Energy Technology Data Exchange (ETDEWEB)
Voss, L.
1986-01-01
The accuracy can be improved, and the risk of complications can be reduced in the case of cytodiagnostic lung puncture, if one optimises the method whereby the puncture needle is inserted into the lesion. The author describes such a procedure incorporating the use of technical aids for marking the exact puncture point of the cannula. At the same time the procedure results in a reduction of radiation exposure of both doctor and patient.
Exact and useful optimization methods for microeconomics
Balder, E.J.
2011-01-01
This paper points out that the treatment of utility maximization in current textbooks on microeconomic theory is deficient in at least three respects: breadth of coverage, completeness-cum-coherence of solution methods and mathematical correctness. Improvements are suggested in the form of a
Improved exact method for the double TSP with multiple stacks
DEFF Research Database (Denmark)
Lusby, Richard Martin; Larsen, Jesper
2011-01-01
The Double TSP with Multiple Stacks is a logistics problem where one must, using a container, transport a given number of orders from a set of pickup customers to a set of delivery customers at minimum cost. Each order corresponds to the movement of one pallet, all pickups must be completed before...... the first delivery, and the container cannot be repacked once packed. In this paper we improve the previously proposed exact method of Lusby et al. (Int Trans Oper Res 17 (2010), 637–652) through an additional preprocessing technique that uses the longest common subsequence between the respective pickup...... and delivery problems. The results suggest an impressive improvement, and we report, for the first time, optimal solutions to several unsolved instances from the literature containing 18 customers. Instances with 28 customers are also shown to be solvable within a few percent of optimality. © 2011 Wiley...
The functional variable method for finding exact solutions of some ...
Indian Academy of Sciences (India)
Abstract. In this paper, we implemented the functional variable method and the modified. Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled. KdV system. This method is extremely simple ...
A new type of descent conjugate gradient method with exact line search
Hajar, Nurul; Mamat, Mustafa; Rivaie, Mohd.; Jusoh, Ibrahim
2016-06-01
Nowadays, conjugate gradient (CG) methods are impressive for solving nonlinear unconstrained optimization problems. In this paper, a new CG method is proposed and analyzed. This new CG method satisfies descent condition and its global convergence is established using exact line search. Numerical results show that this new CG method substantially outperforms the previous CG methods. This new CG method is considered robust, efficient and provided faster and stable convergence.
Path Following in the Exact Penalty Method of Convex Programming.
Zhou, Hua; Lange, Kenneth
2015-07-01
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.
Exact Methods for Solving the Train Departure Matching Problem
DEFF Research Database (Denmark)
Haahr, Jørgen Thorlund; Bull, Simon Henry
In this paper we consider the train departure matching problem which is an important subproblem of the Rolling Stock Unit Management on Railway Sites problem introduced in the ROADEF/EURO Challenge 2014. The subproblem entails matching arriving train units to scheduled departing trains at a railway...... site while respecting multiple physical and operational constraints. In this paper we formally define that subproblem, prove its NP- hardness, and present two exact method approaches for solving the problem. First, we present a compact Mixed Integer Program formulation which we solve using a MIP solver...
Exact extraction method for road rutting laser lines
Hong, Zhiming
2018-02-01
This paper analyzes the importance of asphalt pavement rutting detection in pavement maintenance and pavement administration in today's society, the shortcomings of the existing rutting detection methods are presented and a new rutting line-laser extraction method based on peak intensity characteristic and peak continuity is proposed. The intensity of peak characteristic is enhanced by a designed transverse mean filter, and an intensity map of peak characteristic based on peak intensity calculation for the whole road image is obtained to determine the seed point of the rutting laser line. Regarding the seed point as the starting point, the light-points of a rutting line-laser are extracted based on the features of peak continuity, which providing exact basic data for subsequent calculation of pavement rutting depths.
Exact rebinning methods for three-dimensional PET.
Liu, X; Defrise, M; Michel, C; Sibomana, M; Comtat, C; Kinahan, P; Townsend, D
1999-08-01
The high computational cost of data processing in volume PET imaging is still hindering the routine application of this successful technique, especially in the case of dynamic studies. This paper describes two new algorithms based on an exact rebinning equation, which can be applied to accelerate the processing of three-dimensional (3-D) PET data. The first algorithm, FOREPROJ, is a fast-forward projection algorithm that allows calculation of the 3-D attenuation correction factors (ACF's) directly from a two-dimensional (2-D) transmission scan, without first reconstructing the attenuation map and then performing a 3-D forward projection. The use of FOREPROJ speeds up the estimation of the 3-D ACF's by more than a factor five. The second algorithm, FOREX, is a rebinning algorithm that is also more than five times faster, compared to the standard reprojection algorithm (3DRP) and does not suffer from the image distortions generated by the even faster approximate Fourier rebinning (FORE) method at large axial apertures. However, FOREX is probably not required by most existing scanners, as the axial apertures are not large enough to show improvements over FORE with clinical data. Both algorithms have been implemented and applied to data simulated for a scanner with a large axial aperture (30 degrees), and also to data acquired with the ECAT HR and the ECAT HR+ scanners. Results demonstrate the excellent accuracy achieved by these algorithms and the important speedup when the sinogram sizes are powers of two.
On the integration of image sources in exact image method of field analysis
Lindell, I. V.
1988-01-01
Convergence conditions of image integration in the exact image method of field calculation have been investigated, and the method is extended to include more general media than previously considered. It is demonstrated that the integral is well behaved and the method works best when the field is calculated in a medium with less loss. If the medium has more loss, it is shown that the image line may enter the improper half-space and still produce valid results. Means of correctly selecting the integration path branch for the case of crossing branch cuts of the Green function in complex integration planes are proposed.
Exactly Embedded Wavefunction Methods for Characterizing Nitrogen Reduction Catalysis
2015-01-15
two in preparation: • “A simple, exact density-functional-theory embedding scheme,” F. R. Manby, M. Stella , J. D. Goodpaster, and T. F. Miller III, J...and Kaito Miyamoto (U. Bristol / Toyota Co.). Miller, FA9550-11-1-0288 Final Report - 5 [1] F. R. Manby, M. Stella , J. D. Goodpaster, and T. F. Miller
Multishell method: Exact treatment of a cluster in an effective medium
International Nuclear Information System (INIS)
Gonis, A.; Garland, J.W.
1977-01-01
A method is presented for the exact determination of the Green's function of a cluster embedded in a given effective medium. This method, the multishell method, is applicable even to systems with off-diagonal disorder, extended-range hopping, multiple bands, and/or hybridization, and is computationally practicable for any system described by a tight-binding or interpolation-scheme Hamiltonian. It allows one to examine the effects of local environment on the densities of states and site spectral weight functions of disordered systems. For any given analytic effective medium characterized by a non-negative density of states the method yields analytic cluster Green's functions and non-negative site spectral weight functions. Previous methods used for the calculation of the Green's function of a cluster embedded in a given effective medium have not been exact. The results of numerical calculations for model systems show that even the best of these previous methods can lead to substantial errors, at least for small clusters in two- and three-dimensional lattices. These results also show that fluctuations in local environment have large effects on site spectral weight functions, even in cases in which the single-site coherent-potential approximation yields an accurate overall density of states
A new conjugate gradient method and its global convergence under the exact line search
Omer, Osman; Rivaie, Mohd; Mamat, Mustafa; Abdalla, Awad
2014-12-01
The conjugate gradient methods are numerously used for solving nonlinear unconstrained optimization problems, especially of large scale. Their wide applications are due to their simplicity and low memory requirement. To analyze conjugate gradient methods, two types of line searches are used; exact and inexact. In this paper, we present a new method of nonlinear conjugate gradient methods under the exact line search. The theoretical analysis shows that the new method generates a descent direction in each iteration and globally convergent under the exact line search. Moreover, numerical experiments based on comparing the new method with other well known conjugate gradient methods show that the new is efficient for some unconstrained optimization problems.
The quasi-exactly solvable potentials method applied to the three-body problem
International Nuclear Information System (INIS)
Chafa, F.; Chouchaoui, A.; Hachemane, M.; Ighezou, F.Z.
2007-01-01
The quasi-exactly solved potentials method is used to determine the energies and the corresponding exact eigenfunctions for three families of potentials playing an important role in the description of interactions occurring between three particles of equal mass. The obtained results may also be used as a test in evaluating the performance of numerical methods
The functional variable method for finding exact solutions of some ...
Indian Academy of Sciences (India)
solvers and aids in the stability analysis of solutions. In the past few years, many new approaches to nonlinear equations were proposed to search for solitary solutions, among which the variational iteration method [3–7], the homotopy perturbation method [8–12], parameter-expansion method [13–15], the variational method ...
Exact methods for time constrained routing and related scheduling problems
DEFF Research Database (Denmark)
Kohl, Niklas
1995-01-01
, Desrosiers and Solomon (1992) who were able to solve 50 of the problems, and Halse (1992) who solved 33. The main reason for the success of the algorithm is the exploitation of valid inequalities. The increase in speed of computers since 1992 play only a minor role. In the last part of the dissertation...... application of valid inequalities on the VRPTW. The algorithm developed represents a major step forward in terms of computational ability to solve the VRPTW. Solutions to a large number of previously unsolved problems are reported....... can be improved further by incorporation of valid inequalities . We show how this can be done computationally and we introduce a number of valid inequalities for the VRPTW. Finally we present a number of strategies, primarily branch-and-bound, to obtain integer solutions. In the computational part...
Exact solution of some linear matrix equations using algebraic methods
Djaferis, T. E.; Mitter, S. K.
1977-01-01
A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.
Exact Group Sequential Methods for Estimating a Binomial Proportion
Directory of Open Access Journals (Sweden)
Zhengjia Chen
2013-01-01
Full Text Available We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, we establish the uniform controllability of coverage probability and the asymptotic optimality for such a family of sampling schemes. Our theoretical results establish the possibility that the parameters of this family of sampling schemes can be determined so that the prescribed level of confidence is guaranteed with little waste of samples. Analytic bounds for the cumulative distribution functions and expectations of sample numbers are derived. Moreover, we discuss the inherent connection of various sampling schemes. Numerical issues are addressed for improving the accuracy and efficiency of computation. Computational experiments are conducted for comparing sampling schemes. Illustrative examples are given for applications in clinical trials.
Multiuser detection and channel estimation: Exact and approximate methods
DEFF Research Database (Denmark)
Fabricius, Thomas
2003-01-01
propose here to use accurate approximations borrowed from statistical mechanics and machine learning. These give us various algorithms that all can be formulated in a subtractive interference cancellation formalism. The suggested algorithms can e ectively be seen as bias corrections to standard...... subtractive interference cancellation with hyperbolic tangent tentative decision device, in statistical mechanics and machine learning called the naive mean field approach. The differences between the proposed algorithms lie in how the bias is estimated/approximated. We propose approaches based on a second...... analysis of the convexity and bifurcations of the naive mean field free energy and optima. This proves that we can avoid local minima by tracking a global convex solution into the non-convex region, effectively avoiding error propagation. This method is in statistical physics denoted mean field annealing...
Astronavigation a method for determining exact position by the stars
Zischka, K A
2018-01-01
This book acts as a manual for the ancient methods of navigating by the stars, which continue to provide the sailor or pilot with a timeless means of determining location. Despite the prevalence of GPS, a comprehensive set of formulae that can be evaluated on any inexpensive scientific calculator in the event of a catastrophic software or systems failure is a vital failsafe. It also serves as a living link to centuries of explorers from centuries past. Beginning with the basics of positional astronomy, this guide moves on to the more complex math necessary to understand the ephemerides, tables showing the future positions of the stars and planets. These astronomical almanacs were the satellite navigation of their day. The objective of this book is twofold: to provide the reader with a concise, comprehensible manual on positional astronomy as it applies to astro-navigation and to furnish the concise algorithms for finding the position of the Sun and various navigational stars at any given instant. In a worl...
Structures in the Universe by Exact Methods: Formation, Evolution, Interactions
Bolejko, Krzysztof; Krasiński, Andrzej; Hellaby, Charles; Célérier, Marie-Noëlle
2009-10-01
As the structures in our Universe are mapped out on ever larger scales, and with increasing detail, the use of inhomogeneous models is becoming an essential tool for analyzing and understanding them. This book reviews a number of important developments in the application of inhomogeneous solutions of Einstein's field equations to cosmology. It shows how inhomogeneous models can be employed to study the evolution of structures such as galaxy clusters and galaxies with central black holes, and to account for cosmological observations like supernovae dimming, the cosmic microwave background, baryon acoustic oscillations or the dependence of the Hubble parameter on redshift within classical general relativity. Whatever 'dark matter' and 'dark energy' turn out to be, inhomogeneities exist on many scales and need to be investigated with all appropriate methods. This book is of great value to all astrophysicists and researchers working in cosmology, from graduate students to academic researchers. - Presents inhomogeneous cosmological models, allowing readers to familiarise themselves with basic properties of these models - Shows how inhomogeneous models can be used to analyse cosmological observations such as supernovae, cosmic microwave background, and baryon acoustic oscillations - Reviews important developments in the application of inhomogeneous solutions of Einstein's field equations to cosmology
Simo, J. C.; Posbergh, T. A.; Marsden, J. E.
1990-01-01
This paper develops and applies the energy-momentum method to the problem of nonlinear stability of relative equilibria. The method is applied in detail to the stability analysis of uniformly rotating states of geometrically exact rod models, and a rigid body with an attached flexible appendage. Here, the flexible appendage is modeled as a geometrically exact rod capable of accommodating arbitrarily large deformations in three dimensions; including extension, shear, flexure and twist. The mod...
Ghani, N. H. A.; Mohamed, N. S.; Zull, N.; Shoid, S.; Rivaie, M.; Mamat, M.
2017-09-01
Conjugate gradient (CG) method is one of iterative techniques prominently used in solving unconstrained optimization problems due to its simplicity, low memory storage, and good convergence analysis. This paper presents a new hybrid conjugate gradient method, named NRM1 method. The method is analyzed under the exact and inexact line searches in given conditions. Theoretically, proofs show that the NRM1 method satisfies the sufficient descent condition with both line searches. The computational result indicates that NRM1 method is capable in solving the standard unconstrained optimization problems used. On the other hand, the NRM1 method performs better under inexact line search compared with exact line search.
The exact solutions of nonlinear problems by Homotopy Analysis Method (HAM
Directory of Open Access Journals (Sweden)
Hafiz Abdul Wahab
2016-06-01
Full Text Available The present paper presents the comparison of analytical techniques. We establish the existence of the phenomena of the noise terms in the perturbation series solution and find the exact solution of the nonlinear problems. If the noise terms exist, the Homotopy Analysis method gives the same series solution as in Adomian Decomposition Method as well as homotopy Perturbation Method (Wahab et al, 2015 and we get the exact solution using the initial guess in Homotopy Analysis Method using the results obtained by Adomian Decomposition Method.
Directory of Open Access Journals (Sweden)
Özkan Güner
2014-01-01
Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.
Directory of Open Access Journals (Sweden)
Ji Juan-Juan
2017-01-01
Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.
Short overview of PSA quantification methods, pitfalls on the road from approximate to exact results
International Nuclear Information System (INIS)
Banov, Reni; Simic, Zdenko; Sterc, Davor
2014-01-01
Over time the Probabilistic Safety Assessment (PSA) models have become an invaluable companion in the identification and understanding of key nuclear power plant (NPP) vulnerabilities. PSA is an effective tool for this purpose as it assists plant management to target resources where the largest benefit for plant safety can be obtained. PSA has quickly become an established technique to numerically quantify risk measures in nuclear power plants. As complexity of PSA models increases, the computational approaches become more or less feasible. The various computational approaches can be basically classified in two major groups: approximate and exact (BDD based) methods. In recent time modern commercially available PSA tools started to provide both methods for PSA model quantification. Besides availability of both methods in proven PSA tools the usage must still be taken carefully since there are many pitfalls which can drive to wrong conclusions and prevent efficient usage of PSA tool. For example, typical pitfalls involve the usage of higher precision approximation methods and getting a less precise result, or mixing minimal cuts and prime implicants in the exact computation method. The exact methods are sensitive to selected computational paths in which case a simple human assisted rearrangement may help and even switch from computationally non-feasible to feasible methods. Further improvements to exact method are possible and desirable which opens space for a new research. In this paper we will show how these pitfalls may be detected and how carefully actions must be done especially when working with large PSA models. (authors)
Electrostatics of a Point Charge between Intersecting Planes: Exact Solutions and Method of Images
Mei, W. N.; Holloway, A.
2005-01-01
In this work, the authors present a commonly used example in electrostatics that could be solved exactly in a conventional manner, yet expressed in a compact form, and simultaneously work out special cases using the method of images. Then, by plotting the potentials and electric fields obtained from these two methods, the authors demonstrate that…
New exact solutions of coupled Boussinesq–Burgers equations by Exp-function method
Directory of Open Access Journals (Sweden)
L.K. Ravi
2017-03-01
Full Text Available In the present paper, we build the new analytical exact solutions of a nonlinear differential equation, specifically, coupled Boussinesq–Burgers equations by means of Exp-function method. Then, we analyze the results by plotting the three dimensional soliton graphs for each case, which exhibit the simplicity and effectiveness of the proposed method. The primary purpose of this paper is to employ a new approach, which allows us victorious and efficient derivation of the new analytical exact solutions for the coupled Boussinesq–Burgers equations.
An exactly conservative particle method for one dimensional scalar conservation laws
International Nuclear Information System (INIS)
Farjoun, Yossi; Seibold, Benjamin
2009-01-01
A particle scheme for scalar conservation laws in one space dimension is presented. Particles representing the solution are moved according to their characteristic velocities. Particle interaction is resolved locally, satisfying exact conservation of area. Shocks stay sharp and propagate at correct speeds, while rarefaction waves are created where appropriate. The method is variation diminishing, entropy decreasing, exactly conservative, and has no numerical dissipation away from shocks. Solutions, including the location of shocks, are approximated with second order accuracy. Source terms can be included. The method is compared to CLAWPACK in various examples, and found to yield a comparable or better accuracy for similar resolutions.
Construction of exact solutions to a family of wave equations by the functional variable method
Zerarka, A.; Ouamane, S.; Attaf, A.
2011-02-01
The method developed in this work uses an alternative functional variable method to construct exact travelling solutions to a class of nonlinear wave equations. It is shown that it is possible to obtain by a direct treatment the general solutions to some important nonlinear model equations which arise in a wide variety of physical problems. We have also presented some interesting typical examples to illustrate the application of this method.
An FDTD method with FFT-accelerated exact absorbing boundary conditions
Sirenko, Kostyantyn
2011-07-01
An accurate and efficient finite-difference time-domain (FDTD) method for analyzing axially symmetric structures is presented. The method achieves its accuracy and efficiency using exact absorbing conditions (EACs) for terminating the computation domain and a blocked-FFT based scheme for accelerating the computation of the temporal convolutions present in non-local EACs. The method is shown to be especially useful in characterization of long-duration resonant wave interactions. © 2011 IEEE.
A new convergent conjugate gradient method under the exact line search
Omer, Osman; Mamat, Mustafa; Rivaie, Mohd
2015-05-01
Conjugate gradient methods are widely used for unconstrained optimization problems, especially large scale problems. That is, for its simplicity, low memory requirement, and global convergence properties. In this paper, we study the global convergence properties of a new conjugate gradient method under the exact line search. Under some assumptions, the proofs of the sufficient descent property and the global convergence are given. The numerical results show that our new method is efficient for some unconstrained optimization problems.
International Nuclear Information System (INIS)
Chen Yong; Wang Qi; Li Biao
2005-01-01
Based on a new general ansatz and a general subepuation, a new general algebraic method named elliptic equation rational expansion method is devised for constructing multiple travelling wave solutions in terms of rational special function for nonlinear evolution equations (NEEs). We apply the proposed method to solve Whitham-Broer-Kaup equation and explicitly construct a series of exact solutions which include rational form solitary wave solution, rational form triangular periodic wave solutions and rational wave solutions as special cases. In addition, the links among our proposed method with the method by Fan [Chaos, Solitons and Fractals 2004;20:609], are also clarified generally
International Nuclear Information System (INIS)
Zhang Huiqun
2009-01-01
By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.
Directory of Open Access Journals (Sweden)
Zayed El-Sayed Mohamed El-Sayed
2016-01-01
Full Text Available The generalized Kudryashov method is applied in this article for finding the exact solutions of nonlinear partial differential equations (PDEs in mathematical physics. Solitons and other solutions are given. To illustrate the validity of this method, we apply it to three nonlinear PDEs, namely, the diffusive predator-prey system, the nonlinear Bogoyavlenskii equations and the nonlinear telegraph equation. These equations are related to signal analysis for transmission and propagation of electrical signals. As a result, many analytical exact solutions of these equations are obtained including symmetrical Fibonacci function solutions and hyperbolic function solutions. Physical explanations for some solutions of the given three nonlinear PDEs are obtained. Comparison our new results with the well-known results are given.
A comparative study of three new conjugate gradient methods with exact line search
Hamoda, Mohamed; Rivaie, Mohd; Abshar, Abdelrhaman; Mamat, Mustafa
2015-10-01
Conjugate Gradient methods play an important role in solving unconstrained optimization, especially for large scale problems. In this paper, we compared the performance profile of the classical conjugate gradient coefficients FR, PRP with three new βk. These three new βk possess global convergence properties using the exact line search. Preliminary numerical results show that the three new βk are very promising and efficient when compared to CG coefficients FR, PRP.
Construction of exact solutions to the modified forms of DP and CH equations by analytical methods
Directory of Open Access Journals (Sweden)
Jalil Manafian Heris
2015-11-01
Full Text Available In this work, we establish the exact solutions to the modified forms of Degasperis–Procesi (DP and Camassa–Holm (CH equations. The generalized (G’/G-expansion and generalized tanh-coth methods were used to construct solitary wave solutions of nonlinear evolution equations. The generalized (G’/G-expansion method presents a wider applicability for handling nonlinear wave equations. It is shown that the (G’/G-expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
Exact solution to the Coulomb wave using the linearized phase-amplitude method
Directory of Open Access Journals (Sweden)
Shuji Kiyokawa
2015-08-01
Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.
International Nuclear Information System (INIS)
Zekri, L.; Zekri, N.; Bouamrane, R.
1999-10-01
We present a new numerical method for determining exactly the effective conductivity and the local field for random RLC networks. This method is compared to a real space renormalization group method and the Frank and Lobb method. Although our method is slower than the Frank and Lobb method, it also computes exactly the local field for large size systems. We also show that the renormalization group method fails in determining the local field. (author)
The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2018-02-01
Full Text Available In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.
Meleshko, Sergey V
2005-01-01
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
A fast exact simulation method for a class of Markov jump processes.
Li, Yao; Hu, Lili
2015-11-14
A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.
Exact traveling wave solutions to the Klein–Gordon equation using the novel (G′/G-expansion method
Directory of Open Access Journals (Sweden)
M.G. Hafez
2014-01-01
Full Text Available The novel (G′/G-expansion method is one of the powerful methods that appeared in recent times for establishing exact traveling wave solutions of nonlinear partial differential equations. Exact traveling wave solutions in terms of hyperbolic, trigonometric and rational functions to the cubic nonlinear Klein–Gordon equation via this method are obtained in this article. The efficiency of this method for finding exact solutions and traveling wave solutions has been demonstrated. It is shown that the novel (G′/G-expansion method is a simple and valuable mathematical tool for solving nonlinear evolution equations (NLEEs in applied mathematics, mathematical physics and engineering.
Exact traveling wave solutions to the Klein-Gordon equation using the novel (G‧/G)-expansion method
Hafez, M. G.; Alam, Md. Nur; Akbar, M. Ali
The novel (G‧/G)-expansion method is one of the powerful methods that appeared in recent times for establishing exact traveling wave solutions of nonlinear partial differential equations. Exact traveling wave solutions in terms of hyperbolic, trigonometric and rational functions to the cubic nonlinear Klein-Gordon equation via this method are obtained in this article. The efficiency of this method for finding exact solutions and traveling wave solutions has been demonstrated. It is shown that the novel (G‧/G)-expansion method is a simple and valuable mathematical tool for solving nonlinear evolution equations (NLEEs) in applied mathematics, mathematical physics and engineering.
de Klerk, Etienne; Glineur, Francois; Taylor, Adrien
2016-01-01
We consider the gradient (or steepest) descent method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-case rate of convergence of this scheme, and show that this worst-case behavior is exhibited by a certain convex
de Klerk, Etienne; Glineur, Francois; Taylor, Adrien
2017-01-01
We consider the gradient (or steepest) descent method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-case rate of convergence of this scheme, and show that this worst-case behavior is exhibited by a certain convex
An efficient method to calculate the aggregated isotopic distribution and exact center-masses.
Claesen, Jürgen; Dittwald, Piotr; Burzykowski, Tomasz; Valkenborg, Dirk
2012-04-01
In this article, we present a computation- and memory-efficient method to calculate the probabilities of occurrence and exact center-masses of the aggregated isotopic distribution of a molecule. The method uses fundamental mathematical properties of polynomials given by the Newton-Girard theorem and Viete's formulae. The calculation is based on the atomic composition of the molecule and the natural abundances of the elemental isotopes in normal terrestrial matter. To evaluate the performance of the proposed method, which we named BRAIN, we compare it with the results obtained from five existing software packages (IsoPro, Mercury, Emass, NeutronCluster, and IsoDalton) for 10 biomolecules. Additionally, we compare the computed mass centers with the results obtained by calculating, and subsequently aggregating, the fine isotopic distribution for two of the exemplary biomolecules. The algorithm will be made available as a Bioconductor package in R, and is also available upon request.
Discretization error estimation and exact solution generation using the method of nearby problems.
Energy Technology Data Exchange (ETDEWEB)
Sinclair, Andrew J. (Auburn University Auburn, AL); Raju, Anil (Auburn University Auburn, AL); Kurzen, Matthew J. (Virginia Tech Blacksburg, VA); Roy, Christopher John (Virginia Tech Blacksburg, VA); Phillips, Tyrone S. (Virginia Tech Blacksburg, VA)
2011-10-01
The Method of Nearby Problems (MNP), a form of defect correction, is examined as a method for generating exact solutions to partial differential equations and as a discretization error estimator. For generating exact solutions, four-dimensional spline fitting procedures were developed and implemented into a MATLAB code for generating spline fits on structured domains with arbitrary levels of continuity between spline zones. For discretization error estimation, MNP/defect correction only requires a single additional numerical solution on the same grid (as compared to Richardson extrapolation which requires additional numerical solutions on systematically-refined grids). When used for error estimation, it was found that continuity between spline zones was not required. A number of cases were examined including 1D and 2D Burgers equation, the 2D compressible Euler equations, and the 2D incompressible Navier-Stokes equations. The discretization error estimation results compared favorably to Richardson extrapolation and had the advantage of only requiring a single grid to be generated.
Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations
Zhi, Longxiao; Gu, Hanming
2018-03-01
The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.
Statistical Physics Methods Provide the Exact Solution to a Long-Standing Problem of Genetics
Samal, Areejit; Martin, Olivier C.
2015-06-01
Analytic and computational methods developed within statistical physics have found applications in numerous disciplines. In this Letter, we use such methods to solve a long-standing problem in statistical genetics. The problem, posed by Haldane and Waddington [Genetics 16, 357 (1931)], concerns so-called recombinant inbred lines (RILs) produced by repeated inbreeding. Haldane and Waddington derived the probabilities of RILs when considering two and three genes but the case of four or more genes has remained elusive. Our solution uses two probabilistic frameworks relatively unknown outside of physics: Glauber's formula and self-consistent equations of the Schwinger-Dyson type. Surprisingly, this combination of statistical formalisms unveils the exact probabilities of RILs for any number of genes. Extensions of the framework may have applications in population genetics and beyond.
Directory of Open Access Journals (Sweden)
E Ghasemikhah
2012-03-01
Full Text Available This study investigated the electronic properties of antiferromagnetic UBi2 metal by using ab initio calculations based on the density functional theory (DFT, employing the augmented plane waves plus local orbital method. We used the exact exchange for correlated electrons (EECE method to calculate the exchange-correlation energy under a variety of hybrid functionals. Electric field gradients (EFGs at the uranium site in UBi2 compound were calculated and compared with the experiment. The EFGs were predicted experimentally at the U site to be very small in this compound. The EFG calculated by the EECE functional are in agreement with the experiment. The densities of states (DOSs show that 5f U orbital is hybrided with the other orbitals. The plotted Fermi surfaces show that there are two kinds of charges on Fermi surface of this compound.
An implicit enumeration method for an exact test of weighted kappa.
Brusco, Michael J; Stahl, Stephanie; Steinley, Douglas
2008-11-01
The kappa coefficient is one of the most widely used measures for evaluating the agreement between two raters asked to assign N objects to one of K nominal categories. Weighted versions of kappa enable partial credit to be awarded for near agreement, most notably in the case of ordinal categories. An exact significance test for weighted kappa can be conducted by enumerating all rater agreement tables with the same fixed marginal frequencies as the observed table, and accumulating the probabilities for all tables that produce a weighted kappa index that is greater than or equal to the observed measure. Unfortunately, complete enumeration of all tables is computationally unwieldy for modest values of N and K. We present an implicit enumeration algorithm for conducting an exact test of weighted kappa, which can be applied to tables of non-trivial size. The algorithm is particularly efficient for 'good' to 'excellent' values of weighted kappa that typically have very small p-values. Therefore, our method is beneficial for situations where resampling tests are of limited value because the number of trials needed to estimate the p-value tends to be large.
Subramanian, Ramanathan Vishnampet Ganapathi
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvement. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs. Such methods have enabled sensitivity analysis and active control of turbulence at engineering flow conditions by providing gradient information at computational cost comparable to that of simulating the flow. They accelerate convergence of numerical design optimization algorithms, though this is predicated on the availability of an accurate gradient of the discretized flow equations. This is challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. We analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space--time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge--Kutta-like scheme
de Klerk, Etienne; Glineur, François; Taylor, Adrien B.
2016-01-01
We consider the gradient (or steepest) descent method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-case rate of convergence of this scheme, and show that this worst-case behavior is exhibited by a certain convex quadratic function. We also give the tight worst-case complexity bound for a noisy variant of gradient descent method, where exact line-search is performed in a search direction that differs from negative...
Naeimi, Ghasem; Alipour, Samira; Khademi, Siamak
2016-01-01
Recently, the master equations for the interaction of two-mode photons with a three-level Λ-type atom are exactly solved for the coherence terms. In this paper the exact absorption spectrum is applied for the presentation of a non-demolition photon counting method, for a few number of coupling photons, and its benefits are discussed. The exact scheme is also applied where the coupling photons are squeezed and the photon counting method is also developed for the measurement of the squeezing parameter of the coupling photons.
DFT-SAPT intermolecular interaction energies employing exact-exchange Kohn-Sham response methods.
Hesselmann, Andreas
2018-03-22
Intermolecular interaction energies have been calculated by symmetry-adapted perturbation theory based on density-functional theory monomer properties (DFT-SAPT) employing response functions from time-dependent exact-exchange (TDEXX) kernels. Combined with a new asymptotic correction scheme for the xc potentials of the monomers, it is shown that this DFT-SAPT[TDEXX] method delivers highly accurate intermolecular interaction energies for the S22, S66 and IonHB benchmark data bases by Hobza et al.. A corresponding DFT-SAPT approach employing the adiabatic TDEXX kernel in the response calculations has also been tested. While exhibiting a similar performance than DFT-SAPT[TDEXX] for dispersion-dominated dimer systems, it was found found that the accuracies of the interaction energies for hydrogen-bonded dimers deteriorate with this DFT-SAPT[ATDEXX] method. Compared to this, the DFT-SAPT[TDEXX] yields a balanced description of the interaction energies for various interaction-type motifs, similar to the standard DFT-SAPT method that utilises the ALDA xc kernel to compute the response functions.
Exact solutions of the dirac equation for an electron in magnetic field with shape invariant method
International Nuclear Information System (INIS)
Setare, M.R.; Hatami, O.
2008-01-01
Based on the shape invariance property we obtain exact solutions of the Virac equation for an electron moving in the presence of a certain varying magnetic Geld, then we also show its non-relativistic limit. (authors)
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2017-11-01
Full Text Available In this article, a variety of solitary wave solutions are observed for microtubules (MTs. We approach the problem by treating the solutions as nonlinear RLC transmission lines and then find exact solutions of Nonlinear Evolution Equations (NLEEs involving parameters of special interest in nanobiosciences and biophysics. We determine hyperbolic, trigonometric, rational and exponential function solutions and obtain soliton-like pulse solutions for these equations. A comparative study against other methods demonstrates the validity of the technique that we developed and demonstrates that our method provides additional solutions. Finally, using suitable parameter values, we plot 2D and 3D graphics of the exact solutions that we observed using our method. Keywords: Analytical method, Exact solutions, Nonlinear evolution equations (NLEEs of microtubules, Nonlinear RLC transmission lines
Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G′/G-Expansion Method
Directory of Open Access Journals (Sweden)
Muhammad Shakeel
2014-01-01
Full Text Available The fractional derivatives are used in the sense modified Riemann-Liouville to obtain exact solutions for BBM-Burger equation of fractional order. This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. The performance of the method is reliable, useful, and gives newer general exact solutions with more free parameters than the existing methods. Numerical results coupled with the graphical representation completely reveal the trustworthiness of the method.
International Nuclear Information System (INIS)
Abdolsalami, F.; Abdolsalami, M.; Perez, L.; Gomez, P.
1995-01-01
The authors have applied the finite-element method to electron-molecule collision with the exchange effect implemented rigorously. All the calculations are done in the body-frame within the fixed-nuclei approximation, where the exact treatment of exchange as a nonlocal effect results in a set of coupled integro-differential equations. The method is applied to e-H 2 and e-N 2 scatterings and the cross sections obtained are in very good agreement with the corresponding results the authors have generated from the linear-algebraic approach. This confirms the significant difference observed between their results generated by linear-algebraic method and the previously published e-N 2 cross sections. Their studies show that the finite-element method is clearly superior to the linear-algebraic approach in both memory usage and CPU time especially for large systems such as e-N 2 . The system coefficient matrix obtained from the finite-element method is often sparse and smaller in size by a factor of 12 to 16, compared to the linear-algebraic technique. Moreover, the CPU time required to obtain stable results with the finite-element method is significantly smaller than the linear-algebraic approach for one incident electron energy. The usage of computer resources in the finite-element method can even be reduced much further when (1) scattering calculations involving multiple electron energies are performed in one computer run and (2) exchange, which is a short range effect, is approximated by a sparse matrix. 17 refs., 7 figs., 5 tabs
Exact method for numerically analyzing a model of local denaturation in superhelically stressed DNA
International Nuclear Information System (INIS)
Fye, R.M.; Benham, C.J.
1999-01-01
Local denaturation, the separation at specific sites of the two strands comprising the DNA double helix, is one of the most fundamental processes in biology, required to allow the base sequence to be read both in DNA transcription and in replication. In living organisms this process can be mediated by enzymes which regulate the amount of superhelical stress imposed on the DNA. We present a numerically exact technique for analyzing a model of denaturation in superhelically stressed DNA. This approach is capable of predicting the locations and extents of transition in circular superhelical DNA molecules of kilobase lengths and specified base pair sequences. It can also be used for closed loops of DNA which are typically found in vivo to be kilobases long. The analytic method consists of an integration over the DNA twist degrees of freedom followed by the introduction of auxiliary variables to decouple the remaining degrees of freedom, which allows the use of the transfer matrix method. The algorithm implementing our technique requires O(N 2 ) operations and O(N) memory to analyze a DNA domain containing N base pairs. However, to analyze kilobase length DNA molecules it must be implemented in high precision floating point arithmetic. An accelerated algorithm is constructed by imposing an upper bound M on the number of base pairs that can simultaneously denature in a state. This accelerated algorithm requires O(MN) operations, and has an analytically bounded error. Sample calculations show that it achieves high accuracy (greater than 15 decimal digits) with relatively small values of M (M<0.05N) for kilobase length molecules under physiologically relevant conditions. Calculations are performed on the superhelical pBR322 DNA sequence to test the accuracy of the method. With no free parameters in the model, the locations and extents of local denaturation predicted by this analysis are in quantitatively precise agreement with in vitro experimental measurements
Sirenko, Kostyantyn
2013-07-01
Exact absorbing and periodic boundary conditions allow to truncate grating problems\\' infinite physical domains without introducing any errors. This work presents exact absorbing boundary conditions for 3D diffraction gratings and describes their discretization within a high-order time-domain discontinuous Galerkin finite element method (TD-DG-FEM). The error introduced by the boundary condition discretization matches that of the TD-DG-FEM; this results in an optimal solver in terms of accuracy and computation time. Numerical results demonstrate the superiority of this solver over TD-DG-FEM with perfectly matched layers (PML)-based domain truncation. © 2013 IEEE.
The exact realisation of the Lanczos method for a quantum many-body system
International Nuclear Information System (INIS)
Witte, N.S.
1997-01-01
The Lanczos process has been analytically and exactly carried out for the spin 1/2 isotropic XY chain in the thermodynamic limit, yielding a form for the Lanczos coefficient β 2 (s). This coefficient has a monotonic variation for real positive s and confirms a general theorem on the ground state properties of extensive Many-body Systems. The Taylor expansion of the coefficient about s = 0 has a finite radius of convergence, and ground state estimates based on a finite truncation of this are shown to be asymptotic
Raslan, K. R.; EL-Danaf, Talaat S.; Ali, Khalid K.
2017-07-01
In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.
International Nuclear Information System (INIS)
Raslan, K. R.; Ali, Khalid K.; EL-Danaf, Talaat S.
