A recursive Monte Carlo method for estimating importance functions in deep penetration problems

International Nuclear Information System (INIS)

Goldstein, M.

1980-04-01

A pratical recursive Monte Carlo method for estimating the importance function distribution, aimed at importance sampling for the solution of deep penetration problems in three-dimensional systems, was developed. The efficiency of the recursive method was investigated for sample problems including one- and two-dimensional, monoenergetic and and multigroup problems, as well as for a practical deep-penetration problem with streaming. The results of the recursive Monte Carlo calculations agree fairly well with Ssub(n) results. It is concluded that the recursive Monte Carlo method promises to become a universal method for estimating the importance function distribution for the solution of deep-penetration problems, in all kinds of systems: for many systems the recursive method is likely to be more efficient than previously existing methods; for three-dimensional systems it is the first method that can estimate the importance function with the accuracy required for an efficient solution based on importance sampling of neutron deep-penetration problems in those systems

Isotope decay equations solved by means of a recursive method

International Nuclear Information System (INIS)

Grant, Carlos

2009-01-01

The isotope decay equations have been solved using forward finite differences taking small time steps, among other methods. This is the case of the cell code WIMS, where it is assumed that concentrations of all fissionable isotopes remain constant during the integration interval among other simplifications. Even when the problem could be solved running through a logical tree, all algorithms used for resolution of these equations used an iterative programming formulation. That happened because nearly all computer languages used up to a recent past by the scientific programmers did not support recursion, such as the case of the old versions of FORTRAN or BASIC. Nowadays also an integral form of the depletion equations is used in Monte Carlo simulation. In this paper we propose another programming solution using a recursive algorithm, running through all descendants of each isotope and adding their contributions to all isotopes in each generation. The only assumption made for this solution is that fluxes remain constant during the whole time step. Recursive process is interrupted when a stable isotope was attained or the calculated contributions are smaller than a given precision. These algorithms can be solved by means an exact analytic method that can have some problems when circular loops appear for isotopes with alpha decay, and a more general polynomial method. Both methods are shown. (author)

Improved Undecidability Results for Reachability Games on Recursive Timed Automata

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Shankara Narayanan Krishna

2014-08-01

Full Text Available We study reachability games on recursive timed automata (RTA that generalize Alur-Dill timed automata with recursive procedure invocation mechanism similar to recursive state machines. It is known that deciding the winner in reachability games on RTA is undecidable for automata with two or more clocks, while the problem is decidable for automata with only one clock. Ouaknine and Worrell recently proposed a time-bounded theory of real-time verification by claiming that restriction to bounded-time recovers decidability for several key decision problem related to real-time verification. We revisited games on recursive timed automata with time-bounded restriction in the hope of recovering decidability. However, we found that the problem still remains undecidable for recursive timed automata with three or more clocks. Using similar proof techniques we characterize a decidability frontier for a generalization of RTA to recursive stopwatch automata.

The Method of Recursive Counting: Can one go further?

International Nuclear Information System (INIS)

Creutz, M.; Horvath, I.

1993-12-01

After a short review of the Method of Recursive Counting we introduce a general algebraic description of recursive lattice building. This provides a rigorous framework for discussion of method's limitations

Recursion Operators for Dispersionless KP Hierarchy

International Nuclear Information System (INIS)

Cheng Qiusheng; He Jingsong

2012-01-01

Based on the corresponding theorem between dispersionless KP (dKP) hierarchy and ħ-dependent KP (ħKP) hierarchy, a general formal representation of the recursion operators for dKP hierarchy under n-reduction is given in a systematical way from the corresponding ħKP hierarchy. To illustrate this method, the recursion operators for dKP hierarchy under 2-reduction and 3-reduction are calculated in detail.

Recursive representation of Wronskians in confluent supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Contreras-Astorga, Alonso; Schulze-Halberg, Axel

2017-01-01

A recursive form of arbitrary-order Wronskian associated with transformation functions in the confluent algorithm of supersymmetric quantum mechanics (SUSY) is constructed. With this recursive form regularity conditions for the generated potentials can be analyzed. Moreover, as byproducts we obtain new representations of solutions to Schrödinger equations that underwent a confluent SUSY-transformation. (paper)

Recursion theory computational aspects of definability

CERN Document Server

Chong, Chi Tat

2015-01-01

This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion theory. These include structure theory, hyperarithmetic determinacy and rigidity, basis theorems, independence results on Turing degrees, as well as applications to higher randomness.

Parallelizable approximate solvers for recursions arising in preconditioning

Energy Technology Data Exchange (ETDEWEB)

Shapira, Y. [Israel Inst. of Technology, Haifa (Israel)

1996-12-31

For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

Science.gov (United States)

Rodriguez, G.; Scheid, R. E., Jr.

1987-01-01

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Discovery of a Recursive Principle: An Artificial Grammar Investigation of Human Learning of a Counting Recursion Language.

Science.gov (United States)

Cho, Pyeong Whan; Szkudlarek, Emily; Tabor, Whitney

2016-01-01

Learning is typically understood as a process in which the behavior of an organism is progressively shaped until it closely approximates a target form. It is easy to comprehend how a motor skill or a vocabulary can be progressively learned-in each case, one can conceptualize a series of intermediate steps which lead to the formation of a proficient behavior. With grammar, it is more difficult to think in these terms. For example, center embedding recursive structures seem to involve a complex interplay between multiple symbolic rules which have to be in place simultaneously for the system to work at all, so it is not obvious how the mechanism could gradually come into being. Here, we offer empirical evidence from a new artificial language (or "artificial grammar") learning paradigm, Locus Prediction, that, despite the conceptual conundrum, recursion acquisition occurs gradually, at least for a simple formal language. In particular, we focus on a variant of the simplest recursive language, a (n) b (n) , and find evidence that (i) participants trained on two levels of structure (essentially ab and aabb) generalize to the next higher level (aaabbb) more readily than participants trained on one level of structure (ab) combined with a filler sentence; nevertheless, they do not generalize immediately; (ii) participants trained up to three levels (ab, aabb, aaabbb) generalize more readily to four levels than participants trained on two levels generalize to three; (iii) when we present the levels in succession, starting with the lower levels and including more and more of the higher levels, participants show evidence of transitioning between the levels gradually, exhibiting intermediate patterns of behavior on which they were not trained; (iv) the intermediate patterns of behavior are associated with perturbations of an attractor in the sense of dynamical systems theory. We argue that all of these behaviors indicate a theory of mental representation in which recursive

