro-slip. For joints not undergoing macro-slip, when load reversal occurs the tangent stiffness immediately rebounds to its maximum value. This occurs due to stiction effects at the interface. Thus, for periodic loads, a softening and rebound hardening cycle is produced which defines a hysteretic, energy absorbing trajectory. For many jointed sub-structures, this hysteretic trajectory can be approximated using simple polynomial representations. This allows for complex joint substructures to be represented using simple non-linear models. In this paper a simple one dimensional model is discussed.
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante
Truthful approximations to range voting
DEFF Research Database (Denmark)
Filos-Ratsika, Aris; Miltersen, Peter Bro
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare maximi...
Analytical Approximations to Galaxy Clustering
Mo, H. J.
1997-01-01
We discuss some recent progress in constructing analytic approximations to the galaxy clustering. We show that successful models can be constructed for the clustering of both dark matter and dark matter haloes. Our understanding of galaxy clustering and galaxy biasing can be greatly enhanced by these models.
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
2013-01-01
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and
Approximation by Penultimate Stable Laws
L.F.M. de Haan (Laurens); L. Peng (Liang); H. Iglesias Pereira
1997-01-01
textabstractIn certain cases partial sums of i.i.d. random variables with finite variance are better approximated by a sequence of stable distributions with indices \\\\alpha_n \\\\to 2 than by a normal distribution. We discuss when this happens and how much the convergence rate can be improved by using
Approximation properties of haplotype tagging
Directory of Open Access Journals (Sweden)
Dreiseitl Stephan
2006-01-01
Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.
Low Rank Approximation in $G_0W_0$ Approximation
Shao, Meiyue; Yang, Chao; Liu, Fang; da Jornada, Felipe H; Deslippe, Jack; Louie, Steven G
2016-01-01
The single particle energies obtained in a Kohn--Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The $G_0W_0$ approximation is a widely used technique in which the self energy is expressed as the convolution of a non-interacting Green's function ($G_0$) and a screened Coulomb interaction ($W_0$) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating $W_0$ at multiple frequencies. In this paper, we discuss how the cos...
Vašátko, Jiří; Munzar, Dominik
2016-03-01
The influence of Zn and Ni impurities on the normal-state pseudogap of underdoped high-Tc cuprate superconductors is studied using exact diagonalization of effective t -J -like Hamiltonians describing low energy electronic excitations of the CuO2 plane with some of the copper ions replaced with Zn/Ni. The Ni case Hamiltonian has been obtained by a sequence of approximations from a more complete model involving Cu 3 d , Ni 3 d , and O 2 p orbitals. Our main findings are: (i) The width ΩPG of the pseudogap occurring in the many body density of states, and manifesting itself also in the c -axis infrared conductivity, decreases with increasing Zn concentration as a consequence of a suppression of short range spin correlations. (ii) In the case of one hole and one Ni impurity, the hole is—for realistic values of the model parameters—weakly bound to the Ni site. This causes a slight increase of ΩPG with respect to the pure case. (iii) Based on this result and further results for 1-2 holes and 1-2 Ni impurities, we suggest that in the real Ni substituted CuO2 plane ΩPG is larger than in the pure case due to the binding of the doped holes to the Ni sites and effective underdoping. Our findings clarify the trends observed in the c -axis infrared conductivity data of Zn and Ni substituted (Sm,Nd)Ba2Cu3O7 -δ crystals.
International Nuclear Information System (INIS)
A new method, mixed diagonalization, is introduced in which an effective Hamiltonian operator acting on a reduced dimensional space is constructed using the similarity transformations of canonical Van Vleck perturbation theory (CVPT). This construction requires the characterization of modes into two categories, global and local, which in the bound vibrational problem are tantamount to the large and small amplitude vibrations, respectively. The local modes in the Hamiltonian are projected out by CVPT, and the resulting Hamiltonian operator acts only on the space of global modes. The method affords the treatment of energy levels of bound systems in which some vibrational assignments are possible. In addition, it systematically provides a reduced dimensional Hamiltonian which is more amenable to exact numerical solution than the original full-dimensional Hamiltonian. In recent work, a semiclassical transition state theory (SCTST) rate expression has been written in terms of a Hamiltonian operator parameterized by the imaginary action along the local reaction path in the transition state region [Chem. Phys. Lett. 214, 129 (1993)]. We show that the Hamiltonian constructed by mixed diagonalization has this form, and can be used to obtain more accurate semiclassical rate expressions
International Nuclear Information System (INIS)
We describe a scheme for efficient large-scale electronic-structure calculations based on the combination of the pole expansion and selected inversion (PEXSI) technique with the SIESTA method, which uses numerical atomic orbitals within the Kohn–Sham density functional theory (KSDFT) framework. The PEXSI technique can efficiently utilize the sparsity pattern of the Hamiltonian and overlap matrices generated in SIESTA, and for large systems it has a much lower computational complexity than that associated with the matrix diagonalization procedure. The PEXSI technique can be used to evaluate the electron density, free energy, atomic forces, density of states and local density of states without computing any eigenvalue or eigenvector of the Kohn–Sham Hamiltonian. It can achieve accuracy fully comparable to that obtained from a matrix diagonalization procedure for general systems, including metallic systems at low temperature. The PEXSI method is also highly scalable. With the recently developed massively parallel PEXSI technique, we can make efficient use of more than 10 000 processors on high performance machines. We demonstrate the performance and accuracy of the SIESTA-PEXSI method using several examples of large scale electronic structure calculations, including 1D, 2D and bulk problems with insulating, semi-metallic, and metallic character. (paper)
Côrtes, A.M.A.