2017-01-01
In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels. (paper)
Directory of Open Access Journals (Sweden)
Jiang Ying
2017-01-01
Full Text Available In this work, we study the (2+1-D Broer-Kaup equation. The composite periodic breather wave, the exact composite kink breather wave and the solitary wave solutions are obtained by using the coupled degradation technique and the consistent Riccati expansion method. These results may help us to investigate some complex dynamical behaviors and the interaction between composite non-linear waves in high dimensional models
Zayed, E. M. E.; Hoda, S. A.; Arnous, Ibrahim A. H.
2013-10-01
In this paper, the functional variable method is proposed to seek the exact solutions of some nonlinear evolution equations. The validity and advantages of the proposed method is illustrated by the applications to the Asymmetric Nizhnik-Novikov-Vesselov equation, the breaking soliton equation, the Nizhnik-Novikov-Vesselov equation and the Painlevé integrable Burgers equations, which play an important role in mathematical physics. It is shown that the proposed method provides a very effective and powerful tool for solving nonlinear evolution equations.
Mohamed, Nur Syarafina; Mamat, Mustafa; Rivaie, Mohd
2016-11-01
Conjugate gradient (CG) methods are one of the tools in optimization. Due to its low computational memory requirement, this method is used in solving several of nonlinear unconstrained optimization problems from designs, economics, physics and engineering. In this paper, a new modification of CG family coefficient (βk) is proposed and posses global convergence under exact line search direction. Numerical experimental results based on the number of iterations and central processing unit (CPU) time show that the new βk performs better than some other well known CG methods under some standard test functions.
International Nuclear Information System (INIS)
Li Liang; Chen Zhiqiang; Xing Yuxiang; Zhang Li; Kang Kejun; Wang Ge
2006-01-01
In recent years, image reconstruction methods for cone-beam computed tomography (CT) have been extensively studied. However, few of these studies discussed computing parallel-beam projections from cone-beam projections. In this paper, we focus on the exact synthesis of complete or incomplete parallel-beam projections from cone-beam projections. First, an extended central slice theorem is described to establish a relationship between the Radon space and the Fourier space. Then, data sufficiency conditions are proposed for computing parallel-beam projection data from cone-beam data. Using these results, a general filtered backprojection algorithm is formulated that can exactly synthesize parallel-beam projection data from cone-beam projection data. As an example, we prove that parallel-beam projections can be exactly synthesized in an angular range in the case of circular cone-beam scanning. Interestingly, this angular range is larger than that derived in the Feldkamp reconstruction framework. Numerical experiments are performed in the circular scanning case to verify our method
Rotational degree-of-freedom synthesis: An optimised finite difference method for non-exact data
Gibbons, T. J.; Öztürk, E.; Sims, N. D.
2018-01-01
Measuring the rotational dynamic behaviour of a structure is important for many areas of dynamics such as passive vibration control, acoustics, and model updating. Specialist and dedicated equipment is often needed, unless the rotational degree-of-freedom is synthesised based upon translational data. However, this involves numerically differentiating the translational mode shapes to approximate the rotational modes, for example using a finite difference algorithm. A key challenge with this approach is choosing the measurement spacing between the data points, an issue which has often been overlooked in the published literature. The present contribution will for the first time prove that the use of a finite difference approach can be unstable when using non-exact measured data and a small measurement spacing, for beam-like structures. Then, a generalised analytical error analysis is used to propose an optimised measurement spacing, which balances the numerical error of the finite difference equation with the propagation error from the perturbed data. The approach is demonstrated using both numerical and experimental investigations. It is shown that by obtaining a small number of test measurements it is possible to optimise the measurement accuracy, without any further assumptions on the boundary conditions of the structure.
An Exact Method to Determine the Conductivity of Aqueous Solutions in Acid-Base Titrations
Directory of Open Access Journals (Sweden)
Norma Rodríguez-Laguna
2015-01-01
Full Text Available Several works in the literature show that it is possible to establish the analytic equations to estimate the volume V of a strong base or a strong acid (Vb and Va, resp. being added to a solution of a substance or a mix of substances during an acid-base titration, as well as the equations to estimate the first derivative of the titration plot dpH/dV, and algebraic expressions to determine the buffer β capacity with dilution βdil. This treatment allows establishing the conditions of thermodynamic equilibria for all species within a system containing a mix of species from one or from various polyacid systems. The present work shows that it is possible to determine exactly the electric conductivity of aqueous solutions for these Brønsted acid-base titrations, because the functional relation between this property and the composition of the system in equilibrium is well known; this is achieved using the equivalent conductivity λi values of each of the ions present in a given system. The model employed for the present work confirms the experimental outcomes with the H2SO4, B(OH3, CH3COOH, and H3PO4 aqueous solutions’ titration.
A New Lagrangian Relaxation Method Considering Previous Hour Scheduling for Unit Commitment Problem
Khorasani, H.; Rashidinejad, M.; Purakbari-Kasmaie, M.; Abdollahi, A.
2009-08-01
Generation scheduling is a crucial challenge in power systems especially under new environment of liberalization of electricity industry. A new Lagrangian relaxation method for unit commitment (UC) has been presented for solving generation scheduling problem. This paper focuses on the economical aspect of UC problem, while the previous hour scheduling as a very important issue is studied. In this paper generation scheduling of present hour has been conducted by considering the previous hour scheduling. The impacts of hot/cold start-up cost have been taken in to account in this paper. Case studies and numerical analysis presents significant outcomes while it demonstrates the effectiveness of the proposed method.
International Nuclear Information System (INIS)
Ma Songhua; Fang Jianping; Zheng Chunlong
2009-01-01
By means of an extended mapping method and a variable separation method, a series of solitary wave solutions, periodic wave solutions and variable separation solutions to the (2 + 1)-dimensional breaking soliton system is derived.
Sakamoto, Hiroki; Yamamoto, Toshihiro
2017-09-01
This paper presents improvement and performance evaluation of the "perturbation source method", which is one of the Monte Carlo perturbation techniques. The formerly proposed perturbation source method was first-order accurate, although it is known that the method can be easily extended to an exact perturbation method. A transport equation for calculating an exact flux difference caused by a perturbation is solved. A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system. The source term of the transport equation is defined by the unperturbed flux and the cross section (or optical parameter) changes. The unperturbed flux is provided by an "on-the-fly" technique during the course of the ordinary fixed source calculation for the unperturbed system. A set of perturbation particle is started at the collision point in the perturbed region and tracked until death. For a perturbation in a smaller portion of the whole domain, the efficiency of the perturbation source method can be improved by using a virtual scattering coefficient or cross section in the perturbed region, forcing collisions. Performance is evaluated by comparing the proposed method to other Monte Carlo perturbation methods. Numerical tests performed for a particle transport in a two-dimensional geometry reveal that the perturbation source method is less effective than the correlated sampling method for a perturbation in a larger portion of the whole domain. However, for a perturbation in a smaller portion, the perturbation source method outperforms the correlated sampling method. The efficiency depends strongly on the adjustment of the new virtual scattering coefficient or cross section.
Coley, Alan
2010-05-01
In this book the use of inhomogeneous models in cosmology, both in modelling structure formation and interpreting cosmological observations, is discussed. The authors concentrate on exact solutions, and particularly the Lemaitre-Tolman (LT) and Szekeres models (the important topic of averaging is not discussed). The book serves to demonstrate that inhomogeneous metrics can generate realistic models of cosmic structure formation and nonlinear evolution and shows that general relativity has a lot more to offer to cosmology than just the standard spatially homogeneous FLRW model. I would recommend this book to people working in theoretical cosmology. In the introduction (and in the concluding chapter and throughout the book) a reasonable discussion of the potential problems with the standard FLRW cosmology is presented, and a list of examples illustrating the limitations of standard FLRW cosmology are discussed (including potential problems with perturbation methods). In particular, the authors argue that the assumptions of isotropy and spatial homogeneity (and consequently the Copernican principle) must be properly challenged and revisited. Indeed, it is possible for `good old general relativity' to be used to explain cosmological observations without introducing speculative elements. In part I of the book the necessary background is presented (readers need a background in general relativity theory at an advanced undergraduate or graduate level). There is a good (and easy to read) review of the exact spherically symmetric dust Lemaitre-Tolman model (LT) (often denoted the LTB model) and the Lemaitre and Szekeres models. Light propogation (i.e. null geodesics, for both central and off-center observers) in exact inhomogeneous (LT) models is reviewed. In part II a number of applications of exact inhomogeneous models are presented (taken mainly from the authors' own work). In chapter 4, the evolution of exact inhomogeneous models (primarily the LT model, but also the
Weatherford, C. A.; Onda, K.; Temkin, A.
1985-01-01
The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.
Zedan, Hassan A.; Barakati, W.; Hamad, Nada
2013-01-01
We introduce two powerful methods to solve the Davey-Stewartson equations: one is the homotopy perturbation method (HPM) and the other is the homotopy analysis method (HAM). HAM is a strong and easy to use analytic tool for nonlinear problems. Comparison of the HPM results with the HAM results, and compute the absolute errors between the exact solutions of the DS equations with the HPM solutions and HAM solutions are obtained.
National Research Council Canada - National Science Library
Mitchell, Jason
2002-01-01
A method is presented for the generation of exact numerical coefficients found in two families of implicit Chebyshev methods for the numerical integration of first- and second-order ordinary differential equations...
Exact and approximate interior corner problem in neutron diffusion by integral transform methods
Energy Technology Data Exchange (ETDEWEB)
Bareiss, E.H.; Chang, K.S.J.; Constatinescu, D.A.
1976-09-01
The mathematical solution of the neutron diffusion equation exhibits singularities in its derivatives at material corners. A mathematical treatment of the nature of these singularities and its impact on coarse network approximation methods in computational work is presented. The mathematical behavior is deduced from Green's functions, based on a generalized theory for two space dimensions, and the resulting systems of integral equations, as well as from the Kontorovich--Lebedev Transform. The effect on numerical calculations is demonstrated for finite difference and finite element methods for a two-region corner problem.
Pinski, Peter; Neese, Frank
2018-01-01
Electron correlation methods based on pair natural orbitals (PNOs) have gained an increasing degree of interest in recent years, as they permit energy calculations to be performed on systems containing up to many hundred atoms, while maintaining chemical accuracy for reaction energies. We present an approach for taking exact analytical first derivatives of the energy contributions in the simplest method of the family of Domain-based Local Pair Natural Orbital (DLPNO) methods, closed-shell DLPNO-MP2. The Lagrangian function contains constraints to account for the relaxation of PNOs. RI-MP2 reference geometries are reproduced accurately, as exemplified for four systems with a substantial degree of nonbonding interactions. By the example of electric field gradients, we demonstrate that omitting PNO-specific constraints can lead to dramatic errors for orbital-relaxed properties.
Simo, J. C.; Posbergh, T. A.; Marsden, J. E.
1990-10-01
This paper develops and applies the energy-momentum method to the problem of nonlinear stability of relative equilibria. The method is applied in detail to the stability of uniformily rotating states of geometrically exact rod models, and a rigid body with an attached flexible appendage. Here, the flexible appendage is modeled as a geometrically exact rod capable of accomodating arbitrarily large deformations in three dimensions; including extension, shear, flexure and twist. The model is said to be ‘geometrically exact’ because of the lack of restrictions of the allowable deformations, and the full invariance properties of the model under superposed rigid body motions. We show that a (sharp) necessary condition for nonlinear stability is that the whole assemblage be in uniform (stationary) rotation about the shortest axis of a precisely defined ‘locked’ inertia dyadic. Sufficient conditions are obtained by appending the restriction that the angular velocity of the stationary motion be bounded from above by the square root of the minimum eigenvalue of an associated linear operator. Specific examples are worked out, including the case of a rod attached to a rigid body in uniform rotation. Our technique depends crucially on a special choice of variables, introduced in this paper and referred to as the block diagonalization procedure, in which the second variation of the energu augmented with the linear and angular momentum block diagonalizes, separating the rotational from the internal vibration modes.
Applications of algebraic method to exactly solve some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)]. E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)]. E-mail: aramady@yahoo.com
2007-08-15
A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear evolution equations is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDE's) are obtained. Graphs of the solutions are displayed.
Exact Travelling Wave Solutions for Isothermal Magnetostatic Atmospheres by Fan Subequation Method
Directory of Open Access Journals (Sweden)
Hossein Jafari
2012-01-01
ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is carried out. These equations transform to a single nonlinear elliptic equation for the magnetic vector potential . This equation depends on an arbitrary function of that must be specified. With choices of the different arbitrary functions, we obtain analytical solutions of elliptic equation using the Fan subequation method.
International Nuclear Information System (INIS)
Zeger, J.
1993-01-01
Organized criminals also tried to illegally transfer nuclear material through Austria. Two important questions have to be answered after the material is sized by police authorities: What is the composition of the material and where does it come from? By application of a broad range of analytical techniques, which were developed or refined by our experts, it is possible to measure the exact amount and isotopic composition of uranium and plutonium in any kind of samples. The criminalistic application is only a byproduct of the large scale work on controlling the peaceful application of nuclear energy, which is done in contract with the IAEA in the context of the 'Network of Analytical Laboratories'
Exact traveling wave solutions of the bbm and kdv equations using (G'/G)-expansion method
International Nuclear Information System (INIS)
Saddique, I.; Nazar, K.
2009-01-01
In this paper, we construct the traveling wave solutions involving parameters of the Benjamin Bona-Mahony (BBM) and KdV equations in terms of the hyperbolic, trigonometric and rational functions by using the (G'/G)-expansion method, where G = G(zeta) satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the Solitary was are derived from the traveling waves. (author)
Eslami, M.; Mirzazadeh, M.
2014-09-01
The KdV equation plays an important role in describing motions of long waves in shallow water under gravity, one-dimensional nonlinear lattice, fluid mechanics, quantum mechanics, plasma physics, nonlinear optics and other areas. The KdV equation is a well-known model for the description of nonlinear long internal waves in a fluid stratified by both density and current. The aim of this paper is to present solitary wave solutions of the fifth-order KdV equations with time-dependent coefficients. The Kudryashov method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving high-order nonlinear partial differential equations with time-dependent coefficients in mathematical physics.
Directory of Open Access Journals (Sweden)
Xudong Chen
2016-01-01
Full Text Available Comparison study on free vibration of circular cylindrical shells between thin and moderately thick shell theories when using the exact dynamic stiffness method (DSM formulation is presented. Firstly, both the thin and moderately thick dynamic stiffness formulations are examined. Based on the strain and kinetic energy, the vibration governing equations are expressed in the Hamilton form for both thin and moderately thick circular cylindrical shells. The dynamic stiffness is assembled in a similar way as that in classic skeletal theory. With the employment of the Wittrick-Williams algorithm, natural frequencies of circular cylindrical shells can be obtained. A FORTRAN code is written and used to compute the modal characteristics. Numerical examples are presented, verifying the proposed computational framework. Since the DSM is an exact approach, the advantages of high accuracy, no-missing frequencies, and good adaptability to various geometries and boundary conditions are demonstrated. Comprehensive parametric studies on the thickness to radius ratio (h/r and the length to radius ratio (L/r are performed. Applicable ranges of h/r are found for both thin and moderately thick DSM formulations, and influences of L/r on frequencies are also investigated. The following conclusions are reached: frequencies of moderately thick shells can be considered as alternatives to those of thin shells with high accuracy where h/r is small and L/r is large, without any observation of shear locking.
Volokitin, V.; Liniov, A.; Meyerov, I.; Hartmann, M.; Ivanchenko, M.; Hänggi, P.; Denisov, S.
2017-11-01
Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dim H =N ≲300 , while the direct long-time numerical integration of the master equation becomes increasingly problematic for N ≳400 , especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η1,η2,...,ηn} , one could propagate a quantum trajectory (with ηi's as norm thresholds) in a numerically exact way. By using a scalable N -particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N =2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.
Saïdou, Abdoulkary; Alidou, Mohamadou; Ousmanou, Dafounansou; Serge Yamigno, Doka
2014-12-01
We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete (G'/G)-expansion method, we solve the nonlinear differential—difference equations associated with the network. We obtain some exact traveling wave solutions which include hyperbolic function solution, trigonometric function solution, rational solutions with arbitrary function, bright as well as dark solutions.
Poreba, R; Dudkiewicz, D; Drygalski, M; Poreba, A; Sipiński, A
2000-04-01
121 women after previous caesarean section were examined. The amount of successful labours were compared (according to the own diagnostic card) with the foreseeing probability of vaginal labours according to Weinstein's score. 63% pregnant woman was classified to the natural labour on the base of the own diagnostic card, probability of natural labour according to Weinstein's score were more or equal than 67%. There were no agreement between prognostic Weinstein's scale and our own method in the cases of failed attempt of labour followed by caesarean section.
Kucmin, Tomasz; Płowaś-Goral, Małgorzata; Nogalski, Adam
2015-02-01
Cardiopulmonary resuscitation (CPR) is relatively novel branch of medical science, however first descriptions of mouth-to-mouth ventilation are to be found in the Bible and literature is full of descriptions of different resuscitation methods - from flagellation and ventilation with bellows through hanging the victims upside down and compressing the chest in order to stimulate ventilation to rectal fumigation with tobacco smoke. The modern history of CPR starts with Kouwenhoven et al. who in 1960 published a paper regarding heart massage through chest compressions. Shortly after that in 1961Peter Safar presented a paradigm promoting opening the airway, performing rescue breaths and chest compressions. First CPR guidelines were published in 1966. Since that time guidelines were modified and improved numerously by two leading world expert organizations ERC (European Resuscitation Council) and AHA (American Heart Association) and published in a new version every 5 years. Currently 2010 guidelines should be obliged. In this paper authors made an attempt to present history of development of resuscitation techniques and methods and assess the influence of previous lifesaving methods on nowadays technologies, equipment and guidelines which allow to help those women and men whose life is in danger due to sudden cardiac arrest. © 2015 MEDPRESS.
Chiu, Y. T.; Hilton, H. H.
1977-01-01
Exact closed-form solutions to the solar force-free magnetic-field boundary-value problem are obtained for constant alpha in Cartesian geometry by a Green's function approach. The uniqueness of the physical problem is discussed. Application of the exact results to practical solar magnetic-field calculations is free of series truncation errors and is at least as economical as the approximate methods currently in use. Results of some test cases are presented.
Nikitin, A. V.; Rey, M.; Tyuterev, Vl. G.
2015-03-01
A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB4 molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q)-2 type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH4 molecule is demonstrated.
Exact piecewise flat gravitational waves
van de Meent, M.
2011-01-01
We generalize our previous linear result (van de Meent 2011 Class. Quantum Grav 28 075005) in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly how to
Royce, S; Khann, S; Yadav, RP; Mao, ET; Cattamanchi, A; Sam, S; Handley, MA
2014-01-01
SUMMARY Setting Previously treated tuberculosis (TB) patients are a priority for drug susceptibility testing (DST) to identify cases with multidrug resistance (MDR). In Cambodia, a recent study found that only one-third of smear-positive previously treated patients had DST results. Objective To quantify the gaps in detecting MDR in previously treated TB patients in Cambodia, and describe health workers’ perspectives on barriers, facilitators and potential interventions. Design We analyzed case notifications in Cambodia (2004–2012) and conducted semi-structured interviews with key stakeholders Results The proportion of previously treated notifications varied significantly across provinces 2010–12, in the context of longer term trends of decreasing relapse and increasing “other” retreatment notifications. Correct classification of patients’ TB treatment history and ensuring specimens from previously-treated patients are collected and reach the laboratory could nearly double the number of detected MDR-TB cases. Identified barriers include patients’ reluctance to disclose and staff difficulty eliciting treatment history, partly due to availability of streptomycin only in hospitals. Facilitators include trained health workers, collection of sputum for DST even if previously treated patients are not taking streptomycin, streamlining sputum transportation and promptly reporting results. Conclusion Improved monitoring, supportive supervision, and correctly classifying previously treated patients are essential for improving detection of MDR-TB. PMID:25299861
Energy Technology Data Exchange (ETDEWEB)
Sabry, R.; Zahran, M.A.; Fan Engui
2004-05-31
A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found.
Directory of Open Access Journals (Sweden)
Farhad A. Namin
2016-08-01
Full Text Available A rigorous method for obtaining the diffraction patterns of quasicrystals is presented. Diffraction patterns are an essential analytical tool in the study of quasicrystals, since they can be used to determine their photonic resonances. Previous methods for approximating the diffraction patterns of quasicrystals have relied on evaluating the Fourier transform of finite-sized super-lattices. Our approach, on the other hand, is exact in the sense that it is based on a technique that embeds quasicrystals into higher dimensional periodic hyper-lattices, thereby completely capturing the properties of the infinite structure. The periodicity of the unit cell in the higher dimensional space can be exploited to obtain the Fourier series expansion in closed-form of the corresponding atomic surfaces. The utility of the method is demonstrated by applying it to one-dimensional Fibonacci and two-dimensional Penrose quasicrystals. The results are verified by comparing them to those obtained by using the conventional super-lattice method. It is shown that the conventional super-cell approach can lead to inaccurate results due to the continuous nature of the Fourier transform, since quasicrystals have a discrete spectrum, whereas the approach introduced in this paper generates discrete Fourier harmonics. Furthermore, the conventional approach requires very large super-cells and high-resolution sampling of the reciprocal space in order to produce accurate results leading to a very large computational burden, whereas the proposed method generates accurate results with a relatively small number of terms. Finally, we propose how this approach can be generalized from the vertex model, which assumes identical particles at all vertices, to a more realistic case where the quasicrystal is composed of different atoms.
International Nuclear Information System (INIS)
Zhao Dun; Luo Honggang; Wang Shunjin; Zuo Wei
2005-01-01
We suggest a direct truncation technique for finding exact solutions of nonlinear differential equation, this method is based on the WTC test. As an application, abundant new exact stationary solutions of the one-dimensional higher-order nonlinear Schroedinger equation are obtained. These solutions include bright, dark, kink or anti-kink solitary wave solutions, which are dependent of the model and free parameters in the solutions. Algebraic solitary-like solution and new periodic solutions are also obtained. An interesting fact is that some solitary solutions can convert into the periodic solutions and vice versa when the free parameters are changed
International Nuclear Information System (INIS)
Dubrovsky, V.G.; Formusatik, I.B.
2003-01-01
The scheme for calculating via Zakharov-Manakov ∂-macron-dressing method of new rational solutions with constant asymptotic values at infinity of the famous two-dimensional Veselov-Novikov (VN) integrable nonlinear evolution equation and new exact rational potentials of two-dimensional stationary Schroedinger (2DSchr) equation with multiple pole wave functions is developed. As examples new lumps of VN nonlinear equation and new exact rational potentials of 2DSchr equation with multiple pole of order two wave functions are calculated. Among the constructed rational solutions are as nonsingular and also singular
Perturbation of an exact strong gravity solution
International Nuclear Information System (INIS)
Baran, S.A.
1982-10-01
Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)
Method for restoring contaminants to base levels in previously leached formations
International Nuclear Information System (INIS)
Strom, E.T.; Espencheid, W.F.
1983-01-01
The present invention relates to a method for restoring to environmentally acceptable levels the soluble contaminants in a subterranean formation that has been subjected to oxidative leaching. The contaminants are defined as those ionic species that when subjected to calcium ions form precipitates which are insoluble in the formation fluids. In accordance with the present invention, soluble calcium values are introduced into the formation. The level of contaminants is monitored and when such reaches the desired level, the introduction of soluble calcium values is stopped. The introduction of calcium values may be achieved in several ways one of which is to inject into the formation an aqueous solution containing therein solubilized calcium values. Another method of introducing calcium values into a formation, is to inject into the formation an aqueous solution containing carbon dioxide to solubilize calcium values, such as calcium carbonates, found in the formation
International Nuclear Information System (INIS)
Helbig, N.; Fuks, J.I.; Tokatly, I.V.; Appel, H.; Gross, E.K.U.; Rubio, A.
2011-01-01
Graphical abstract: We solve a 1D N-electron system, with N small, by mapping it onto an N-dimensional one-electron problem. We compare the exact solutions to the results from adiabatic density and density matrix functionals for different physical situations. Highlights: ► Static and dynamical correlations. ► Memory dependence of exchange-correlation functionals in TDDFT. ► Linear and non-linear response. ► Laser-induced population control. - Abstract: To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem is solved exactly by exploiting the mapping of the 1D N-electron problem onto an N-dimensional single electron problem. We analyze the performance of the recently derived 1D local density approximation as well as the exact-exchange orbital functional for those systems. We show that the interaction with an external resonant laser field shows Rabi oscillations which are detuned due to the lack of memory in adiabatic approximations. To investigate situations where static correlations play a role, we consider the time-evolution of the natural occupation numbers associated to the reduced one-body density matrix. Those studies shed light on the non-locality and time-dependence of the exchange and correlation functionals in time-dependent density and density-matrix functional theories.
International Nuclear Information System (INIS)
Pan, X.; Metz, C.E.
1995-01-01
A general approach that the authors proposed elsewhere reveals the intrinsic relationship among methods for inversion of the 2-D exponential Radon transform described by Bellini et al., by Tretiak and Metz, by Hawkins et al., and by Inouye et al. Moreover, the approach provides an infinite class of linear methods for inverting the 2-D exponential Radon transform. In the work reported here, they systematically investigated the noise characteristics of the methods in this class, obtaining analytical forms for the autocovariance and the variance of the images reconstructed by use of various methods. The noise properties of a new quasi-optimal method were then compared theoretically to those of other methods of the class. The analysis demonstrates that the quasi-optimal method achieves smaller global variance in the reconstructed images than do the other methods of the class. Extensive numerical simulation studies confirm this prediction
Exact analysis of discrete data
Hirji, Karim F
2005-01-01
Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...
Sirenko, Kostyantyn
2013-01-01
A scheme that discretizes exact absorbing boundary conditions (EACs) to incorporate them into a time-domain discontinuous Galerkin finite element method (TD-DG-FEM) is described. The proposed TD-DG-FEM with EACs is used for accurately characterizing transient electromagnetic wave interactions on two-dimensional waveguides. Numerical results demonstrate the proposed method\\'s superiority over the TD-DG-FEM that employs approximate boundary conditions and perfectly matched layers. Additionally, it is shown that the proposed method can produce the solution with ten-eleven digit accuracy when high-order spatial basis functions are used to discretize the Maxwell equations as well as the EACs. © 1963-2012 IEEE.
International Nuclear Information System (INIS)
Ushveridze, A.G.
1992-01-01
This paper reports that quasi-exactly solvable (QES) models realize principally new type of exact solvability in quantum physics. These models are distinguished by the fact that the Schrodinger equations for them can be solved exactly only for certain limited parts of the spectrum, but not for the whole spectrum. They occupy an intermediate position between the exactly the authors solvable (ES) models and all the others. The number of energy levels for which the spectral problems can be solved exactly refer below to as the order of QES model. From the mathematical point of view the existence of QES models is not surprising. Indeed, if the term exact solvability expresses the possibility of total explicit diagonalization of infinite Hamiltonian matrix, then the term quasi-exact solvability implies the situation when the Hamiltonian matrix can be reduced explicitly to the block-diagonal form with one of the appearing blocks being finite
Exact tests for Hardy-Weinberg proportions.
Engels, William R
2009-12-01
Exact conditional tests are often required to evaluate statistically whether a sample of diploids comes from a population with Hardy-Weinberg proportions or to confirm the accuracy of genotype assignments. This requirement is especially common when the sample includes multiple alleles and sparse data, thus rendering asymptotic methods, such as the common chi(2)-test, unreliable. Such an exact test can be performed using the likelihood ratio as its test statistic rather than the more commonly used probability test. Conceptual advantages in using the likelihood ratio are discussed. A substantially improved algorithm is described to permit the performance of a full-enumeration exact test on sample sizes that are too large for previous methods. An improved Monte Carlo algorithm is also proposed for samples that preclude full enumeration. These algorithms are about two orders of magnitude faster than those currently in use. Finally, methods are derived to compute the number of possible samples with a given set of allele counts, a useful quantity for evaluating the feasibility of the full enumeration procedure. Software implementing these methods, ExactoHW, is provided.
Constructing exact symmetric informationally complete measurements from numerical solutions
Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne
2018-04-01
Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.
Representing exact number visually using mental abacus.
Frank, Michael C; Barner, David
2012-02-01
Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation.
Czech Academy of Sciences Publication Activity Database
Bulant, P.; Klimeš, L.; Pšenčík, Ivan; Vavryčuk, Václav
2004-01-01
Roč. 48, č. 4 (2004), s. 675-688 ISSN 0039-3169 R&D Projects: GA ČR GA205/04/1104; GA AV ČR IAA3012309; GA AV ČR KSK3012103 Institutional research plan: CEZ:AV0Z3012916 Keywords : coupling ray theory * quasi-isotropic approximation * ray methods Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 0.447, year: 2004
Kubota, Masaru; Kobayashi, Hirosuke; Quanjer, Philip H; Omori, Hisamitsu; Tatsumi, Koichiro; Kanazawa, Minoru
2014-07-01
Reference values for lung function tests should be periodically updated because of birth cohort effects and improved technology. This study updates the spirometric reference values, including vital capacity (VC), for Japanese adults and compares the new reference values with previous Japanese reference values. Spirometric data from healthy non-smokers (20,341 individuals aged 17-95 years, 67% females) were collected from 12 centers across Japan, and reference equations were derived using the LMS method. This method incorporates modeling skewness (lambda: L), mean (mu: M), and coefficient of variation (sigma: S), which are functions of sex, age, and height. In addition, the age-specific lower limits of normal (LLN) were calculated. Spirometric reference values for the 17-95-year age range and the age-dependent LLN for Japanese adults were derived. The new reference values for FEV(1) in males are smaller, while those for VC and FVC in middle age and elderly males and those for FEV(1), VC, and FVC in females are larger than the previous values. The LLN of the FEV(1)/FVC for females is larger than previous values. The FVC is significantly smaller than the VC in the elderly. The new reference values faithfully reflect spirometric indices and provide an age-specific LLN for the 17-95-year age range, enabling improved diagnostic accuracy. Compared with previous prediction equations, they more accurately reflect the transition in pulmonary function during young adulthood. In elderly subjects, the FVC reference values are not interchangeable with the VC values. Copyright © 2014 The Japanese Respiratory Society. Published by Elsevier B.V. All rights reserved.
Jo, Bum Seak; Myong, Jun Pyo; Rhee, Chin Kook; Yoon, Hyoung Kyu; Koo, Jung Wan; Kim, Hyoung Ryoul
2018-01-15
The present study aimed to update the prediction equations for spirometry and their lower limits of normal (LLN) by using the lambda, mu, sigma (LMS) method and to compare the outcomes with the values of previous spirometric reference equations. Spirometric data of 10,249 healthy non-smokers (8,776 females) were extracted from the fourth and fifth versions of the Korea National Health and Nutrition Examination Survey (KNHANES IV, 2007-2009; V, 2010-2012). Reference equations were derived using the LMS method which allows modeling skewness (lambda [L]), mean (mu [M]), and coefficient of variation (sigma [S]). The outcome equations were compared with previous reference values. Prediction equations were presented in the following form: predicted value = e{a + b × ln(height) + c × ln(age) + M - spline}. The new predicted values for spirometry and their LLN derived using the LMS method were shown to more accurately reflect transitions in pulmonary function in young adults than previous prediction equations derived using conventional regression analysis in 2013. There were partial discrepancies between the new reference values and the reference values from the Global Lung Function Initiative in 2012. The results should be interpreted with caution for young adults and elderly males, particularly in terms of the LLN for forced expiratory volume in one second/forced vital capacity in elderly males. Serial spirometry follow-up, together with correlations with other clinical findings, should be emphasized in evaluating the pulmonary function of individuals. Future studies are needed to improve the accuracy of reference data and to develop continuous reference values for spirometry across all ages. © 2018 The Korean Academy of Medical Sciences.
Anderson, Jeff R; Diaz, Orlando; Klucznik, Richard; Zhang, Y Jonathan; Britz, Gavin W; Grossman, Robert G; Lv, Nan; Huang, Qinghai; Karmonik, Christof
2014-01-01
A new concept of rapid 3D prototyping was implemented using cost-effective 3D printing for creating anatomically correct replica of cerebral aneurysms. With a dedicated flow loop set-up in a full body human MRI scanner, flow measurements were performed using 4D phase contrast magnetic resonance imaging to visualize and quantify intra-aneurysmal flow patterns. Ultrashort TE sequences were employed to obtain high-resolution 3D image data to visualize the lumen inside the plastic replica. In-vitro results were compared with retrospectively obtained in-vivo data and results from computational fluid dynamics simulations (CFD). Rapid prototyping of anatomically realistic 3D models may have future impact in treatment planning, design of image acquisition methods for MRI and angiographic systems and for the design and testing of advanced image post-processing technologies.
Energy Technology Data Exchange (ETDEWEB)
Singleton, Robert Jr. [Los Alamos National Laboratory; Israel, Daniel M. [Los Alamos National Laboratory; Doebling, Scott William [Los Alamos National Laboratory; Woods, Charles Nathan [Los Alamos National Laboratory; Kaul, Ann [Los Alamos National Laboratory; Walter, John William Jr [Los Alamos National Laboratory; Rogers, Michael Lloyd [Los Alamos National Laboratory
2016-05-09
For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.
Exact rotamer optimization for protein design.
Gordon, D Benjamin; Hom, Geoffrey K; Mayo, Stephen L; Pierce, Niles A
2003-01-30
Computational methods play a central role in the rational design of novel proteins. The present work describes a new hybrid exact rotamer optimization (HERO) method that builds on previous dead-end elimination algorithms to yield dramatic performance enhancements. Measured on experimentally validated physical models, these improvements make it possible to perform previously intractable designs of entire protein core, surface, or boundary regions. Computational demonstrations include a full core design of the variable domains of the light and heavy chains of catalytic antibody 48G7 FAB with 74 residues and 10(128) conformations, a full core/boundary design of the beta1 domain of protein G with 25 residues and 10(53) conformations, and a full surface design of the beta1 domain of protein G with 27 residues and 10(60) conformations. In addition, a full sequence design of the beta1 domain of protein G is used to demonstrate the strong dependence of algorithm performance on the exact form of the potential function and the fidelity of the rotamer library. These results emphasize that search algorithm performance for protein design can only be meaningfully evaluated on physical models that have been subjected to experimental scrutiny. The new algorithm greatly facilitates ongoing efforts to engineer increasingly complex protein features. Copyright 2002 Wiley Periodicals, Inc.
Torigoe, Ikuyo; Shorten, Allison
2018-02-01
Opportunities for women and providers to use decision aids and share decisions about birth after caesarean in practice are currently limited in Japan. This is despite known benefits of decision aids to support value-sensitive healthcare decisions. To explore Japanese women's decision making experiences using a decision aid program for birth choices after caesarean. A mixed methods study was conducted among 33 consenting pregnant women with previous caesarean in five obstetrics institutions located in the western part of Japan. Outcome measures included change in level of decisional conflict, change in knowledge, and preference for birth method. Semi-structured interviews examined women's decision making experiences, and qualitative data were analyzed using thematic analysis. The participants in the program experienced a statistically significant improvement in knowledge and reduction in decisional conflict about birth after caesarean. Four themes were identified in the qualitative data related to decision making: change in women's knowledge about birth choices, clarifying women's birth preference, feelings about shared decision making, and contrasting feelings after receiving information. This study confirmed potential benefits of using the decision aid program. However, uncertainty about mode of birth continued for some women immediately prior to the birth. This finding emphasized the need to identify additional ways to support women emotionally throughout the process of decision making about birth after caesarean. It was feasible to adapt the decision aid for use in clinical practice. Future research is necessary to examine its effectiveness when implemented in Japanese clinical settings. Copyright © 2017 Australian College of Midwives. Published by Elsevier Ltd. All rights reserved.
Endom, Joerg
2014-05-01
negligible any more. Locating for example the exact position of joints, rebars on site, getting correct calibration information or overlaying measurements of independent methods requires high accuracy positioning for all data. Different technologies of synchronizing and stabilizing are discussed in this presentation. Furthermore a scale problem for interdisciplinary work between the geotechnical engineer, the civil engineer, the surveyor and the geophysicist is presented. Manufacturers as well as users are addressed to work on a unified methodology that could be implemented in future. This presentation is a contribution to COST Action TU1208.
EXACT LOGISTIC MODELS FOR NESTED BINARY DATA
TROXLER, STEVEN; LALONDE, TRENT; WILSON, JEFFREY R.
2011-01-01
The use of logistic models for independent binary data has relied first on asymptotic theory and later on exact distributions for small samples. However, the use of logistic models for dependent analysis based on exact analysis is not as common. Moreover attention is usually given to one-stage clustering. In this paper we extend the exact techniques to address hypothesis testing (estimation is not addressed) for data with second-stage and probably higher levels of clustering. The methods are ...
Exact models for isotropic matter
Thirukkanesh, S.; Maharaj, S. D.
2006-04-01
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.
Bagherinejad, Jafar; Niknam, Azar
2018-03-01
In this paper, a leader-follower competitive facility location problem considering the reactions of the competitors is studied. A model for locating new facilities and determining levels of quality for the facilities of the leader firm is proposed. Moreover, changes in the location and quality of existing facilities in a competitive market where a competitor offers the same goods or services are taken into account. The competitor could react by opening new facilities, closing existing ones, and adjusting the quality levels of its existing facilities. The market share, captured by each facility, depends on its distance to customer and its quality that is calculated based on the probabilistic Huff's model. Each firm aims to maximize its profit subject to constraints on quality levels and budget of setting up new facilities. This problem is formulated as a bi-level mixed integer non-linear model. The model is solved using a combination of Tabu Search with an exact method. The performance of the proposed algorithm is compared with an upper bound that is achieved by applying Karush-Kuhn-Tucker conditions. Computational results show that our algorithm finds near the upper bound solutions in a reasonable time.