On Recursion

Directory of Open Access Journals (Sweden)

Jeffrey eWatumull

2014-01-01

Full Text Available It is a truism that conceptual understanding of a hypothesis is required for its empirical investigation. However the concept of recursion as articulated in the context of linguistic analysis has been perennially confused. Nowhere has this been more evident than in attempts to critique and extend Hauser, Chomsky, and Fitch’s (2002 articulation. These authors put forward the hypothesis that what is uniquely human and unique to the faculty of language—the faculty of language in the narrow sense (FLN—is a recursive system that generates and maps syntactic objects to conceptual-intentional and sensory-motor systems. This thesis was based on the standard mathematical definition of recursion as understood by Gödel and Turing, and yet has commonly been interpreted in other ways, most notably and incorrectly as a thesis about the capacity for syntactic embedding. As we explain, the recursiveness of a function is defined independent of such output, whether infinite or finite, embedded or unembedded—existent or nonexistent. And to the extent that embedding is a sufficient, though not necessary, diagnostic of recursion, it has not been established that the apparent restriction on embedding in some languages is of any theoretical import. Misunderstanding of these facts has generated research that is often irrelevant to the FLN thesis as well as to other theories of language competence that focus on its generative power of expression. This essay is an attempt to bring conceptual clarity to such discussions as well as to future empirical investigations by explaining three criterial properties of recursion: computability (i.e., rules in intension rather than lists in extension; definition by induction (i.e., rules strongly generative of structure; and mathematical induction (i.e., rules for the principled—and potentially unbounded—expansion of strongly generated structure. By these necessary and sufficient criteria, the grammars of all natural

Is recursion language-specific? Evidence of recursive mechanisms in the structure of intentional action.

Science.gov (United States)

Vicari, Giuseppe; Adenzato, Mauro

2014-05-01

In their 2002 seminal paper Hauser, Chomsky and Fitch hypothesize that recursion is the only human-specific and language-specific mechanism of the faculty of language. While debate focused primarily on the meaning of recursion in the hypothesis and on the human-specific and syntax-specific character of recursion, the present work focuses on the claim that recursion is language-specific. We argue that there are recursive structures in the domain of motor intentionality by way of extending John R. Searle's analysis of intentional action. We then discuss evidence from cognitive science and neuroscience supporting the claim that motor-intentional recursion is language-independent and suggest some explanatory hypotheses: (1) linguistic recursion is embodied in sensory-motor processing; (2) linguistic and motor-intentional recursions are distinct and mutually independent mechanisms. Finally, we propose some reflections about the epistemic status of HCF as presenting an empirically falsifiable hypothesis, and on the possibility of testing recursion in different cognitive domains. Copyright © 2014 Elsevier Inc. All rights reserved.

On Modified Bar recursion

DEFF Research Database (Denmark)

Oliva, Paulo Borges

2002-01-01

Modified bar recursion is a variant of Spector's bar recursion which can be used to give a realizability interpretation of the classical axiom of dependent choice. This realizability allows for the extraction of witnesses from proofs of forall-exists-formulas in classical analysis. In this talk I...... shall report on results regarding the relationship between modified and Spector's bar recursion. I shall also show that a seemingly weak form of modified bar recursion is as strong as "full" modified bar recursion in higher types....

On the Relation between Spector's Bar Recursion and Modified Bar Recursion

DEFF Research Database (Denmark)

Oliva, Paulo Borges

2002-01-01

We introduce a variant of Spector's Bar Recursion in finite types to give a realizability interpretation of the classical axiom of dependent choice allowing for the extraction of witnesses from proofs of Sigma_1 formulas in classical analysis. We also give a bar recursive definition of the fan...... functional and study the relationship of our variant of Bar Recursion with others....

Cobham recursive set functions

Czech Academy of Sciences Publication Activity Database

Beckmann, A.; Buss, S.; Friedman, S.-D.; Müller, M.; Thapen, Neil

2016-01-01

Roč. 167, č. 3 (2016), s. 335-369 ISSN 0168-0072 R&D Projects: GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : set function * polynomial time * Cobham recursion Subject RIV: BA - General Mathematics Impact factor: 0.647, year: 2016 http://www.sciencedirect.com/science/article/pii/S0168007215001293

Recursive automatic classification algorithms

Energy Technology Data Exchange (ETDEWEB)

Bauman, E V; Dorofeyuk, A A

1982-03-01

A variational statement of the automatic classification problem is given. The dependence of the form of the optimal partition surface on the form of the classification objective functional is investigated. A recursive algorithm is proposed for maximising a functional of reasonably general form. The convergence problem is analysed in connection with the proposed algorithm. 8 references.

Recursion relations for AdS/CFT correlators

International Nuclear Information System (INIS)

Raju, Suvrat

2011-01-01

We expand on the results of our recent letter [Phys. Rev. Lett. 106, 091601 (2011)], where we presented new recursion relations for correlation functions of the stress-tensor and conserved currents in conformal field theories with an AdS d+1 dual for d≥4. These recursion relations are derived by generalizing the Britto-Cachazo-Feng-Witten (BCFW) relations to amplitudes in anti-de Sitter space (AdS) that are dual to boundary correlators, and are usually computed perturbatively by Witten diagrams. Our results relate vacuum-correlation functions to integrated products of lower-point transition amplitudes, which correspond to correlators calculated between states dual to certain normalizable modes. We show that the set of ''polarization vectors'' for which amplitudes behave well under the BCFW extension is smaller than in flat-space. We describe how transition amplitudes for more general external polarizations can be constructed by combining answers obtained by different pairs of BCFW shifts. We then generalize these recursion relations to supersymmetric theories. In AdS, unlike flat-space, even maximal supersymmetry is insufficient to permit the computation of all correlators of operators in the same multiplet as a stress-tensor or conserved current. Finally, we work out some simple examples to verify our results.

