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
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
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
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
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.
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
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
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.
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
''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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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.
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
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
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, ...
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
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
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
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.
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.)
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.)
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
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.
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
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
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.
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
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
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
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
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
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
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
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
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
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.)
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
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
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...
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
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
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
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
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
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
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...