Cheng, Lan; Wang, Fan; Stanton, John F.; Gauss, Jürgen
2018-01-01
A scheme is reported for the perturbative calculation of spin-orbit coupling (SOC) within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e) in combination with the equation-of-motion coupled-cluster singles and doubles method. Benchmark calculations of the spin-orbit splittings in 2Π and 2P radicals show that the accurate inclusion of scalar-relativistic effects using the SFX2C-1e scheme extends the applicability of the perturbative treatment of SOC to molecules that contain heavy elements. The contributions from relaxation of the coupled-cluster amplitudes are shown to be relatively small; significant contributions from correlating the inner-core orbitals are observed in calculations involving third-row and heavier elements. The calculation of term energies for the low-lying electronic states of the PtH radical, which serves to exemplify heavy transition-metal containing systems, further demonstrates the quality that can be achieved with the pragmatic approach presented here.
Bagherinejad, Jafar; Niknam, Azar
2017-06-01
In this paper, a leader-follower competitive facility location problem considering the reactions of the competitors is studied. A model for locating new facilities and determining levels of quality for the facilities of the leader firm is proposed. Moreover, changes in the location and quality of existing facilities in a competitive market where a competitor offers the same goods or services are taken into account. The competitor could react by opening new facilities, closing existing ones, and adjusting the quality levels of its existing facilities. The market share, captured by each facility, depends on its distance to customer and its quality that is calculated based on the probabilistic Huff's model. Each firm aims to maximize its profit subject to constraints on quality levels and budget of setting up new facilities. This problem is formulated as a bi-level mixed integer non-linear model. The model is solved using a combination of Tabu Search with an exact method. The performance of the proposed algorithm is compared with an upper bound that is achieved by applying Karush-Kuhn-Tucker conditions. Computational results show that our algorithm finds near the upper bound solutions in a reasonable time.
Directory of Open Access Journals (Sweden)
Weiguo Rui
2015-01-01
Full Text Available By using Frobenius’ idea together with integral bifurcation method, we study a third order nonlinear equation of generalization form of the modified KdV equation, which is an important water wave model. Some exact traveling wave solutions such as smooth solitary wave solutions, nonsmooth peakon solutions, kink and antikink wave solutions, periodic wave solutions of Jacobian elliptic function type, and rational function solution are obtained. And we show their profiles and discuss their dynamic properties aim at some typical solutions. Though the types of these solutions obtained in this work are not new and they are familiar types, they did not appear in any existing literatures because the equation ut+ux+νuxxt+βuxxx + αuux+1/3να(uuxxx+2uxuxx+3μα2u2ux+νμα2(u2uxxx+ux3+4uuxuxx + ν2μα2(ux2uxxx+2uxuxx2 = 0 is very complex. Particularly, compared with the cited references, all results obtained in this paper are new.
Cheng, Lan; Wang, Fan; Stanton, John F; Gauss, Jürgen
2018-01-28
A scheme is reported for the perturbative calculation of spin-orbit coupling (SOC) within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e) in combination with the equation-of-motion coupled-cluster singles and doubles method. Benchmark calculations of the spin-orbit splittings in 2 Π and 2 P radicals show that the accurate inclusion of scalar-relativistic effects using the SFX2C-1e scheme extends the applicability of the perturbative treatment of SOC to molecules that contain heavy elements. The contributions from relaxation of the coupled-cluster amplitudes are shown to be relatively small; significant contributions from correlating the inner-core orbitals are observed in calculations involving third-row and heavier elements. The calculation of term energies for the low-lying electronic states of the PtH radical, which serves to exemplify heavy transition-metal containing systems, further demonstrates the quality that can be achieved with the pragmatic approach presented here.
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
... integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Exact soliton solution is constructed through the established first integrals. This method is a powerful tool for searching exact travelling solutions of nonlinear partial differential equations (NPDEs) in mathematical physics.
Quasi exact solution of the Rabi Hamiltonian
Koç, R; Tuetuencueler, H
2002-01-01
A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.
Su, Min; Zhou, Zhongliang; Si, Yafei; Wei, Xiaolin; Xu, Yongjian; Fan, Xiaojing; Chen, Gang
2018-03-07
China has three basic health insurance schemes: Urban Employee Basic Medical Insurance (UEBMI), Urban Resident Basic Medical Insurance (URBMI) and New Rural Cooperative Medical Scheme (NRCMS). This study aimed to compare the equity of health-related quality of life (HRQoL) of residents under any two of the schemes. Using data from the 5th National Health Services Survey of Shaanxi Province, China, coarsened exact matching method was employed to control confounding factors. We included a matched sample of 6802 respondents between UEBMI and URBMI, 34,169 respondents between UEBMI and NRCMS, and 36,928 respondents between URBMI and NRCMS. HRQoL was measured by EQ-5D-3L based on the Chinese-specific value set. Concentration index was adopted to assess health inequality and was decomposed into its contributing factors to explain health inequality. After matching, the horizontal inequity indexes were 0.0036 and 0.0045 in UEBMI and URBMI, 0.0035 and 0.0058 in UEBMI and NRCMS, and 0.0053 and 0.0052 in URBMI and NRCMS respectively, which were mainly explained by age, educational and economic statuses. The findings demonstrated the pro-rich health inequity was much higher for the rural scheme than that for the urban ones. This study highlights the need to consolidate all three schemes by administrating uniformly, merging funds pooling and benefit packages. Based on the contributing factors, strategies aim to facilitate health conditions of the elderly, narrow economic gap, and reduce educational inequity, are essential. This study will provide evidence-based strategies on consolidating the fragmented health schemes towards reducing health inequity in both China and other developing countries.
Discrete compactons: some exact results
International Nuclear Information System (INIS)
Kevrekidis, P G; Konotop, V V; Bishop, A R; Takeno, S
2002-01-01
In this letter, we use the method of constructing exact solutions on lattices proposed by Kinnersley and described in Schmidt (1979 Phys. Rev. B 20 4397), to obtain exact compacton solutions in discrete models. We examine the linear stability of such solutions, both for the bright compacton and for the dark compacton cases. We focus on a 'quantization condition' that the width of the profile should satisfy. We also use this quantization condition to examine the possibility of compact coherent structures travelling in discrete settings. Our results are obtained for sinusoidal profiles and then generalized to elliptic functions of arbitrary modulus. The possibility of multi-compacton solutions is considered. (letter to the editor)
Exact approaches for scaffolding
Weller, Mathias; Chateau, Annie; Giroudeau, Rodolphe
2015-01-01
This paper presents new structural and algorithmic results around the scaffolding problem, which occurs prominently in next generation sequencing. The problem can be formalized as an optimization problem on a special graph, the "scaffold graph". We prove that the problem is polynomial if this graph is a tree by providing a dynamic programming algorithm for this case. This algorithm serves as a basis to deduce an exact algorithm for general graphs using a tree decomposition of the input. We ex...
Directory of Open Access Journals (Sweden)
Knaus William A
2006-03-01
Full Text Available Abstract Background Data mining can be utilized to automate analysis of substantial amounts of data produced in many organizations. However, data mining produces large numbers of rules and patterns, many of which are not useful. Existing methods for pruning uninteresting patterns have only begun to automate the knowledge acquisition step (which is required for subjective measures of interestingness, hence leaving a serious bottleneck. In this paper we propose a method for automatically acquiring knowledge to shorten the pattern list by locating the novel and interesting ones. Methods The dual-mining method is based on automatically comparing the strength of patterns mined from a database with the strength of equivalent patterns mined from a relevant knowledgebase. When these two estimates of pattern strength do not match, a high "surprise score" is assigned to the pattern, identifying the pattern as potentially interesting. The surprise score captures the degree of novelty or interestingness of the mined pattern. In addition, we show how to compute p values for each surprise score, thus filtering out noise and attaching statistical significance. Results We have implemented the dual-mining method using scripts written in Perl and R. We applied the method to a large patient database and a biomedical literature citation knowledgebase. The system estimated association scores for 50,000 patterns, composed of disease entities and lab results, by querying the database and the knowledgebase. It then computed the surprise scores by comparing the pairs of association scores. Finally, the system estimated statistical significance of the scores. Conclusion The dual-mining method eliminates more than 90% of patterns with strong associations, thus identifying them as uninteresting. We found that the pruning of patterns using the surprise score matched the biomedical evidence in the 100 cases that were examined by hand. The method automates the acquisition of
Poul, J; Urbášek, K; Ročák, K
2013-01-01
The aim of the study was to compare the exactness of correction of proximal femoral deformities between the patients treated with AO angled blade plates and those managed by the cannulated paediatric osteotomy system (CAPOS). In the period from 1994 to 2003, corrective osteotomy of the proximal femur using the conventional AO angled blade plate (90°, 120°, 130°) was performed on 57 hips in 42 children. In the period 2004-2012, 68 hips in 59 children were treated by the CAPOS method. In each child, the pre- and post-operative X-ray views were compared and a real deviation from the pre-operative plan was determined. A deviation larger than 10° in the frontal plane was recorded as an error. Penetration of the blade into either the posterior or the anterior femoral neck cortex seen on axial views was regarded as an error as well. Corrective osteotomy with AO angled blade plates performed on 57 hips failed in 12 (21.1%) on anteroposterior views and six hips (10.5%) on axial views. Of 68 hips treated by the CAPOS, failure was recorded in four (5.9%) and one (1.5%) on anteroposterior and axial views, respectively. DISCUSSION No information on the CAPOS technique is available in either international or national literature, with the exception of our preliminary report. On the other hand, locking compression plates for paediatric hips, developed later, have been described in several publications. The authors appreciate a higher accuracy of bone correction and higher stability for the whole fixation, which results in earlier mobilisation of the treated extremity. These advantages are also true for CAPOS instrumentation. The CAPOS can be seen as an intermediate stage of development between conventional angled blade plates and locking compression plates for paediatric hips. However, it should be noted that surgery involving insertion of an angled blade plate takes less time than insertion of a locking compression plate. For this reason, in procedures combining femoral
Energy Technology Data Exchange (ETDEWEB)
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
AbouEisha, Hassan M.
2014-01-01
The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts with minimum cardinality. This algorithm transforms the initial table to a decision table of a special kind, apply a set of simplification steps to this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. I present results of computer experiments for a collection of decision tables from UCIML Repository. For many of the experimented tables, the simplification steps solved the problem.
Haule, Kristjan
2015-11-06
We propose a continuum representation of the dynamical mean field theory, in which we were able to derive an exact overlap between the dynamical mean field theory and band structure methods, such as the density functional theory; double counting. The implementation of this exact double counting shows improved agreement between the theory and experiment in several correlated solids, such as the transition metal oxides and lanthanides. Previously introduced nominal double counting is in much better agreement with the exact double counting than the most widely used fully localized limit formula.
Vacaru, Sergiu I.; Yazici, Enis
2014-01-01
We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.
Vacaru, Sergiu I.; Veliev, Elşen Veli; Yazici, Enis
2014-09-01
We show that geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in f(R, T)-modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. Some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
On the exact calculation of the scattering lengths for long range potentials
International Nuclear Information System (INIS)
Szmytkowski, R.
1991-01-01
The potentials vanishing asymptotically as Lenz potentials are considered and an exact method of calculating of the scattering lengths for them is presented. This method is especially useful for Buckingham polarization potential. Formulae obtained are the generalization of those derived in the previous paper for the inverse power potentials. (author)
AESS: Accelerated Exact Stochastic Simulation
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
Yang, Zong-Lin; Li, Hui; Wang, Bing; Liu, Shu-Ying
2016-02-15
Neurotransmitters (NTs) and their metabolites are known to play an essential role in maintaining various physiological functions in nervous system. However, there are many difficulties in the detection of NTs together with their metabolites in biological samples. A new method for NTs and their metabolites detection by high performance liquid chromatography coupled with Q Exactive hybrid quadruple-orbitrap high-resolution accurate mass spectrometry (HPLC-HRMS) was established in this paper. This method was a great development of the applying of Q Exactive MS in the quantitative analysis. This method enabled a rapid quantification of ten compounds within 18min. Good linearity was obtained with a correlation coefficient above 0.99. The concentration range of the limit of detection (LOD) and the limit of quantitation (LOQ) level were 0.0008-0.05nmol/mL and 0.002-25.0nmol/mL respectively. Precisions (relative standard deviation, RSD) of this method were at 0.36-12.70%. Recovery ranges were between 81.83% and 118.04%. Concentrations of these compounds in mouse hypothalamus were detected by Q Exactive LC-MS technology with this method. Copyright © 2016 Elsevier B.V. All rights reserved.
New exact solutions for two nonlinear equations
International Nuclear Information System (INIS)
Wang Quandi; Tang Minying
2008-01-01
In this Letter, we investigate two nonlinear equations given by u t -u xxt +3u 2 u x =2u x u xx +uu xxx and u t -u xxt +4u 2 u x =3u x u xx +uu xxx . Through some special phase orbits we obtain four new exact solutions for each equation above. Some previous results are extended
Exact integrability in quantum field theory
International Nuclear Information System (INIS)
Thacker, H.B.
1980-08-01
The treatment of exactly integrable systems in various branches of two-dimensional classical and quantum physics has recently been placed in a unified framework by the development of the quantum inverse method. This method consolidates a broad range of developments in classical nonlinear wave (soliton) physics, statistical mechanics, and quantum field theory. The essential technique for analyzing exactly integrable quantum systems was invested by Bethe in 1931. The quantum-mechanical extension of the inverse scattering method and its relationship to the methods associated with Bethe's ansatz are examined here
arXiv Integrable flows between exact CFTs
Georgiou, George
2017-11-14
We explicitly construct families of integrable σ-model actions smoothly inter-polating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels k$_{1}$ and k$_{2}$. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for a single matrix deformation it is given by the ultraviolet direct product theories but at levels k$_{1}$ and k$_{2}$ − k$_{1}$. For isotropic deformations we demonstrate integrability. In this case we also compute the exact beta-function for the deformation parameters using gravitational methods. This is shown to coincide with previous results obtained using perturbation theory and non-perturbative symmetries.
On exact solutions of the Bogoyavlenskii equation
Indian Academy of Sciences (India)
Abstract. Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method. It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical field is still a solution of the equation of interest, except for a ...
Crawford, Elizabeth; Musselman, Brian
2012-07-01
Rapid screening of pesticides present on the surfaces of fruits and vegetables has been facilitated by using a Direct Analysis in Real Time (DART(®)) open air surface desorption ionization source coupled to an Exactive(®) high-resolution accurate mass benchtop orbitrap mass spectrometer. The use of cotton and polyester cleaning swabs to collect and retain pesticides for subsequent open air desorption ionization is demonstrated by sampling the surface of various produce to which solutions of pesticides have been applied at levels 10 and 100 times below the tolerance levels established by the United States Environmental Protection Agency (US EPA). Samples analyzed include cherry tomatoes, oranges, peaches and carrots each chosen for their surface characteristics which include: smooth, pitted, fuzzy, and rough respectively. Results from the direct analysis of fungicides on store-bought oranges are also described. In all cases, the swabs were introduced directly into the heated ionizing gas of the DART source resulting in production of protonated pesticide molecules within seconds of sampling. Operation of the orbitrap mass spectrometer at 25,000 full-width half maximum resolution was sufficient to generate high-quality accurate mass data. Stable external mass calibration eliminated the need for addition of standards typically required for mass calibration, thus allowing multiple analyses to be completed without instrument recalibration.
Barbian, Jeff
2001-01-01
Explains how low-tech experiential methods thrive in companies interested in fostering the human touch. Examples include NASA's paper airplane simulation, total immersion simulation, and fantasy multisensory environments. (JOW)
CONDITIONS FOR EXACT CAVALIERI ESTIMATION
Directory of Open Access Journals (Sweden)
Mónica Tinajero-Bravo
2014-03-01
Full Text Available Exact Cavalieri estimation amounts to zero variance estimation of an integral with systematic observations along a sampling axis. A sufficient condition is given, both in the continuous and the discrete cases, for exact Cavalieri sampling. The conclusions suggest improvements on the current stereological application of fractionator-type sampling.
Exact Optimum Design of Segmented Thermoelectric Generators
Directory of Open Access Journals (Sweden)
M. Zare
2016-01-01
Full Text Available A considerable difference between experimental and theoretical results has been observed in the studies of segmented thermoelectric generators (STEGs. Because of simplicity, the approximate methods are widely used for design and optimization of the STEGs. This study is focused on employment of exact method for design and optimization of STEGs and comparison of exact and approximate results. Thus, using new highly efficient thermoelectric materials, four STEGs are proposed to operate in the temperature range of 300 to 1300 kelvins. The proposed STEGs are optimally designed to achieve maximum efficiency. Design and performance characteristics of the optimized generators including maximum conversion efficiency and length of elements are calculated through both exact and approximate methods. The comparison indicates that the approximate method can cause a difference up to 20% in calculation of some design characteristics despite its appropriate results in efficiency calculation. The results also show that the maximum theoretical efficiency of 23.08% is achievable using the new proposed STEGs. Compatibility factor of the selected materials for the proposed STEGs is also calculated using both exact and approximate methods. The comparison indicates a negligible difference in calculation of compatibility factor, despite the considerable difference in calculation of reduced efficiency (temperature independence efficiency.
Directory of Open Access Journals (Sweden)
J. Caesar
2018-03-01
Full Text Available Chlorophyll concentrations of biological soil crust (biocrust samples are commonly determined to quantify the relevance of photosynthetically active organisms within these surface soil communities. Whereas chlorophyll extraction methods for freshwater algae and leaf tissues of vascular plants are well established, there is still some uncertainty regarding the optimal extraction method for biocrusts, where organism composition is highly variable and samples comprise major amounts of soil. In this study we analyzed the efficiency of two different chlorophyll extraction solvents, the effect of grinding the soil samples prior to the extraction procedure, and the impact of shaking as an intermediate step during extraction. The analyses were conducted on four different types of biocrusts. Our results show that for all biocrust types chlorophyll contents obtained with ethanol were significantly lower than those obtained using dimethyl sulfoxide (DMSO as a solvent. Grinding of biocrust samples prior to analysis caused a highly significant decrease in chlorophyll content for green algal lichen- and cyanolichen-dominated biocrusts, and a tendency towards lower values for moss- and algae-dominated biocrusts. Shaking of the samples after each extraction step had a significant positive effect on the chlorophyll content of green algal lichen- and cyanolichen-dominated biocrusts. Based on our results we confirm a DMSO-based chlorophyll extraction method without grinding pretreatment and suggest the addition of an intermediate shaking step for complete chlorophyll extraction (see Supplement S6 for detailed manual. Determination of a universal chlorophyll extraction method for biocrusts is essential for the inter-comparability of publications conducted across all continents.
Exact solutions of some nonlinear partial differential equations using ...
Indian Academy of Sciences (India)
The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...
Exact solutions for nonlinear foam drainage equation
Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani
2017-02-01
In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G)-expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.
International Nuclear Information System (INIS)
Morishita, Junji; Katsuragawa, Shigehiko; Kondo, Keisuke; Doi, Kunio
2001-01-01
An automated patient recognition method for correcting 'wrong' chest radiographs being stored in a picture archiving and communication system (PACS) environment has been developed. The method is based on an image-matching technique that uses previous chest radiographs. For identification of a 'wrong' patient, the correlation value was determined for a previous image of a patient and a new, current image of the presumed corresponding patient. The current image was shifted horizontally and vertically and rotated, so that we could determine the best match between the two images. The results indicated that the correlation values between the current and previous images for the same, 'correct' patients were generally greater than those for different, 'wrong' patients. Although the two histograms for the same patient and for different patients overlapped at correlation values greater than 0.80, most parts of the histograms were separated. The correlation value was compared with a threshold value that was determined based on an analysis of the histograms of correlation values obtained for the same patient and for different patients. If the current image is considered potentially to belong to a 'wrong' patient, then a warning sign with the probability for a 'wrong' patient is provided to alert radiology personnel. Our results indicate that at least half of the 'wrong' images in our database can be identified correctly with the method described in this study. The overall performance in terms of a receiver operating characteristic curve showed a high performance of the system. The results also indicate that some readings of 'wrong' images for a given patient in the PACS environment can be prevented by use of the method we developed. Therefore an automated warning system for patient recognition would be useful in correcting 'wrong' images being stored in the PACS environment
DEFF Research Database (Denmark)
Alenius, Malin; Hammarlund-Udenaes, Margareta; Honoré, Per Gustaf Hartvig
2009-01-01
; underestimating residual symptoms, negative symptoms, and side effects; or being to open for individual interpretation. The aim of this study was to present and evaluate a new method of classification according to treatment response and, thus, to identify patients in functional remission. METHOD: A naturalistic......, cross-sectional study was performed using patient interviews and information from patient files. The new classification method CANSEPT, which combines the Camberwell Assessment of Need rating scale, the Udvalg for Kliniske Undersøgelser side effect rating scale (SE), and the patient's previous treatment...... history (PT), was used to group the patients according to treatment response. CANSEPT was evaluated by comparison of expected and observed results. RESULTS: In the patient population (n = 123), the patients in functional remission, as defined by CANSEPT, had higher quality of life, fewer hospitalizations...
International Nuclear Information System (INIS)
Witte, N.S.
1997-01-01
The exact solution to the problem of reflection and diffraction of atomic de Broglie waves by a travelling evanescent wave is found starting with a bare-state formulation. The solution for the wavefunctions, the tunnelling losses and the non-adiabatic losses are given exactly in terms of hyper-Bessel functions, and are valid for all detuning and Rabi frequencies, thus generalizing previous approximate methods. Furthermore we give the limiting cases of all amplitudes in the uniform semiclassical limit, which is valid in all regions including near the classical turning points, and in the large and weak coupling cases. Exact results for the zero detuning case are obtained in terms of Bessel functions. We find our uniform semiclassical limit to be closer to the exact result over the full range of parameter values than the previously reported calculations. The current knowledge of hyper-Bessel function properties is reviewed in order to apply this to the physical problems imposed
International Nuclear Information System (INIS)
Belmont, G.
1981-01-01
Intense natural waves are commonly observed onboard satellites in the outer earth's magnetosphere, inside a narrow frequency range, including the electron plasma and upper hybrid frequencies. In order to progress in the understanding of their emission processes, it is necessary to determine precisely the relationship which exists between their frequencies and the characteristic frequencies of the magnetospheric plasma. For this purpose, it is necessary to take into account the fact that some of these characteristic frequencies, which are provided by active sounding of the plasma, not only depend on the total density, but also on the shape of the distribution function (which has generally been assumed to be Maxwellian). A method providing a fine diagnosis of general non-Maxwellian plasmas is developed. This method of analysis of the experimental data is based on a theoretical study which points out the influence of the shape of the distribution function on the dispersion curves (for wave vectors perpendicular to the static magnetic field)
When 'exact recovery' is exact recovery in compressed sensing simulation
DEFF Research Database (Denmark)
Sturm, Bob L.
2012-01-01
In a simulation of compressed sensing (CS), one must test whether the recovered solution \\(\\vax\\) is the true solution \\(\\vx\\), i.e., ``exact recovery.'' Most CS simulations employ one of two criteria: 1) the recovered support is the true support; or 2) the normalized squared error is less than...... \\(\\epsilon^2\\). We analyze these exact recovery criteria independent of any recovery algorithm, but with respect to signal distributions that are often used in CS simulations. That is, given a pair \\((\\vax,\\vx)\\), when does ``exact recovery'' occur with respect to only one or both of these criteria...... for a given distribution of \\(\\vx\\)? We show that, in a best case scenario, \\(\\epsilon^2\\) sets a maximum allowed missed detection rate in a majority sense....
Energy vs. density on paths toward more exact density functionals.
Kepp, Kasper P
2018-03-14
Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a "path". Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness and "straying" from the "path" by separating errors in ρ and E[ρ]. A consistent path toward exactness involves minimizing both errors. Second, a suitably diverse test set of trial densities ρ' can be used to estimate the significance of errors in ρ without knowing the exact densities which are often inaccessible. To illustrate this, the systems previously studied by Medvedev et al., the first ionization energies of atoms with Z = 1 to 10, the ionization energy of water, and the bond dissociation energies of five diatomic molecules were investigated using CCSD(T)/aug-cc-pV5Z as benchmark at chemical accuracy. Four functionals of distinct designs was used: B3LYP, PBE, M06, and S-VWN. For atomic cations regardless of charge and compactness up to Z = 10, the energy effects of the different ρ are energy-wise insignificant. An interesting oscillating behavior in the density sensitivity is observed vs. Z, explained by orbital occupation effects. Finally, it is shown that even large "normal" problems such as the Co-C bond energy of cobalamins can use simpler (e.g. PBE) trial densities to drastically speed up computation by loss of a few kJ mol -1 in accuracy. The proposed method of using a test set of trial densities to estimate the sensitivity and significance of density errors of functionals may be useful for testing and designing new balanced functionals with more systematic improvement of densities and energies.
Directory of Open Access Journals (Sweden)
L.L. Glazyrina
2016-12-01
Full Text Available In this paper, the initial-boundary problem for two nonlinear parabolic combined equations has been considered. One of the equations is set on the bounded domain Ω from R2, another equation is set along the curve lying in Ω. Both of the equations are parabolic equations with double degeneration. The degeneration can be present at the space operator. Furthermore, the nonlinear function which is under the sign of partial derivative with respect to the variable t, can be bound to zero. This problem has an applied character: such structure is needed to describe the process of surface and ground water combined movement. In this case, the desired function determines the level of water above the given impenetrable bottom, the section simulates the riverbed. The Bussinesk equation has been used for mathematical description of the groundwater filtration process in the domain Ω; a diffusion analogue of the Saint-Venant's system has been used on the section for description of the process of water level change in the open channel. Earlier, the authors proved the theorems of generalized solution existence and uniqueness for the considered problem from the functions classes which are called strengthened Sobolev spaces in the literature. To obtain these results, we used the technique which was created by the German mathematicians (H.W. Alt, S. Luckhaus, F. Otto to establish the correctness of the problems with a double degeneration. In this paper, we have proposed and investigated an approximate solution method for the above-stated problem. This method has been constructed using semidiscretization with respect to the variable t and the finite element method for space variables. Triangulation of the domain has been accomplished by triangles. The mesh has been set on the section line. On each segment of the line section lying between the nearby mesh points, on both side of this segment we have constructed the triangles with a common side which matches with
Laparoscopy After Previous Laparotomy
Directory of Open Access Journals (Sweden)
Zulfo Godinjak
2006-11-01
Full Text Available Following the abdominal surgery, extensive adhesions often occur and they can cause difficulties during laparoscopic operations. However, previous laparotomy is not considered to be a contraindication for laparoscopy. The aim of this study is to present that an insertion of Veres needle in the region of umbilicus is a safe method for creating a pneumoperitoneum for laparoscopic operations after previous laparotomy. In the last three years, we have performed 144 laparoscopic operations in patients that previously underwent one or two laparotomies. Pathology of digestive system, genital organs, Cesarean Section or abdominal war injuries were the most common causes of previouslaparotomy. During those operations or during entering into abdominal cavity we have not experienced any complications, while in 7 patients we performed conversion to laparotomy following the diagnostic laparoscopy. In all patients an insertion of Veres needle and trocar insertion in the umbilical region was performed, namely a technique of closed laparoscopy. Not even in one patient adhesions in the region of umbilicus were found, and no abdominal organs were injured.
Directory of Open Access Journals (Sweden)
Abdelhalim Ebaid
2014-01-01
Full Text Available The exact solution for any physical model is of great importance in the applied science. Such exact solution leads to the correct physical interpretation and it is also useful in validating the approximate analytical or numerical methods. The exact solution for the peristaltic transport of a Jeffrey fluid with variable viscosity through a porous medium in an asymmetric channel has been achieved. The main advantage of such exact solution is the avoidance of any kind of restrictions on the viscosity parameter α, unlike the previous study in which the restriction α ≪ 1 has been put to achieve the requirements of the regular perturbation method. Hence, various plots have been introduced for the exact effects of the viscosity parameter, Daray’s number, porosity, amplitude ratio, Jeffrey fluid parameter, and the amplitudes of the waves on the pressure rise and the axial velocity. These exact effects have been discussed and further compared with those approximately obtained in the literature by using the regular perturbation method. The comparisons reveal that remarkable differences have been detected between the current exact results and those approximately obtained in the literature for the axial velocity profile and the pressure rise.
Exactly energy conserving semi-implicit particle in cell formulation
Energy Technology Data Exchange (ETDEWEB)
Lapenta, Giovanni, E-mail: giovanni.lapenta@kuleuven.be
2017-04-01
We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conserves energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These
Alenius, Malin; Hammarlund-Udenaes, Margareta; Hartvig, Per; Sundquist, Staffan; Lindström, Leif
2009-01-01
Various approaches have been made over the years to classify psychotic patients according to inadequate treatment response, using terms such as treatment resistant or treatment refractory. Existing classifications have been criticized for overestimating positive symptoms; underestimating residual symptoms, negative symptoms, and side effects; or being to open for individual interpretation. The aim of this study was to present and evaluate a new method of classification according to treatment response and, thus, to identify patients in functional remission. A naturalistic, cross-sectional study was performed using patient interviews and information from patient files. The new classification method CANSEPT, which combines the Camberwell Assessment of Need rating scale, the Udvalg for Kliniske Undersøgelser side effect rating scale (SE), and the patient's previous treatment history (PT), was used to group the patients according to treatment response. CANSEPT was evaluated by comparison of expected and observed results. In the patient population (n = 123), the patients in functional remission, as defined by CANSEPT, had higher quality of life, fewer hospitalizations, fewer psychotic symptoms, and higher rate of workers than those with the worst treatment outcome. In the evaluation, CANSEPT showed validity in discriminating the patients of interest and was well tolerated by the patients. CANSEPT could secure inclusion of correct patients in the clinic or in research.
Weights of Exact Threshold Functions
DEFF Research Database (Denmark)
Babai, László; Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.
2010-01-01
We consider Boolean exact threshold functions defined by linear equations, and in general degree d polynomials. We give upper and lower bounds on the maximum magnitude (absolute value) of the coefficients required to represent such functions. These bounds are very close and in the linear case in ...... leave a substantial gap, a challenge for future work....
Exact expression for information distance
P.M.B. Vitányi (Paul)
2017-01-01
textabstractInformation distance can be defined not only between two strings but also in a finite multiset of strings of cardinality greater than two. We determine a best upper bound on the information distance. It is exact, since the upper bound on the information distance for all multisets is the
On exact algorithms for treewidth
Bodlaender, H.L.; Fomin, F.V.; Koster, A.M.C.A.; Kratsch, D.; Thilikos, D.M.
2006-01-01
We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a
New exact travelling wave solutions of bidirectional wave equations
Indian Academy of Sciences (India)
where , , and d are real constants. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution systems. In this paper, we obtain exact travelling wave solutions of system (1) using the modiﬁed tanh–coth function method with computerized symbolic ...
A characterisation of algebraic exactness
Garner, Richard
2011-01-01
An algebraically exact category in one that admits all of the limits and colimits which every variety of algebras possesses and every forgetful functor between varieties preserves, and which verifies the same interactions between these limits and colimits as hold in any variety. Such categories were studied by Ad\\'amek, Lawvere and Rosick\\'y: they characterised them as the categories with small limits and sifted colimits for which the functor taking sifted colimits is continuous. They conject...
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025
Exact image theory for field calculation in layered biological medium
International Nuclear Information System (INIS)
Alanen, E.; Lindell, I.V.
1985-01-01
A method based on the exact image theory to calculate the near field distribution of a horn antenna in direct contact with the skin is introduced. Being exact, the method is not restricted by parameter values and can be applied in optimization of horn aperture function to produce focus fields in the human body. The method observes the effect of the skin layer and can be applied for an arbitrary aperture function. The optimization is demonstrated with few examples
PREVIOUS SECOND TRIMESTER ABORTION
African Journals Online (AJOL)
PNLC
PREVIOUS SECOND TRIMESTER ABORTION: A risk factor for third trimester uterine rupture in three ... for accurate diagnosis of uterine rupture. KEY WORDS: Induced second trimester abortion - Previous uterine surgery - Uterine rupture. ..... scarred uterus during second trimester misoprostol- induced labour for a missed ...
Exact solutions of nonlinear differential equations using continued fractions
International Nuclear Information System (INIS)
Ditto, W.L.; Pickett, T.J.
1990-01-01
The continued-fraction conversion method (J. Math. Phys. (N.Y.), 29, 1761 (1988)) is used to generate a homologous family of exact solutions to the Lane-Emden equation φ(r) '' + 2φ(r)'/r + αφ(r) p = 0, for p=5. An exact solution is also obtained for a generalization of the Lane-Emden equation of the form -φ '' (r) -2φ(r)'/r + αφ(r) 2p+1 + λφ(r) 4p+1 = 0 for arbitrary α, γ and p. A condition is established for the generation of exact solutions from the method
Exactly solvable models for multiatomic molecular Bose-Einstein condensates
Energy Technology Data Exchange (ETDEWEB)
Santos, G, E-mail: gfilho@if.ufrgs.br, E-mail: gfilho@cbpf.br [Instituto de Fisica da UFRGS, Av. Bento Goncalves, 9500, Agronomia, Porto Alegre, RS (Brazil)
2011-08-26
I introduce two families of exactly solvable models for multiatomic hetero-nuclear and homo-nuclear molecular Bose-Einstein condensates through the algebraic Bethe ansatz method. The conserved quantities of the respective models are also shown. (paper)
Exact renormalization group as a scheme for calculations
International Nuclear Information System (INIS)
Mack, G.
1985-10-01
In this lecture I report on recent work to use exact renormalization group methods to construct a scheme for calculations in quantum field theory and classical statistical mechanics on the continuum. (orig./HSI)
Two exact solutions of the DPL non-Fourier heat conduction equation with special conditions
Zhang, Youtong; Zheng, Changsong; Liu, Yongfeng; Shao, Liang; Gou, Chenhua
2009-04-01
This paper presents two exact explicit solutions for the three dimensional dual-phase lag (DLP) heat conduction equation, during the derivation of which the method of trial and error and the authors’ previous experiences are utilized. To the authors’ knowledge, most solutions of 2D or 3D DPL models available in the literature are obtained by numerical methods, and there are few exact solutions up to now. The exact solutions in this paper can be used as benchmarks to validate numerical solutions and to develop numerical schemes, grid generation methods and so forth. In addition, they are of theoretical significance since they correspond to physically possible situations. The main goal of this paper is to obtain some possible exact explicit solutions of the dual-phase lag heat conduction equation as the benchmark solutions for computational heat transfer, rather than specific solutions for some given initial and boundary conditions. Therefore, the initial and boundary conditions are indeterminate before derivation and can be deduced from the solutions afterwards. Actually, all solutions given in this paper can be easily proven by substituting them into the governing equation.
Familial sinistrals avoid exact numbers.
Directory of Open Access Journals (Sweden)
Uli Sauerland
Full Text Available We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals--individuals who are left-handed themselves or have a left-handed close blood-relative--with those of pure familial dextrals--right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd's (1988, Language in Society index of the roundness of a number and report that familial sinistrals' responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere.
Dissociation between exact and approximate addition in developmental dyslexia.
Yang, Xiujie; Meng, Xiangzhi
2016-09-01
Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.
Exact renormalization group equations: an introductory review
Bagnuls, C.; Bervillier, C.
2001-07-01
We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.
Exact anisotropic polytropic cylindrical solutions
Sharif, M.; Sadiq, Sobia
2018-03-01
In this paper, we study anisotropic compact stars with static cylindrically symmetric anisotropic matter distribution satisfying polytropic equation of state. We formulate the field equations as well as the corresponding mass function for the particular form of gravitational potential z(x)=(1+bx)^{η } (η =1, 2, 3) and explore exact solutions of the field equations for different values of the polytropic index. The values of arbitrary constants are determined by taking mass and radius of compact star (Her X-1). We find that resulting solutions show viable behavior of physical parameters (density, radial as well as tangential pressure, anisotropy) and satisfy the stability condition. It is concluded that physically acceptable solutions exist only for η =1, 2.
Exact wording: Consequences after Gundremmingen
International Nuclear Information System (INIS)
Anon.
1975-01-01
In connection with the accident at the Kernkraftwerk Gundremmingen, the exact wording of the answer of the undersecretary of state of the Ministry of the Interior is given to an inquiry concerning the consequences the accident has on safety precautions relating to staff and of a technical nature. According to this statement, a report is to be written by the highest nuclear supervisory authorities on the state and implementation of recommendations on maintenance and repair work, to be followed by an examination in how far these recommendations are uniform, and in how far they serve a useful function. In the meantime, maintenance and repair work is admissible only after it has been endorsed and sanctioned by an independent safety expert. (ORU) [de
Exact solutions in bouncing cosmology
Energy Technology Data Exchange (ETDEWEB)
Stachowiak, Tomasz [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244 Cracow (Poland)]. E-mail: toms@oa.uj.edu.pl; Szydlowski, Marek [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244 Cracow (Poland); M. Kac Complex Systems Research Centre, Jagiellonian University, Reymonta 4, 30-059 Cracow (Poland)
2007-03-22
We discuss the effects of a (possibly) negative (1+z){sup 6} type contribution to the Friedmann equation in a spatially flat universe. No definite answer can be given as to the presence and magnitude of a particular mechanism, because any test using the general relation H(z) is able to estimate only the total of all sources of such a term. That is why we describe four possibilities: (1) geometric effects of loop quantum cosmology, (2) braneworld cosmology, (3) metric-affine gravity, and (4) cosmology with spinning fluid. We find the exact solutions for the models with {rho}{sup 2} correction in terms of elementary functions, and show all evolutional paths on their phase plane. Instead of the initial singularity, the generic feature is now a bounce.