Recursive utility in a Markov environment with stochastic growth.

Science.gov (United States)

Hansen, Lars Peter; Scheinkman, José A

2012-07-24

Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron-Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility.

Thinking recursively

CERN Document Server

Roberts, Eric S

1986-01-01

Concentrating on the practical value of recursion, this text, the first of its kind, is essential to computer science students' education. In this text, students will learn the concept and programming applications of recursive thinking. This will ultimately prepare students for advanced topics in computer science such as compiler construction, formal language theory, and the mathematical foundations of computer science.

Dissecting CFT Correlators and String Amplitudes. Conformal Blocks and On-Shell Recursion for General Tensor Fields

International Nuclear Information System (INIS)

Hansen, Tobias

2015-07-01

This thesis covers two main topics: the tensorial structure of quantum field theory correlators in general spacetime dimensions and a method for computing string theory scattering amplitudes directly in target space. In the first part tensor structures in generic bosonic CFT correlators and scattering amplitudes are studied. To this end arbitrary irreducible tensor representations of SO(d) (traceless mixed-symmetry tensors) are encoded in group invariant polynomials, by contracting with sets of commuting and anticommuting polarization vectors which implement the index symmetries of the tensors. The tensor structures appearing in CFT d correlators can then be inferred by studying these polynomials in a d + 2 dimensional embedding space. It is shown with an example how these correlators can be used to compute general conformal blocks describing the exchange of mixed-symmetry tensors in four-point functions, which are crucial for advancing the conformal bootstrap program to correlators of operators with spin. Bosonic string theory lends itself as an ideal example for applying the same methods to scattering amplitudes, due to its particle spectrum of arbitrary mixed-symmetry tensors. This allows in principle the definition of on-shell recursion relations for string theory amplitudes. A further chapter introduces a different target space definition of string scattering amplitudes. As in the case of on-shell recursion relations, the amplitudes are expressed in terms of their residues via BCFW shifts. The new idea here is that the residues are determined by use of the monodromy relations for open string theory, avoiding the infinite sums over the spectrum arising in on-shell recursion relations. Several checks of the method are presented, including a derivation of the Koba-Nielsen amplitude in the bosonic string. It is argued that this method provides a target space definition of the complete S-matrix of string theory at tree-level in a at background in terms of a small

Tracking of Multiple Moving Sources Using Recursive EM Algorithm

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Böhme Johann F

2005-01-01

Full Text Available We deal with recursive direction-of-arrival (DOA estimation of multiple moving sources. Based on the recursive EM algorithm, we develop two recursive procedures to estimate the time-varying DOA parameter for narrowband signals. The first procedure requires no prior knowledge about the source movement. The second procedure assumes that the motion of moving sources is described by a linear polynomial model. The proposed recursion updates the polynomial coefficients when a new data arrives. The suggested approaches have two major advantages: simple implementation and easy extension to wideband signals. Numerical experiments show that both procedures provide excellent results in a slowly changing environment. When the DOA parameter changes fast or two source directions cross with each other, the procedure designed for a linear polynomial model has a better performance than the general procedure. Compared to the beamforming technique based on the same parameterization, our approach is computationally favorable and has a wider range of applications.

On Recursion Operator of the q -KP Hierarchy

International Nuclear Information System (INIS)

Tian Ke-Lei; Zhu Xiao-Ming; He Jing-Song

2016-01-01

It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy. The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived. (paper)

A strange recursion operator demystified

International Nuclear Information System (INIS)

Sergyeyev, A

2005-01-01

We show that a new integrable two-component system of KdV type studied by Karasu (Kalkanli) et al (2004 Acta Appl. Math. 83 85-94) is bi-Hamiltonian, and its recursion operator, which has a highly unusual structure of nonlocal terms, can be written as a ratio of two compatible Hamiltonian operators found by us. Using this we prove that the system in question possesses an infinite hierarchy of local commuting generalized symmetries and conserved quantities in involution, and the evolution systems corresponding to these symmetries are bi-Hamiltonian as well. We also show that upon introduction of suitable nonlocal variables the nonlocal terms of the recursion operator under study can be written in the usual form, with the integration operator D -1 x appearing in each term at most once. (letter to the editor)

Language and Recursion

Science.gov (United States)

Lowenthal, Francis

2010-11-01

This paper examines whether the recursive structure imbedded in some exercises used in the Non Verbal Communication Device (NVCD) approach is actually the factor that enables this approach to favor language acquisition and reacquisition in the case of children with cerebral lesions. For that a definition of the principle of recursion as it is used by logicians is presented. The two opposing approaches to the problem of language development are explained. For many authors such as Chomsky [1] the faculty of language is innate. This is known as the Standard Theory; the other researchers in this field, e.g. Bates and Elman [2], claim that language is entirely constructed by the young child: they thus speak of Language Acquisition. It is also shown that in both cases, a version of the principle of recursion is relevant for human language. The NVCD approach is defined and the results obtained in the domain of language while using this approach are presented: young subjects using this approach acquire a richer language structure or re-acquire such a structure in the case of cerebral lesions. Finally it is shown that exercises used in this framework imply the manipulation of recursive structures leading to regular grammars. It is thus hypothesized that language development could be favored using recursive structures with the young child. It could also be the case that the NVCD like exercises used with children lead to the elaboration of a regular language, as defined by Chomsky [3], which could be sufficient for language development but would not require full recursion. This double claim could reconcile Chomsky's approach with psychological observations made by adherents of the Language Acquisition approach, if it is confirmed by researches combining the use of NVCDs, psychometric methods and the use of Neural Networks. This paper thus suggests that a research group oriented towards this problematic should be organized.