2015-02-20
The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and pointwise divergence-free. When applied to discretized Stokes equations, these spaces generate a symmetric and indefinite saddle-point linear system. Krylov subspace methods are usually the most efficient procedures to solve such systems. One of such methods, for symmetric systems, is the Minimum Residual Method (MINRES). However, the efficiency and robustness of Krylov subspace methods is closely tied to appropriate preconditioning strategies. For the discrete Stokes system, in particular, block-diagonal strategies provide efficient preconditioners. In this article, we compare the performance of block-diagonal preconditioners for several block choices. We verify how the eigenvalue clustering promoted by the preconditioning strategies affects MINRES convergence. We also compare the number of iterations and wall-clock timings. We conclude that among the building blocks we tested, the strategy with relaxed inner conjugate gradients preconditioned with incomplete Cholesky provided the best results.
Approximate Matching of Hierarchial Data
DEFF Research Database (Denmark)
Augsten, Nikolaus
formally proof that the pq-gram index can be incrementally updated based on the log of edit operations without reconstructing intermediate tree versions. The incremental update is independent of the data size and scales to a large number of changes in the data. We introduce windowed pq-grams for the......-gram based distance between streets, introduces a global greedy matching that guarantees stable pairs, and links addresses that are stored with different granularity. The connector has been successfully tested with public administration databases. Our extensive experiments on both synthetic and real world......The goal of this thesis is to design, develop, and evaluate new methods for the approximate matching of hierarchical data represented as labeled trees. In approximate matching scenarios two items should be matched if they are similar. Computing the similarity between labeled trees is hard as in...
Approximate Privacy: Foundations and Quantification
Feigenbaum, Joan; Schapira, Michael
2009-01-01
Increasing use of computers and networks in business, government, recreation, and almost all aspects of daily life has led to a proliferation of online sensitive data about individuals and organizations. Consequently, concern about the privacy of these data has become a top priority, particularly those data that are created and used in electronic commerce. There have been many formulations of privacy and, unfortunately, many negative results about the feasibility of maintaining privacy of sensitive data in realistic networked environments. We formulate communication-complexity-based definitions, both worst-case and average-case, of a problem's privacy-approximation ratio. We use our definitions to investigate the extent to which approximate privacy is achievable in two standard problems: the second-price Vickrey auction and the millionaires problem of Yao. For both the second-price Vickrey auction and the millionaires problem, we show that not only is perfect privacy impossible or infeasibly costly to achieve...
Hydrogen: Beyond the Classic Approximation
International Nuclear Information System (INIS)
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Concentration Bounds for Stochastic Approximations
Frikha, Noufel
2012-01-01
We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic time and its empirical mean obtained by the Monte-Carlo procedure. We then give some estimates concerning the deviation between the value at a given time-step of a stochastic approximation algorithm and its target. Under suitable assumptions both concentration bounds turn out to be Gaussian. The key tool consists in exploiting accurately the concentration properties of the increments of the schemes. For the first case, as opposed to the previous work of Lemaire and Menozzi (EJP, 2010), we do not have any systematic bias in our estimates. Also, no specific non-degeneracy conditions are assumed.
Waveless Approximation Theories of Gravity
Isenberg, J A
2007-01-01
The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability -- are associated with the presence of gravitational waves. We have developed a number of ``waveless approximation theories'' (WAT) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.
On Approximability of Block Sorting
Narayanaswamy, N S
2011-01-01
Block Sorting is a well studied problem, motivated by its applications in Optical Character Recognition (OCR), and Computational Biology. Block Sorting has been shown to be NP-Hard, and two separate polynomial time 2-approximation algorithms have been designed for the problem. But questions like whether a better approximation algorithm can be designed, and whether the problem is APX-Hard have been open for quite a while now. In this work we answer the latter question by proving Block Sorting to be Max-SNP-Hard (APX-Hard). The APX-Hardness result is based on a linear reduction of Max-3SAT to Block Sorting. We also provide a new lower bound for the problem via a new parametrized problem k-Block Merging.