Directory of Open Access Journals (Sweden)
Weiguo Rui
2014-01-01
Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.
QCD in the infrared with exact angular integrations
Atkinson, D; Bloch, J.C R
1998-01-01
In a previous paper we have shown that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole. These results were obtained after angular averaging, but here we go beyond this approximation and perform an exact
Exact and Efficient Sampling of Conditioned Walks
Adorisio, Matteo; Pezzotta, Alberto; de Mulatier, Clélia; Micheletti, Cristian; Celani, Antonio
2018-01-01
A computationally challenging and open problem is how to efficiently generate equilibrated samples of conditioned walks. We present here a general stochastic approach that allows one to produce these samples with their correct statistical weight and without rejections. The method is illustrated for a jump process conditioned to evolve within a cylindrical channel and forced to reach one of its ends. We obtain analytically the exact probability density function of the jumps and offer a direct method for gathering equilibrated samples of a random walk conditioned to stay in a channel with suitable boundary conditions. Unbiased walks of arbitrary length can thus be generated with linear computational complexity—even when the channel width is much smaller than the typical bond length of the unconditioned walk. By profiling the metric properties of the generated walks for various bond lengths we characterize the crossover between weak and strong confinement regimes with great detail.
New exact travelling wave solutions of bidirectional wave equations
Indian Academy of Sciences (India)
finding travelling wave solutions to nonlinear evolution equations. However, practically there is no unified method that can be used to handle all types of nonlinearity. The tanh-function method is an effective and direct algebraic method for finding the exact solutions of nonlinear evolution problems [22,23]. The concept of ...
Giannakis, Stefanos; Gamarra Vives, Franco Alejandro; Grandjean, Dominique; Magnet, Anoys; De Alencastro, Luiz Felippe; Pulgarin, César
2015-11-01
In this study, wastewater from the output of three different secondary treatment facilities (Activated Sludge, Moving Bed Bioreactor and Coagulation-Flocculation) present in the municipal wastewater treatment plant of Vidy, Lausanne (Switzerland), was further treated with various oxidation processes (UV, UV/H2O2, solar irradiation, Fenton, solar photo-Fenton), at laboratory scale. For this assessment, 6 organic micropollutants in agreement with the new environmental legislation requirements in Switzerland were selected (Carbamazepine, Clarithromycin, Diclofenac, Metoprolol, Benzotriazole, Mecoprop) and monitored throughout the treatment. Also, the overall removal of the organic load was assessed. After each secondary treatment, the efficiency of the AOPs increased in the following order: Coagulation-Flocculation municipal wastewater subjected to biological treatment followed by UV/H2O2 resulted in the highest elimination levels. Wastewater previously treated by physicochemical treatment demonstrated considerably inhibited micropollutant degradation rates. The degradation kinetics were determined, yielding: k (UV) < k (UV/H2O2) and k (Fenton) < k (solar irradiation) < k (photo-Fenton). Finally, the evolution of global pollution parameters (COD & TOC elimination) was followed and the degradation pathways for the effluent organic matter are discussed. Copyright © 2015 Elsevier Ltd. All rights reserved.
Hamnerius, Nils; Wallin, Ewa; Svensson, Åke; Stenström, Pernilla; Svensjö, Tor
2016-01-01
Chronic leg ulcers remain a challenge to the treating physician. Such wounds often need skin grafts to heal. This necessitates a readily available, fast, simple, and standardized procedure for grafting. The aim of this work was to test a novel method developed for outpatient transplant procedures. The procedure employs a handheld disposable dermatome and a roller mincer that cut the skin into standardized micrografts that can be spread out onto a suitable graft bed. Wounds were followed until healed and photographed. The device was successfully used to treat and close a traumatic lower limb wound and a persistent chronic venous leg ulcer. The donor site itself healed by secondary intent with minimal cosmetic impairment. The method was successfully used to graft 2 lower extremity wounds.
Ruffin, Mack T.; Creswell, John W.; Jimbo, Masahito; Fetters, Michael D.
2009-01-01
We investigated factors that influence choice of colorectal cancer (CRC) screening test and assessed the most- and least-preferred options among fecal occult blood testing (FOBT), flexible sigmoidoscopy, colonoscopy, and double contrast barium enema among adults with varied race, gender, and geographic region demographics. Mixed methods data collection consisted of 10 focus group interviews and a survey of the 93 focus group participants. Participants were ≥50 years of age and reported not ha...
Ruffin, Mack T.; Creswell, John W.; Jimbo, Masahito
2014-01-01
We investigated factors that influence choice of colorectal cancer (CRC) screening test and assessed the most- and least-preferred options among fecal occult blood testing (FOBT), flexible sigmoidoscopy, colonoscopy, and double contrast barium enema among adults with varied race, gender, and geographic region demographics. Mixed methods data collection consisted of 10 focus group interviews and a survey of the 93 focus group participants. Participants were ≥50 years of age and reported not having been screened for colorectal cancer in the last ten years. Analyses examined differences by race, gender, and geographic location. Participants had modest knowledge about CRC and there were fewer correct answers to knowledge questions by African Americans. Participants recognized value of early detection, and identified health symptoms and their doctor's recommendation as influential for obtaining CRC screening. They chose colonoscopy and FOBT as the most preferred tests, while barium enema was least preferred. The analysis revealed intra-group variations in preference, though there were no significant differences by race, gender, or location. Openness of discussing this sensitive topic, lack of knowledge about colorectal cancer and screening costs, and diversity of preferences expressed within study groups suggest the importance of patient-physician dialogue about colorectal cancer screening options. New approaches to promoting colorectal cancer screening need to explore methods to facilitate patients establishing and expressing preferences among the screening options. PMID:19082695
International Nuclear Information System (INIS)
Pulkkanen, V.-M.; Nordman, H.
2010-03-01
Traditional radionuclide transport models overestimate significantly some phenomena, or completely ignore them. This motivates the development of new more precise models. As a result, this work is a description of commissioning of a new KBS-3V near-field radionuclide transport model, which has been done with a commercial software called GoldSim. According to earlier models, GoldSim model uses rz coordinates, but the solubilities of radionuclides have been treated more precisely. To begin with, the physical phenomena concerning near-field transport have been introduced according to GoldSim way of thinking. Also, the computational methods of GoldSim have been introduced and compared to methods used earlier. The actual verification of GoldSim model has been carried out by comparing the GoldSim results from simple cases to the corresponding results obtained with REPCOM, a software developed by VTT and used in several safety assessments. The results agree well. Finally, a few complicated cases were studied. In these cases, the REPCOM's limitations in handling of some phenomena become evident. The differences in the results are caused especially by the extension of the solubility limit to the whole computational domain, and the element-wise treatment of the solubilities which was used instead of nuclide-wise treatment. This work has been carried out as a special assignment to the former laboratory of Advanced Energy Systems in Helsinki University of Technology. The work was done at VTT. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Pulkkanen, V.-M.; Nordman, H. (VTT Technical Research Centre, Espoo (Finland))
2010-03-15
Traditional radionuclide transport models overestimate significantly some phenomena, or completely ignore them. This motivates the development of new more precise models. As a result, this work is a description of commissioning of a new KBS-3V near-field radionuclide transport model, which has been done with a commercial software called GoldSim. According to earlier models, GoldSim model uses rz coordinates, but the solubilities of radionuclides have been treated more precisely. To begin with, the physical phenomena concerning near-field transport have been introduced according to GoldSim way of thinking. Also, the computational methods of GoldSim have been introduced and compared to methods used earlier. The actual verification of GoldSim model has been carried out by comparing the GoldSim results from simple cases to the corresponding results obtained with REPCOM, a software developed by VTT and used in several safety assessments. The results agree well. Finally, a few complicated cases were studied. In these cases, the REPCOM's limitations in handling of some phenomena become evident. The differences in the results are caused especially by the extension of the solubility limit to the whole computational domain, and the element-wise treatment of the solubilities which was used instead of nuclide-wise treatment. This work has been carried out as a special assignment to the former laboratory of Advanced Energy Systems in Helsinki University of Technology. The work was done at VTT. (orig.)
Quantifying risks with exact analytical solutions of derivative pricing distribution
Zhang, Kun; Liu, Jing; Wang, Erkang; Wang, Jin
2017-04-01
Derivative (i.e. option) pricing is essential for modern financial instrumentations. Despite of the previous efforts, the exact analytical forms of the derivative pricing distributions are still challenging to obtain. In this study, we established a quantitative framework using path integrals to obtain the exact analytical solutions of the statistical distribution for bond and bond option pricing for the Vasicek model. We discuss the importance of statistical fluctuations away from the expected option pricing characterized by the distribution tail and their associations to value at risk (VaR). The framework established here is general and can be applied to other financial derivatives for quantifying the underlying statistical distributions.
Exhaustive generation of orthomodular lattices with exactly one nonquantum state
Pavičić, Mladen
2009-12-01
We propose a kind of reverse Kochen-Specker theorem that amounts to generating orthomodular lattices with exactly one state that do not admit properties of the Hilbert space. We apply MMP algorithms to obtain smallest orthomodular lattices with 35 atoms and 35 blocks (35-35) and all other ones up to 38-38. We find out that all but one of them admit exactly one state and discover several other properties of them. Previously known such orthomodular lattices have 44 atoms and 44 blocks or more. We present some of them in our notation.
Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2013-01-01
Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.
Exact Power Constraints in Smart Grid Control
DEFF Research Database (Denmark)
Trangbæk, K; Petersen, Mette Højgaard; Bendtsen, Jan Dimon
2011-01-01
This paper deals with hierarchical model predictive control (MPC) of smart grid systems. The objective is to accommodate load variations on the grid, arising from varying consumption and natural variations in the power production e.g. from wind turbines. This balancing between supply and demand...... is performed by distributing power to consumers in an optimal manner, subject to the requirement that each consumer receives the specific amount of energy the consumer is entitled to within a specific time horizon. However, in order to do so, the high-level controller requires knowledge of how much energy...... consumer models. The example illustrates that the exact bounds computed by the proposed method leads to a better power distribution than a conventional, conservative approach in case of fast changes in the load....
On truncations of the exact renormalization group
Morris, T R
1994-01-01
We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.
Exact solutions to operator differential equations
International Nuclear Information System (INIS)
Bender, C.M.
1992-01-01
In this talk we consider the Heisenberg equations of motion q = -i(q, H), p = -i(p, H), for the quantum-mechanical Hamiltonian H(p, q) having one degree of freedom. It is a commonly held belief that such operator differential equations are intractable. However, a technique is presented here that allows one to obtain exact, closed-form solutions for huge classes of Hamiltonians. This technique, which is a generalization of the classical action-angle variable methods, allows us to solve, albeit formally and implicitly, the operator differential equations of two anharmonic oscillators whose Hamiltonians are H = p 2 /2 + q 4 /4 and H = p 4 /4 + q 4 /4
Directory of Open Access Journals (Sweden)
INTAN S. AHMAD
2008-04-01
Full Text Available This work presents the application of a primal-dual interior point method to minimax optimisation problems. The algorithm differs significantly from previous approaches as it involves a novel non-monotone line search procedure, which is based on the use of standard penalty methods as the merit function used for line search. The crucial novel concept is the discretisation of the penalty parameter used over a finite range of orders of magnitude and the provision of a memory list for each such order. An implementation within a logarithmic barrier algorithm for bounds handling is presented with capabilities for large scale application. Case studies presented demonstrate the capabilities of the proposed methodology, which relies on the reformulation of minimax models into standard nonlinear optimisation models. Some previously reported case studies from the open literature have been solved, and with significantly better optimal solutions identified. We believe that the nature of the non-monotone line search scheme allows the search procedure to escape from local minima, hence the encouraging results obtained.
Pröschel, Bernhard; Lehmkuhl, Frank
2017-04-01
Reconstructing paleo-landscapes in urban areas is always a special challenge since the research area often witnessed constant human impact over long time periods. Dense building development is a major difficulty, particularly in regard to accessibility to in-situ soils and archaeological findings. It is therefore necessary to use data from various sources and combine methods from different fields to gain a detailed picture of the former topography. The area, which is occupied by the city of Aachen today, looks back on a long history of human influence. Traces of human activity can be dated back to Neolithic time. The first architectural structures and the first road network were built by the Romans about 2000 years ago. From then on, the area of Aachen was more or less continuously inhabited forming today's city. This long history is represented by archaeological findings throughout the city. Several meters of settlement deposits, covering different eras, are present in many locations. Therefore, it can be assumed that the modern topography significantly differs from the pre-roman topography. The main objective of this project is a reconstruction of the paleo-topography of Aachen in order to gain new insights on the spatial preconditions that the first settlers found. Moreover, further attention is given to the question whether and to what extent a paleo-DEM can help to clarify specific open archaeological and historical questions. The main database for the reconstruction are the archaeological excavation reports of the past 150 years, provided by municipal and regional archives. After analyzing these written accounts, we linked this information to drill data, provided by the Geological Service of North Rhine-Westphalia. Together with additional sources like geological and hydrological maps, we generated a GIS-based terrain model. The result is a high-resolution terrain model, representing the undisturbed pre-roman topography of the inner city of Aachen without any
Exact Heat Kernel on a Hypersphere and Its Applications in Kernel SVM
Directory of Open Access Journals (Sweden)
Chenchao Zhao
2018-01-01
Full Text Available Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector machine compared to other competing similarity measures. Specifically, the idea of using heat diffusion on a hypersphere to measure similarity has been previously proposed and tested by Lafferty and Lebanon [1], demonstrating promising results based on a heuristic heat kernel obtained from the zeroth order parametrix expansion; however, how well this heuristic kernel agrees with the exact hyperspherical heat kernel remains unknown. This paper presents a higher order parametrix expansion of the heat kernel on a unit hypersphere and discusses several problems associated with this expansion method. We then compare the heuristic kernel with an exact form of the heat kernel expressed in terms of a uniformly and absolutely convergent series in high-dimensional angular momentum eigenmodes. Being a natural measure of similarity between sample points dwelling on a hypersphere, the exact kernel often shows superior performance in kernel SVM classifications applied to text mining, tumor somatic mutation imputation, and stock market analysis.
New exact solutions of the generalized Zakharov–Kuznetsov ...
Indian Academy of Sciences (India)
YUSUF PANDIR. Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey ... The extended trial equation method; generalized Zakharov–Kuznetsov equation; soliton solution; elliptic ... these, some new exact solutions are obtained by using the trial equation methods. Some of them ...
New exact solutions of the generalized Zakharov–Kuznetsov ...
Indian Academy of Sciences (India)
In this paper, new exact solutions, including soliton, rational and elliptic integral function solutions, for the generalized Zakharov–Kuznetsov modified equal-width equation are obtained using a new approach called the extended trial equation method. In this discussion, a new version of the trial equation method for the ...
Exact Internal Controllability of Maxwell's Equations
International Nuclear Information System (INIS)
Zhang, X.
2000-01-01
In this paper we obtain two exact internal controllability results of Maxwell's equations in a general region by using multiplier techniques. The first one is exact controllability in a short time, in which we obtain the 'optimal' (observability) estimates when the location and the shape of the controller is fixed. What happens if we allow the controller to change? Under some conditions, we show that by doing that the system can be exactly controllable within any given time duration, which is our second exact controllability result
Exact renormalization group for gauge theories
International Nuclear Information System (INIS)
Balaban, T.; Imbrie, J.; Jaffe, A.
1984-01-01
Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study
Exact algorithms for the Steiner tree problem
Wang, Xinhui
2008-01-01
The Steiner tree problem is one of the original 21 NP complete problems, which has wide application in theorey and industry. There are no polynomial time algorithms for it, and exact (acceptable exponential time) algorithms are the best we can obtain for pursuing the exact solution for the all these
Exact, almost and delayed fault detection
DEFF Research Database (Denmark)
Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.
1999-01-01
Considers the problem of fault detection and isolation while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems....... The l-step delayed fault detection problem is also considered for discrete-time systems....
Exact Monte Carlo for molecules
Energy Technology Data Exchange (ETDEWEB)
Lester, W.A. Jr.; Reynolds, P.J.
1985-03-01
A brief summary of the fixed-node quantum Monte Carlo method is presented. Results obtained for binding energies, the classical barrier height for H + H2, and the singlet-triplet splitting in methylene are presented and discussed. 17 refs.
Directory of Open Access Journals (Sweden)
M.G. Hafez
2015-03-01
Full Text Available The (1+1-dimensional nonlinear Klein-Gordon-Zakharov equation considered as a model equation for describing the interaction of the Langmuir wave and the ion acoustic wave in high frequency plasma. By the execution of the exp(-Φ(ξ-expansion, we obtain new explicit and exact traveling wave solutions to this equation. The obtained solutions include kink, singular kink, periodic wave solutions, soliton solutions and solitary wave solutions of bell types. The variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in plasma physics and engineering.
Affine Toda field theory and exact S-matrices
International Nuclear Information System (INIS)
Braden, H.W.; Corrigan, E.; Dorey, P.E.; Sasaki, R.
1989-10-01
The masses and three-point couplings for all affine Toda theories are calculated. The exact factorisable S-matrices are conjectured on the basis of the classical masses and couplings and found, in the case of theories based on simply-laced algebras, to give consistent solutions to the bootstrap. An investigation of the properties of the exact S-matrices in perturbation theory is begun but non-perturbative methods will be required to understand the conjectured duality between weak and strong coupling which appears to be a striking feature of these theories. (author)
New exact solutions of the generalized Zakharov–Kuznetsov ...
Indian Academy of Sciences (India)
soliton, elliptic integral function and Jacobi elliptic function solutions. Apart from all these, some new exact solutions are obtained by using the trial equation methods. Some of them are elliptic integral F, E and functions, Jacobi elliptic function solutions etc. These types of solutions are very important and encounter in various ...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
arising in mathematical physics. Keywords. Exact travelling wave solutions; nonlinear physical models; Kudryashov method. PACS Nos 02.30.Jr; 02.70.Wz; 04.20.Jb. 1. Introduction. The study of nonlinear partial differential equations is an active area of research in applied mathematics, theoretical physics and engineering ...
Thermodynamics of Rh nuclear spins calculated by exact diagonalization
DEFF Research Database (Denmark)
Lefmann, K.; Ipsen, J.; Rasmussen, F.B.
2000-01-01
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 positi...
Exact solutions of some coupled nonlinear diffusion-reaction ...
Indian Academy of Sciences (India)
Exact solutions of some coupled nonlinear diffusion-reaction equations using auxiliary equation method. RANJIT KUMAR. Department of Physics, Dyal Singh College, University of Delhi, Delhi 110 003, India. E-mail: du.ranjit@gmail.com. MS received 1 January 2012; revised 29 February 2012; accepted 10 May 2012.
New exact travelling wave solutions of bidirectional wave equations
Indian Academy of Sciences (India)
The travelling wave solutions may be useful in the theoretical and numerical studies of the model systems. The computer symbolic systems such as Maple and Mathematica allow us to perform complicated and tedious calculations. 2. Exact travelling wave solutions. The standard tanh method was developed by Malfliet [22], ...
A procedure to construct exact solutions of nonlinear evolution ...
Indian Academy of Sciences (India)
Exact solutions; the functional variable method; nonlinear wave equations. PACS Nos 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg. 1. Introduction. The theory of nonlinear dispersive and dissipative wave motion has recently undergone much research. Phenomena in physics and other fields are often described by nonlinear.
The exact probability law for the approximated similarity from the ...
African Journals Online (AJOL)
The exact probability law for the approximated similarity from the Minhashing method. Soumaila Dembele, Gane Samb Lo. Abstract. We propose a probabilistic setting in which we study the probability law of the Rajaraman and Ullman RU algorithm and a modied version of it denoted by RUM. These algorithms aim at ...
Quaternionic formulation of the exact parity model
International Nuclear Information System (INIS)
Brumby, S.P.; Foot, R.; Volkas, R.R.
1996-01-01
The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs
Exact Soft Confidence-Weighted Learning
Wang, Jialei; Zhao, Peilin; Hoi, Steven C. H.
2012-01-01
In this paper, we propose a new Soft Confidence-Weighted (SCW) online learning scheme, which enables the conventional confidence-weighted learning method to handle non-separable cases. Unlike the previous confidence-weighted learning algorithms, the proposed soft confidence-weighted learning method enjoys all the four salient properties: (i) large margin training, (ii) confidence weighting, (iii) capability to handle non-separable data, and (iv) adaptive margin. Our experimental results show ...
Exact Algorithms for Solving Stochastic Games
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels
2012-01-01
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....
Some remarks on exact wormhole solutions
Kuhfittig, Peter K. F.
2010-01-01
Exact wormhole solutions, while eagerly sought after, often have the appearance of being overly specialized or highly artificial. A case for the possible existence of traversable wormholes would be more compelling if an abundance of solutions could be found. It is shown in this note that for many of the wormhole geometries in the literature, the exact solutions obtained imply the existence of large sets of additional solutions.
Exact Fit of Simple Finite Mixture Models
Directory of Open Access Journals (Sweden)
Dirk Tasche
2014-11-01
Full Text Available How to forecast next year’s portfolio-wide credit default rate based on last year’s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year’s portfolio-wide default rate. We point out that the maximum-likelihood (ML approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fixed. From this observation we can conclude that the standard default rate forecast based on last year’s conditional default rates will always be located between last year’s portfolio-wide default rate and the ML forecast for next year. As an application example, cost quantification is then discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem.
Exact controllability for a Thermodiffusion System with locally distributed controls
de Moraes, F. G.; Schulz, R. A.; Soriano, J. A.
2018-03-01
In this work we establish a exact controllability result for a thermodiffusion system, modeled by Cattaneo's law, posed in a one-dimensional domain. In the present model the control mechanisms are effective in a small subinterval of the domain. To obtain the desired results, we prove an observability inequality for the adjoint system which, together with the multiplier methods and the Hilbert Uniqueness Method (HUM) developed by J.L. Lions, gives the controllability.
Hard ellipsoids: Analytically approaching the exact overlap distance
Guevara-Rodríguez, F. de J.; Odriozola, G.
2011-08-01
Following previous work [G. Odriozola and F. de J. Guevara-Rodríguez, J. Chem. Phys. 134, 201103 (2011)], 10.1063/1.3596728, the replica exchange Monte Carlo technique is used to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. Here, in addition to the analytical approximation of the overlap distance given by Berne and Pechukas (BP) and the exact numerical solution of Perram and Wertheim, we tested a simple modification of the original BP approximation (MBP) which corrects the known T-shape mismatch of BP for all aspect ratios. We found that the MBP equation of state shows a very good quantitative agreement with the exact solution. The MBP analytical expression allowed us to study size effects on the previously reported results. For the thermodynamic limit, we estimated the exact 1:5 hard ellipsoid isotropic-nematic transition at the volume fraction 0.343 ± 0.003, and the nematic-solid transition in the volume fraction interval (0.592 ± 0.006) - (0.634 ± 0.008).
Aesthetic Responses to Exact Fractals Driven by Physical Complexity.
Bies, Alexander J; Blanc-Goldhammer, Daryn R; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E
2016-01-01
pattern. Conceptualizations such as Berlyne's and Redies' theories of aesthetics also provide a suitable framework for interpretation of our data with respect to the individual differences that we detect. Future studies that incorporate physiological methods to measure the human aesthetic response to exact fractal patterns would further elucidate our responses to such timeless patterns.
International Nuclear Information System (INIS)
Yang Zonghang
2007-01-01
We find new exact travelling wave solutions for two potential KdV equations which are presented by Foursov [Foursov MV. J Math Phys 2000;41:6173-85]. Compared with the extended tanh-function method, the algorithm used in our paper can obtain some new kinds of exact travelling wave solutions. With the aid of symbolic computation, some novel exact travelling wave solutions of the potential KdV equations are constructed
Energy vs. density on paths toward exact density functionals
DEFF Research Database (Denmark)
Kepp, Kasper Planeta
2018-01-01
Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a “path”. Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness...... inaccessible. To illustrate this, the systems previously studied by Medvedev et al., the first ionization energies of atoms with Z = 1 to 10, the ionization energy of water, and the bond dissociation energies of five diatomic molecules were investigated using CCSD(T)/aug-cc-pV5Z as benchmark at chemical...... accuracy. Four functionals of distinct designs was used: B3LYP, PBE, M06, and S-VWN. For atomic cations regardless of charge and compactness up to Z = 10, the energy effects of the different ρ are
On the exact interpolating function in ABJ theory
Energy Technology Data Exchange (ETDEWEB)
Cavaglià, Andrea [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); Gromov, Nikolay [Mathematics Department, King’s College London,The Strand, London WC2R 2LS (United Kingdom); St. Petersburg INP,Gatchina, 188 300, St.Petersburg (Russian Federation); Levkovich-Maslyuk, Fedor [Mathematics Department, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Nordita, KTH Royal Institute of Technology and Stockholm University,Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden)
2016-12-16
Based on the recent indications of integrability in the planar ABJ model, we conjecture an exact expression for the interpolating function h(λ{sub 1},λ{sub 2}) in this theory. Our conjecture is based on the observation that the integrability structure of the ABJM theory given by its Quantum Spectral Curve is very rigid and does not allow for a simple consistent modification. Under this assumption, we revised the previous comparison of localization results and exact all loop integrability calculations done for the ABJM theory by one of the authors and Grigory Sizov, fixing h(λ{sub 1},λ{sub 2}). We checked our conjecture against various weak coupling expansions, at strong coupling and also demonstrated its invariance under the Seiberg-like duality. This match also gives further support to the integrability of the model. If our conjecture is correct, it extends all the available integrability results in the ABJM model to the ABJ model.
Exact solutions in three-dimensional gravity
Garcia-Diaz, Alberto A
2017-01-01
A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...
Exact black hole formation in three dimensions
Directory of Open Access Journals (Sweden)
Wei Xu
2014-11-01
Full Text Available We consider three dimensional Einstein gravity non-minimally coupled to a real scalar field with a self-interacting scalar potential and present the exact black hole formation in three dimensions. Firstly we obtain an exact time-dependent spherically symmetric solution describing the gravitational collapse to a scalar black hole at the infinite time, i.e. in the static limit. The solution can only be asymptotically AdS because of the No–Go theorem in three dimensions which is resulting from the existence of a smooth black hole horizon. Then we analyze their geometric properties and properties of the time evolution. We also get the exact time-dependent solution in the minimal coupling model after taking a conformal transformation.
Exact solution of the hidden Markov processes
Saakian, David B.
2017-11-01
We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .
Classes of exact Einstein Maxwell solutions
Komathiraj, K.; Maharaj, S. D.
2007-12-01
We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.
Inverse Schroedinger equation and the exact wave function
International Nuclear Information System (INIS)
Nakatsuji, Hiroshi
2002-01-01
Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem
Nonlocal Symmetries and Exact Solutions for PIB Equation
Xin, Xiang-Peng; Miao, Qian; Chen, Yong
2012-09-01
In this paper, the symmetry group of the (2+1)-dimensional Painlevé integrable Burgers (PIB) equations is studied by means of the classical symmetry method. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.
Exact Closed-form Solutions for Lamb's Problem
Feng, X.
2017-12-01
In this work, we report on an exact closedform solution for the displacement at the surfaceof an elastic halfspace elicited by a buried point source that acts at some point underneath thatsurface. This is commonly referred to as the 3D Lamb's problem, for which previous solutionswere restricted to sources and receivers placed at the free surface. By means of the reciprocitytheorem, our solution should also be valid as a means to obtain the displacements at interior pointswhen the source is placed at the free surface. We manage to obtain explicit results by expressingthe solution in terms of elementary algebraic expression as well as elliptic integrals. We anchorour developments on Poissons ratio 0.25 starting from Johnson's numerical, integral transformsolutions. Furthermore, the spatial derivatives of our solutions can be easily acquired in termsof our methods. In the end, our closed-form results agree perfectly with the numerical results ofJohnson, which strongly conrms the correctness of our explicit formulas. It is hoped that in duetime, these formulas may constitute a valuable canonical solution that will serve as a yardstickagainst which other numerical solutions can be compared and measured.In addition, we abstract some terms from our solutions as the generator of the Rayleigh waves.Some basic properties of the Rayleigh waves in the time domain will be indicated in terms of thegenerator. The fareld radiation patterns of P-wave and S-wave elicited by the double-couple forcein the uniform half-space medium could also be acquired from our results.
Exactly marginal deformations from exceptional generalised geometry
Energy Technology Data Exchange (ETDEWEB)
Ashmore, Anthony [Merton College, University of Oxford,Merton Street, Oxford, OX1 4JD (United Kingdom); Mathematical Institute, University of Oxford,Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Gabella, Maxime [Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Graña, Mariana [Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Université, UPMC Paris 05, UMR 7589, LPTHE,75005 Paris (France); Waldram, Daniel [Department of Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)
2017-01-27
We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS{sub 5} flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS{sub 5} flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.
On Exact and Inexact Differentials and Applications
Cortez, L. A. B.; de Oliveira, E. Capelas
2017-01-01
Considering the important role played by mathematical derivatives in the study of physical-chemical processes, this paper discusses the different possibilities and formulations of this concept and its application. In particular, in Chemical Thermodynamics, we study exact differentials associated with the so-called state functions and inexact…
Solitons in nonlocal nonlinear media: Exact solutions
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole
2001-01-01
We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties...... of these solitons and show their stability....
Python for Education: The Exact Cover Problem
Directory of Open Access Journals (Sweden)
2011-06-01
Full Text Available
Python implementation of Algorithm X by Knuth is presented.
Algorithm X finds all solutions to the exact cover problem.
The exemplary results for pentominoes, Latin squares and Sudoku
are given.
Exact nonradial input, output, and productivity measurement
Robert G. Chambers
2002-01-01
The use of measures originally suggested by Bennet, Bowley, and Hicks in the context of cost of living, welfare, and consumer surplus measurement to measure inputs, outputs, and productivity is examined. Suitably normalized versions of the Bennet-Bowley measures are shown to be exact and superlative measures of input, output, and productivity indicators.
Exactly marginal deformations from exceptional generalised geometry
International Nuclear Information System (INIS)
Ashmore, Anthony; Gabella, Maxime; Graña, Mariana; Petrini, Michela; Waldram, Daniel
2017-01-01
We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS 5 flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS 5 flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.
Symmetry Approach and Exact Solutions in Hydrodynamics
Golovin, Sergey V.
2005-01-01
The application of symmetry analysis in hydrodynamics is illustrated by two examples. First is a description of all irrotational barochronous motions of ideal gas. The second is an exact solution of magnetohydrodynamics equations for infinitely conducting media, which describes the flow of so called “special vortex” type.
Exact solutions of holonomic quantum computation
International Nuclear Information System (INIS)
Tanimura, Shogo; Hayashi, Daisuke; Nakahara, Mikio
2004-01-01
Holonomic quantum computation is analyzed from geometrical viewpoint. We develop an optimization scheme in which an arbitrary unitary gate is implemented with a small circle in a complex projective space. Exact solutions for the Hadamard, CNOT and 2-qubit discrete Fourier transformation gates are explicitly constructed
Exactly solvable models of baryon structure
Energy Technology Data Exchange (ETDEWEB)
Bijker, R. [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico. Apartado Postal 70-543, 04510 Mexico D.F. (Mexico); Leviatan, A. [Racah Institute of Physics, The Hebrew University. Jerusalem 91904, Israel (Israel)
1998-12-31
We present a qualitative analysis of the gross features of baryon spectroscopy (masses and form factors) in terms of various exactly solvable models. It is shown that a collective model, in which baryon resonances are interpreted as rotations and vibrations of an oblate symmetric top, provides a good starting point for a more detailed quantitative study. (Author)
Exactly solvable models of baryon structure
International Nuclear Information System (INIS)
Bijker, R.; Leviatan, A.
1998-01-01
We present a qualitative analysis of the gross features of baryon spectroscopy (masses and form factors) in terms of various exactly solvable models. It is shown that a collective model, in which baryon resonances are interpreted as rotations and vibrations of an oblate symmetric top, provides a good starting point for a more detailed quantitative study. (Author)
CAD optimization design of exact mechanism
International Nuclear Information System (INIS)
Wang Yongxue; Liu Jianbo; Ma Yue; Zhao Yingfeng
2001-01-01
Based on the study of the 'laser light magnifier bearing device', the CAD optimization-design technology of exact mechanism is discussed and the design of 'magnifier bearing device' by using CAD software 'PRO/E', CAE software 'ANSYS' and engineering drawing software 'AUTOCAD' as the optimization-design tool is accomplished
Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems
International Nuclear Information System (INIS)
Zabrodin, A.V.
1995-01-01
The algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method is clarified. The quasi-exactly solvable Hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with non-periodic boundary conditions. Applications to Azbel-Hofstadter problem are outlined. 39 refs
Dissipative motion perturbation theory and exact solutions
International Nuclear Information System (INIS)
Lodder, J.J.
1976-06-01
Dissipative motion of classical and quantum systems is described. In particular, attention is paid to systems coupled to the radiation field. A dissipative equation of motion for a particle in an arbitrary potential coupled to the radiation field is derived by means of perturbation theory. The usual divrgencies associated with the radiation field are eliminated by the application of a theory of generalized functions. This theory is developed as a subject in its own right and is presented independently. The introduction of classical zero-point energy makes the classical equa tion of motion for the phase density formally the same as its quantum counterpart. In particular, it is shown that the classical zero-point energy prevents the collapse of a classical H-atom and gives rise to a classical ground state. For systems with a quadratic Hamiltoian, the equation of motion can be solved exactly, even in the continuum limit for the radiation field, by means of the new generalized functions. Classically, the Fokker-Planck equation is found without any approximations, and quantum mechanically, the only approximation is the neglect of the change in the ground state caused by the interaction. The derivation is valid even for strong damping and arbitrarily short times. There is no transient time. For harmonic oscillators complete equivalence is shown to exist between quantum mechanics and classical mechanics with zero-point energy. A discussion of the derivation of the Pauli equation is given and perturbation theory is compared with the exact derivation. The exactly solvable models are used to calculate the Langevin force of the radiation field. The result is that the classical Langevin force is exactly delta-correlated, while the quantum Langevin force is not delta-correlated at all. The fluctuation-dissipation theorem is shown to be an exact consequence of the solution to the equations of motion
Exact renormalization group equation for the Lifshitz critical point
Bervillier, C.
2004-10-01
An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.
Exact solutions for the spin tune for model storage rings
Mane, S R
2002-01-01
We present exact analytical expressions for the spin tune for arbitrary values of the orbital action for several storage ring models. The models we treat contain Siberian Snakes, the use of which is essential to preserve the polarization of beams in high-energy proton storage rings. Our solutions contain some novel features. We also prove a previously conjectured claim about the behavior of spin tuneshifts in rings with multiple Snakes. The conjecture is based on numerical simulations, but our proof is analytical, and also nonperturbative.
Comparison of an exact and moments calculation of reliability
International Nuclear Information System (INIS)
Hockenbury, R.W.; Yeater, M.L.; Hawkins, J.M.; Wilkinson, J.W.
1976-01-01
Present methods for calculating the reliability of reactor systems usually assume constant failure rates for individual components of the system. In principle, if the uncertainty in component failure rates can be expressed in terms of a probability density function, then the probability density function for the overall system reliability can be obtained. The system reliability distribution can then be used to calculate confidence bounds, for example. The probability distribution for the system reliability can also be found by an approximate method, namely the method of moments. In order to compare the exact and approximate results, a simple two element series system is modeled
Exact S matrices and extended supersymmetry
Abdalla, Elcio
1993-01-01
In this revised version we correct some mistakes, realizing the supersymmetry algebra on the exact S matrix, taking into account several phase factros. We study the constraint imposed by supersymmetry on the exact $S$-matrix of $\\Complex P^{n-1}$ model, and compute a non-trivial phase factor in the relation between the $S$-matrix and one of the supersymmetry generators. We discuss several features connected with the physical interpretation of the result. The supersymmetry current is studied in such context as well, and we find some operators appearing in the conservation equation of the supersymmetry current that might be connected with such phase factors. The relation with the literature on the subject is also discussed. hep-th/yymmnnn
Model checking exact cost for attack scenarios
DEFF Research Database (Denmark)
Aslanyan, Zaruhi; Nielson, Flemming
2017-01-01
. However, current model checking does not encompass the exact cost analysis of an attack, which is standard for attack trees. Our first contribution is the logic erPCTL with cost-related operators. The extended logic allows to analyse the probability of an event satisfying given cost bounds and to compute......Attack trees constitute a powerful tool for modelling security threats. Many security analyses of attack trees can be seamlessly expressed as model checking of Markov Decision Processes obtained from the attack trees, thus reaping the benefits of a coherent framework and a mature tool support...... the exact cost of an event. Our second contribution is the model checking algorithm for erPCTL. Finally, we apply our framework to the analysis of attack trees....
Exact computation of the 9-j symbols
International Nuclear Information System (INIS)
Lai Shantao; Chiu Jingnan
1992-01-01
A useful algebraic formula for the 9-j symbol has been rewritten for convenient use on a computer. A simple FORTRAN program for the exact computation of 9-j symbols has been written for the VAX with VMS version V5,4-1 according to this formula. The results agree with the approximate values in existing literature. Some specific values of 9-j symbols needed for the intensity and alignments of three-photon nonresonant transitions are tabulated. Approximate 9-j symbol values beyond the limitation of the computer can also be computed by this program. The computer code of the exact computation of 3-j, 6-j and 9-j symbols are available through electronic mail upon request. (orig.)