Recursive Trees for Practical ORAM

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Moataz Tarik

2015-06-01

Full Text Available We present a new, general data structure that reduces the communication cost of recent tree-based ORAMs. Contrary to ORAM trees with constant height and path lengths, our new construction r-ORAM allows for trees with varying shorter path length. Accessing an element in the ORAM tree results in different communication costs depending on the location of the element. The main idea behind r-ORAM is a recursive ORAM tree structure, where nodes in the tree are roots of other trees. While this approach results in a worst-case access cost (tree height at most as any recent tree-based ORAM, we show that the average cost saving is around 35% for recent binary tree ORAMs. Besides reducing communication cost, r-ORAM also reduces storage overhead on the server by 4% to 20% depending on the ORAM’s client memory type. To prove r-ORAM’s soundness, we conduct a detailed overflow analysis. r-ORAM’s recursive approach is general in that it can be applied to all recent tree ORAMs, both constant and poly-log client memory ORAMs. Finally, we implement and benchmark r-ORAM in a practical setting to back up our theoretical claims.

Kerr generalized solution

International Nuclear Information System (INIS)

Papoyan, V.V.

1989-01-01

A Kerr generalized solution for a stationary axially-symmetric gravitational field of rotating self-gravitational objects is given. For solving the problem Einstein equations and their combinations are used. The particular cases: internal and external Schwarzschild solutions are considered. The external solution of the stationary problem is a Kerr solution generalization. 3 refs

CP-Recursion in Danish

DEFF Research Database (Denmark)

Nyvad, Anne Mette; Christensen, Ken Ramshøj; Vikner, Sten

2017-01-01

Based on data from extraction, embedded V2, and complementizer stacking, this paper proposes a cP/CP-analysis of CP-recursion in Danish. Because extraction can be shown to be possible from relative clauses, wh-islands, and adverbial clauses, and given that long extraction is successive......-cyclic, an extra specifier position has to be available as an escape hatch. Consequently, such extractions require a CP-recursion analysis, as has been argued for embedded V2 and for complementizer stacking. Given that CP-recursion in embedded V2 clauses does not allow extraction, whereas other types of CP......-recursion do, we suggest that embedded V2 is fundamentally different, in that main clause V2 and embedded V2 involve a CP (“big CP”), whereas all other clausal projections above IP are instances of cP (“little cP”). The topmost “little” c° has an occurrence feature that enables extraction but bars spell...

Conjugate gradient algorithms using multiple recursions

Energy Technology Data Exchange (ETDEWEB)

Barth, T.; Manteuffel, T.

1996-12-31

Much is already known about when a conjugate gradient method can be implemented with short recursions for the direction vectors. The work done in 1984 by Faber and Manteuffel gave necessary and sufficient conditions on the iteration matrix A, in order for a conjugate gradient method to be implemented with a single recursion of a certain form. However, this form does not take into account all possible recursions. This became evident when Jagels and Reichel used an algorithm of Gragg for unitary matrices to demonstrate that the class of matrices for which a practical conjugate gradient algorithm exists can be extended to include unitary and shifted unitary matrices. The implementation uses short double recursions for the direction vectors. This motivates the study of multiple recursion algorithms.

Recursive Bayesian recurrent neural networks for time-series modeling.

Science.gov (United States)

Mirikitani, Derrick T; Nikolaev, Nikolay

2010-02-01

This paper develops a probabilistic approach to recursive second-order training of recurrent neural networks (RNNs) for improved time-series modeling. A general recursive Bayesian Levenberg-Marquardt algorithm is derived to sequentially update the weights and the covariance (Hessian) matrix. The main strengths of the approach are a principled handling of the regularization hyperparameters that leads to better generalization, and stable numerical performance. The framework involves the adaptation of a noise hyperparameter and local weight prior hyperparameters, which represent the noise in the data and the uncertainties in the model parameters. Experimental investigations using artificial and real-world data sets show that RNNs equipped with the proposed approach outperform standard real-time recurrent learning and extended Kalman training algorithms for recurrent networks, as well as other contemporary nonlinear neural models, on time-series modeling.

One-particle many-body Green's function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms.

Science.gov (United States)

Hirata, So; Doran, Alexander E; Knowles, Peter J; Ortiz, J V

2017-07-28

A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.

Recursions of Symmetry Orbits and Reduction without Reduction

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Andrei A. Malykh

2011-04-01

Full Text Available We consider a four-dimensional PDE possessing partner symmetries mainly on the example of complex Monge-Ampère equation (CMA. We use simultaneously two pairs of symmetries related by a recursion relation, which are mutually complex conjugate for CMA. For both pairs of partner symmetries, using Lie equations, we introduce explicitly group parameters as additional variables, replacing symmetry characteristics and their complex conjugates by derivatives of the unknown with respect to group parameters. We study the resulting system of six equations in the eight-dimensional space, that includes CMA, four equations of the recursion between partner symmetries and one integrability condition of this system. We use point symmetries of this extended system for performing its symmetry reduction with respect to group parameters that facilitates solving the extended system. This procedure does not imply a reduction in the number of physical variables and hence we end up with orbits of non-invariant solutions of CMA, generated by one partner symmetry, not used in the reduction. These solutions are determined by six linear equations with constant coefficients in the five-dimensional space which are obtained by a three-dimensional Legendre transformation of the reduced extended system. We present algebraic and exponential examples of such solutions that govern Legendre-transformed Ricci-flat Kähler metrics with no Killing vectors. A similar procedure is briefly outlined for Husain equation.