Approximating Metal-Insulator Transitions
Danieli, C.; Rayanov, K.; Pavlov, B.; Martin, G.; Flach, S
2014-01-01
We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We propose an iterative construction of quasiperiodic potentials from sequences of potentials with increasing spatial period. At each finite iteration step the eigenstates reflect the properties of the limiting quasiperiodic potential properties up to a controlled maximum system size. We then observe approximate metal-insulator transitions (MIT) at the finite iteration steps. We also report evidence on mobility ed...
Saddlepoint approximations to option prices
Rogers, L. C. G.; Zane, O.
1999-01-01
The use of saddlepoint approximations in statistics is a well-established technique for computing the distribution of a random variable whose moment generating function is known. In this paper, we apply the methodology to computing the prices of various European-style options, whose returns processes are not the Brownian motion with drift assumed in the Black-Scholes paradigm. Through a number of examples, we show that the methodology is generally accurate and fast.
Approximate maximizers of intricacy functionals
Buzzi, Jerome; Zambotti, Lorenzo
2009-01-01
G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the neural complexity of a family of random variables. This functional is a special case of intricacy, i.e., an average of the mutual information of subsystems whose weights have good mathematical properties. Moreover, its maximum value grows at a definite speed with the size of the system. In this work, we compute exactly this speed of growth by building "approximate maximizers" subject to an entropy condition. These appr...
Stochastic approximation algorithms and applications
Kushner, Harold J
1997-01-01
In recent years algorithms of the stochastic approximation type have found applications in new and diverse areas, and new techniques have been developed for proofs of convergence and rate of convergence. The actual and potential applications in signal processing have exploded. New challenges have arisen in applications to adaptive control. This book presents a thorough coverage of the ODE method used to analyze these algorithms.
Quantum Tunneling Beyond Semiclassical Approximation
Banerjee, Rabin; Majhi, Bibhas Ranjan
2008-01-01
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black h...
Approximate quantum and acoustic cloaking
Greenleaf, Allan; Lassas, Matti; Uhlmann, Gunther
2008-01-01
At any energy E > 0, we construct a sequence of bounded potentials $V^E_{n}, n\\in\\N$, supported in an annular region $B_{out}\\setminus B_{inn}$ in three-space, which act as approximate cloaks for solutions of Schr\\"odinger's equation: For any potential $V_0\\in L^\\infty(B_{inn})$ such that E is not a Neumann eigenvalue of $-\\Delta+V_0$ in $B_{inn}$, the scattering amplitudes $a_{V_0+V_n^E}(E,\\theta,\\omega)\\to 0$ as $n\\to\\infty$. The $V^E_{n}$ thus not only form a family of approximately transparent potentials, but also function as approximate invisibility cloaks in quantum mechanics. On the other hand, for $E$ close to interior eigenvalues, resonances develop and there exist {\\it almost trapped states} concentrated in $B_{inn}$. We derive the $V_n^E$ from singular, anisotropic transformation optics-based cloaks by a de-anisotropization procedure, which we call \\emph{isotropic transformation optics}. This technique uses truncation, inverse homogenization and spectral theory to produce nonsingular, isotropic app...
Computer Experiments for Function Approximations
Energy Technology Data Exchange (ETDEWEB)
Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C
2007-10-15
This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.
Product Approximation of Grade and Precision
Institute of Scientific and Technical Information of China (English)
ZHANG Xian-yong; MO Zhi-wen
2005-01-01
The normal graded approximation and variable precision approximation are defined in approximate space. The relationship between graded approximation and variable precision approximation is studied, and an important formula of conversion between them is achieved. The product approximation of gradeand precision is defined and its basic properties are studied.
Federal Laboratory Consortium — The Joint Quantum Institute (JQI) is pursuing that goal through the work of leading quantum scientists from the Department of Physics of the University of Maryland...
... Working It Out: Common Techniques for Conflict Resolution Workplace Diversity & Team Performance CME & MOC Understanding MOC ACR's MOC ... infection is suspected, aspirating the joint to gather cultures is ... Communications and Marketing. This patient information is provided for ...
... Therapist? Media Find a Hand Surgeon MP Joint Arthritis Email to a friend * required fields From * To * ... in to name and customize your collection. DESCRIPTION Arthritis is the wearing away of the cartilage at ...