Exact Relativistic Magnetized Haloes around Rotating Disks
Directory of Open Access Journals (Sweden)
Antonio C. Gutiérrez-Piñeres
2015-01-01
Full Text Available The study of the dynamics of magnetic fields in galaxies is one of important problems in formation and evolution of galaxies. In this paper, we present the exact relativistic treatment of a rotating disk surrounded by a magnetized material halo. The features of the halo and disk are described by the distributional energy-momentum tensor of a general fluid in canonical form. All the relevant quantities and the metric and electromagnetic potentials are exactly determined by an arbitrary harmonic function only. For instance, the generalized Kuzmin-disk potential is used. The particular class of solutions obtained is asymptotically flat and satisfies all the energy conditions. Moreover, the motion of a charged particle on the halo is described. As far as we know, this is the first relativistic model describing analytically the magnetized halo of a rotating disk.
Exact BPS bound for noncommutative baby Skyrmions
Energy Technology Data Exchange (ETDEWEB)
Domrin, Andrei, E-mail: domrin@mi.ras.ru [Department of Mathematics and Mechanics, Moscow State University, Leninskie gory, 119992, GSP-2, Moscow (Russian Federation); Lechtenfeld, Olaf, E-mail: lechtenf@itp.uni-hannover.de [Institut für Theoretische Physik and Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover (Germany); Linares, Román, E-mail: lirr@xanum.uam.mx [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, C.P. 09340, México D.F. (Mexico); Maceda, Marco, E-mail: mmac@xanum.uam.mx [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, C.P. 09340, México D.F. (Mexico)
2013-11-25
The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory.
Exact solutions and singularities in string theory
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail
Exact diagonalization library for quantum electron models
Iskakov, Sergei; Danilov, Michael
2018-04-01
We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models, including the single-band finite Hubbard cluster and the multi-orbital impurity Anderson model. The observables that can be computed using EDLib are single particle Green's functions and spin-spin correlation functions. This code provides three different types of Hamiltonian matrix storage that can be chosen based on the model.
Tamm's problem in Schwinger's and exact approaches
International Nuclear Information System (INIS)
Afanas'ev, G.N.; Kartavenko, V.G.; Ruzicka, J.
2000-01-01
Schwinger's approach gives a fresh look on Tamm's problem (charge, being initially at rest, exhibits an instant acceleration, moves with a finite velocity, and, after an instant deceleration, goes to the state of rest). Schwinger's angular and frequency distributions are compared with Tamm's ones, which in their turn are compared with exact distributions. Criteria for the validity of Tamm's formulae are checked by numerical calculations
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan
2004-01-01
We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating...... and differentiating these circuits in time linear in their size. We report on experimental results showing the successful compilation, and efficient inference, on relational Bayesian networks whose {\\primula}--generated propositional instances have thousands of variables, and whose jointrees have clusters...
Exact Theory of Compressible Fluid Turbulence
Drivas, Theodore; Eyink, Gregory
2017-11-01
We obtain exact results for compressible turbulence with any equation of state, using coarse-graining/filtering. We find two mechanisms of turbulent kinetic energy dissipation: scale-local energy cascade and ``pressure-work defect'', or pressure-work at viscous scales exceeding that in the inertial-range. Planar shocks in an ideal gas dissipate all kinetic energy by pressure-work defect, but the effect is omitted by standard LES modeling of pressure-dilatation. We also obtain a novel inverse cascade of thermodynamic entropy, injected by microscopic entropy production, cascaded upscale, and removed by large-scale cooling. This nonlinear process is missed by the Kovasznay linear mode decomposition, treating entropy as a passive scalar. For small Mach number we recover the incompressible ``negentropy cascade'' predicted by Obukhov. We derive exact Kolmogorov 4/5th-type laws for energy and entropy cascades, constraining scaling exponents of velocity, density, and internal energy to sub-Kolmogorov values. Although precise exponents and detailed physics are Mach-dependent, our exact results hold at all Mach numbers. Flow realizations at infinite Reynolds are ``dissipative weak solutions'' of compressible Euler equations, similarly as Onsager proposed for incompressible turbulence.
On the exactness of soft theorems
Guerrieri, Andrea L.; Huang, Yu-tin; Li, Zhizhong; Wen, Congkao
2017-12-01
Soft behaviours of S-matrix for massless theories reflect the underlying symmetry principle that enforces its masslessness. As an expansion in soft momenta, sub-leading soft theorems can arise either due to (I) unique structure of the fundamental vertex or (II) presence of enhanced broken-symmetries. While the former is expected to be modified by infrared or ultraviolet divergences, the latter should remain exact to all orders in perturbation theory. Using current algebra, we clarify such distinction for spontaneously broken (super) Poincaré and (super) conformal symmetry. We compute the UV divergences of DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft theorems, while type (I) are shown to be broken and the soft-modifying higher-dimensional operators are identified. As further evidence for the exactness of type (II) soft theorems, we consider the α' expansion of both super and bosonic open strings amplitudes, and verify the validity of the translation symmetry breaking soft-theorems up to O({α}^' 6}) . Thus the massless S-matrix of string theory "knows" about the presence of D-branes.
Piezoelectric vibration damping using resonant shunt circuits: an exact solution
International Nuclear Information System (INIS)
Soltani, P; Kerschen, G; Tondreau, G; Deraemaeker, A
2014-01-01
The objective of this paper is to propose an exact closed-form solution to the H ∞ optimization of piezoelectric materials shunted with inductive-resistive passive electrical circuits. Realizing that Den Hartog's method which imposes fixed points of equal height in the receptance transfer function is approximate, the parameters of the piezoelectric tuned vibration absorber are calculated through the direct minimization of the maxima of the receptance. The method is applied to a one-degree-of-freedom primary oscillator considering various values of the electromechanical coupling coefficients. (paper)
Ghinita, Gabriel
2010-12-15
Mobile devices with global positioning capabilities allow users to retrieve points of interest (POI) in their proximity. To protect user privacy, it is important not to disclose exact user coordinates to un-trusted entities that provide location-based services. Currently, there are two main approaches to protect the location privacy of users: (i) hiding locations inside cloaking regions (CRs) and (ii) encrypting location data using private information retrieval (PIR) protocols. Previous work focused on finding good trade-offs between privacy and performance of user protection techniques, but disregarded the important issue of protecting the POI dataset D. For instance, location cloaking requires large-sized CRs, leading to excessive disclosure of POIs (O({pipe}D{pipe}) in the worst case). PIR, on the other hand, reduces this bound to O(√{pipe}D{pipe}), but at the expense of high processing and communication overhead. We propose hybrid, two-step approaches for private location-based queries which provide protection for both the users and the database. In the first step, user locations are generalized to coarse-grained CRs which provide strong privacy. Next, a PIR protocol is applied with respect to the obtained query CR. To protect against excessive disclosure of POI locations, we devise two cryptographic protocols that privately evaluate whether a point is enclosed inside a rectangular region or a convex polygon. We also introduce algorithms to efficiently support PIR on dynamic POI sub-sets. We provide solutions for both approximate and exact NN queries. In the approximate case, our method discloses O(1) POI, orders of magnitude fewer than CR- or PIR-based techniques. For the exact case, we obtain optimal disclosure of a single POI, although with slightly higher computational overhead. Experimental results show that the hybrid approaches are scalable in practice, and outperform the pure-PIR approach in terms of computational and communication overhead. © 2010
Stereospecific assignments in proteins using exact NOEs
Energy Technology Data Exchange (ETDEWEB)
Orts, Julien; Vögeli, Beat; Riek, Roland, E-mail: roland.riek@phys.chem.ethz.ch [Swiss Federal Institute of Technology, Laboratory of Physical Chemistry (Switzerland); Güntert, Peter, E-mail: guentert@em.uni-frankfurt.de [Goethe University Frankfurt am Main, Center for Biomolecular Magnetic Resonance, Institute of Biophysical Chemistry (Germany)
2013-10-18
Recently developed methods to measure distances in proteins with high accuracy by “exact” nuclear Overhauser effects (eNOEs) make it possible to determine stereospecific assignments, which are particularly important to fully exploit the accuracy of the eNOE distance measurements. Stereospecific assignments are determined by comparing the eNOE-derived distances to protein structure bundles calculated without stereospecific assignments, or an independently determined crystal structure. The absolute and relative CYANA target function difference upon swapping the stereospecific assignment of a diastereotopic group yields the respective stereospecific assignment. We applied the method to the eNOE data set that has recently been obtained for the third immunoglobulin-binding domain of protein G (GB3). The 884 eNOEs provide relevant data for 47 of the total of 75 diastereotopic groups. Stereospecific assignments could be established for 45 diastereotopic groups (96 %) using the X-ray structure, or for 27 diastereotopic groups (57 %) using structures calculated with the eNOE data set without stereospecific assignments, all of which are in agreement with those determined previously. The latter case is relevant for structure determinations based on eNOEs. The accuracy of the eNOE distance measurements is crucial for making stereospecific assignments because applying the same method to the traditional NOE data set for GB3 with imprecise upper distance bounds yields only 13 correct stereospecific assignments using the X-ray structure or 2 correct stereospecific assignments using NMR structures calculated without stereospecific assignments.
A Large Class of Exact Solutions to the One-Dimensional Schrodinger Equation
Karaoglu, Bekir
2007-01-01
A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrodinger equation. The method is simple and easy to implement. (Contains 1 table and 1 figure.)
Exact path-integral evaluation of locally interacting systems: The subtlety of operator ordering
Taniguchi, Nobuhiko
2017-10-01
We discuss how one calculates the coherent path integrals for locally interacting systems, where some inconsistencies with exact results have been reported previously. It is shown that the operator ordering subtlety that is hidden in the local interaction term modifies the Hubbard-Stratonovich transformation in the continuous time formulation, and it helps reproduce known results by the operator method. We also demonstrate that many-body effects in the strong interaction limit can be well characterized by the free-particle theory that is subject to annealed random potentials and dynamical gauge (or phase) fields. The present treatment expands the conventional paradigm of the one-particle description, and it provides a simple, viable picture for strongly correlated materials of either bosonic or fermionic systems.
An exact solution in Einstein-Cartan
International Nuclear Information System (INIS)
Roque, W.L.
1982-01-01
The exact solution of the field equations of the Einstein-Cartan theory is obtained for an artificial dust of radially polarized spins, with spherical symmetry and static. For a best estimation of the effect due the spin, the energy-momentum metric tensor is considered null. The gravitational field dynamics is studied for several torsion strengths, through the massive and spinless test-particle moviment, in particular for null torsion Schwarzschild solutions is again obtained. It is observed that the gravitational effects related to the torsin (spin) sometimes are attractives sometimes are repulsives, depending of the torsion values and of the test-particle position and velocity. (L.C.) [pt
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark
2006-01-01
We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...... by evaluating and differentiating these circuits in time linear in their size. We report on experimental results showing successful compilation and efficient inference on relational Bayesian networks, whose PRIMULA--generated propositional instances have thousands of variables, and whose jointrees have clusters...
International Nuclear Information System (INIS)
Abdou, M.A.
2008-01-01
The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics
A fast, exact code for scattered thermal radiation compared with a two-stream approximation
International Nuclear Information System (INIS)
Cogley, A.C.; Pandey, D.K.
1980-01-01
A two-stream accuracy study for internally (thermal) driven problems is presented by comparison with a recently developed 'exact' adding/doubling method. The resulting errors in external (or boundary) radiative intensity and flux are usually larger than those for the externally driven problems and vary substantially with the radiative parameters. Error predictions for a specific problem are difficult. An unexpected result is that the exact method is computationally as fast as the two-stream approximation for nonisothermal media
Exact simulation of Brown-Resnick random fields at a finite number of locations
DEFF Research Database (Denmark)
Dieker, Ton; Mikosch, Thomas Valentin
2015-01-01
We propose an exact simulation method for Brown-Resnick random fields, building on new representations for these stationary max-stable fields. The main idea is to apply suitable changes of measure.......We propose an exact simulation method for Brown-Resnick random fields, building on new representations for these stationary max-stable fields. The main idea is to apply suitable changes of measure....
Off-diagonal Bethe ansatz for exactly solvable models
Wang, Yupeng; Cao, Junpeng; Shi, Kangjie
2015-01-01
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.
Exact combinatorial approach to finite coagulating systems
Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr
2018-02-01
This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.
Exact Solution for a Gravitational Wave Detector
Rabounski, Dmitri; Borissova, Larissa
2008-04-01
The experimental statement on gravitational waves proceeds from the equation for deviating geodesic lines and the equation for deviating non-geodesics. Weber's result was not based upon an exact solution to the equations, but on an approximate analysis of what could be expected: he expected that a plane weak wave of the space metric may displace two resting particles with respect to each other. In this work, exact solutions are presented for the deviation equation of both free and spring-connected particles. The solutions show that a gravitational wave may displace particles in a two-particle system only if they are in motion with respect to each other or the local space (there is no effect if they are at rest). Thus, gravitational waves produce a parametric effect on a two-particle system. According to the solutions, an altered detector construction can be proposed such that it might interact with gravitational waves: 1) a horizontally suspended cylindrical pig, whose butt-ends have basic relative oscillations induced by a laboratory source; 2) a free-mass detector where suspended mirrors have laboratory induced basic oscillations relative to each other.
Exact multi-restricted Schur polynomial correlators
International Nuclear Information System (INIS)
Bhattacharyya, Rajsekhar; Koch, Robert de Mello; Stephanou, Michael
2008-01-01
We derive a product rule satisfied by restricted Schur polynomials. We focus mostly on the case that the restricted Schur polynomial is built using two matrices, although our analysis easily extends to more than two matrices. This product rule allows us to compute exact multi-point correlation functions of restricted Schur polynomials, in the free field theory limit. As an example of the use of our formulas, we compute two point functions of certain single trace operators built using two matrices and three point functions of certain restricted Schur polynomials, exactly, in the free field theory limit. Our results suggest that gravitons become strongly coupled at sufficiently high energy, while the restricted Schur polynomials for totally antisymmetric representations remain weakly interacting at these energies. This is in perfect accord with the half-BPS (single matrix) results of hep-th/0512312. Finally, by studying the interaction of two restricted Schur polynomials we suggest a physical interpretation for the labels of the restricted Schur polynomial: the composite operator χ R,(r n ,r m ) (Z,X) is constructed from the half BPS 'partons' χ r n (Z) and χ r m (X).
Transversal magnetotransport in Weyl semimetals: Exact numerical approach
Behrends, Jan; Kunst, Flore K.; Sbierski, Björn
2018-02-01
Magnetotransport experiments on Weyl semimetals are essential for investigating the intriguing topological and low-energy properties of Weyl nodes. If the transport direction is perpendicular to the applied magnetic field, experiments have shown a large positive magnetoresistance. In this work we present a theoretical scattering matrix approach to transversal magnetotransport in a Weyl node. Our numerical method confirms and goes beyond the existing perturbative analytical approach by treating disorder exactly. It is formulated in real space and is applicable to mesoscopic samples as well as in the bulk limit. In particular, we study the case of clean and strongly disordered samples.
Directory of Open Access Journals (Sweden)
Matthew J Simpson
Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0
Directory of Open Access Journals (Sweden)
Márcio Alves Vieira Belo
2004-08-01
describe the knowledge, attitudes and practices related to previous contraceptive methods used among pregnant teenagers as well as to outline some sociodemographic characteristics and sexual practices. METHODS: An observational study associated to the KAP (Knowledge, Attitudes, and Practices survey was carried out in 156 pregnant teenagers aged 19 years or more. A structured questionnaire was applied before their first prenatal visit from October 1999 to August 2000. Univariate and bivariate analyses were performed using Pearson's and Yates' chi-square test and logistic regression. RESULTS: The adolescents had an average age of 16.1 years and most were in their first pregnancy (78.8%. Average age of menarche was 12.2 years and their first sexual intercourse was at the age of 14.5 years. Condoms (99.4% and oral contraceptives (98% were the most common contraceptive methods known. Of all, 67.3% were not using any contraceptive method before getting pregnant. The main reason reported for not using any contraceptive method was wanting to get pregnant (24.5%. The older ones who reported having religious beliefs and had a higher socioeconomic status had better knowledge on contraceptive methods. Teenagers who had had previous pregnancies reported more often use of contraceptive methods before getting pregnant. CONCLUSIONS: The pregnant teenagers showed to have adequate knowledge of contraceptive methods and agreed to use them throughout their teenage years. Religion, age group, and socioeconomic status were directly related to their knowledge on contraceptive methods, and multiple pregnancies brought more awareness on that. Of all, 54% had used any contraceptive on first sexual intercourse but their use decreased over time and shortly after their first intercourse the studied teenagers got pregnant.
Some exact BPS solutions for exotic vortices and monopoles
Directory of Open Access Journals (Sweden)
Handhika S. Ramadhan
2016-07-01
Full Text Available We present several analytical solutions of BPS vortices and monopoles in the generalized Abelian Maxwell–Higgs and Yang–Mills–Higgs theories, respectively. These models have recently been extensively studied and several exact solutions have already been obtained in [1,2]. In each theory, the dynamics is controlled by the additional two positive scalar-field-dependent functions, f(|ϕ| and w(|ϕ|. For the case of vortices, we work in the ordinary symmetry-breaking Higgs potential, while for the case of monopoles we have the ordinary condition of the Prasad–Sommerfield limit. Our results generalize the exact solutions found previously. We also present solutions for BPS vortices with higher winding number. These solutions suffer from the condition that w(|ϕ| has negative value at some finite range of r, but we argue that since it satisfies the weaker positive-value conditions then the corresponding energy density is still positive-definite and, thus, they are acceptable BPS solutions.
Some exact BPS solutions for exotic vortices and monopoles
Ramadhan, Handhika S.
2016-07-01
We present several analytical solutions of BPS vortices and monopoles in the generalized Abelian Maxwell-Higgs and Yang-Mills-Higgs theories, respectively. These models have recently been extensively studied and several exact solutions have already been obtained in [1,2]. In each theory, the dynamics is controlled by the additional two positive scalar-field-dependent functions, f (| ϕ |) and w (| ϕ |). For the case of vortices, we work in the ordinary symmetry-breaking Higgs potential, while for the case of monopoles we have the ordinary condition of the Prasad-Sommerfield limit. Our results generalize the exact solutions found previously. We also present solutions for BPS vortices with higher winding number. These solutions suffer from the condition that w (| ϕ |) has negative value at some finite range of r, but we argue that since it satisfies the weaker positive-value conditions then the corresponding energy density is still positive-definite and, thus, they are acceptable BPS solutions.
A new auxiliary equation and exact travelling wave solutions of nonlinear equations
International Nuclear Information System (INIS)
Sirendaoreji
2006-01-01
A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations
An Exact Method for the Double TSP with Multiple Stacks
DEFF Research Database (Denmark)
Larsen, Jesper; Lusby, Richard Martin; Ehrgott, Matthias
The double travelling salesman problem with multiple stacks (DTSPMS) is a pickup and delivery problem in which all pickups must be completed before any deliveries can be made. The problem originates from a real-life application where a 40 foot container (configured as 3 columns of 11 rows) is used...
An Exact Method for the Double TSP with Multiple Stacks
DEFF Research Database (Denmark)
Lusby, Richard Martin; Larsen, Jesper; Ehrgott, Matthias
2010-01-01
The double travelling salesman problem with multiple stacks (DTSPMS) is a pickup and delivery problem in which all pickups must be completed before any deliveries can be made. The problem originates from a real-life application where a 40 foot container (configured as 3 columns of 11 rows) is used...
Optimization of the drayage problem using exact methods
DEFF Research Database (Denmark)
Reinhardt, Line Blander; Pisinger, David; Spoorendonk, Simon
2016-01-01
vehicle routing problems to schedule pre- and end-haulage of containers, and perform tests on data from a major liner shipping company. The paper considers several versions of the scheduling problem such as having multiple empty container depots, and having to balance the empty container depot levels....... The influence of the side constraints on the overall cost is analysed. By exploring the fact that the number of possible routes in the considered case is quite limited, we show that the model can be solved within a minute by use of column enumeration. Alternative constraints and problem formulations...
An Exact Method for a Discrete Multiobjective Linear Fractional Optimization
Directory of Open Access Journals (Sweden)
Mohamed El-Amine Chergui
2008-01-01
Full Text Available Integer linear fractional programming problem with multiple objective (MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated.
Exact Molecular Typing of Aspergillus fumigatus. Methods and Applications.
Valk-van Haren, J.A. de
2008-01-01
Aspergillus species are widely distributed fungi that release large amounts of airborne conidia that are dispersed in the environment. Aspergillus fumigatus is the species most frequently isolated from human infections. In this thesis a novel assay for fingerprinting A. fumigatus is described and
Exactly solvable cellular automaton traffic jam model.
Kearney, Michael J
2006-12-01
A detailed study is undertaken of the v{max}=1 limit of the cellular automaton traffic model proposed by Nagel and Paczuski [Phys. Rev. E 51, 2909 (1995)]. The model allows one to analyze the behavior of a traffic jam initiated in an otherwise freely flowing stream of traffic. By mapping onto a discrete-time queueing system, itself related to various problems encountered in lattice combinatorics, exact results are presented in relation to the jam lifetime, the maximum jam length, and the jam mass (the space-time cluster size or integrated vehicle waiting time), both in terms of the critical and the off-critical behavior. This sets existing scaling results in their natural context and also provides several other interesting results in addition.
An exact operator that knows its location
Anand, N.; Chen, Hongbin; Fitzpatrick, A. Liam; Kaplan, Jared; Li, Daliang
2018-02-01
We use conformal symmetry to define an AdS3 proto-field ϕ as an exact linear combination of Virasoro descendants of a CFT2 primary operator O . We find that both symmetry considerations and a gravitational Wilson line formalism lead to the same results. The operator ϕ has many desirable properties; in particular it has correlators that agree with gravitational perturbation theory when expanded at large c, and that automatically take the correct form in all vacuum AdS3 geometries, including BTZ black hole backgrounds. In the future it should be possible to use ϕ to probe bulk locality and black hole horizons at a non-perturbative level.
Exactly solvable cellular automaton traffic jam model
Kearney, Michael J.
2006-12-01
A detailed study is undertaken of the vmax=1 limit of the cellular automaton traffic model proposed by Nagel and Paczuski [Phys. Rev. E 51, 2909 (1995)]. The model allows one to analyze the behavior of a traffic jam initiated in an otherwise freely flowing stream of traffic. By mapping onto a discrete-time queueing system, itself related to various problems encountered in lattice combinatorics, exact results are presented in relation to the jam lifetime, the maximum jam length, and the jam mass (the space-time cluster size or integrated vehicle waiting time), both in terms of the critical and the off-critical behavior. This sets existing scaling results in their natural context and also provides several other interesting results in addition.
Exactly soluble QCD and confinement of quarks
International Nuclear Information System (INIS)
Rusakov, B.
1997-01-01
An exactly soluble non-perturbative model of the pure gauge QCD is derived as a weak coupling limit of the lattice theory in plaquette formulation [B. Rusakov, Phys. Lett. B 398 (1997) 331]. The model represents QCD as a theory of the weakly interacting field strength fluxes. The area law behavior of the Wilson loop average is a direct result of this representation: the total flux through macroscopic loop is the additive (due to the weakness of the interaction) function of the elementary fluxes. The compactness of the gauge group is shown to be the factor which prevents the elementary fluxes contributions from cancellation. There is no area law in the non-compact theory. (orig.)
An exactly solvable system from quantum optics
Energy Technology Data Exchange (ETDEWEB)
Maciejewski, Andrzej J., E-mail: maciejka@astro.ia.uz.zgora.pl [J. Kepler Institute of Astronomy, University of Zielona Góra, Licealna 9, PL-65-417 Zielona Góra (Poland); Przybylska, Maria, E-mail: M.Przybylska@if.uz.zgora.pl [Institute of Physics, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra (Poland); Stachowiak, Tomasz, E-mail: stachowiak@cft.edu.pl [Center for Theoretical Physics PAS, Al. Lotników 32/46, 02-668 Warsaw (Poland)
2015-07-31
We investigate a generalisation of the Rabi system in the Bargmann–Fock representation. In this representation the eigenproblem of the considered quantum model is described by a system of two linear differential equations with one independent variable. The system has only one irregular singular point at infinity. We show how the quantisation of the model is related to asymptotic behaviour of solutions in a vicinity of this point. The explicit formulae for the spectrum and eigenfunctions of the model follow from an analysis of the Stokes phenomenon. An interpretation of the obtained results in terms of differential Galois group of the system is also given. - Highlights: • New exactly solvable system from quantum optics is found. • Normalisation condition for system in Bargmann representation is used. • Formulae for spectrum and eigenfunctions from analysis of Stokes phenomenon are given.
Exact integrability in quantum field theory and statistical systems
International Nuclear Information System (INIS)
Thacker, H.B.
1981-01-01
The properties of exactly integrable two-dimensional quantum systems are reviewed and discussed. The nature of exact integrability as a physical phenomenon and various aspects of the mathematical formalism are explored by discussing several examples, including detailed treatments of the nonlinear Schroedinger (delta-function gas) model, the massive Thirring model, and the six-vertex (ice) model. The diagonalization of a Hamiltonian by Bethe's Ansatz is illustrated for the nonlinear Schroedinger model, and the integral equation method of Lieb for obtaining the spectrum of the many-body system from periodic boundary conditions is reviewed. Similar methods are applied to the massive Thirring model, where the fermion-antifermion and bound-state spectrum are obtained explicitly by the integral equation method. After a brief review of the classical inverse scattering method, the quantum inverse method for the nonlinear Schroedinger model is introduced and shown to be an algebraization of the Bethe Ansatz technique. In the quantum inverse method, an auxiliary linear problem is used to define nonlocal operators which are functionals of the original local field on a fixed-time string of arbitrary length. The particular operators for which the string is infinitely long (free boundary conditions) or forms a closed loop around a cylinder (periodic boundary conditions) correspond to the quantized scattering data and have a special significance. One of them creates the Bethe eigenstates, while the other is the generating function for an infinite number of conservation laws. The analogous operators on a lattice are constructed for the symmetric six-vertex model, where the object which corresponds to a solution of the auxiliary linear problem is a string of vertices contracted over horizontal links (arrows). The relationship between the quantum inverse method and the transfer matrix formalism is exhibited
Exact supersymmetric string solutions in curved gravitational backgrounds
Antoniadis, Ignatios; Kounnas, Costas
1994-01-01
We construct a new class of exact and stable superstring solutions based on $N=4$ superconformal world-sheet symmetry. In a subclass of these, the full spectrum of string excitations is derived in a modular-invariant way. In the weak curvature limit, our solutions describe a target space with non-trivial metric and topology, and generalize the previously known (semi) wormhole. The effective field theory limit is identified in certain cases, with solutions of the $N=4$ and $N=8$ extended gauged supergravities, in which the number of space-time supersymmetries is reduced by a factor of 2 because of the presence of non-trivial dilaton, gravitational and/or gauge backgrounds. In the context of string theory, our solutions correspond to stable non-critical superstrings in the strong coupling region; the super-Liouville field couples to a unitary matter system with central charge $5\\le{\\hat c}_M\\le 9$.
Exact marginality in open string field theory. A general framework
International Nuclear Information System (INIS)
Kiermaier, M.
2007-07-01
We construct analytic solutions of open bosonic string field theory for any exactly marginal deformation in any boundary conformal field theory when properly renormalized operator products of the marginal operator are given. We explicitly provide such renormalized operator products for a class of marginal deformations which include the deformations of flat D-branes in flat backgrounds by constant massless modes of the gauge field and of the scalar fields on the D-branes, the cosine potential for a space-like coordinate, and the hyperbolic cosine potential for the time-like coordinate. In our construction we use integrated vertex operators, which are closely related to finite deformations in boundary conformal field theory, while previous analytic solutions were based on unintegrated vertex operators. We also introduce a modified star product to formulate string field theory around the deformed background. (orig.)
Jargalsaikhan, Bolor
2013-01-01
Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out
Exact traveling wave solutions for system of nonlinear evolution equations.
Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H
2016-01-01
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.
Propagation of nuclear data uncertainty: Exact or with covariances
Directory of Open Access Journals (Sweden)
van Veen D.
2010-10-01
Full Text Available Two distinct methods of propagation for basic nuclear data uncertainties to large scale systems will be presented and compared. The “Total Monte Carlo” method is using a statistical ensemble of nuclear data libraries randomly generated by means of a Monte Carlo approach with the TALYS system. These libraries are then directly used in a large number of reactor calculations (for instance with MCNP after which the exact probability distribution for the reactor parameter is obtained. The second method makes use of available covariance files and can be done in a single reactor calculation (by using the perturbation method. In this exercise, both methods are using consistent sets of data files, which implies that covariance files used in the second method are directly obtained from the randomly generated nuclear data libraries from the first method. This is a unique and straightforward comparison allowing to directly apprehend advantages and drawbacks of each method. Comparisons for different reactions and criticality-safety benchmarks from 19F to actinides will be presented. We can thus conclude whether current methods for using covariance data are good enough or not.
On a revisit to the Painlevé test for integrability and exact solutions ...
Indian Academy of Sciences (India)
... the same equations and keeping the singularity manifold completely general in nature. It has been found that the equations, in real form, pass the Painlevé test for integrability. The truncation procedure of the same analysis leads to non-trivial exact solutions obtained previously and auto-Backlund transformation between ...
Generation of exact solutions to the Einstein field equations for homogeneous space--time
International Nuclear Information System (INIS)
Hiromoto, R.E.
1978-01-01
A formalism is presented capable of finding all homogeneous solutions of the Einstein field equations with an arbitrary energy-stress tensor. Briefly the method involves the classification of the four-dimensional Lie algebra over the reals into nine different broad classes, using only the Lorentz group. Normally the classification of Lie algebras means that one finds all essentially different solutions of the Jacobi identities, i.e., there exists no nonsingular linear transformation which transforms two sets of structure constants into the other. This approach is to utilize the geometrical considerations of the homogeneous spacetime and field equations to be solved. Since the set of orthonormal basis vectors is not only endowed with a Minkowskian metric, but also constitutes the vector space of our four-dimensional Lie algebras, the Lie algebras are classified against the Lorentz group restricts the linear group of transformations, denoting the essentially different Lie algebras, into nine different broad classes. The classification of the four-dimensional Lie algebras represents the unification of various methods previously introduced by others. Where their methods found only specific solutions to the Einstein field equations, systematic application of the nine different classes of Lie algebras guarantees the extraction of all solutions. Therefore, the methods of others were extended, and their foundations of formalism which goes beyond the present literature of exact homogeneous solutions to the Einstein field equations is built upon
Duality invariant class of exact string backgrounds
Klimcík, C
1994-01-01
We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.
STELLAR: fast and exact local alignments
Directory of Open Access Journals (Sweden)
Weese David
2011-10-01
Full Text Available Abstract Background Large-scale comparison of genomic sequences requires reliable tools for the search of local alignments. Practical local aligners are in general fast, but heuristic, and hence sometimes miss significant matches. Results We present here the local pairwise aligner STELLAR that has full sensitivity for ε-alignments, i.e. guarantees to report all local alignments of a given minimal length and maximal error rate. The aligner is composed of two steps, filtering and verification. We apply the SWIFT algorithm for lossless filtering, and have developed a new verification strategy that we prove to be exact. Our results on simulated and real genomic data confirm and quantify the conjecture that heuristic tools like BLAST or BLAT miss a large percentage of significant local alignments. Conclusions STELLAR is very practical and fast on very long sequences which makes it a suitable new tool for finding local alignments between genomic sequences under the edit distance model. Binaries are freely available for Linux, Windows, and Mac OS X at http://www.seqan.de/projects/stellar. The source code is freely distributed with the SeqAn C++ library version 1.3 and later at http://www.seqan.de.
Pure N=2 super Yang-Mills and exact WKB
Energy Technology Data Exchange (ETDEWEB)
Kashani-Poor, Amir-Kian; Troost, Jan [Laboratoire de Physique Théorique, Ecole Normale Supérieure,24 rue Lhomond, 75005 Paris (France)
2015-08-31
We apply exact WKB methods to the study of the partition function of pure N=2ϵ{sub i}-deformed gauge theory in four dimensions in the context of the 2d/4d correspondence. We study the partition function at leading order in ϵ{sub 2}/ϵ{sub 1} (i.e. at large central charge) and in an expansion in ϵ{sub 1}. We find corrections of the form ∼exp [−((/tiny SW periods)/(ϵ{sub 1}))] to this expansion. We attribute these to the exchange of the order of summation over gauge instanton number and over powers of ϵ{sub 1} when passing from the Nekrasov form of the partition function to the topological string theory inspired form. We conjecture that such corrections should be computable from a worldsheet perspective on the partition function. Our results follow upon the determination of the Stokes graphs associated to the Mathieu equation with complex parameters and the application of exact WKB techniques to compute the Mathieu characteristic exponent.
Pure N=2 super Yang-Mills and exact WKB
International Nuclear Information System (INIS)
Kashani-Poor, Amir-Kian; Troost, Jan
2015-01-01
We apply exact WKB methods to the study of the partition function of pure N=2ϵ i -deformed gauge theory in four dimensions in the context of the 2d/4d correspondence. We study the partition function at leading order in ϵ 2 /ϵ 1 (i.e. at large central charge) and in an expansion in ϵ 1 . We find corrections of the form ∼exp [−((/tiny SW periods)/(ϵ 1 ))] to this expansion. We attribute these to the exchange of the order of summation over gauge instanton number and over powers of ϵ 1 when passing from the Nekrasov form of the partition function to the topological string theory inspired form. We conjecture that such corrections should be computable from a worldsheet perspective on the partition function. Our results follow upon the determination of the Stokes graphs associated to the Mathieu equation with complex parameters and the application of exact WKB techniques to compute the Mathieu characteristic exponent.
Exact and Approximate Solutions for Transient Squeezing Flow
Lang, Ji; Santhanam, Sridhar; Wu, Qianhong
2017-11-01
In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration is negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear, and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process, and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity of the analytical approaches. The study presented herein fills the gap in the literature, and will have a broad impact in industrial and biomedical applications. This work is supported by National Science Foundation CBET Fluid Dynamics Program under Award #1511096, and supported by the Seed Grant from The Villanova Center for the Advancement of Sustainability in Engineering (VCASE).
Exact complexity: The spectral decomposition of intrinsic computation
Energy Technology Data Exchange (ETDEWEB)
Crutchfield, James P., E-mail: chaos@ucdavis.edu [Complexity Sciences Center and Department of Physics, University of California at Davis, One Shields Avenue, Davis, CA 95616 (United States); Ellison, Christopher J., E-mail: cellison@wisc.edu [Center for Complexity and Collective Computation, University of Wisconsin-Madison, Madison, WI 53706 (United States); Riechers, Paul M., E-mail: pmriechers@ucdavis.edu [Complexity Sciences Center and Department of Physics, University of California at Davis, One Shields Avenue, Davis, CA 95616 (United States)
2016-03-06
We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full eigenvalue spectrum of the mixed-state presentation of a process's ϵ-machine causal-state dynamic. Measures include correlation functions, power spectra, past-future mutual information, transient and synchronization informations, and many others. As a result, a direct and complete analysis of intrinsic computation is now available for the temporal organization of finitary hidden Markov models and nonlinear dynamical systems with generating partitions and for the spatial organization in one-dimensional systems, including spin systems, cellular automata, and complex materials via chaotic crystallography. - Highlights: • We provide exact, closed-form expressions for a hidden stationary process' intrinsic computation. • These include information measures such as the excess entropy, transient information, and synchronization information and the entropy-rate finite-length approximations. • The method uses an epsilon-machine's mixed-state presentation. • The spectral decomposition of the mixed-state presentation relies on the recent development of meromorphic functional calculus for nondiagonalizable operators.
Supersymmetric non-Abelian gauge models; the exact β-function from one loop of perturbation theory
International Nuclear Information System (INIS)
Vainshtein, A.I.; Zakharov, V.I.; Shifman, M.A.
1986-01-01
A method for calculating the exact β-function (in all orders in the coupling constant), proposed earlier in supersymmetric electrodynamics, is generalized. The starting point is the observation that the low-energy effective action is exhausted by one loop, provided that the theory is supersymmetrically regularized both in the ultraviolet and in the infrared region in four dimensions. For the ultraviolet regularization the Pauli-Villars method is used, while for the infrared regularization two variants are considered. The first: quantization in a box of finite volume L 3 : is universally applicable to any gauge theory. The second variant is based on an effective Higgs mechanism for generation of mass, and requires the presence of certain matter superfields in the Lagrangian. For the second method a necessary condition is the existence of flat directions: so-called valleys along which the energy of the vacuum vanishes. We quantize the field near a nonzero value of the scalar field from the bottom of the valley. After calculation of the one-loop effective action both variants give for the β-function the same exact expression which, in addition, coincides with our previous result extracted from instanton calculus. A few remarks on the problem of anomalies in supersymmetric gauge theories are presented
Directory of Open Access Journals (Sweden)
Heng Wang
2016-01-01
Full Text Available By using the method of dynamical system, the exact travelling wave solutions of the higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms are studied. Based on this method, all phase portraits of the system in the parametric space are given with the aid of the Maple software. All possible bounded travelling wave solutions, such as solitary wave solutions, kink and anti-kink wave solutions, and periodic travelling wave solutions, are obtained, respectively. The results presented in this paper improve the related previous conclusions.
Concomitant and previous osteoporotic vertebral fractures.