Syntactic Recursion Facilitates and Working Memory Predicts Recursive Theory of Mind

Science.gov (United States)

Arslan, Burcu; Hohenberger, Annette; Verbrugge, Rineke

2017-01-01

In this study, we focus on the possible roles of second-order syntactic recursion and working memory in terms of simple and complex span tasks in the development of second-order false belief reasoning. We tested 89 Turkish children in two age groups, one younger (4;6–6;5 years) and one older (6;7–8;10 years). Although second-order syntactic recursion is significantly correlated with the second-order false belief task, results of ordinal logistic regressions revealed that the main predictor of second-order false belief reasoning is complex working memory span. Unlike simple working memory and second-order syntactic recursion tasks, the complex working memory task required processing information serially with additional reasoning demands that require complex working memory strategies. Based on our results, we propose that children’s second-order theory of mind develops when they have efficient reasoning rules to process embedded beliefs serially, thus overcoming a possible serial processing bottleneck. PMID:28072823

Syntactic Recursion Facilitates and Working Memory Predicts Recursive Theory of Mind.

Directory of Open Access Journals (Sweden)

Burcu Arslan

Full Text Available In this study, we focus on the possible roles of second-order syntactic recursion and working memory in terms of simple and complex span tasks in the development of second-order false belief reasoning. We tested 89 Turkish children in two age groups, one younger (4;6-6;5 years and one older (6;7-8;10 years. Although second-order syntactic recursion is significantly correlated with the second-order false belief task, results of ordinal logistic regressions revealed that the main predictor of second-order false belief reasoning is complex working memory span. Unlike simple working memory and second-order syntactic recursion tasks, the complex working memory task required processing information serially with additional reasoning demands that require complex working memory strategies. Based on our results, we propose that children's second-order theory of mind develops when they have efficient reasoning rules to process embedded beliefs serially, thus overcoming a possible serial processing bottleneck.

Numerical solution of recirculating flow by a simple finite element recursion relation

Energy Technology Data Exchange (ETDEWEB)

Pepper, D W; Cooper, R E

1980-01-01

A time-split finite element recursion relation, based on linear basis functions, is used to solve the two-dimensional equations of motion. Recirculating flow in a rectangular cavity and free convective flow in an enclosed container are analyzed. The relation has the advantage of finite element accuracy and finite difference speed and simplicity. Incorporating dissipation parameters in the functionals decreases numerical dispersion and improves phase lag.

The ABCD of topological recursion

DEFF Research Database (Denmark)

Andersen, Jorgen Ellegaard; Borot, Gaëtan; Chekhov, Leonid O.

Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of math-ph/0702045, seeing it as a quantization of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial data a quantum Airy structure...... the 2d TQFT partition function as a special case), non-commutative Frobenius algebras, loop spaces of Frobenius algebras and a Z2-invariant version of the latter. This Z2-invariant version in the case of a semi-simple Frobenius algebra corresponds to the topological recursion of math-ph/0702045....

Continued development of recursive thinking in adolescence : Longitudinal analyses with a revised recursive thinking test

NARCIS (Netherlands)

van den Bos, E.; de Rooij, M.; Sumter, S.R.; Westenberg, P.M.

2016-01-01

The present study adds to the emerging literature on the development of social cognition in adolescence by investigating the development of recursive thinking (i.e., thinking about thinking). Previous studies have indicated that the development of recursive thinking is not completed during

On an analytical representation of the solution of the one-dimensional transport equation for a multi-group model in planar geometry

Energy Technology Data Exchange (ETDEWEB)

Fernandes, Julio C.L.; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: julio.lombaldo@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada; Dulla, Sandra; Ravetto, Piero, E-mail: sandra.dulla@polito.it, E-mail: piero.ravetto@polito.it [Dipartimento di Energia, Politecnico di Torino, Piemonte (Italy)

2015-07-01

In this work we generalize the solution of the one-dimensional neutron transport equation to a multi- group approach in planar geometry. The basic idea of this work consists in consider the hierarchical construction of a solution for a generic number G of energy groups, starting from a mono-energetic solution. The hierarchical method follows the reasoning of the decomposition method. More specifically, the additional terms from adding energy groups is incorporated into the recursive scheme as source terms. This procedure leads to an analytical representation for the solution with G energy groups. The recursion depth is related to the accuracy of the solution, that may be evaluated after each recursion step. The authors present a heuristic analysis of stability for the results. Numerical simulations for a specific example with four energy groups and a localized pulsed source. (author)

A Recursive Formula for the Evaluation of Earth Return Impedance on Buried Cables

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Reynaldo Iracheta

2015-09-01

Full Text Available This paper presents an alternative solution based on infinite series for the accurate and efficient evaluation of cable earth return impedances. This method uses Wedepohl and Wilcox’s transformation to decompose Pollaczek’s integral in a set of Bessel functions and a definite integral. The main feature of Bessel functions is that they are easy to compute in modern mathematical software tools such as Matlab. The main contributions of this paper are the approximation of the definite integral by an infinite series, since it does not have analytical solution; and its numerical solution by means of a recursive formula. The accuracy and efficiency of this recursive formula is compared against the numerical integration method for a broad range of frequencies and cable  configurations. Finally, the proposed method is used as a subroutine for cable parameter calculation in the inverse Numerical Laplace Transform (NLT to obtain accurate transient responses in the time domain.

Recursive definition of global cellular-automata mappings

DEFF Research Database (Denmark)

Feldberg, Rasmus; Knudsen, Carsten; Rasmussen, Steen

1994-01-01

A method for a recursive definition of global cellular-automata mappings is presented. The method is based on a graphical representation of global cellular-automata mappings. For a given cellular-automaton rule the recursive algorithm defines the change of the global cellular-automaton mapping...... as the number of lattice sites is incremented. A proof of lattice size invariance of global cellular-automata mappings is derived from an approximation to the exact recursive definition. The recursive definitions are applied to calculate the fractal dimension of the set of reachable states and of the set...