... may have problems with infection, loosening, or even dislocation of the new hip joint. Over time the artificial ... Professor, Chief, Sports Medicine and Shoulder Service, UCSF Department of Orthopaedic Surgery, San Francisco, ...
Temporomandibular Joint Disorder
... 2008 Previous Next Related Articles: Temporomandibular Joint Disorder (TMD) Are You Biting Off More Than You Can Chew? Equilibration May Lessen TMD Pain Fender-benders: Source of TMD? First Comes ...
... dietary supplements, such as green tea and various vitamins, to see if they can keep your joints ... body, such as your ears, nose, and windpipe. Fibromyalgia (fi-bro-my-AL-juh). A condition that ...
Johnson, Ellsworth K.; Paton, Bryan H.; Threat, Edward W.; Haptonstall, Lisa A.
2005-01-01
The purpose of this Master of Business Administration (MBA) Professional Report is to investigate and analyze the means by which Contingency Contracting Officers (CCO) can effectively operate in a Joint contingency environment and to validate the Defense Contract Management Agency's (DCMA) entry and exit criteria for contingency contracting missions. Joint contingencies encompass regional conflicts, humanitarian and peacekeeping missions, and international or domestic disaster relief missions...
Joint Aspiration: Arthrocentesis
Mackie, John William
1987-01-01
Joint aspiration is an easily mastered procedure used to confirm or rule out joint sepsis and crystal-induced arthrosis. It is routinely performed with or without local anaesthetic, or with cooling spray. The time spent obtaining the fluid is short. The procedure is safe, requiring no hospitalization, except in the case of diagnosed sepsis. Arthrocentesis is a necessary procedure to prove beyond reasonable doubt that infection is not the cause of the arthritis. The family physician must be fa...
Pimentel, Dinarco
2015-01-01
Joint Venture contracts are contracting models typically designed to reach international markets. In spite of being used at the national level, a joint venture is based on single or multiple contracts between two individuals, two institutions, two organizations or two different entrepreneurial entities joining forces, meeting synergies to reach a common goal.Initially, these types of contracts were justifiable based on the need of different economic agents penetrating the most inaccessible ma...
A symptomatic coracoclavicular joint.
Cheung, T F S; Boerboom, A L; Wolf, R F E; Diercks, R L
2006-11-01
Bilateral coracoclavicular joints were found in a 44-year-old male patient following a fall. He had an Indonesian mother and a Dutch father. Prior to the injury he was asymptomatic and had full range of movement in both shoulders but the trauma resulted in pain and limitation of movement in the left shoulder which required resection of the anomalous joint, after which full pain-free movement was restored. PMID:17075101
Rotation-vibrational states of H3+ and the adiabatic approximation.
Alijah, Alexander; Hinze, Juergen
2006-11-15
We discuss recent progress in the calculation and identification of rotation-vibrational states of H3+ at intermediate energies up to 13,000 cm(-1). Our calculations are based on the potential energy surface of Cencek et al. which is of sub-microhartree accuracy. As this surface includes diagonal adiabatic and relativistic corrections to the fixed nuclei electronic energies, the remaining discrepancies between our calculated and experimental data should be due to the neglect of non-adiabatic coupling to excited electronic states in the calculations. To account for this, our calculated energy values were adjusted empirically by a simple correction formula. Based on our understanding of the adiabatic approximation, we suggest two new approaches to account for the off-diagonal adiabatic correction, which should work; however, they have not been tested yet for H3+. Theoretical predictions made for the above-barrier energy region of recent experimental interest are accurate to 0.35 cm(-1) or better. PMID:17015396
Joint discrete universality of Hurwitz zeta functions
Laurinčikas, A.
2014-11-01
We obtain a joint discrete universality theorem for Hurwitz zeta functions. Here the parameters of zeta functions and the step of shifts of these functions approximating a given family of analytic functions are connected by some condition of linear independence. Nesterenko's theorem gives an example satisfying this condition. The universality theorem is applied to estimate the number of zeros of a linear combination of Hurwitz zeta functions. Bibliography: 20 titles.
José Roberto Ortale; José Meciano Filho; Ana Maria Ferreira Paccola; Júlia Guedes Pereira Garcia Leal; Carolina Alves Scaranari
2005-01-01
OBJETIVO: O objetivo deste trabalho é a descrição dos ramos lateral, diagonal e ântero-superior, no tecido adiposo epicárdico do ventrículo esquerdo, e a análise da freqüência e do diâmetro destes, conforme o tipo de circulação coronariana. O conhecimento preciso desses ramos tem aplicabilidade na abordagem cirúrgica para a sua revascularização ou durante a injeção de substâncias cardioplégicas nos mesmos. MÉTODO: Dissecados 50 corações obtidos de necropsias de adultos, fixados em solução de ...