Lenski, Markus; Büser, Natalie; Scherer, Michael
2017-04-01
Background and purpose - Patients with osteoporosis who present with an acute onset of back pain often have multiple fractures on plain radiographs. Differentiation of an acute osteoporotic vertebral fracture (AOVF) from previous fractures is difficult. The aim of this study was to investigate the incidence of concomitant AOVFs and previous OVFs in patients with symptomatic AOVFs, and to identify risk factors for concomitant AOVFs. Patients and methods - This was a prospective epidemiological study based on the Registry of Pathological Osteoporotic Vertebral Fractures (REPAPORA) with 1,005 patients and 2,874 osteoporotic vertebral fractures, which has been running since February 1, 2006. Concomitant fractures are defined as at least 2 acute short-tau inversion recovery (STIR-) positive vertebral fractures that happen concomitantly. A previous fracture is a STIR-negative fracture at the time of initial diagnostics. Logistic regression was used to examine the influence of various variables on the incidence of concomitant fractures. Results - More than 99% of osteoporotic vertebral fractures occurred in the thoracic and lumbar spine. The incidence of concomitant fractures at the time of first patient contact was 26% and that of previous fractures was 60%. The odds ratio (OR) for concomitant fractures decreased with a higher number of previous fractures (OR =0.86; p = 0.03) and higher dual-energy X-ray absorptiometry T-score (OR =0.72; p = 0.003). Interpretation - Concomitant and previous osteoporotic vertebral fractures are common. Risk factors for concomitant fractures are a low T-score and a low number of previous vertebral fractures in cases of osteoporotic vertebral fracture. An MRI scan of the the complete thoracic and lumbar spine with STIR sequence reduces the risk of under-diagnosis and under-treatment.
Exact association test for small size sequencing data.
Lee, Joowon; Lee, Seungyeoun; Jang, Jin-Young; Park, Taesung
2018-04-20
Recent statistical methods for next generation sequencing (NGS) data have been successfully applied to identifying rare genetic variants associated with certain diseases. However, most commonly used methods (e.g., burden tests and variance-component tests) rely on large sample sizes. Notwithstanding, due to its-still high cost, NGS data is generally restricted to small sample sizes, that cannot be analyzed by most existing methods. In this work, we propose a new exact association test for sequencing data that does not require a large sample approximation, which is applicable to both common and rare variants. Our method, based on the Generalized Cochran-Mantel-Haenszel (GCMH) statistic, was applied to NGS datasets from intraductal papillary mucinous neoplasm (IPMN) patients. IPMN is a unique pancreatic cancer subtype that can turn into an invasive and hard-to-treat metastatic disease. Application of our method to IPMN data successfully identified susceptible genes associated with progression of IPMN to pancreatic cancer. Our method is expected to identify disease-associated genetic variants more successfully, and corresponding signal pathways, improving our understanding of specific disease's etiology and prognosis.
The exact solution of self-consistent equations in the scanning near-field optic microscopy problem
DEFF Research Database (Denmark)
Lozovski, Valeri; Bozhevolnyi, Sergey I.
1999-01-01
The macroscopic approach that allows one to obtain an exact solution of the self-consistent equation of the Lippmann-Schwinger type is developed. The main idea of our method consist in usage of diagram technque for exact summation of the infinite series corresponding to the iteration procedure fo...
International Nuclear Information System (INIS)
Castro Moreira, I. de.
1983-01-01
A method introduced by Lewis and Leach for the obtention of exact invariants of the form I = Σ p sup(n) F sub(n) (q,t) for hamiltonian systems, is generalized and applied directly on the equations of motion. It gives us a general procedure to generates exact invariants also for non hamiltonian systems. (Author) [pt
Exact derivation of the Hawking effect in canonical formulation
Barman, Subhajit; Hossain, Golam Mortuza; Singha, Chiranjeeb
2018-01-01
The Hawking effect is one of the most extensively studied topics in modern physics, yet it remains relatively underexplored within the framework of canonical quantization. The key difficulty lies in the fact that the Hawking effect is principally understood using the relation between the ingoing modes which leave past null infinity and the outgoing modes which arrive at future null infinity. Naturally, these modes are described using advanced and retarded null coordinates instead of the usual Schwarzschild coordinates. However, null coordinates do not lead to a true Hamiltonian that describes the evolution of these modes. In order to overcome these hurdles in a canonical formulation, we introduce here a set of near-null coordinates which allows one to perform an exact Hamiltonian-based derivation of the Hawking effect. This derivation opens up an avenue to explore the Hawking effect using different canonical quantization methods such as polymer quantization.
An Exactly Solvable Supersymmetric Model of Semimagic Nuclei
International Nuclear Information System (INIS)
Balantekin, A. B.; Gueven, Nurtac; Pehlivan, Yamac
2008-01-01
A simple model of nucleons coupled to angular momentum zero (s-pairs) occupying the valance shell of a semi-magic nuclei is considered. The model has a separable, orbit dependent pairing interaction which dominates over the kinetic term. It is shown that such an interaction leads to an exactly solvable model whose (0 + ) eigenstates and energies can be computed very easily with the help of the algebraic Bethe ansatz method. It is also shown that the model has a supersymmetry which connects the spectra of some semimagic nuclei. The results obtained from this model for the semimagic Ni isotopes from 58 Ni to 68 Ni are given. In addition, a new and easier technique for calculating the energy eigenvalues from the Bethe ansatz equations is also presented.
Exact partition functions of Higgsed 5d TN theories
International Nuclear Information System (INIS)
Hayashi, Hirotaka; Zoccarato, Gianluca
2015-01-01
We present a general prescription by which we can systematically compute exact partition functions of five-dimensional supersymmetric theories which arise in Higgs branches of the T N theory. The theories may be realised by webs of 5-branes whose dual geometries are non-toric. We have checked our method by calculating the partition functions of the theories realised in various Higgs branches of the T 3 theory. A particularly interesting example is the E 8 theory which can be obtained by Higgsing the T 6 theory. We explicitly compute the partition function of the E 8 theory and find agreement with the field theory result as well as enhancement of the global symmetry to E 8 .
An Exact Analytical Solution to Exponentially Tapered Piezoelectric Energy Harvester
Directory of Open Access Journals (Sweden)
H. Salmani
2015-01-01
Full Text Available It has been proven that tapering the piezoelectric beam through its length optimizes the power extracted from vibration based energy harvesting. This phenomenon has been investigated by some researchers using semianalytical, finite element and experimental methods. In this paper, an exact analytical solution is presented to calculate the power generated from vibration of exponentially tapered unimorph and bimorph with series and parallel connections. The mass normalized mode shapes of the exponentially tapered piezoelectric beam with tip mass are implemented to transfer the proposed electromechanical coupled equations into modal coordinates. The steady states harmonic solution results are verified both numerically and experimentally. Results show that there exist values for tapering parameter and electric resistance in a way that the output power per mass of the energy harvester will be maximized. Moreover it is concluded that the electric resistance must be higher than a specified value for gaining more power by tapering the beam.
Mathematics of epidemics on networks from exact to approximate models
Kiss, István Z; Simon, Péter L
2017-01-01
This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...
Tempel, David G.; Aspuru-Guzik, Alán
2011-11-01
The dissipative dynamics of many-electron systems interacting with a thermal environment has remained a long-standing challenge within time-dependent density functional theory (TDDFT). Recently, the formal foundations of open quantum systems time-dependent density functional theory (OQS-TDDFT) within the master equation approach were established. It was proven that the exact time-dependent density of a many-electron open quantum system evolving under a master equation can be reproduced with a closed (unitarily evolving) and non-interacting Kohn-Sham system. This potentially offers a great advantage over previous approaches to OQS-TDDFT, since with suitable functionals one could obtain the dissipative open-systems dynamics by simply propagating a set of Kohn-Sham orbitals as in usual TDDFT. However, the properties and exact conditions of such open-systems functionals are largely unknown. In the present article, we examine a simple and exactly-solvable model open quantum system: one electron in a harmonic well evolving under the Lindblad master equation. We examine two different representitive limits of the Lindblad equation (relaxation and pure dephasing) and are able to deduce a number of properties of the exact OQS-TDDFT functional. Challenges associated with developing approximate functionals for many-electron open quantum systems are also discussed.
Energy Technology Data Exchange (ETDEWEB)
Dubrovsky, V. G.; Topovsky, A. V. [Novosibirsk State Technical University, Karl Marx prosp. 20, Novosibirsk 630092 (Russian Federation)
2013-03-15
New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.
A class of exactly solvable many-body models
International Nuclear Information System (INIS)
Dzyubenko, A.B.; Lozovik, Yu.E.
1991-01-01
A class of quantum many-body models of arbitrary dimension and arbitrary statistics of particles, for which exact eigenstates may be obtained is found. Exact many-body eigenstates correspond to a condensation of noninteracting composite particles (excitons), which are not exactly bosons, into a single quantum state, and to excitations over the condensate. The class of such models includes, in particular, two-dimensional electron-hole systems in strong magnetic field
Upper bounds on minimum cardinality of exact and approximate reducts
Chikalov, Igor
2010-01-01
In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.
Pressure in an exactly solvable model of active fluid
Marini Bettolo Marconi, Umberto; Maggi, Claudio; Paoluzzi, Matteo
2017-07-01
We consider the pressure in the steady-state regime of three stochastic models characterized by self-propulsion and persistent motion and widely employed to describe the behavior of active particles, namely, the Active Brownian particle (ABP) model, the Gaussian colored noise (GCN) model, and the unified colored noise approximation (UCNA) model. Whereas in the limit of short but finite persistence time, the pressure in the UCNA model can be obtained by different methods which have an analog in equilibrium systems, in the remaining two models only the virial route is, in general, possible. According to this method, notwithstanding each model obeys its own specific microscopic law of evolution, the pressure displays a certain universal behavior. For generic interparticle and confining potentials, we derive a formula which establishes a correspondence between the GCN and the UCNA pressures. In order to provide explicit formulas and examples, we specialize the discussion to the case of an assembly of elastic dumbbells confined to a parabolic well. By employing the UCNA we find that, for this model, the pressure determined by the thermodynamic method coincides with the pressures obtained by the virial and mechanical methods. The three methods when applied to the GCN give a pressure identical to that obtained via the UCNA. Finally, we find that the ABP virial pressure exactly agrees with the UCNA and GCN results.
Wang, Gang-wei; Liu, Xi-qiang; Zhang, Ying-yuan
2013-09-01
In this paper, by applying Lie symmetry method, we get the corresponding Lie algebra and similarity reductions of a new fifth-order nonlinear integrable equation. At the same time, the explicit and exact analytic solutions are obtained by means of the power series method. At last, we also give the conservation laws.
Exact norm-conserving stochastic time-dependent Hartree-Fock
International Nuclear Information System (INIS)
Tessieri, Luca; Wilkie, Joshua; Cetinbas, Murat
2005-01-01
We derive an exact single-body decomposition of the time-dependent Schroedinger equation for N pairwise interacting fermions. Each fermion obeys a stochastic time-dependent norm-preserving wave equation. As a first test of the method, we calculate the low energy spectrum of helium. An extension of the method to bosons is outlined
Exact travelling wave solutions for the generalized shallow water wave equation
International Nuclear Information System (INIS)
Elwakil, S.A.; El-labany, S.K.; Zahran, M.A.; Sabry, R.
2003-01-01
Using homogeneous balance method an auto-Baecklund transformation for the generalized shallow water wave equation is obtained. Then solitary wave solutions are found. Also, modified extended tanh-function method is applied and new exact travelling wave solutions are obtained. The obtained solutions include rational, periodical, singular and solitary wave solutions
Exact travelling wave solutions for the generalized shallow water wave equation
Energy Technology Data Exchange (ETDEWEB)
Elwakil, S.A.; El-labany, S.K.; Zahran, M.A.; Sabry, R
2003-07-01
Using homogeneous balance method an auto-Baecklund transformation for the generalized shallow water wave equation is obtained. Then solitary wave solutions are found. Also, modified extended tanh-function method is applied and new exact travelling wave solutions are obtained. The obtained solutions include rational, periodical, singular and solitary wave solutions.
Exact travelling wave solutions of the (3+1)-dimensional mKdV-ZK ...
Indian Academy of Sciences (India)
Abstract. In this paper, the new generalized (G /G)-expansion method is executed to find the travelling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation. The efficiency of this method for finding exact and travelling wave solu- tions has been demonstrated.
Exact travelling wave solutions of the (3+1)-dimensional mKdV-ZK ...
Indian Academy of Sciences (India)
In this paper, the new generalized (′/)-expansion method is executed to find the travelling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation. The efficiency of this method for finding exact and travelling wave solutions has been demonstrated. It is shown ...
DEFF Research Database (Denmark)
Garde, Henrik
2018-01-01
. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method...
A Class of Quasi-exact Solutions of Rabi Hamiltonian
International Nuclear Information System (INIS)
Pan Feng; Yao Youkun; Xie Mingxia; Han Wenjuan; Draayer, J.P.
2007-01-01
A class of quasi-exact solutions of the Rabi Hamiltonian, which describes a two-level atom interacting with a single-mode radiation field via a dipole interaction without the rotating-wave approximation, are obtained by using a wavefunction ansatz. Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and the field frequency satisfy certain relations. As an example, the lowest exact energy level and the corresponding atom-field entanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings and counter-rotating cases of the Rabi Hamiltonian.
Configured-groups hypothesis: fast comparison of exact large quantities without counting.
Miravete, Sébastien; Tricot, André; Kalyuga, Slava; Amadieu, Franck
2017-11-01
Our innate number sense cannot distinguish between two large exact numbers of objects (e.g., 45 dots vs 46). Configured groups (e.g., 10 blocks, 20 frames) are traditionally used in schools to represent large numbers. Previous studies suggest that these external representations make it easier to use symbolic strategies such as counting ten by ten, enabling humans to differentiate exactly two large numbers. The main hypothesis of this work is that configured groups also allow for a differentiation of large exact numbers, even when symbolic strategies become ineffective. In experiment 1, the children from grade 3 were asked to compare two large collections of objects for 5 s. When the objects were organized in configured groups, the success rate was over .90. Without this configured grouping, the children were unable to make a successful comparison. Experiments 2 and 3 controlled for a strategy based on non-numerical parameters (areas delimited by dots or the sum areas of dots, etc.) or use symbolic strategies. These results suggest that configured grouping enables humans to distinguish between two large exact numbers of objects, even when innate number sense and symbolic strategies are ineffective. These results are consistent with what we call "the configured group hypothesis": configured groups play a fundamental role in the acquisition of exact numerical abilities.
Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model
Pont, Federico M.; Osenda, Omar; Serra, Pablo
2018-05-01
The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.
Exactly solvable quantum Sturm-Liouville problems
Buyukasik, Sirin A.; Pashaev, Oktay K.; Tigrak-Ulas, Esra
The harmonic oscillator with time-dependent parameters covers a broad spectrum of physical problems from quantum transport, quantum optics, and quantum information to cosmology. Several methods have been developed to quantize this fundamental system, such as the path integral method, the
Exact complex integrals in two dimensions for shifted harmonic ...
Indian Academy of Sciences (India)
With a view of constructing complex integral for some cases here, in this section we use methods discussed in the previous section. To start with, we first consider the case of shifted harmonic oscillator systems within the framework of rationalization method. Note that for shifted harmonic oscillator in complex plane. H = 1. 2.
Fast, Exact Bootstrap Principal Component Analysis forp> 1 million.
Fisher, Aaron; Caffo, Brian; Schwartz, Brian; Zipunnikov, Vadim
Many have suggested a bootstrap procedure for estimating the sampling variability of principal component analysis (PCA) results. However, when the number of measurements per subject ( p ) is much larger than the number of subjects ( n ), calculating and storing the leading principal components from each bootstrap sample can be computationally infeasible. To address this, we outline methods for fast, exact calculation of bootstrap principal components, eigenvalues, and scores. Our methods leverage the fact that all bootstrap samples occupy the same n -dimensional subspace as the original sample. As a result, all bootstrap principal components are limited to the same n -dimensional subspace and can be efficiently represented by their low dimensional coordinates in that subspace. Several uncertainty metrics can be computed solely based on the bootstrap distribution of these low dimensional coordinates, without calculating or storing the p -dimensional bootstrap components. Fast bootstrap PCA is applied to a dataset of sleep electroencephalogram recordings ( p = 900, n = 392), and to a dataset of brain magnetic resonance images (MRIs) ( p ≈ 3 million, n = 352). For the MRI dataset, our method allows for standard errors for the first 3 principal components based on 1000 bootstrap samples to be calculated on a standard laptop in 47 minutes, as opposed to approximately 4 days with standard methods.
Exact RG flow equations and quantum gravity
de Alwis, S. P.
2018-03-01
We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg's asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.
Exact Algorithms for the Clustered Vehicle Routing Problem
Battarra, M.; Erdogan, G.; Vigo, D.
2014-01-01
This study presents new exact algorithms for the clustered vehicle routing problem (CluVRP). The CluVRP is a generalization of the capacitated vehicle routing problem (CVRP), in which the customers are grouped into clusters. As in the CVRP, all the customers must be visited exactly once, but a
Exact Boundary Controllability of Electromagnetic Fields in a General Region
International Nuclear Information System (INIS)
Eller, M. M.; Masters, J. E.
2002-01-01
We prove exact controllability for Maxwell's system with variable coefficients in a bounded domain by a current flux in the boundary. The proof relies on a duality argument which reduces the proof of exact controllability to the proof of continuous observability for the homogeneous adjoint system. There is no geometric restriction imposed on the domain
Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions
Directory of Open Access Journals (Sweden)
Armando Martínez-Pérez
2017-10-01
Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.
Exact solution for the generalized Telegraph Fisher's equation
International Nuclear Information System (INIS)
Abdusalam, H.A.; Fahmy, E.S.
2009-01-01
In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.
Exact solutions of a nonpolynomially nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Parwani, R.; Tan, H.S.
2007-01-01
A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics
Exact simulation of conditioned Wright-Fisher models.
Zhao, Lei; Lascoux, Martin; Waxman, David
2014-12-21
Forward and backward simulations play an increasing role in population genetics, in particular when inferring the relative importance of evolutionary forces. It is therefore important to develop fast and accurate simulation methods for general population genetics models. Here we present an exact simulation method that generates trajectories of an allele׳s frequency in a finite population, as described by a general Wright-Fisher model. The method generates conditioned trajectories that start from a known frequency at a known time, and which achieve a specific final frequency at a known final time. The simulation method applies irrespective of the smallness of the probability of the transition between the initial and final states, because it is not based on rejection of trajectories. We illustrate the method on several different populations where a Wright-Fisher model (or related) applies, namely (i) a locus with 2 alleles, that is subject to selection and mutation; (ii) a locus with 3 alleles, that is subject to selection; (iii) a locus in a metapopulation consisting of two subpopulations of finite size, that are subject to selection and migration. The simulation method allows the generation of conditioned trajectories that can be used for the purposes of visualisation, the estimation of summary statistics, and the development/testing of new inferential methods. The simulated trajectories provide a very simple approach to estimating quantities that cannot easily be expressed in terms of the transition matrix, and can be applied to finite Markov chains other than the Wright-Fisher model. Copyright © 2014 Elsevier Ltd. All rights reserved.
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
than other traditional techniques. The study indicates the validity and great potential of the first integral method in solving complicated solitary wave problems. References. [1] W M Taha, M S M Noorani and I Hashim, J. King Saud University-Science 26, 75 (2014). [2] G Ebadi and A Biswas, Commun. Nonlinear Sci. Numer.
Fixed-J moments: exact calculations
International Nuclear Information System (INIS)
Jacquemin, C.
1980-01-01
We show that the two first fixed J moments of the Hamiltonian operator can be easily calculated over the whole fixed particle number shell model space as well as over configurations. The method may be extended to higher moments of H and to include the isotopic spin T
Exact solutions of the spherically symmetric multidimensional ...
African Journals Online (AJOL)
The complete orthonormalised energy eigenfunctions and the energy eigenvalues of the spherically symmetric isotropic harmonic oscillator in N dimensions, are obtained through the methods of separation of variables. Also, the degeneracy of the energy levels are examined. KEY WORDS: - Schrödinger Equation, Isotropic ...
Simpson, Matthew J
2015-01-01
Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).
New version of PLNoise: a package for exact numerical simulation of power-law noises
Milotti, Edoardo
2007-08-01
In a recent paper I have introduced a package for the exact simulation of power-law noises and other colored noises [E. Milotti, Comput. Phys. Comm. 175 (2006) 212]: in particular, the algorithm generates 1/f noises with 0Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler RAM: The code of the test program is very compact (about 60 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B.W. Brown, J. Lovato, K. Russell: ranlib, available from Netlib, http://www.netlib.org/random/index.html, select the C version ranlib.c], but it has also been successfully tested with the random number routines in Numerical Recipes [W.H. Press, S.A. Teulkolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press., Cambridge, 1992, pp. 274-290]. Notice that ranlib requires a pair of routines from the linear algebra package LINPACK, and that the distribution of ranlib includes the C source of these routines, in case LINPACK is not installed on the target machine. No. of lines in distributed program, including test data, etc.:2975 No. of bytes in distributed program, including test data, etc.:194 588 Distribution format:tar.gz Catalogue identifier of previous version: ADXV_v1_0 Journal reference of previous version: Comput. Phys. Comm. 175 (2006) 212 Does the new version supersede the previous version?: Yes Nature of problem: Exact generation of different types of colored noise. Solution method: Random superposition of relaxation processes [E. Milotti, Phys. Rev. E 72 (2005) 056701
Exact solutions of the Bach field equations of general relativity
Fiedler, B.; Schimming, R.
1980-02-01
Conformally invariant gravitational field equations on the hand and fourth order field equations on the other were discussed in the early history of general relativity (Weyl Einstein, Bach et al.) and have recently gained some new interest (Deser, P. Günther, Treder, et al.). The equations Bαβ=0 or Bαβ= ϰTαβ, where Bαβ denotes the Bach tensor and Tαβ a suitable energy-momentum tensor, possess both the mentioned properties. We construct exact solutions ds2= gαβdxαdxβ of the Bach equations: (2, 2)-decomposable, centrally symmetric and pp-wave solutions. The gravitational field gαβ is coupled by Bαβ= ϰTαβ to an electromagnetic field Fαβ=- Fαβ obeying the Maxwell equations or to a neutrino field ϕ A obeying the Weyl equations respectively. Among interesting new metrics ds2 there appear some physically well-known ones, such as the De Sitter universe, the Weyl-Trefftz metric. and the plane-fronted gravitational waves with parallel rays (pp-waves) known from Einstein's theory. The solutions are built up by means of special techniques: A separation method for (2, 2)-decomposable solutions, simplification of centrally symmetric metrics by a suitable conformal transformation, and complex function methods for pp-wave solutions.
Exact cone beam CT with a spiral scan
International Nuclear Information System (INIS)
Tam, K.C.; Samarasekera, S.; Sauer, F.
1998-01-01
A method is developed which makes it possible to scan and reconstruct an object with cone beam x-rays in a spiral scan path with area detectors much shorter than the length of the object. The method is mathematically exact. If only a region of interest of the object is to be imaged, a top circle scan at the top level of the region of interest and a bottom circle scan at the bottom level of the region of interest are added. The height of the detector is required to cover only the distance between adjacent turns in the spiral projected at the detector. To reconstruct the object, the Radon transform for each plane intersecting the object is computed from the totality of the cone beam data. This is achieved by suitably combining the cone beam data taken at different source positions on the scan path; the angular range of the cone beam data required at each source position can be determined easily with a mask which is the spiral scan path projected on the detector from the current source position. The spiral scan algorithm has been successfully validated with simulated cone beam data. (author)
General and exact pressure evolution equation
Toutant, Adrien
2017-11-01
A crucial issue in fluid dynamics is related to the knowledge of the fluid pressure. A new general pressure equation is derived from compressible Navier-Stokes equation. This new pressure equation is valid for all real dense fluids for which the pressure tensor is isotropic. It is argued that this new pressure equation allows unifying compressible, low-Mach and incompressible approaches. Moreover, this equation should be able to replace the Poisson equation in isothermal incompressible fluids. For computational fluid dynamics, it can be seen as an alternative to Lattice Boltzmann methods and as the physical justification of artificial compressibility.
An exact approach for aggregated formulations
DEFF Research Database (Denmark)
Gamst, Mette; Spoorendonk, Simon
Aggregating formulations is a powerful approach for transforming problems into taking more tractable forms. Aggregated formulations can, though, have drawbacks: some information may get lost in the aggregation and { put in a branch-and-bound context { branching may become very di_cult and even....... The paper includes general considerations on types of problems for which the method is of particular interest. Furthermore, we prove the correctness of the procedure and consider how to include extensions such as cutting planes and advanced branching strategies....
Exact Witten index in D=2 supersymmetric Yang-Mills quantum mechanics
International Nuclear Information System (INIS)
Campostrini, M.; Wosiek, J.
2002-01-01
A new, recursive method of calculating matrix elements of polynomial hamiltonians is proposed. It is particularly suitable for the recent algebraic studies of the supersymmetric Yang-Mills quantum mechanics in any dimensions. For the D=2 system with the SU(2) gauge group, considered here, the technique gives exact, closed expressions for arbitrary matrix elements of the hamiltonian and of the supersymmetric charge, in the occupation number representation. Subsequent numerical diagonalization provides spectrum and restricted Witten index of the system with very high precision (taking into account up to 10 5 quanta). Independently, the exact value of the restricted Witten index is derived analytically for the first time
International Nuclear Information System (INIS)
Castejon, F.; Pavlov, S. S.
2006-01-01
The fully relativistic plasma dielectric tensor for any wave and plasma parameter is estimated on the basis of the exact plasma dispersion functions concept. The inclusion of this concept allows one to write the tensor in a closed and compact form and to reduce the tensor evaluation to the calculation of those functions. The main analytical properties of these functions are studied and two methods are given for their evaluation. The comparison between the exact dielectric tensor with the weakly relativistic approximation, widely used presently in plasma waves calculations, is given as well as the range of plasma temperature, harmonic number, and propagation angle in which the weakly relativistic approximation is valid
Polyanin, A. D.; Sorokin, V. G.
2017-12-01
The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.
Exact probability distribution function for multifractal random walk models of stocks
Saakian, D. B.; Martirosyan, A.; Hu, Chin-Kun; Struzik, Z. R.
2011-07-01
We investigate the multifractal random walk (MRW) model, popular in the modelling of stock fluctuations in the financial market. The exact probability distribution function (PDF) is derived by employing methods proposed in the derivation of correlation functions in string theory, including the analytical extension of Selberg integrals. We show that the recent results by Y. V. Fyodorov, P. Le Doussal and A. Rosso obtained with the logarithmic Random Energy Model (REM) model are sufficient to derive exact formulas for the PDF of the log returns in the MRW model.
Quasi-exact evaluation of time domain MFIE MOT matrix elements
Shi, Yifei
2013-07-01
A previously proposed quasi-exact scheme for evaluating matrix elements resulting from the marching-on-in-time (MOT) discretization of the time domain electric field integral equation (EFIE) is extended to matrix entries resulting from the discretization of its magnetic field integral equation (MFIE) counterpart. Numerical results demonstrate the accuracy of the scheme as well as the late-time stability of the resulting MOT-MFIE solver. © 2013 IEEE.
Exact solutions of the Drinfel'd–Sokolov–Wilson equation using ...
Indian Academy of Sciences (India)
1Department of Engineering Mathematics and Physics, Higher Institute of Engineering,. El Shorouk, Egypt. 2Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran. 3Department of ... mation method of Riccati equation to look for new exact solutions of nonlinear fractional. PDEs.
An hp-adaptive strategy for the solution of the exact kernel curved wire Pocklington equation
D.J.P. Lahaye (Domenico); P.W. Hemker (Piet)
2007-01-01
textabstractIn this paper we introduce an adaptive method for the numerical solution of the Pocklington integro-differential equation with exact kernel for the current induced in a smoothly curved thin wire antenna. The hp-adaptive technique is based on the representation of the discrete solution,
Energy Technology Data Exchange (ETDEWEB)
Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T., E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br, E-mail: ftvdl@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica. Grupo de Pesquisas Radiologicas; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio G., E-mail: phd.marcio@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Tramandai, RS (Brazil). Departamento Interdisciplinar do Campus Litoral Norte
2015-07-01
This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)
Bifurcations of Exact Traveling Wave Solutions for (2+1)-Dimensional HNLS Equation
International Nuclear Information System (INIS)
Xu Yuanfen
2012-01-01
For the (2+1)-Dimensional HNLS equation, what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems. Ten exact explicit parametric representations of the traveling wave solutions are given. (general)
Exactly solvable models for tri-atomic molecular Bose-Einstein condensates
Energy Technology Data Exchange (ETDEWEB)
Santos, G; Roditi, I; Santos, Z V T [CBPF-Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro RJ (Brazil); Foerster, A [Instituto de Fisica da UFRGS, Porto Alegre, RS (Brazil); Tonel, A P [CCET da Universidade Federal do Pampa/Unipampa, Bage, RS (Brazil)], E-mail: gfilho@cbpf.br
2008-07-25
We construct a family of tri-atomic models for heteronuclear and homonuclear molecular Bose-Einstein condensates. We show that these new generalized models are exactly solvable through the algebraic Bethe ansatz method and derive their corresponding Bethe ansatz equations and energies.
Exactly solvable models for triatomic-molecular Bose-Einstein Condensates
Energy Technology Data Exchange (ETDEWEB)
Santos, G.; Roditi, I.; Santos, Z.V.T. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Foerster, A. [Instituto de Fisica da UFRGS, Porto Alegre, RS (Brazil); Tonel, A.P. [CCET da Universidade Federal do Pampa/Unipampa, Bage, RS (Brazil)
2014-11-15
We construct a family of triatomic models for heteronuclear and homonuclear molecular Bose-Einstein condensates. We show that these new generalized models are exactly solvable through the algebraic Bethe Ansatz method and derive their corresponding Bethe Ansatz equations and energies. (author)
Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.
2018-04-01
We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.
Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation
Directory of Open Access Journals (Sweden)
Hongwei Yang
2012-01-01
Full Text Available We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.
Tisdell, C. C.
2017-01-01
Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…
The fractional coupled KdV equations: Exact solutions and white noise functional approach
International Nuclear Information System (INIS)
Ghany, Hossam A.; El Bab, A. S. Okb; Zabel, A. M.; Hyder, Abd-Allah
2013-01-01
Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated. By using the modified fractional sub-equation method, Hermite transform, and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained, including the generalized exponential, hyperbolic, and trigonometric types. (general)
Exact Electromagnetic Fields Produced by a Finite Wire with Constant Current
Jimenez, J. L.; Campos, I.; Aquino, N.
2008-01-01
We solve exactly the problem of calculating the electromagnetic fields produced by a finite wire with a constant current, by using two methods: retarded potentials and Jefimenko's formalism. One result in this particular case is that the usual Biot-Savart law of magnetostatics gives the correct magnetic field of the problem. We also show…
Exact Sampling and Decoding in High-Order Hidden Markov Models
Carter, S.; Dymetman, M.; Bouchard, G.
2012-01-01
We present a method for exact optimization and sampling from high order Hidden Markov Models (HMMs), which are generally handled by approximation techniques. Motivated by adaptive rejection sampling and heuristic search, we propose a strategy based on sequentially refining a lower-order language
New exact solutions for a generalized variable coefficients 2D KdV equation
Energy Technology Data Exchange (ETDEWEB)
Elwakil, S.A.; El-labany, S.K.; Zahran, M.A. E-mail: m_zahran1@mans.edu.eg; Sabry, R. E-mail: refaatsabry@mans.edu.eg
2004-03-01
Using homogeneous balance method an auto-Baecklund transformation for a generalized variable coefficients 2D KdV equation is obtained. Then new exact solutions are found which include solitary one. Also, we have found certain new analytical soliton-typed solution in terms of the variable coefficients of the studied 2D KdV equation.
Directory of Open Access Journals (Sweden)
Zhanhua Yu
2011-01-01
Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.
Exact vibration analysis of variable thickness thick annular isotropic and FGM plates
Efraim, E.; Eisenberger, M.
2007-02-01
Annular plates are used in many engineering structures. In many cases variable thickness is used in order to save weight and improve structural characteristics. In recent years functionally graded materials (FGM) are used in many engineering applications. A FGM plate is an inhomogeneous composite made of two constituents (usually ceramic and metal), with both the composition and the material properties varying smoothly through the thickness of the plate. An optimal distribution of material properties may be obtained. The plate vibrations will have a strong bending-stretching coupling effect. The equations of motion including the effect of shear deformations using the first-order shear deformation theory are derived and solved exactly for various combinations of boundary conditions. The solution is obtained by using the exact element method. Exact vibration frequencies and modes are given for several examples for the first time.
Painlevé Integrability and New Exact Solutions of the (4 + 1-Dimensional Fokas Equation
Directory of Open Access Journals (Sweden)
Sheng Zhang
2015-01-01
Full Text Available The Painlevé integrability of the (4+1-dimensional Fokas equation is verified by the WTC method of Painlevé analysis combined with a new and more general transformation. By virtue of the truncated Painlevé expansion, two new exact solutions with arbitrary differentiable functions are obtained. Thanks to the arbitrariness of the included functions, the obtained exact solutions not only possess rich spatial structures but also help to bring about two-wave solutions and three-wave solutions. It is shown that the transformation adopted in this work plays a key role in testing the Painlevé integrability and constructing the exact solutions of the Fokas equation.
Exact and approximate computations of watersheds on triangulated terrains
DEFF Research Database (Denmark)
Tsirogiannis, Konstantinos; de Berg, Mark
2011-01-01
or they perform computations using inexact arithmetic, which leads to inexact and sometimes inconsistent results. We perform a detailed study of various issues concerning the exact or approximate computation of watersheds according to the dsd model. Our main contributions are the following. • We provide the first...... implementation that computes watersheds on triangulated terrains following strictly the dsd model and using exact arithmetic, and we experimentally investigate its computational cost. Our experiments show that the algorithm cannot handle large data sets effectively, due to the bit-sizes needed in the exact...
How hairpin vortices emerge from exact invariant solutions
Schneider, Tobias M.; Farano, Mirko; de Palma, Pietro; Robinet, Jean-Christoph; Cherubini, Stefania
2017-11-01
Hairpin vortices are among the most commonly observed flow structures in wall-bounded shear flows. However, within the dynamical system approach to turbulence, those structures have not yet been described. They are not captured by known exact invariant solutions of the Navier-Stokes equations nor have other state-space structures supporting hairpins been identified. We show that hairpin structures are observed along an optimally growing trajectory leaving a well known exact traveling wave solution of plane Poiseuille flow. The perturbation triggering hairpins does not correspond to an unstable mode of the exact traveling wave but lies in the stable manifold where non-normality causes strong transient amplification.
The exact mass-gaps of the principal chiral models
Hollowood, Timothy J
1994-01-01
An exact expression for the mass-gap, the ratio of the physical particle mass to the $\\Lambda$-parameter, is found for the principal chiral sigma models associated to all the classical Lie algebras. The calculation is based on a comparison of the free-energy in the presence of a source coupling to a conserved charge of the theory computed in two ways: via the thermodynamic Bethe Ansatz from the exact scattering matrix and directly in perturbation theory. The calculation provides a non-trivial test of the form of the exact scattering matrix.
Exact and approximation algorithms for DNA tag set design.
Măndoiu, Ion I; Trincă, Dragoş
2006-04-01
In this paper, we propose new solution methods for designing tag sets for use in universal DNA arrays. First, we give integer linear programming formulations for two previous formalizations of the tag set design problem. We show that these formulations can be solved to optimality for problem instances of moderate size by using general purpose optimization packages and also give more scalable algorithms based on an approximation scheme for packing linear programs. Second, we note the benefits of periodic tags and establish an interesting connection between the tag design problem and the problem of packing the maximum number of vertex-disjoint directed cycles in a given graph. We show that combining a simple greedy cycle packing algorithm with a previously proposed alphabetic tree search strategy yields an increase of over 40% in the number of tags compared to previous methods.
Kalmykov, Yu. P.; Coffey, W. T.; Waldron, J. T.
1996-08-01
The correlation time of the positional autocorrelation function is calculated exactly for one-dimensional translational Brownian motion of a particle in a 2-4 double-well potential in the noninertial limit. The calculations are carried out using the method of direct conversion (by averaging) of the Langevin equation for a nonlinear stochastic system to a set of differential-recurrence relations. These, in the present problem, reduce on taking the Laplace transform, to a three-term recurrence relation. Thus the correlation time Tc of the positional autocorrelation function may be formally expressed as a sum of products of infinite continued fractions which may be represented in series form as a sum of two term products of Whittaker's parabolic cylinder functions. The sum of this series may be expressed as an integral using the integral representation of the parabolic cylinder functions and subsequently the Taylor expansion of the error function, thus yielding the exact solution for Tc. This solution is in numerical agreement with that obtained by Perico et al. [J. Chem. Phys. 98, 564 (1993)] using the first passage time approach while previous asymptotic results obtained by solving the underlying Smoluchowski equation are recovered in the limit of high barrier heights. A simple empirical formula which provides a close approximation to the exact solution for all barrier heights is also given.
Exact Analysis of the Cache Behavior of Nested Loops
National Research Council Canada - National Science Library
Chatterjee, Siddhartha; Parker, Erin; Hanlon, Philip J; Lebeck, Alvin R
2001-01-01
The authors develop from first principles an exact model of the behavior of loop nests executing in a memory hierarchy by using a nontraditional classification of misses that has the key property of composability...
Dynamical generation of interaction in an exactly solvable model
International Nuclear Information System (INIS)
Avdeev, L.V.; Chizhov, M.V.
1984-01-01
The dynamical generation of interaction in the chiral-invariant Gross-Neveu model leads to an asymptotically free charge behaviour and a correlation between coupling constants. The known exact solution possesses similar properties
Exact evolution equations for SU(2) quasidistribution functions
International Nuclear Information System (INIS)
Klimov, A.B.