How Learning Logic Programming Affects Recursion Comprehension

Science.gov (United States)

Haberman, Bruria

2004-01-01

Recursion is a central concept in computer science, yet it is difficult for beginners to comprehend. Israeli high-school students learn recursion in the framework of a special modular program in computer science (Gal-Ezer & Harel, 1999). Some of them are introduced to the concept of recursion in two different paradigms: the procedural…

General predictive control using the delta operator

DEFF Research Database (Denmark)

Jensen, Morten Rostgaard; Poulsen, Niels Kjølstad; Ravn, Ole

1993-01-01

This paper deals with two-discrete-time operators, the conventional forward shift-operator and the δ-operator. Both operators are treated in view of construction of suitable solutions to the Diophantine equation for the purpose of prediction. A general step-recursive scheme is presented. Finally...... a general predictive control (GPC) is formulated and applied adaptively to a continuous-time plant...

Recursive solutions for multi-group neutron kinetics diffusion equations in homogeneous three-dimensional rectangular domains with time dependent perturbations

Energy Technology Data Exchange (ETDEWEB)

Petersen, Claudio Z. [Universidade Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Bodmann, Bardo E.J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-graduacao em Engenharia Mecanica; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ (Brazil). Inst. Politecnico

2014-12-15

In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i.e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.

Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion

Science.gov (United States)

Alexandrov, A.; Chapuy, G.; Eynard, B.; Harnad, J.

2017-12-01

A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2D Toda {τ} -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel-Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers.

Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion

Science.gov (United States)

Alexandrov, A.; Chapuy, G.; Eynard, B.; Harnad, J.

2018-06-01

A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2 D Toda {τ} -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel-Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers.

Recursive definition of global cellular-automata mappings

International Nuclear Information System (INIS)

Feldberg, R.; Knudsen, C.; Rasmussen, S.

1994-01-01

A method for a recursive definition of global cellular-automata mappings is presented. The method is based on a graphical representation of global cellular-automata mappings. For a given cellular-automaton rule the recursive algorithm defines the change of the global cellular-automaton mapping as the number of lattice sites is incremented. A proof of lattice size invariance of global cellular-automata mappings is derived from an approximation to the exact recursive definition. The recursive definitions are applied to calculate the fractal dimension of the set of reachable states and of the set of fixed points of cellular automata on an infinite lattice

One loop integration with hypergeometric series by using recursion relations

International Nuclear Information System (INIS)

Watanabe, Norihisa; Kaneko, Toshiaki

2014-01-01

General one-loop integrals with arbitrary mass and kinematical parameters in d-dimensional space-time are studied. By using Bernstein theorem, a recursion relation is obtained which connects (n + 1)-point to n-point functions. In solving this recursion relation, we have shown that one-loop integrals are expressed by a newly defined hypergeometric function, which is a special case of Aomoto-Gelfand hypergeometric functions. We have also obtained coefficients of power series expansion around 4-dimensional space-time for two-, three- and four-point functions. The numerical results are compared with ''LoopTools'' for the case of two- and three-point functions as examples

Recursive sequences in first-year calculus

Science.gov (United States)

Krainer, Thomas

2016-02-01

This article provides ready-to-use supplementary material on recursive sequences for a second-semester calculus class. It equips first-year calculus students with a basic methodical procedure based on which they can conduct a rigorous convergence or divergence analysis of many simple recursive sequences on their own without the need to invoke inductive arguments as is typically required in calculus textbooks. The sequences that are accessible to this kind of analysis are predominantly (eventually) monotonic, but also certain recursive sequences that alternate around their limit point as they converge can be considered.

Cosymmetries and Nijenhuis recursion operators for difference equations

International Nuclear Information System (INIS)

Mikhailov, Alexander V; Xenitidis, Pavlos; Wang, Jing Ping

2011-01-01

In this paper we discuss the concept of cosymmetries and co-recursion operators for difference equations and present a co-recursion operator for the Viallet equation. We also discover a new type of factorization for the recursion operators of difference equations. This factorization enables us to give an elegant proof that the pseudo-difference operator R presented in Mikhailov et al 2011 Theor. Math. Phys. 167 421–43 is a recursion operator for the Viallet equation. Moreover, we show that the operator R is Nijenhuis and thus generates infinitely many commuting local symmetries. The recursion operator R and its factorization into Hamiltonian and symplectic operators have natural applications to Yamilov's discretization of the Krichever–Novikov equation

A step-indexed Kripke model of hidden state via recursive properties on recursively defined metric spaces

DEFF Research Database (Denmark)

Birkedal, Lars; Schwinghammer, Jan; Støvring, Kristian

2010-01-01

for Chargu´eraud and Pottier’s type and capability system including frame and anti-frame rules, based on the operational semantics and step-indexed heap relations. The worlds are constructed as a recursively defined predicate on a recursively defined metric space, which provides a considerably simpler...

A Survey on Teaching and Learning Recursive Programming

Science.gov (United States)

Rinderknecht, Christian

2014-01-01

We survey the literature about the teaching and learning of recursive programming. After a short history of the advent of recursion in programming languages and its adoption by programmers, we present curricular approaches to recursion, including a review of textbooks and some programming methodology, as well as the functional and imperative…

A Step-Indexed Kripke Model of Hidden State via Recursive Properties on Recursively Defined Metric Spaces

DEFF Research Database (Denmark)

Schwinghammer, Jan; Birkedal, Lars; Støvring, Kristian

2011-01-01

´eraud and Pottier’s type and capability system including both frame and anti-frame rules. The model is a possible worlds model based on the operational semantics and step-indexed heap relations, and the worlds are constructed as a recursively defined predicate on a recursively defined metric space. We also extend...

Relationship between Maximum Principle and Dynamic Programming for Stochastic Recursive Optimal Control Problems and Applications

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Jingtao Shi

2013-01-01

Full Text Available This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.

Recursion method in the k-space representation

International Nuclear Information System (INIS)

Anlage, S.M.; Smith, D.L.