2002-01-01
We derive an exact (differential) evolution equation for a class of SU(2) quasiprobability distribution functions. Linear and quadratic cases are considered as well as the quasiclassical limit of the large dimension of representation, S>>1
Exact and Asymptotic Scaling Solutions for Fragmentation with Mass Loss
Cai, M.; Edwards, Boyd F.; Han, H.
1991-01-01
Exact and asymptotic solutions to a linear rate equation for fragmentation with mass loss are presented. Solutions for spatially discrete random bond annihilation illustrate the mutual exclusiveness of the fragmentation and recession terms in the rate equation. Exact solutions for deterministic equal fragment recession show that continuous mass loss between fragmentation events can be approximated by discrete mass loss during fragmentation events when this mass loss is small. Evidence ...
Exact Dimensional Reduction of Linear Dynamics: Application to Confined Diffusion
Kalinay, Pavol; Percus, Jerome K.
2006-06-01
In their stochastic versions, dynamical systems take the form of the linear dynamics of a probability distribution. We show that exact dimensional reduction of such systems can be carried out, and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior, disappearing under typical coarse graining. Application is made to non-uniform quasi-low dimensional diffusion, resulting in a systematic extension of the "classical" Fick-Jacobs approximate reduction to an exact subdynamics.
Exact 2-point function in Hermitian matrix model
International Nuclear Information System (INIS)
Morozov, A.; Shakirov, Sh.
2009-01-01
J. Harer and D. Zagier have found a strikingly simple generating function [1,2] for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function - arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.
Exact Lagrangian caps and non-uniruled Lagrangian submanifolds
Dimitroglou Rizell, Georgios
2015-04-01
We make the elementary observation that the Lagrangian submanifolds of C n , n≥3, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and, moreover, have infinite relative Gromov width. The construction of these submanifolds involve exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a contactisation admits an exact Lagrangian cap, then its Chekanov-Eliashberg algebra is acyclic.
Exact generator coordinate wave functions for some simple Hamiltonians
International Nuclear Information System (INIS)
Ullah, Nazakat
1988-01-01
A Gaussian form of the generator coordinate wave function is used to find the exact weight function for the ground state of H-atom using HWG integral equation. Exact pairs of GC wave functions and weight functions are then constructed for other simple Hamiltonians using a simple integral which converts an exponential into a Gaussian. A discussion as to how a GC wave function can be used as a trial variational wave function is also presented. (author). 10 refs
Fast and Exact Fiber Surfaces for Tetrahedral Meshes.
Klacansky, Pavol; Tierny, Julien; Carr, Hamish; Zhao Geng
2017-07-01
Isosurfaces are fundamental geometrical objects for the analysis and visualization of volumetric scalar fields. Recent work has generalized them to bivariate volumetric fields with fiber surfaces, the pre-image of polygons in range space. However, the existing algorithm for their computation is approximate, and is limited to closed polygons. Moreover, its runtime performance does not allow instantaneous updates of the fiber surfaces upon user edits of the polygons. Overall, these limitations prevent a reliable and interactive exploration of the space of fiber surfaces. This paper introduces the first algorithm for the exact computation of fiber surfaces in tetrahedral meshes. It assumes no restriction on the topology of the input polygon, handles degenerate cases and better captures sharp features induced by polygon bends. The algorithm also allows visualization of individual fibers on the output surface, better illustrating their relationship with data features in range space. To enable truly interactive exploration sessions, we further improve the runtime performance of this algorithm. In particular, we show that it is trivially parallelizable and that it scales nearly linearly with the number of cores. Further, we study acceleration data-structures both in geometrical domain and range space and we show how to generalize interval trees used in isosurface extraction to fiber surface extraction. Experiments demonstrate the superiority of our algorithm over previous work, both in terms of accuracy and running time, with up to two orders of magnitude speedups. This improvement enables interactive edits of range polygons with instantaneous updates of the fiber surface for exploration purpose. A VTK-based reference implementation is provided as additional material to reproduce our results.
Nishino, Hitoshi
1992-01-01
We give exact solutions for a recently developed ~$N=1$~ locally supersymmetric self-dual gauge theories in $~(2+2)\\-$dimensions. We give the exact solutions for an $~SL(2)$~ self-dual Yang-Mills multiplet and what we call ``self-dual tensor multiplet'' on the gravitational instanton background by Eguchi-Hanson. We use a general method to get an $~SL(2)$~ self-dual Yang-Mills solution from any known self-dual gravity solution. Our result is the first example of exact solutions for the coupled...
Exact travelling wave solutions of the Whitham-Broer-Kaup and Broer-Kaup-Kupershmidt equations
International Nuclear Information System (INIS)
Xu Guiqiong; Li Zhibin
2005-01-01
In this paper, an interesting fact is found that the auxiliary equation method is also applicable to a coupled system of two different equations involving both even-order and odd-order partial derivative terms. Furthermore, singular travelling wave solutions can also be obtained by considering other types of exact solutions of auxiliary equation. The Whitham-Broer-Kaup and the (2 + 1)-dimensional Broer-Kaup-Kupershmidt equations are chosen as examples to illustrate the effectiveness of the auxiliary equation method
Occupation times and exact asymptotics of small deviations of Bessel processes for Lp-norms with p>0
International Nuclear Information System (INIS)
Fatalov, V R
2007-01-01
We prove theorems on exact asymptotics of the distributions of integral functionals of the occupation time of Bessel processes. Using these results, we obtain exact asymptotics of small deviations for Bessel processes in the L p -norm. We use Laplace's method for the occupation times of Markov processes with continuous time. Computations are carried out for p=2 and p=1. We also solve extremal problems for the action functional
Rates of induced abortion in Denmark according to age, previous births and previous abortions
Directory of Open Access Journals (Sweden)
Marie-Louise H. Hansen
2009-11-01
Full Text Available Background: Whereas the effects of various socio-demographic determinants on a woman's risk of having an abortion are relatively well-documented, less attention has been given to the effect of previous abortions and births. Objective: To study the effect of previous abortions and births on Danish women's risk of an abortion, in addition to a number of demographic and personal characteristics. Data and methods: From the Fertility of Women and Couples Dataset we obtained data on the number of live births and induced abortions by year (1981-2001, age (16-39, county of residence and marital status. Logistic regression analysis was used to estimate the influence of the explanatory variables on the probability of having an abortion in a relevant year. Main findings and conclusion: A woman's risk of having an abortion increases with the number of previous births and previous abortions. Some interactions were was found in the way a woman's risk of abortion varies with calendar year, age and parity. The risk of an abortion for women with no children decreases while the risk of an abortion for women with children increases over time. Furthermore, the risk of an abortion decreases with age, but relatively more so for women with children compared to childless women. Trends for teenagers are discussed in a separate section.
Theoretically exact backprojection filtration algorithm for multi-segment linear trajectory
Wu, Weiwen; Yu, Hengyong; Cong, Wenxiang; Liu, Fenglin
2018-01-01
A theoretically exact backprojection filtration algorithm is proved and implemented for image reconstruction from a multi-segment linear trajectory assuming fan-beam geometry. The reconstruction formula is based on a concept of linear PI-line (L-PI) proposed in our previous work. The proof is completed in two consecutive steps. In the first step, it is proved that theoretically exact image reconstruction can be obtained on an arbitrary L-PI line from an infinite straight-line trajectory. In the second step, it is shown that accurate image reconstruction can be achieved from a multi-segment line trajectory by introducing a weight function to deal with the data redundancy. Numerical implementation and simulation results validate the correctness of our theoretical results.
Sen, Debashis; Pal, Sankar K
2011-05-01
Histogram equalization, which aims at information maximization, is widely used in different ways to perform contrast enhancement in images. In this paper, an automatic exact histogram specification technique is proposed and used for global and local contrast enhancement of images. The desired histogram is obtained by first subjecting the image histogram to a modification process and then by maximizing a measure that represents increase in information and decrease in ambiguity. A new method of measuring image contrast based upon local band-limited approach and center-surround retinal receptive field model is also devised in this paper. This method works at multiple scales (frequency bands) and combines the contrast measures obtained at different scales using L(p)-norm. In comparison to a few existing methods, the effectiveness of the proposed automatic exact histogram specification technique in enhancing contrasts of images is demonstrated through qualitative analysis and the proposed image contrast measure based quantitative analysis.
Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism
Energy Technology Data Exchange (ETDEWEB)
Neto, J.F.S.; Lima, K.A.L.; Carvalho, P.R.S. [Universidade Federal do Piaui, Departamento de Fisica, Teresina, PI (Brazil); Sena-Junior, M.I. [Universidade de Pernambuco, Escola Politecnica de Pernambuco, Recife, PE (Brazil); Universidade Federal de Alagoas, Instituto de Fisica, Maceio, AL (Brazil)
2017-12-15
We probe the two-scale-factor universality hypothesis by evaluating, firstly explicitly and analytically at the one-loop order, the loop quantum corrections to the amplitude ratios for O(N)λφ{sup 4} scalar field theories with rotation symmetry breaking in three distinct and independent methods in which the rotation symmetry-breaking mechanism is treated exactly. We show that the rotation symmetry-breaking amplitude ratios turn out to be identical in the three methods and equal to their respective rotation symmetry-breaking ones, although the amplitudes themselves, in general, depend on the method employed and on the rotation symmetry-breaking parameter. At the end, we show that all these results can be generalized, through an inductive process based on a general theorem emerging from the exact calculation, to any loop level and physically interpreted based on symmetry ideas. (orig.)
Optimizing stochastic trajectories in exact quantum-jump approaches of interacting systems
International Nuclear Information System (INIS)
Lacroix, Denis
2005-01-01
The quantum-jump approach, where pairs of state vectors follow the stochastic Schroedinger equation (SSE) in order to treat the exact quantum dynamics of two interacting systems, is described. In this work the nonuniqueness of such stochastic Schroedinger equations is investigated to propose strategies to optimize the stochastic paths and reduce statistical fluctuations. In the proposed method, called the 'adaptative noise method', a specific SSE is obtained for which the noise depends explicitly on both the initial state and on the properties of the interaction Hamiltonian. It is also shown that this method can be further improved by introduction of a mean-field dynamics. The different optimization procedures are illustrated quantitatively in the case of interacting spins. A significant reduction of the statistical fluctuations is obtained. Consequently a much smaller number of trajectories is needed to accurately reproduce the exact dynamics as compared to the SSE without optimization
Indian Academy of Sciences (India)
of a system under investigation is to model the system in terms of some mathematical equations, which are generally nonlinear, and then find exact analytic solutions of such model equations using a suitable method. By the aid of exact solutions, when they exist, the phenomena modelled by these NLEEs can be better ...
Quasitraces on exact C*-algebras are traces
DEFF Research Database (Denmark)
Haagerup, Uffe
2014-01-01
It is shown that all 2-quasitraces on a unital exact C ∗ -algebra are traces. As consequences one gets: (1) Every stably finite exact unital C ∗ -algebra has a tracial state, and (2) if an AW ∗ -factor of type II 1 is generated (as an AW ∗ -algebra) by an exact C ∗ -subalgebra, then i......, then it is a von Neumann II 1 -factor. This is a partial solution to a well known problem of Kaplansky. The present result was used by Blackadar, Kumjian and Rørdam to prove that RR(A)=0 for every simple non-commutative torus of any dimension...
Electron transfer dynamics: Zusman equation versus exact theory
International Nuclear Information System (INIS)
Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing
2009-01-01
The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.
Fuzziness and Foundations of Exact and Inexact Sciences
Dompere, Kofi Kissi
2013-01-01
The monograph is an examination of the fuzzy rational foundations of the structure of exact and inexact sciences over the epistemological space which is distinguished from the ontological space. It is thus concerned with the demarcation problem. It examines exact science and its critique of inexact science. The role of fuzzy rationality in these examinations is presented. The driving force of the discussions is the nature of the information that connects the cognitive relational structure of the epistemological space to the ontological space for knowing. The knowing action is undertaken by decision-choice agents who must process information to derive exact-inexact or true-false conclusions. The information processing is done with a paradigm and laws of thought that constitute the input-output machine. The nature of the paradigm selected depends on the nature of the information structure that is taken as input of the thought processing. Generally, the information structure received from the ontological space i...
Exact deconstruction of the 6D (2,0) theory
International Nuclear Information System (INIS)
Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodriguez-Gomez, D.
2017-06-01
The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2 , starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: In the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the ''half-BPS'' limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 x T 2 . In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.
Exact semiclassical expansions for one-dimensional quantum oscillators
Energy Technology Data Exchange (ETDEWEB)
Delabaere, E. [UMR CNRS J. A. Dieudonne No. 6621, University of Nice, 06108 Nice Cedex 2 (France); Dillinger, H.; Pham, F. [University of Nice, Department of Maths, UMR CNRS J.A. Dieudonne No. 6621, 06108 Nice Cedex 2 (France)
1997-12-01
A set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. These rules, which include also the case when there are double turning points, are illustrated on various examples, and applied to the study of bound state or resonance spectra. In the case of simple oscillators, it is thus shown that the Rayleigh{endash}Schr{umlt o}dinger series is Borel resummable, yielding the exact energy levels. In the case of the symmetrical anharmonic oscillator, one gets a simple and rigorous justification of the Zinn-Justin quantization condition, and of its solution in terms of {open_quotes}multi-instanton expansions.{close_quotes} {copyright} {ital 1997 American Institute of Physics.}
[Application of Excel programs of Fisher exact probability test for medical data].
Chen, Qing-shan; Wang, Wei; Lin, Pei-xian; Zhong, Qian-hong; Yu, Shou-yi
2009-04-01
To accomplish the computation of Fisher exact probability test for fourfold table data in Excel. The computing program of exact probability method for medical data in fourfold table design was edited by employing the IF statement and the relevant functions, such as SUM, FACT, DSUM, etc in Excel. The computational results are compared and evaluated according to the case studies. The output of Fisher Exact Probability was generated and presented correctly following the input of four numerical values into the computation program in the setting of Excel. The parametric outcomes are in agreement with those produced by SAS and SPSS, in the combination tables containing the P value, two-tailed cumulative P value, left-tailed P-value, right-tailed P-value, Chi2 values and P values both for direct Chi-squared test and corrected Chi-squared test. Direct Chi-squared test, corrected Chi-squared test combined with Fisher Exact Probability test for fourfold table data can be conveniently, rapidly, and accurately accomplished in Excel.
International Nuclear Information System (INIS)
Baxter, Mathew; Van Gorder, Robert A
2013-01-01
We obtain solutions to a transformation of the axially symmetric Ernst equation, which governs a class of exact solutions of Einstein's field equations. Physically, the equation serves as a model of axially symmetric stationary vacuum gravitational fields. By an application of the method of homotopy analysis, we are able to construct approximate analytic solutions to the relevant boundary value problem in the case where exact solutions are not possible. The results presented constitute a solution for a complicated nonlinear and singular initial value problem. Through appropriate selection of the auxiliary linear operator and convergence control parameter, we are able to obtain low order approximations which minimize residual error over the problem domain. The benefit to such approach is that we obtain very accurate approximations after computing very few terms, hence the computational efficiency is high. Finally, an exact solution is provided in a special case, and this corresponds to the analytical solutions obtained in the more general case. The approximate solutions agree qualitatively with the exact solutions. (paper)
Lessons on electronic decoherence in molecules from exact modeling
Hu, Wenxiang; Gu, Bing; Franco, Ignacio
2018-04-01
Electronic decoherence processes in molecules and materials are usually thought and modeled via schemes for the system-bath evolution in which the bath is treated either implicitly or approximately. Here we present computations of the electronic decoherence dynamics of a model many-body molecular system described by the Su-Schrieffer-Heeger Hamiltonian with Hubbard electron-electron interactions using an exact method in which both electronic and nuclear degrees of freedom are taken into account explicitly and fully quantum mechanically. To represent the electron-nuclear Hamiltonian in matrix form and propagate the dynamics, the computations employ the Jordan-Wigner transformation for the fermionic creation/annihilation operators and the discrete variable representation for the nuclear operators. The simulations offer a standard for electronic decoherence that can be used to test approximations. They also provide a useful platform to answer fundamental questions about electronic decoherence that cannot be addressed through approximate or implicit schemes. Specifically, through simulations, we isolate basic mechanisms for electronic coherence loss and demonstrate that electronic decoherence is possible even for one-dimensional nuclear bath. Furthermore, we show that (i) decreasing the mass of the bath generally leads to faster electronic decoherence; (ii) electron-electron interactions strongly affect the electronic decoherence when the electron-nuclear dynamics is not pure-dephasing; (iii) classical bath models with initial conditions sampled from the Wigner distribution accurately capture the short-time electronic decoherence dynamics; (iv) model separable initial superpositions often used to understand decoherence after photoexcitation are only relevant in experiments that employ delta-like laser pulses to initiate the dynamics. These insights can be employed to interpret and properly model coherence phenomena in molecules.
An exact general remeshing scheme applied to physically conservative voxelization
Powell, Devon; Abel, Tom
2015-09-01
We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes. In physics applications this allows one to ensure global mass, momentum, and energy conservation while applying higher-order polynomial interpolation. We elaborate on applications of our algorithm arising in the analysis of cosmological N-body data, computer graphics, and continuum mechanics problems. We focus on the particular case of remeshing tetrahedral cells onto a Cartesian grid such that the volume integral of the polynomial density function given on the input mesh is guaranteed to equal the corresponding integral over the output mesh. We refer to this as "physically conservative voxelization." At the core of our method is an algorithm for intersecting two convex polyhedra by successively clipping one against the faces of the other. This algorithm is an implementation of the ideas presented abstractly by Sugihara [48], who suggests using the planar graph representations of convex polyhedra to ensure topological consistency of the output. This makes our implementation robust to geometric degeneracy in the input. We employ a simplicial decomposition to calculate moment integrals up to quadratic order over the resulting intersection domain. We also address practical issues arising in a software implementation, including numerical stability in geometric calculations, management of cancellation errors, and extension to two dimensions. In a comparison to recent work, we show substantial performance gains. We provide a C implementation intended to be a fast, accurate, and robust tool for geometric calculations on polyhedral mesh elements.
Placental complications after a previous cesarean section
Milošević Jelena; Lilić Vekoslav; Tasić Marija; Radović-Janošević Dragana; Stefanović Milan; Antić Vladimir
2009-01-01
Introduction The incidence of cesarean section has been rising in the past 50 years. With the increased number of cesarean sections, the number of pregnancies with the previous cesarean section rises as well. The aim of this study was to establish the influence of the previous cesarean section on the development of placental complications: placenta previa, placental abruption and placenta accreta, as well as to determine the influence of the number of previous cesarean sections on the complic...
Asymptotically exact solution of a local copper-oxide model
International Nuclear Information System (INIS)
Zhang Guangming; Yu Lu.
1994-03-01
We present an asymptotically exact solution of a local copper-oxide model abstracted from the multi-band models. The phase diagram is obtained through the renormalization-group analysis of the partition function. In the strong coupling regime, we find an exactly solved line, which crosses the quantum critical point of the mixed valence regime separating two different Fermi-liquid (FL) phases. At this critical point, a many-particle resonance is formed near the chemical potential, and a marginal-FL spectrum can be derived for the spin and charge susceptibilities. (author). 15 refs, 1 fig
Exact penalty results for mathematical programs with vanishing constraints
Czech Academy of Sciences Publication Activity Database
Hoheisel, T.; Kanzow, Ch.; Outrata, Jiří
2010-01-01
Roč. 72, č. 5 (2010), s. 2514-2526 ISSN 0362-546X R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10750506 Keywords : Mathematical programs with vanishing constraints * Mathematical programs with equilibrium constraints * Exact penalization * Calmness * Subdifferential calculus * Limiting normal cone Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://library.utia.cas.cz/separaty/2010/MTR/outrata-exact penalty results for mathematical programs with vanishing constraints.pdf
Exact solution of the space-time fractional coupled EW and coupled MEW equations
Raslan, K. R.; S. EL-Danaf, Talaat; K. Ali, Khalid
2017-07-01
In this paper, we obtained a traveling wave solution by using the Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations, such as the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEWE), which are the important soliton equations. Both equations are reduced to ordinary differential equations by use of the fractional complex transform and of the properties of the modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.
DEFF Research Database (Denmark)
Gamst, M.
2014-01-01
an optical network. The problem is formulated as an IP problem and is shown to be NP-hard. An exact solution approach based on Dantzig-Wolfe decomposition is proposed. Also, several heuristic methods are developed by combining heuristics for the job scheduling problem and for the constrained network routing...... problem. The methods are computationally evaluated on test instances arising from telecommunications with up to 500 jobs and 500 machines. Results show that solving the integrated job scheduling and constrained network routing problem to optimality is very difficult. The exact solution approach performs......This paper examines the problem of scheduling a number of jobs on a finite set of machines such that the overall profit of executed jobs is maximized. Each job has a certain demand, which must be sent to the executing machine via constrained paths. A job cannot start before all its demands have...
Prevalence and significance of previously undiagnosed rheumatic diseases in pregnancy.
Spinillo, Arsenio; Beneventi, Fausta; Ramoni, Véronique; Caporali, Roberto; Locatelli, Elena; Simonetta, Margherita; Cavagnoli, Chiara; Alpini, Claudia; Albonico, Giulia; Prisco, Elena; Montecucco, Carlomaurizio
2012-06-01
The objective of this study was to evaluate the rates of previously undiagnosed rheumatic diseases during the first trimester of pregnancy and their impact on the pregnancy outcome. Pregnant women in their first trimester were screened using a two-step approach using a self-administered 10-item questionnaire and subsequent testing for rheumatic autoantibodies (antinuclear antibody, anti-double-stranded DNA, anti-extractable nuclear antigen, anticardiolipin antibodies, anti-β2-glycoprotein I antibodies and lupus anticoagulant) and evaluation by a rheumatologist. Overall, the complications of pregnancy evaluated included fetal loss, pre-eclampsia, gestational diabetes, fetal growth restriction, delivery at less than 34 weeks, neonatal resuscitation and admission to the neonatal intensive care unit. Out of the 2458 women screened, the authors identified 62 (2.5%) women with previously undiagnosed undifferentiated connective tissue disease (UCTD) and 24 (0.98%) women with previously undiagnosed definite systemic rheumatic disease. The prevalences were seven (0.28%) for systemic lupus erythematosus and Sjogren's syndrome, six (0.24%) for rheumatoid arthritis, three (0.12%) for antiphospholipid syndrome and one (0.04%) for systemic sclerosis. In multiple exact logistic regression, after adjustment for potential confounders, the OR of overall complications of pregnancy were 2.81 (95% CI 1.29 to 6.18) in women with UCTD and 4.57 (95% CI 1.57 to 13.57) in those with definite diseases, respectively, compared with asymptomatic controls. In our population approximately 2.5% and 1% of first trimester pregnant women had a previously undiagnosed UCTD and definite systemic rheumatic disease, respectively. These conditions were associated with significant negative effects on the outcome of pregnancy.
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...... to the extent that it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes the effects...
Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.
2016-01-01
We consider the stationary sine-Gordon equation on metric graphs with simple topologies. The vertex boundary conditions are provided by flux conservation and matching of derivatives at the star graph vertex. Exact analytical solutions are obtained. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.
New exact solutions of sixth-order thin-film equation
Directory of Open Access Journals (Sweden)
Wafaa M. Taha
2014-01-01
Full Text Available TheG′G-expansion method is used for the first time to find traveling-wave solutions for the sixth-order thin-film equation, where related balance numbers are not the usual positive integers. New types of exact traveling-wave solutions, such as – solitary wave solutions, are obtained the sixth-order thin-film equation, when parameters are taken at special values.
Shifted axis angular positioning mechanisms – unconventional use of exact constraint design
Szykiedans Ksawery; Bujwan Maciej
2018-01-01
Paper presents some remarks about designing angular positioners having significant angular displacement and shifted axis of rotation. Those driving mechanism are useful in specific applications where mechanism wraps around other object or there is a need of rotation around virtual axis. Examples of those applications like orthotic robots or gimbals for panoramic motions where developed at Faculty of Mechatronics WUT. Usage of exact constraint method was described including its influence to a ...
Pre-selective screening for matrix elements in linear-scaling exact exchange calculations.
Kussmann, Jörg; Ochsenfeld, Christian
2013-04-07
We present a simple but accurate preselection method based on Schwarz integral estimates to determine the significant elements of the exact exchange matrix before its evaluation, thus providing an asymptotical linear-scaling behavior for non-metallic systems. Our screening procedure proves to be highly suitable for exchange matrix calculations on massively parallel computing architectures, such as graphical processing units, for which we present a first linear-scaling exchange matrix evaluation algorithm.
Closed-Form Exact Inverses of the Weakly Singular and Hypersingular Operators On Disks
Hiptmair, Ralf; Jerez-Hanckes, Carlos; Urzua-Torres, Carolina
2017-01-01
We introduce new boundary integral operators which are the exact inverses of the weakly singular and hypersingular operators for the Laplacian on flat disks. Moreover, we provide explicit closed forms for them and prove the continuity and ellipticity of their corresponding bilinear forms in the natural Sobolev trace spaces. This permit us to derive new Calder\\'on-type identities that can provide the foundation for optimal operator preconditioning in Galerkin boundary element methods.
Shifted axis angular positioning mechanisms – unconventional use of exact constraint design
Directory of Open Access Journals (Sweden)
Szykiedans Ksawery
2018-01-01
Full Text Available Paper presents some remarks about designing angular positioners having significant angular displacement and shifted axis of rotation. Those driving mechanism are useful in specific applications where mechanism wraps around other object or there is a need of rotation around virtual axis. Examples of those applications like orthotic robots or gimbals for panoramic motions where developed at Faculty of Mechatronics WUT. Usage of exact constraint method was described including its influence to a kinematic structure of designed mechanism.
Exact solution for suboptimal control of nuclear reactors with distributed parameters
International Nuclear Information System (INIS)
Kim, S.H.; Chang, J.
1981-01-01
An exact solution based on the explicit formulation of the optimal time-displacement operator by using the confluent form of the Sylvester theorem is presented for synthesizing suboptimal control of nuclear reactors with spatially distributed parameters. The Helmholtz mode expansion is used for the application of the optimal theory for lumped parameter systems to the spatially distributed parameter systems. A numerical example is given showing the expedience of the present method. 8 refs
Asymptotically exact localized expansions for signals in the time–frequency domain
International Nuclear Information System (INIS)
Muzhikyan, Aramazd H; Avanesyan, Gagik T
2012-01-01
Based on a unique waveform with strong exponential localization property, an exact mathematical method for solving problems in signal analysis in the time–frequency domain is presented. An analogue of the Gabor frame exposes the non-commutative geometry of the time–frequency plane. Signals are visualized using the constructed graphical representation. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)
Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system
Directory of Open Access Journals (Sweden)
Boris V. Kapitonov
2010-02-01
Full Text Available We present a result on "simultaneous" exact controllability for two models that describe two hyperbolic dynamics. One is the system of Maxwell equations and the other a vector-wave equation with a pressure term. We obtain the main result using modified multipliers in order to generate a necessary observability estimate which allow us to use the Hilbert Uniqueness Method (HUM introduced by Lions.
The potts chain in a random field: an exact solution
International Nuclear Information System (INIS)
Riera, R.; Chaves, C.M.G.F.; Santos, Raimundo R. dos.
1984-01-01
An exact solution is presented for the one-dimensional q-state Potts model in a quenched random field. The ferromagnetic phase is unstable against any small random field perturbation. The correlation function and the Edwards-Anderson order parameter Q are discussed. For finite q only the phase with Q ≠ 0 is present. (Author) [pt
Exact Controllability and Perturbation Analysis for Elastic Beams
International Nuclear Information System (INIS)
Moreles, Miguel Angel
2004-01-01
The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the corresponding solution of the Bernoulli-Euler beam. Convergence is related to a Singular Perturbation Problem. The main tool in solving this perturbation problem is a weak version of a lower bound for hyperbolic polynomials
Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact ...
African Journals Online (AJOL)
Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact solutions and conservation laws. ... In this paper we study the combined sinh-cosh-Gordon equation, which arises in mathematical physics and has a wide range of scientific applications that range from chemical reactions to water surface gravity waves.
Exact rational expectations, cointegration, and reduced rank regression
DEFF Research Database (Denmark)
Johansen, Søren; Swensen, Anders Rygh
We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important role...
Exact rational expectations, cointegration, and reduced rank regression
DEFF Research Database (Denmark)
Johansen, Søren; Swensen, Anders Rygh
2008-01-01
We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important role...
Exact Rational Expectations, Cointegration, and Reduced Rank Regression
DEFF Research Database (Denmark)
Johansen, Søren; Swensen, Anders Rygh
We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important role...
Exact Cover Problem in Milton Babbitt's All-partition Array
DEFF Research Database (Denmark)
Bemman, Brian; Meredith, David
2015-01-01
, A, and a collection of distinct subsets of this set, S, then a subset of S is an exact cover of A if it exhaustively and exclu- sively partitions A. We provide a backtracking algorithm for solving this problem in an all-partition array and compare the output of this algorithm with an analysis...
Exact angular momentum projection based on cranked HFB solution
Energy Technology Data Exchange (ETDEWEB)
Enami, Kenichi; Tanabe, Kosai; Yosinaga, Naotaka [Saitama Univ., Urawa (Japan). Dept. of Physics
1998-03-01
Exact angular momentum projection of cranked HFB solutions is carried out. It is reconfirmed from this calculation that cranked HFB solutions reproduce the intrinsic structure of deformed nucleus. The result also indicates that the energy correction from projection is important for further investigation of nuclear structure. (author)
Construction of an exact solution of time-dependent Ginzburg ...
Indian Academy of Sciences (India)
A new approach is taken to calculate the speed of front propagation at which the interface moves from a superconducting to a normal region in a superconducting sample. Using time-dependent Ginzburg–Landau (TDGL) equations we have calculated the speed by constructing a new exact solution. This approach is based ...
Exact solutions to the generalized Lienard equation and its ...
Indian Academy of Sciences (India)
and the solutions of the equation are applied to solve nonlinear wave equations with nonlin- ... Lienard equation (1) corresponds to the p = 2 case of the generalized Lienard equation. Some exact solutions of the generalized Lienard equation (2) and their applications have been ...... In order to make the left-hand side of eq.
Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.
Pronchik, Jeremy N.; Williams, Brian W.
2003-01-01
Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...
Some exact solutions of magnetized viscous model in string ...
Indian Academy of Sciences (India)
Abstract. In this paper, we study anisotropic Bianchi-V Universe with magnetic field and bulk viscous fluid in string cosmology. Exact solutions of the field equations are obtained by using the equation of state (EoS) for a cloud of strings, and a relationship between bulk viscous coefficient and scalar expansion. The bulk ...
Some exact solutions of magnetized viscous model in string ...
Indian Academy of Sciences (India)
In this paper, we study anisotropic Bianchi-V Universe with magnetic field and bulk viscous fluid in string cosmology. Exact solutions of the field equations are obtained by using the equation of state (EoS) for a cloud of strings, and a relationship between bulk viscous coefficient and scalar expansion. The bulk viscous ...
A SAS/IML algorithm for an exact permutation test
Directory of Open Access Journals (Sweden)
Neuhäuser, Markus
2009-03-01
Full Text Available An algorithm written in SAS/IML is presented that can perform an exact permutation test for a two-sample comparison. All possible permutations are considered. The Baumgartner-Weiß-Schindler statistic is exemplarily used as the test statistic for the permutation test.
Dynamic Programming Approach for Exact Decision Rule Optimization
Amin, Talha
2013-01-01
This chapter is devoted to the study of an extension of dynamic programming approach that allows sequential optimization of exact decision rules relative to the length and coverage. It contains also results of experiments with decision tables from UCI Machine Learning Repository. © Springer-Verlag Berlin Heidelberg 2013.
Exact boundary controllability for a series of membranes elastically connected
Directory of Open Access Journals (Sweden)
Waldemar D. Bastos
2017-01-01
Full Text Available In this article we study the exact controllability with Neumann boundary controls for a system of linear wave equations coupled in parallel by lower order terms on piecewise smooth domains of the plane. We obtain square integrable controls for initial state with finite energy and time of controllability near the optimal value.
Classical charged fluids at equilibrium near an interface: Exact ...
Indian Academy of Sciences (India)
Invited Talks:- Topic 1. Rigorous results and exact solutions; general aspects of statistical physics; thermodynamics Volume 64 Issue 5 May 2005 pp 785-801 ... http://www.ias.ac.in/article/fulltext/pram/064/05/0785-0801. Keywords. Inhomogeneous fluid; Coulomb interaction; screening; density profile; surface tension.
A procedure to construct exact solutions of nonlinear evolution ...
Indian Academy of Sciences (India)
computer science, directly searching for solutions of nonlinear differential equations has become more and more attractive. This is due to the availability of computer symbolic systems like Maple which allows us to perform some complicated and tedious alge- braic calculation using a computer and help us to find new exact ...
New exact models for anisotropic matter with electric field
Indian Academy of Sciences (India)
2017-09-05
Sep 5, 2017 ... We can also obtain particular anisotropic models obtained by Maharaj, Sunzu, and Ray. The exact solutions corresponding to our models are found explicitly in terms of elementary functions. The graphical plots generated for the matter variables and the electric field are well behaved. We also generate ...
Exact Repetition as Input Enhancement in Second Language Acquisition.
Jensen, Eva Dam; Vinther, Thora
2003-01-01
Reports on two studies on input enhancement used to support learners' selection of focus of attention in Spanish second language listening material. Input consisted of video recordings of dialogues between native speakers. Exact repetition and speech rate reduction were examined for effect on comprehension, acquisition of decoding strategies, and…
Exact solution to surface displacement associated with sources ...
African Journals Online (AJOL)
user
Usually an exact solution to the surface displacement in an elastic half space is available for sources parallel to the surface. Here we consider a buried elliptic source ... used Laplace–Hankel mixed transform and transfer matrix techniques along with the Fast Hankel transform algorithm for an impulsive ring source within a ...
The Asymmetric Simple Exclusion Process: An Exactly Solvable ...
Indian Academy of Sciences (India)
Arvind Ayyer, Indian Institute of Science
2017-06-30
Jun 30, 2017 ... An Exactly Solvable Model of Particle Transport. Arvind Ayyer,. Indian Institute of Science. 28th Mid Year Meeting. Faculty Hall, Indian Institute of Science ... System is in thermodynamic equilibrium. Microscopic motion may be present, but macroscopic observables do not change over time. The probability ...
New exact solutions for polynomial oscillators in large dimensions
Czech Academy of Sciences Publication Activity Database
Znojil, Miloslav; Yanovich, D.; Gerdt, VP.
2003-01-01
Roč. 36, č. 23 (2003), s. 6531-6549 ISSN 0305-4470 R&D Projects: GA AV ČR KSK1010104 Keywords : exact solution * large-N limit * anharmonic-oscillators Subject RIV: BE - Theoretical Physics Impact factor: 1.357, year: 2003
Exactly soluble diluted random one-dimensional lattices
Nieuwenhuizen, Th.M.
1984-01-01
Exact solutions for the characteristic function, which determines the density of states and inverse localization length, and one-particle Green function are presented for a class of lattice models with diluted randomness. (Examples are: harmonic, electronic, relaxation and X-Y spin systems.) With
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
Abstract. The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and ...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...
Exact solutions, energy, and charge of stable Q-balls
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D.; Marques, M.A. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)
2016-05-15
In this work we deal with nontopological solutions of the Q-ball type in two spacetime dimensions. We study models of current interest, described by a Higgs-like and other, similar potentials which unveil the presence of exact solutions. We use the analytic results to investigate how to control the energy and charge to make the Q-balls stable. (orig.)
Construction of an exact solution of time-dependent Ginzburg ...
Indian Academy of Sciences (India)
Abstract. A new approach is taken to calculate the speed of front propagation at which the interface moves from a superconducting to a normal region in a superconducting sample. Using time-dependent Ginzburg–Landau (TDGL) equations we have calculated the speed by constructing a new exact solution. This approach ...
Construction of exact complex dynamical invariant of a two ...
Indian Academy of Sciences (India)
physics pp. 999–1009. Construction of exact complex dynamical invariant of a two-dimensional classical system. FAKIR CHAND and S C MISHRA. Department ... namical invariants for both time-dependent and time-independent classical systems. [1–3]. .... where [·, ·] is the Poisson bracket, which in view of the definition eq.
Generalization of quasi-exactly solvable and isospectral potentials
Indian Academy of Sciences (India)
which are exactly solvable for single state. Here, we attain added realism and sophistication by dealing with higher dimensional Schrödinger equation so that the results can easily be applied to any required lower dimension (N > 1). Over and above, the dimensional variable N may be treated as a perturbation parameter (. 1.
Exact relations for energy transfer in self-gravitating isothermal turbulence.
Banerjee, Supratik; Kritsuk, Alexei G
2017-11-01
Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous (not necessarily isotropic) turbulence. A modified definition for the two-point energy correlation functions is used to comply with the requirement of detailed energy equipartition in the acoustic limit. In contrast to the previous relations (S. Galtier and S. Banerjee, Phys. Rev. Lett. 107, 134501 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.134501; S. Banerjee and S. Galtier, Phys. Rev. E 87, 013019 (2013)PLEEE81539-375510.1103/PhysRevE.87.013019), the current exact relation shows that the pressure dilatation terms play practically no role in the energy cascade. Both the flux and source terms are written in terms of two-point differences. Sources enter the relation in a form of mixed second-order structure functions. Unlike the kinetic and thermodynamic potential energies, the gravitational contribution is absent from the flux term. An estimate shows that, for the isotropic case, the correlation between density and gravitational acceleration may play an important role in modifying the energy transfer in self-gravitating turbulence. The exact relation is also written in an alternative form in terms of two-point correlation functions, which is then used to describe scale-by-scale energy budget in spectral space.
Preoperative screening: value of previous tests.
Macpherson, D S; Snow, R; Lofgren, R P
1990-12-15
To determine the frequency of tests done in the year before elective surgery that might substitute for preoperative screening tests and to determine the frequency of test results that change from a normal value to a value likely to alter perioperative management. Retrospective cohort analysis of computerized laboratory data (complete blood count, sodium, potassium, and creatinine levels, prothrombin time, and partial thromboplastin time). Urban tertiary care Veterans Affairs Hospital. Consecutive sample of 1109 patients who had elective surgery in 1988. At admission, 7549 preoperative tests were done, 47% of which duplicated tests performed in the previous year. Of 3096 previous results that were normal as defined by hospital reference range and done closest to the time of but before admission (median interval, 2 months), 13 (0.4%; 95% CI, 0.2% to 0.7%), repeat values were outside a range considered acceptable for surgery. Most of the abnormalities were predictable from the patient's history, and most were not noted in the medical record. Of 461 previous tests that were abnormal, 78 (17%; CI, 13% to 20%) repeat values at admission were outside a range considered acceptable for surgery (P less than 0.001, frequency of clinically important abnormalities of patients with normal previous results with those with abnormal previous results). Physicians evaluating patients preoperatively could safely substitute the previous test results analyzed in this study for preoperative screening tests if the previous tests are normal and no obvious indication for retesting is present.
An exact maternal-fetal genotype incompatibility (MFG) test.
Minassian, Sonia L; Palmer, Christina G S; Sinsheimer, Janet S
2005-01-01
The maternal-fetal genotype incompatibility (MFG) test can be used for a variety of genetic applications concerning disease risk in offspring including testing for the presence of alleles that act directly through offspring genotypes (child allelic effects), alleles that act through maternal genotypes (maternal allelic effects), or maternal-fetal genotype incompatibilities. The log-linear version of the MFG model divides the genotype data into many cells, where each cell represents one of the possible mother, father, and child genotype combinations. Currently, tests of hypotheses about different allelic effects are accomplished by an asymptotic MFG test, but it is unknown if this is appropriate under conditions that produce small cell counts. In this report, we develop an exact MFG test that is based on the permutation distribution of cell counts. We determine by simulation the type I error and power of both the exact MFG test and the asymptotic MFG test for four different biologically relevant scenarios: a test of child allelic effects in the presence of maternal allelic effects, a test of maternal allelic effects in the presence of child allelic effects, and tests of maternal-fetal genotype incompatibility with and without child allelic effects. These simulations show that, in general, the exact test is slightly conservative whereas the asymptotic test is slightly anti-conservative. However, the asymptotic MFG test produces significantly inflated type I error rates under conditions with extreme null allele frequencies and sample sizes of 75, 100, and 150. Under these conditions, the exact test is clearly preferred over the asymptotic test. Under all other conditions that we tested, the user can safely choose either the exact test or the asymptotic test. 2004 Wiley-Liss, Inc.
César Mansur Filho, Júlio; Dickman, Ronald
2011-05-01
We study symmetric sleepy random walkers, a model exhibiting an absorbing-state phase transition in the conserved directed percolation (CDP) universality class. Unlike most examples of this class studied previously, this model possesses a continuously variable control parameter, facilitating analysis of critical properties. We study the model using two complementary approaches: analysis of the numerically exact quasistationary (QS) probability distribution on rings of up to 22 sites, and Monte Carlo simulation of systems of up to 32 000 sites. The resulting estimates for critical exponents β, \\beta /\
Automatic electromagnetic valve for previous vacuum
International Nuclear Information System (INIS)
Granados, C. E.; Martin, F.
1959-01-01
A valve which permits the maintenance of an installation vacuum when electric current fails is described. It also lets the air in the previous vacuum bomb to prevent the oil ascending in the vacuum tubes. (Author)
Exact Solutions of an Extended Bose-Hubbard Model with E 2 Symmetry
Pan, Feng; Zhang, Ningyun; Wang, Qianyun; Draayer, J. P.
2015-07-01
An extended Bose-Hubbard (BH) model with number-dependent multi-site and infinite-range hopping is proposed, which, similar to the original BH model, describes a phase transition between the delocalized superfluid (SF) phase and localized Mott insulator (MI) phase. It is shown that this extended model with local Euclidean E 2 symmetry is exactly solvable when on-site local potentials are included, while the model without local potentials is quasi-exactly solvable, which means only a part of the excited states including the ground state being exactly solvable. As applications of the exact solution for the ground state, phase diagram of the model in 1D without local potential and on-site disorder for filling factor ρ = 1 with M = 6, M = 10, and M = 14 sites are obtained. The ground state probabilities to detect n particles on a single site, P n , for n = 0, 1, 2 as functions of the control parameter U/ t in these cases are also calculated. It is shown that the critical point in P n and in the entanglement measure is away from that of the SF-MI transition determined in the phase analysis. It is also shown that the model-independent entanglement measure is related with P n , which, therefore, may be practically useful because P n is measurable experimentally. The ground state expectation value of local particle numbers, the ground state local particle number fluctuations, the ground state probabilities to detect n particles on every site, and the entanglement measure have also been studied in the model for N = M = 4 with the two-body onsite repulsion and a local confining harmonic potential. The connection between these quantities and the entanglement observed previously is verified.
Saengow, Chaimongkol; Giacomin, A. Jeffrey
2018-03-01
In this paper, we provide a new exact framework for analyzing the most commonly measured behaviors in large-amplitude oscillatory shear flow (LAOS), a popular flow for studying the nonlinear physics of complex fluids. Specifically, the strain rate sweep (also called the strain sweep) is used routinely to identify the onset of nonlinearity. By the strain rate sweep, we mean a sequence of LAOS experiments conducted at the same frequency, performed one after another, with increasing shear rate amplitude. In this paper, we give exact expressions for the nonlinear complex viscosity and the corresponding nonlinear complex normal stress coefficients, for the Oldroyd 8-constant framework for oscillatory shear sweeps. We choose the Oldroyd 8-constant framework for its rich diversity of popular special cases (we list 18 of these). We evaluate the Fourier integrals of our previous exact solution to get exact expressions for the real and imaginary parts of the complex viscosity, and for the complex normal stress coefficients, as functions of both test frequency and shear rate amplitude. We explore the role of infinite shear rate viscosity on strain rate sweep responses for the special case of the corotational Jeffreys fluid. We find that raising η∞ raises the real part of the complex viscosity and lowers the imaginary. In our worked examples, we thus first use the corotational Jeffreys fluid, and then, for greater accuracy, we use the Johnson-Segalman fluid, to describe the strain rate sweep response of molten atactic polystyrene. For our comparisons with data, we use the Spriggs relations to generalize the Oldroyd 8-constant framework to multimode. Our generalization yields unequivocally, a longest fluid relaxation time, used to assign Weissenberg and Deborah numbers to each oscillatory shear flow experiment. We then locate each experiment in the Pipkin space.
Bayesian noninferiority test for 2 binomial probabilities as the extension of Fisher exact test.
Doi, Masaaki; Takahashi, Fumihiro; Kawasaki, Yohei
2017-12-30
Noninferiority trials have recently gained importance for the clinical trials of drugs and medical devices. In these trials, most statistical methods have been used from a frequentist perspective, and historical data have been used only for the specification of the noninferiority margin Δ>0. In contrast, Bayesian methods, which have been studied recently are advantageous in that they can use historical data to specify prior distributions and are expected to enable more efficient decision making than frequentist methods by borrowing information from historical trials. In the case of noninferiority trials for response probabilities π 1 ,π 2 , Bayesian methods evaluate the posterior probability of H 1 :π 1 >π 2 -Δ being true. To numerically calculate such posterior probability, complicated Appell hypergeometric function or approximation methods are used. Further, the theoretical relationship between Bayesian and frequentist methods is unclear. In this work, we give the exact expression of the posterior probability of the noninferiority under some mild conditions and propose the Bayesian noninferiority test framework which can flexibly incorporate historical data by using the conditional power prior. Further, we show the relationship between Bayesian posterior probability and the P value of the Fisher exact test. From this relationship, our method can be interpreted as the Bayesian noninferior extension of the Fisher exact test, and we can treat superiority and noninferiority in the same framework. Our method is illustrated through Monte Carlo simulations to evaluate the operating characteristics, the application to the real HIV clinical trial data, and the sample size calculation using historical data. Copyright © 2017 John Wiley & Sons, Ltd.
CSIR Research Space (South Africa)
Shatalov, M
2012-09-01
Full Text Available Exact solutions of equations of longitudinal vibration of conical and exponential rod are analyzed for the Rayleigh-Love model. These solutions are used as reference results for checking accuracy of the method of lines. It is shown that the method...
Stop: a fast procedure for the exact computation of the performance of complex probabilistic systems
International Nuclear Information System (INIS)
Corynen, G.C.
1982-01-01
A new set-theoretic method for the exact and efficient computation of the probabilistic performance of complex systems has been developed. The core of the method is a fast algorithm for disjointing a collection of product sets which is intended for systems with more than 1000 components and 100,000 cut sets. The method is based on a divide-and-conquer approach, in which a multidimensional problem is progressively decomposed into lower-dimensional subproblems along its dimensions. The method also uses a particular pointer system that eliminates the need to store the subproblems by only requiring the storage of pointers to those problems. Examples of the algorithm and the divide-and-conquer strategy are provided, and comparisons with other significant methods are made. Statistical complexity studies show that the expected time and space complexity of other methods is O(me/sup n/), but that our method is O(nm 3 log(m)). Problems which would require days of Cray-1 computer time with present methods can now be solved in seconds. Large-scale systems that can only be approximated with other techniques can now also be evaluated exactly
Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories
Energy Technology Data Exchange (ETDEWEB)
Carvalho, P.R.S. [Universidade Federal do Piaui, Departamento de Fisica, Teresina, PI (Brazil); Sena-Junior, M.I. [Universidade de Pernambuco, Escola Politecnica de Pernambuco, Recife, PE (Brazil); Universidade Federal de Alagoas, Instituto de Fisica, Maceio, AL (Brazil)
2017-11-15
In this work we evaluate analytically the ultraviolet divergences of Lorentz-violating massive O(N) λφ{sup 4} scalar field theories, which are exact in the Lorentz-violating mechanism, firstly explicitly at next-to-leading order and latter at any loop level through an induction procedure based on a theorem following from the exact approach, for computing the corresponding critical exponents. For attaining that goal, we employ three different and independent field-theoretic renormalization group methods. The results found for the critical exponents show that they are identical in the three distinct methods and equal to their Lorentz-invariant counterparts. Furthermore, we show that the results obtained here, based on the single concept of loop order of the referred terms of the corresponding β-function and anomalous dimensions, reduce to the ones obtained through the earlier non-exact approach based on a joint redefinition of the field and coupling constant of the theory, in the appropriate limit. (orig.)
Construction of an exactly solvable model of the many-body problem
Energy Technology Data Exchange (ETDEWEB)
Zettili, N. [King Fahd Univ. of Petrolium and Minerals, Dhahran (Saudi Arabia). Dept. of Phys.]|[Institut de Physique, Universite de Blida, Blida (Algeria); Bouayad, N. [Institut de Physique, Universite de Blida, Blida (Algeria)
1996-11-11
We propose here a new model for the many-body problem that can be solved exactly through the diagonalization of its Hamiltonian. This model, which is founded on a Lie algebra, serves as a useful tool for testing the accuracy of many-body approximation methods. The model consists of a one-dimensional system of two distinguishable sets of fermions interacting via a schematic two-body force. We construct this model`s Hamiltonian by means of vector operators that are the generators of an SO(2,1) group and which satisfy a Lie algebra. We incorporate into the Hamiltonian a symmetry that yields a constant of the motion which, in turn, renders the size of the Hamiltonian matrix finite. The diagonalization of this finitely dimensional matrix gives the exact values of the energy spectrum. (orig.).
An Enhanced Tire Model for Dynamic Simulation based on Geometrically Exact Shells
Directory of Open Access Journals (Sweden)
Roller Michael
2016-06-01
Full Text Available In the present work, a tire model is derived based on geometrically exact shells. The discretization is done with the help of isoparametric quadrilateral finite elements. The interpolation is performed with bilinear Lagrangian polynomials for the mid-surface as well as for the director field. As time stepping method for the resulting differential algebraic equation a backward differentiation formula is chosen. A multilayer material model for geometrically exact shells is introduced, to describe the anisotropic behavior of the tire material. To handle the interaction with a rigid road surface, a unilateral frictional contact formulation is introduced. Therein a special surface to surface contact element is developed, which rebuilds the shape of the tire.
Schmidt, F; McIntosh, E
2002-01-01
This is a description of the basic ideas behind the ``Polymorphic Tracking Code'' or PTC. PTC is truly a ``kick code'' or symplectic integrator in the tradition of TRACYII, SixTrack, and TEAPOT. However it separates correctly the mathematical atlas of charts and the magnets at a structural level by implementing a ``restricted fibre bundle.'' The resulting structures allow backward propagation and recirculation, something not possible in standard tracking codes. Also PTC is polymorphic in handling real (single, double and even quadruple precision) and Taylor series. Therefore it has all the tools associated to the TPSA packages: Lie methods, Normal Forms, Cosy-Infinity capabilities, beam envelopes for radiation, etc., as well as parameter dependence on-the-fly. However PTC is an integrator, and as such, one must, generally, adhere to the Talman ``exactness'' view of modelling. Incidentally, it supports exact sector and rectangular bends as well. Of course, one can certainly bypass its integrator and the user i...
Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities
Directory of Open Access Journals (Sweden)
Idris Addou
2000-01-01
Full Text Available We consider the boundary-value problem $$displaylines{ -(varphi_p (u'' =lambda f(u mbox{ in }(0,1 cr u(0 = u(1 =0,, }$$ where $p>1$, $lambda >0$ and $varphi_p (x =| x|^{p-2}x$. The nonlinearity $f$ is cubic-like with three distinct roots 0=a less than b less than c. By means of a quadrature method, we provide the exact number of solutions for all $lambda >0$. This way we extend a recent result, for $p=2$, by Korman et al. cite{KormanLiOuyang} to the general case $p>1$. We shall prove that when 1less than $pleq 2$ the structure of the solution set is exactly the same as that studied in the case $p=2$ by Korman et al. cite{KormanLiOuyang}, and strictly different in the case $p>2$.
An exact solution of three interacting friendly walks in the bulk
International Nuclear Information System (INIS)
Tabbara, R; Owczarek, A L; Rechnitzer, A
2016-01-01
We find the exact solution of three interacting friendly directed walks on the square lattice in the bulk, modelling a system of homopolymers that can undergo a multiple polymer fusion or zipping transition by introducing two distinct interaction parameters that differentiate between the zipping of only two or all three walks. We establish functional equations for the model’s corresponding generating function that are subsequently solved exactly by means of the obstinate kernel method. We then proceed to analyse our model, first considering the case where triple-walk interaction effects are ignored, finding that our model exhibits two phases which we classify as free and gelated (or zipped) regions, with the system exhibiting a second-order phase transition. We then analyse the full model where both interaction parameters are incorporated, presenting the full phase diagram and highlighting the additional existence of a first-order gelation (zipping) boundary. (paper)
Uterine rupture without previous caesarean delivery
DEFF Research Database (Denmark)
Thisted, Dorthe L. A.; H. Mortensen, Laust; Krebs, Lone
2015-01-01
OBJECTIVE: To determine incidence and patient characteristics of women with uterine rupture during singleton births at term without a previous caesarean delivery. STUDY DESIGN: Population based cohort study. Women with term singleton birth, no record of previous caesarean delivery and planned...... vaginal delivery (n=611,803) were identified in the Danish Medical Birth Registry (1997-2008). Medical records from women recorded with uterine rupture during labour were reviewed to ascertain events of complete uterine rupture. Relative Risk (RR) and adjusted Relative Risk Ratio (aRR) of complete uterine...... rupture with 95% confidence intervals (95% CI) were ascertained according to characteristics of the women and of the delivery. RESULTS: We identified 20 cases with complete uterine rupture. The incidence of complete uterine rupture among women without previous caesarean delivery was about 3...
Knotted optical vortices in exact solutions to Maxwell's equations
de Klerk, Albertus J. J. M.; van der Veen, Roland I.; Dalhuisen, Jan Willem; Bouwmeester, Dirk
2017-05-01
We construct a family of exact solutions to Maxwell's equations in which the points of zero intensity form knotted lines topologically equivalent to a given but arbitrary algebraic link. These lines of zero intensity, more commonly referred to as optical vortices, and their topology are preserved as time evolves and the fields have finite energy. To derive explicit expressions for these new electromagnetic fields that satisfy the nullness property, we make use of the Bateman variables for the Hopf field as well as complex polynomials in two variables whose zero sets give rise to algebraic links. The class of algebraic links includes not only all torus knots and links thereof, but also more intricate cable knots. While the unknot has been considered before, the solutions presented here show that more general knotted structures can also arise as optical vortices in exact solutions to Maxwell's equations.
Exactly soluble two-state quantum models with linear couplings
International Nuclear Information System (INIS)
Torosov, B T; Vitanov, N V
2008-01-01
A class of exact analytic solutions of the time-dependent Schroedinger equation is presented for a two-state quantum system coherently driven by a nonresonant external field. The coupling is a linear function of time with a finite duration and the detuning is constant. Four special models are considered in detail, namely the shark, double-shark, tent and zigzag models. The exact solution is derived by rotation of the Landau-Zener propagator at an angle of π/4 and is expressed in terms of Weber's parabolic cylinder function. Approximations for the transition probabilities are derived for all four models by using the asymptotics of the Weber function; these approximations demonstrate various effects of physical interest for each model
Exactly solvable string models of curved space-time backgrounds
Russo, J.G.; Russo, J G; Tseytlin, A A
1995-01-01
We consider a new 3-parameter class of exact 4-dimensional solutions in closed string theory and solve the corresponding string model, determining the physical spectrum and the partition function. The background fields (4-metric, antisymmetric tensor, two Kaluza-Klein vector fields, dilaton and modulus) generically describe axially symmetric stationary rotating (electro)magnetic flux-tube type universes. Backgrounds of this class include both the dilatonic Melvin solution and the uniform magnetic field solution discussed earlier as well as some singular space-times. Solvability of the string sigma model is related to its connection via duality to a much simpler looking model which is a "twisted" product of a flat 2-space and a space dual to 2-plane. We discuss some physical properties of this model as well as a number of generalizations leading to larger classes of exact 4-dimensional string solutions.
Mass Deformed Exact S-parameter in Conformal Theories
DEFF Research Database (Denmark)
Sannino, Francesco
2010-01-01
We use the exact expression for the S parameter in the perturbative region of the conformal window to establish its dependence on the explicit introduction of fermion masses. We demonstrate that the relative ordering with which one sends to zero either the fermion mass or the external momentum...... leads to drastically different limiting values of S. Our results apply to any fermion matter representation and can be used as benchmark for the determination of certain relevant properties of the conformal window of any generic vector like gauge theory with fermionic matter. We finally suggest...... the existence of a universal lower bound on the opportunely normalized S parameter and explore its theoretical and phenomenological implications. Our exact results constitute an ideal framework to correctly interpret the lattice studies of the conformal window of strongly interacting theories....
Supersymmetric quantum mechanics on the lattice: II. Exact results
Directory of Open Access Journals (Sweden)
David Baumgartner
2015-08-01
Full Text Available Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper – the second in a series of three – we present such an investigation for N=2 supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.
Exactly solvable models in many-body theory
March, N H
2016-01-01
The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.
Exact performance analysis of decode-and-forward opportunistic relaying
Tourki, Kamel
2010-06-01
In this paper, we investigate a dual-hop decode-and-forward opportunistic relaying scheme where the source may or may not be able to communicate directly with the destination. In our study, we consider a regenerative relaying scheme in which the decision to cooperate takes into account the effect of the possible erroneously detected and transmitted data at the best relay. We derive an exact closed-form expression for the end-to-end bit-error rate (BER) of binary phase-shift keying (BPSK) modulation based on the exact statistics of each hop. Unlike existing works where the analysis focused on high signal-to-noise ratio (SNR) regime, such results are important to enable the designers to take decisions regarding practical systems that operate at low SNR regime. We show that performance simulation results coincide with our analytical results.
Watermelon configurations with wall interaction: exact and asymptotic results
Energy Technology Data Exchange (ETDEWEB)
Krattenthaler, C [Institut Camille Jordan, Universite Claude Bernard Lyon-I, 21, avenue Claude Bernard, F-69622 Villeurbanne Cedex (France)
2006-06-15
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.
Watermelon configurations with wall interaction: exact and asymptotic results
International Nuclear Information System (INIS)
Krattenthaler, C
2006-01-01
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature
Watermelon configurations with wall interaction: exact and asymptotic results
Krattenthaler, C.
2006-06-01
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.
Cesarean section and the manipulation of exact delivery time.
Fabbri, Daniele; Monfardini, Chiara; Castaldini, Ilaria; Protonotari, Adalgisa
2016-07-01
Physicians are often alleged responsible for the manipulation of delivery timing. We investigate this issue in a setting that negates the influence of financial incentives on physician's behavior. Working on a sample of women admitted at the onset of labor in a big public hospital in Italy we estimate a model for the exact time of delivery as driven by individual Indication to Cesarean Section (ICS) and covariates. We find that ICS does not affect the day of delivery but leads to a circadian rhythm in the likelihood of delivery. The pattern is consistent with the postponement of high ICS deliveries in the late night\\early morning shift. Our evidence hardly supports the manipulation of timing of births as driven by medical staff's "demand for leisure". Physicians seem to manipulate the exact timing of delivery to reduce exposure to risk factors extant during off-peak periods. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Nasrin Saharkhiz
2014-11-01
Full Text Available Background: Embryo transfer (ET is one of the most important steps in assisted reproductive technology (ART cycles and affected by many factors namely the depth of embryo deposition in uterus. In this study, the outcomes of intracytoplasmic sperm injection (ICSI cycles after blind embryo transfer and embryo transfer based on previously measured uterine length using vaginal ultrasound were compared. Materials and Methods: This prospective randomised clinical trial included one hundred and forty non-donor fresh embryo transfers during January 2010 to June 2011. In group I, ET was performed using conventional (blind method at 5-6cm from the external os, and in group II, ET was done at a depth of 1-1.5 cm from the uterine fundus based on previously measured uterine length using vaginal sonography. Appropriate statistical analysis was performed using Student’s t test and Chi-square or Fisher’s exact test. The software that we used was PASW statistics version 18. A p value <0.05 was considered statistically significant. Results: Chemical pregnancy rate was 28.7% in group I and 42.1% in group II, while the difference was not statistically significant (p=0.105. Clinical pregnancy, ongoing pregnancy and implantation rates for group I were 21.2%, 17.7%, and 12.8%, while for group II were 33.9%, 33.9%, and 22.1, respectively. In group I and group II, abortion rates were 34.7% and 0%, respectively, indicating a statistically significant difference (p<0.005. No ectopic pregnancy occurred in two groups. Conclusion: The use of uterine length measurement during treatment cycle in order to place embryos at depth of 1-1.5cm from fundus significantly increases clinical and ongoing pregnancy and implantation rates, while leads to a decrease in abortion rate (Registration Number: IRCT2014032512494N1.
Exact and explicit solitary wave solutions to some nonlinear equations
International Nuclear Information System (INIS)
Jiefang Zhang
1996-01-01
Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative Φ 4 -model equation, the generalized Fisher equation, and the elastic-medium wave equation
Comparison of exact pupil astigmatism conditions with Seidel approximations.
Zhao, Chunyu; Burge, James H
2002-12-01
The aberrations of axisymmetric imaging systems can be calculated to third order by use of the Seidel formula. The Coddington equations give aberrations that have quadratic dependence on the pupil, for all field points. The pupil astigmatism conditions were recently developed to predict and control aberrations that have quadratic field dependence and arbitrary pupil dependence. We investigate the relationship between the exact pupil astigmatism conditions and the classical Seidel treatment of pupil aberration.
Exact Controllability of a Piezoelectric Body. Theory and Numerical Simulation
International Nuclear Information System (INIS)
Miara, Bernadette; Muench, Arnaud
2009-01-01
We study the exact controllability of a three-dimensional body made of a material whose constitutive law introduces an elasticity-electricity coupling. We show that a coupled elastic-electric control acting on the whole boundary of the body drives the system to rest after time large enough. Two-dimensional numerical experiments suggest that controllability can still be achieved by relaxing this restrictive condition using either both controls on a reduced support or elastic control alone
Exact solutions to a nonlinear dispersive model with variable coefficients
International Nuclear Information System (INIS)
Yin Jun; Lai Shaoyong; Qing Yin
2009-01-01
A mathematical technique based on an auxiliary differential equation and the symbolic computation system Maple is employed to investigate a prototypical and nonlinear K(n, n) equation with variable coefficients. The exact solutions to the equation are constructed analytically under various circumstances. It is shown that the variable coefficients and the exponent appearing in the equation determine the quantitative change in the physical structures of the solutions.
Unitary-matrix models as exactly solvable string theories
Periwal, Vipul; Shevitz, Danny
1990-01-01
Exact differential equations are presently found for the scaling functions of models of unitary matrices which are solved in a double-scaling limit, using orthogonal polynomials on a circle. For the case of the simplest, k = 1 model, the Painleve II equation with constant 0 is obtained; possible nonperturbative phase transitions exist for these models. Equations are presented for k = 2 and 3, and discussed with a view to asymptotic behavior.
Exactly solvable models for atom-molecule Hamiltonians.
Dukelsky, J; Dussel, G G; Esebbag, C; Pittel, S
2004-07-30
We present a family of exactly solvable generalizations of the Jaynes-Cummings model involving the interaction of an ensemble of SU(2) or SU(1,1) quasispins with a single boson field. They are obtained from the trigonometric Richardson-Gaudin models by replacing one of the SU(2) or SU(1,1) degrees of freedom by an ideal boson. The application to a system of bosonic atoms and molecules is reported.
Exact quantum state for {ital N}=1 supergravity
Energy Technology Data Exchange (ETDEWEB)
Csordas, A.; Graham, R. [Fachbereich Physik, Universitaet-Gesamthochschule Essen, 45117 Essen (Germany)
1995-12-15
For {ital N}=1 supergravity in 3+1 dimensions we determine the graded algebra of the quantized Lorentz generators, supersymmetry generators, and diffeomorphism and Hamiltonian generators and find that, at least formally, it closes in the chosen operator ordering. Following our recent conjecture and generalizing an ansatz for Bianchi-type models we proposed earlier we find an explicit exact quantum solution of all constraints in the metric representation. {copyright} 1995 The American Physical Society.
Exact equivalent straight waveguide model for bent and twisted waveguides
DEFF Research Database (Denmark)
Shyroki, Dzmitry
2008-01-01
Exact equivalent straight waveguide representation is given for a waveguide of arbitrary curvature and torsion. No assumptions regarding refractive index contrast, isotropy of materials, or particular morphology in the waveguide cross section are made. This enables rigorous full-vector modeling...... of in-plane curved or helically wound waveguides with use of available simulators for straight waveguides without the restrictions of the known approximate equivalent-index formulas....
Multijet final states: exact results and the leading pole approximation
International Nuclear Information System (INIS)
Ellis, R.K.; Owens, J.F.
1984-09-01
Exact results for the process gg → ggg are compared with those obtained using the leading pole approximation. Regions of phase space where the approximation breaks down are discussed. A specific example relevant for background estimates to W boson production is presented. It is concluded that in this instance the leading pole approximation may underestimate the standard QCD background by more than a factor of two in certain kinematic regions of physical interest
Exact Solutions of Relativistic Bound State Problem for Spinless Bosons
Aslanzadeh, M.; Rajabi, A. A.
2017-01-01
We investigated in detail the relativistic bound states of spin-zero bosons under the influence of Coulomb-plus-linear potentials with an arbitrary combination of scalar and vector couplings. Through an exact analytical solution of three-dimensional Klein-Gordon equation, closed form expressions were derived for energy eigenvalues and wave functions and some correlations between potential parameters were found. We also presented the relativistic description of bound states and nonrelativistic limit of the problem in some special cases.
New Exact Penalty Functions for Nonlinear Constrained Optimization Problems
Directory of Open Access Journals (Sweden)
Bingzhuang Liu
2014-01-01
Full Text Available For two kinds of nonlinear constrained optimization problems, we propose two simple penalty functions, respectively, by augmenting the dimension of the primal problem with a variable that controls the weight of the penalty terms. Both of the penalty functions enjoy improved smoothness. Under mild conditions, it can be proved that our penalty functions are both exact in the sense that local minimizers of the associated penalty problem are precisely the local minimizers of the original constrained problem.
Exact relativistic solution of disordered radiation with plane symmetry
International Nuclear Information System (INIS)
Fonseca Teixeira, A.F. da; Wolk, I.; Som, M.M.
1976-04-01
An exact solution of Einstein equations corresponding to an equilibrium distribution of disordered electromagnetic radiation with plane symmetry is obtained. This equilibrium is due solely to the gravitational and pressure effects inherent to the radiation. The distribution of radiation is found to be maximum and finite at the plane of symmetry, and to decrease monotonically in directions normal to this plane. The solution tends asymptotically to the static plane symmetric vacuum solution obtained by Levi-Civita. Timelike and null geodesics are discussed
Exact interior solutions in 2 + 1-dimensional spacetime
Energy Technology Data Exchange (ETDEWEB)
Rahaman, Farook; Bhar, Piyali [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Biswas, Ritabrata [Indian Institute of Engineering Sceince and Technology Shibpur, Howrah, West Bengal (India); Usmani, A.A. [Aligarh Muslim University, Department of Physics, Aligarh, Uttar Pradesh (India)
2014-04-15
We provide a new class of exact solutions for the interior in 2 + 1-dimensional spacetime. The solutions obtained for the perfect fluid model both with and without cosmological constant (Λ) are found to be regular and singularity free. It assumes very simple analytical forms that help us to study the various physical properties of the configuration. Solutions without Λ are found to be physically acceptable. (orig.)
Dynamical Response of Networks Under External Perturbations: Exact Results
Chinellato, David D.; Epstein, Irving R.; Braha, Dan; Bar-Yam, Yaneer; de Aguiar, Marcus A. M.
2015-04-01
We give exact statistical distributions for the dynamic response of influence networks subjected to external perturbations. We consider networks whose nodes have two internal states labeled 0 and 1. We let nodes be frozen in state 0, in state 1, and the remaining nodes change by adopting the state of a connected node with a fixed probability per time step. The frozen nodes can be interpreted as external perturbations to the subnetwork of free nodes. Analytically extending and to be smaller than 1 enables modeling the case of weak coupling. We solve the dynamical equations exactly for fully connected networks, obtaining the equilibrium distribution, transition probabilities between any two states and the characteristic time to equilibration. Our exact results are excellent approximations for other topologies, including random, regular lattice, scale-free and small world networks, when the numbers of fixed nodes are adjusted to take account of the effect of topology on coupling to the environment. This model can describe a variety of complex systems, from magnetic spins to social networks to population genetics, and was recently applied as a framework for early warning signals for real-world self-organized economic market crises.
Exact coefficients for higher dimensional operators with sixteen supersymmetries
Energy Technology Data Exchange (ETDEWEB)
Chen, Wei-Ming [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, R.O.C. (China); Huang, Yu-tin [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, R.O.C. (China); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Wen, Congkao [INFN Sezione di Roma “Tor Vergata' ,Via della Ricerca Scientifica, 00133 Roma (Italy)
2015-09-15
We consider constraints on higher-dimensional operators for supersymmetric effective field theories. In four dimensions with maximal supersymmetry and SU(4) R-symmetry, we demonstrate that the coefficients of abelian operators F{sup n} with MHV helicity configurations must satisfy a recursion relation, and are completely determined by that of F{sup 4}. As the F{sup 4} coefficient is known to be one-loop exact, this allows us to derive exact coefficients for all such operators. We also argue that the results are consistent with the SL(2,Z) duality symmetry. Breaking SU(4) to Sp(4), in anticipation for the Coulomb branch effective action, we again find an infinite class of operators whose coefficients are determined exactly. We also consider three-dimensional N=8 as well as six-dimensional N=(2,0),(1,0) and (1,1) theories. In all cases, we demonstrate that the coefficient of dimension-six operator must be proportional to the square of that of dimension-four.
A Generalized Geometric Measurement of Quantum Discord: Exact Treatment
Cui, Hai-Tao; Tian, Jun-Long; Yang, Gui
2016-02-01
A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local measurement. In addition it also does not suffer from the recently raised critiques about quantum discord. The exact result can be obtained for bipartite pure states with arbitrary levels, which is completely determined by the Schmidt decomposition. For bipartite mixed states the exact result can also be found for a special case. Furthermore the generalization into multipartite case is direct. It is shown that it can be evaluated exactly when the measured state is invariant under permutation or translation. In addition the detection of quantum phase transition is also discussed for Lipkin–Meshkov–Glick and Dicke model. Supported by National Natural Science Foundation of China under Grant No. 11005002 and 11475004, New Century Excellent Talent of M.O.E (NCET-11-0937), and Sponsoring Program of Excellent Younger Teachers in universities in Henan Province under Grant No. 2010GGJS-181
Exact EGB models for spherical static perfect fluids
Energy Technology Data Exchange (ETDEWEB)
Hansraj, Sudan; Chilambwe, Brian; Maharaj, Sunil D. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Private Bag 54001, Durban (South Africa)
2015-06-15
We obtain a new exact solution to the field equations for a 5-dimensional spherically symmetric static distribution in the Einstein-Gauss-Bonnet modified theory of gravity. By using a transformation, the study is reduced to the analysis of a single second order nonlinear differential equation. In general the condition of pressure isotropy produces a first order differential equation which is an Abel equation of the second kind. An exact solution is found. The solution is examined for physical admissibility. In particular a set of constants is found which ensures that a pressure-free hypersurface exists which defines the boundary of the distribution. Additionally the isotropic pressure and the energy density are shown to be positive within the radius of the sphere. The adiabatic sound-speed criterion is also satisfied within the fluid ensuring a subluminal sound speed. Furthermore, the weak, strong and dominant conditions hold throughout the distribution. On setting the Gauss-Bonnet coupling to zero, an exact solution for 5-dimensional perfect fluids in the standard Einstein theory is obtained. Plots of the dynamical quantities for the Gauss-Bonnet and the Einstein case reveal that the pressure is unaffected, while the energy density increases under the influence of the Gauss-Bonnet term. (orig.)
Exact coefficients for higher dimensional operators with sixteen supersymmetries
Chen, Wei-Ming; Huang, Yu-tin; Wen, Congkao
2015-09-01
We consider constraints on higher-dimensional operators for supersymmetric effective field theories. In four dimensions with maximal supersymmetry and SU(4) R-symmetry, we demonstrate that the coefficients of abelian operators F n with MHV helicity configurations must satisfy a recursion relation, and are completely determined by that of F 4. As the F 4 coefficient is known to be one-loop exact, this allows us to derive exact coefficients for all such operators. We also argue that the results are consistent with the SL(2,Z) duality symmetry. Breaking SU(4) to Sp(4), in anticipation for the Coulomb branch effective action, we again find an infinite class of operators whose coefficients are determined exactly. We also consider three-dimensional N = 8 as well as six-dimensional N = (2 ,0) ,(1 ,0) and (1 ,1) theories. In all cases, we demonstrate that the coefficient of dimension-six operator must be proportional to the square of that of dimension-four.
Exactly solvable models of proton and neutron interacting bosons
International Nuclear Information System (INIS)
Lerma, S.H.; Errea, B.; Dukelsky, J.; Pittel, S.; Van Isacker, P.
2006-01-01
We describe a class of exactly-solvable models of interacting bosons based on the algebra SO(3, 2). Each copy of the algebra represents a system of neutron and proton bosons in a given bosonic level interacting via a pairing interaction. The model that includes s and d bosons is a specific realization of the IBM2, restricted to the transition regime between vibrational and γ-soft nuclei. By including additional copies of the algebra, we can generate proton-neutron boson models involving other boson degrees of freedom, while still maintaining exact solvability. In each of these models, we can study not only the states of maximal symmetry, but also those of mixed symmetry, albeit still in the vibrational to γ-soft transition regime. Furthermore, in each of these models we can study some features of F-spin symmetry breaking. We report systematic calculations as a function of the pairing strength for models based on s,d, and g bosons and on s,d, and f bosons. The formalism of exactly-solvable models based on the SO(3, 2) algebra is not limited to systems of proton and neutron bosons, however, but can also be applied to other scenarios that involve two species of interacting bosons
Molecular geometric phase from the exact electron-nuclear factorization
Requist, Ryan; Tandetzky, Falk; Gross, E. K. U.
2016-04-01
The Born-Oppenheimer electronic wave function ΦRBO(r ) picks up a topological phase factor ±1 , a special case of Berry phase, when it is transported around a conical intersection of two adiabatic potential energy surfaces in R space. We show that this topological quantity reverts to a geometric quantity ei γ if the geometric phase γ =∮Im .d Rμ is evaluated with the conditional electronic wave function ΦR(r ) from the exact electron-nuclear factorization ΦR(r ) χ (R ) instead of the adiabatic function ΦRBO(r ) . A model of a pseudorotating triatomic molecule, also applicable to dynamical Jahn-Teller ions in bulk crystals, provides examples of nontrivial induced vector potentials and molecular geometric phase from the exact factorization. The induced vector potential gives a contribution to the circulating nuclear current that cannot be removed by a gauge transformation. The exact potential energy surface is calculated and found to contain a term depending on the Fubini-Study metric for the conditional electronic wave function.