1986-01-01

We show that by using a unitary transformation to k space and the special-k-point method for evaluating Brillouin-zone sums, the recursion method can be very effectively applied to translationally invariant systems. We use this approach to perform recursion calculations for realistic tight-binding Hamiltonians which describe diamond- and zinc-blende-structure semiconductors. Projected densities of states for these Hamiltonians have band gaps and internal van Hove singularities. We calculate coefficients for 63 recursion levels exactly and for about 200 recursion levels to a good approximation. Comparisons are made for materials with different magnitude band gaps (diamond, Si, α-Sn). Comparison is also made between materials with one (e.g., diamond) and two (e.g., GaAs) band gaps. The asymptotic behavior of the recursion coefficients is studied by Fourier analysis. Band gaps in the projected density of states dominate the asymptotic behavior. Perturbation analysis describes the asymptotic behavior rather well. Projected densities of states are calculated using a very simple termination scheme. These densities of states compare favorably with the results of Gilat-Raubenheimer integration

Hopf algebras and topological recursion

International Nuclear Information System (INIS)

Esteves, João N

2015-01-01

We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293–309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347–452). (paper)

On Recursive Modification in Child L1 French

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Yves Roberge

2018-03-01

Full Text Available This paper investigates nominal recursive modification (RM in the L1 acquisition of French. Although recursion is considered the fundamental property of human languages, recursive self-embedding is found to be difficult for children in a variety of languages and constructions. Despite these challenges, the acquisition of RM proves to be resilient; acquirable even under severely degraded input conditions. From a minimalist perspective on the operations of narrow syntax, recursive embedding is essentially the application of a sequence of Merge operations (Chomsky 1995; Trotzke and Zwart 2014; therefore, given the universality of Merge, we do not expect to find cross-linguistic differences in how difficult recursion is. But if the challenging nature of recursion stems from factors which might differ from language to language, we expect different outcomes cross-linguistically. We compare new data from French to existing English data (Pérez-Leroux et al. 2012 in order to examine to what extent language-specific properties of RM structures determine the acquisition path. While children’s production differs significantly from their adult’s counterparts, we find no differences between French-speaking and English-speaking children. Our findings suggest that the challenging nature of recursion does not stem from the grammar itself and that what shapes the acquisition path is the interaction between universal properties of language and considerations not specific to language, namely computational efficiency.

Recursive approach for non-Markovian time-convolutionless master equations

Science.gov (United States)

Gasbarri, G.; Ferialdi, L.

2018-02-01

We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which provides a useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We eventually apply our formalism to the evolution of the observables of the reduced system, by showing how the method can be applied to the adjoint master equation, and by developing a diagrammatic description of the associated series.

Recursive relations for a quiver gauge theory

International Nuclear Information System (INIS)

Park, Jaemo; Sim, Woojoo

2006-01-01

We study the recursive relations for a quiver gauge theory with the gauge group SU(N 1 ) x SU(N 2 ) with bifundamental fermions transforming as (N 1 , N-bar 2 ). We work out the recursive relation for the amplitudes involving a pair of quark and antiquark and gluons of each gauge group. We realize directly in the recursive relations the invariance under the order preserving permutations of the gluons of the first and the second gauge group. We check the proposed relations for MHV, 6-point and 7-point amplitudes and find the agreements with the known results and the known relations with the single gauge group amplitudes. The proposed recursive relation is much more efficient in calculating the amplitudes than using the known relations with the amplitudes of the single gauge group

Deformation of the three-term recursion relation and generation of new orthogonal polynomials

International Nuclear Information System (INIS)

Alhaidari, A D

2002-01-01

We find solutions for a linear deformation of the three-term recursion relation. The orthogonal polynomials of the first and second kind associated with the deformed relation are obtained. The new density (weight) function is written in terms of the original one and the deformation parameters

CFT and topological recursion

CERN Document Server

Kostov, Ivan

2010-01-01

We study the quasiclassical expansion associated with a complex curve. In a more specific context this is the 1/N expansion in U(N)-invariant matrix integrals. We compare two approaches, the CFT approach and the topological recursion, and show their equivalence. The CFT approach reformulates the problem in terms of a conformal field theory on a Riemann surface, while the topological recursion is based on a recurrence equation for the observables representing symplectic invariants on the complex curve. The two approaches lead to two different graph expansions, one of which can be obtained as a partial resummation of the other.

Some recursive formulas for Selberg-type integrals

Energy Technology Data Exchange (ETDEWEB)

Iguri, Sergio [Instituto de AstronomIa y Fisica del Espacio (CONICET-UBA). C. C. 67, Suc. 28, 1428 Buenos Aires (Argentina); Mansour, Toufik, E-mail: siguri@iafe.uba.a, E-mail: toufik@math.haifa.ac.i [Department of Mathematics, University of Haifa, Haifa 31905 (Israel)

2010-02-12

A set of recursive relations satisfied by Selberg-type integrals involving monomial symmetric polynomials are derived, generalizing previous results in Aomoto (1987) SIAM J. Math. Anal. 18 545-49 and Iguri (2009) Lett. Math. Phys. 89 141-58. These formulas provide a well-defined algorithm for computing Selberg-Schur integrals whenever the Kostka numbers relating Schur functions and the corresponding monomial polynomials are explicitly known. We illustrate the usefulness of our results discussing some interesting examples.

Primitive recursive realizability and basic propositional logic

NARCIS (Netherlands)

Plisko, Valery

2007-01-01

Two notions of primitive recursive realizability for arithmetic sentences are considered. The first one is strictly primitive recursive realizability introduced by Z. Damnjanovic in 1994. We prove that intuitionistic predicate logic is not sound with this kind of realizability. Namely there

ETHICS AND KNOWLEDGE OF RECURSIVITY IN PSYCHOLOGISTS TRAINING

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Ramón Sanz Ferramola

2008-07-01

Full Text Available This work deals with the characterization of psychology as a science and profession. Thisfeature is part of the Argentine academic tradition which goes from the origins of psychology as an undergraduate program by the end of the 1950s to the present day. In relation to this topic, four issues are analysed: a the knowledges of psychology showing the necessity of two epistemic dimensions closely related, namely the discursivity and recursivity, or knowledge and metaknowledge, b the role of psychology as a profession within the praxis, rather than in the poiesis, according to the Greek distinction between the implications of these two modalities of the “doing”, c the concurrence and difference of ethics and deontology, their roles, bounds and potentialities within the psychological field in general, and that of scientific-professional morality in particular, and d the definition and characterization of ethics and epistemology as knowledge of recursivity in psychologists’ training.

Recursion to food plants by free-ranging Bornean elephant.

Science.gov (United States)

English, Megan; Gillespie, Graeme; Goossens, Benoit; Ismail, Sulaiman; Ancrenaz, Marc; Linklater, Wayne

2015-01-01

Plant recovery rates after herbivory are thought to be a key factor driving recursion by herbivores to sites and plants to optimise resource-use but have not been investigated as an explanation for recursion in large herbivores. We investigated the relationship between plant recovery and recursion by elephants (Elephas maximus borneensis) in the Lower Kinabatangan Wildlife Sanctuary, Sabah. We identified 182 recently eaten food plants, from 30 species, along 14 × 50 m transects and measured their recovery growth each month over nine months or until they were re-browsed by elephants. The monthly growth in leaf and branch or shoot length for each plant was used to calculate the time required (months) for each species to recover to its pre-eaten length. Elephant returned to all but two transects with 10 eaten plants, a further 26 plants died leaving 146 plants that could be re-eaten. Recursion occurred to 58% of all plants and 12 of the 30 species. Seventy-seven percent of the re-eaten plants were grasses. Recovery times to all plants varied from two to twenty months depending on the species. Recursion to all grasses coincided with plant recovery whereas recursion to most browsed plants occurred four to twelve months before they had recovered to their previous length. The small sample size of many browsed plants that received recursion and uneven plant species distribution across transects limits our ability to generalise for most browsed species but a prominent pattern in plant-scale recursion did emerge. Plant recovery time was a good predictor of time to recursion but varied as a function of growth form (grass, ginger, palm, liana and woody) and differences between sites. Time to plant recursion coincided with plant recovery time for the elephant's preferred food, grasses, and perhaps also gingers, but not the other browsed species. Elephants are bulk feeders so it is likely that they time their returns to bulk feed on these grass species when quantities have

Adaptable recursive binary entropy coding technique

Science.gov (United States)

Kiely, Aaron B.; Klimesh, Matthew A.

2002-07-01

We present a novel data compression technique, called recursive interleaved entropy coding, that is based on recursive interleaving of variable-to variable length binary source codes. A compression module implementing this technique has the same functionality as arithmetic coding and can be used as the engine in various data compression algorithms. The encoder compresses a bit sequence by recursively encoding groups of bits that have similar estimated statistics, ordering the output in a way that is suited to the decoder. As a result, the decoder has low complexity. The encoding process for our technique is adaptable in that each bit to be encoded has an associated probability-of-zero estimate that may depend on previously encoded bits; this adaptability allows more effective compression. Recursive interleaved entropy coding may have advantages over arithmetic coding, including most notably the admission of a simple and fast decoder. Much variation is possible in the choice of component codes and in the interleaving structure, yielding coder designs of varying complexity and compression efficiency; coder designs that achieve arbitrarily small redundancy can be produced. We discuss coder design and performance estimation methods. We present practical encoding and decoding algorithms, as well as measured performance results.

Anti-Authoritarian Metrics: Recursivity as a strategy for post-capitalism

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David Adam Banks

2016-12-01

Full Text Available This essay proposes that those seeking to build counter-power institutions and communities learn to think in terms of what I call “recursivity.” Recursivity is an anti-authoritarian metric that helps bring about a sensitivity to feedback loops at multiple levels of organization. I begin by describing how technological systems and the socio-economic order co-constitute one-another around efficiency metrics. I then go on to define recursivity as social conditions that contain within them all of the parts and practices for their maturation and expansion, and show how organizations that demonstrate recursivity, like the historical English commons, have been marginalized or destroyed all together. Finally, I show how the ownership of property is inherently antithetical to the closed loops of recursivity. All of this is bookended by a study of urban planning’s recursive beginnings.

Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems

DEFF Research Database (Denmark)

Frison, Gianluca; Jørgensen, John Bagterp

2013-01-01

In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration....... In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky...... factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver....

A new algorithm for recursive estimation of ARMA parameters in reactor noise analysis

International Nuclear Information System (INIS)

Tran Dinh Tri

1992-01-01

In this paper a new recursive algorithm for estimating the parameters of the Autoregressive Moving Average (ARMA) model from measured data is presented. The Yule-Walker equations for the case of the ARMA model are derived from the ARMA equation with innovations. The recursive algorithm is based on choosing an appropriate form of the operator functions and suitable representation of the (n + 1)-th order operator functions according to those with lower order. Two cases, when the order of the AR part is equal to that of the MA part, and the general case, were considered. (Author)

Recursive Definitions of Monadic Functions

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Alexander Krauss

2010-12-01

Full Text Available Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's imperative programming extension, which results in a convenient definition principle for imperative programs, which were previously hard to define. For such monadic functions, the recursion equation can always be derived without preconditions, even if the function is partial. The construction is easy to automate, and convenient induction principles can be derived automatically.

Real-time recursive hyperspectral sample and band processing algorithm architecture and implementation

CERN Document Server

Chang, Chein-I

2017-01-01

This book explores recursive architectures in designing progressive hyperspectral imaging algorithms. In particular, it makes progressive imaging algorithms recursive by introducing the concept of Kalman filtering in algorithm design so that hyperspectral imagery can be processed not only progressively sample by sample or band by band but also recursively via recursive equations. This book can be considered a companion book of author’s books, Real-Time Progressive Hyperspectral Image Processing, published by Springer in 2016. Explores recursive structures in algorithm architecture Implements algorithmic recursive architecture in conjunction with progressive sample and band processing Derives Recursive Hyperspectral Sample Processing (RHSP) techniques according to Band-Interleaved Sample/Pixel (BIS/BIP) acquisition format Develops Recursive Hyperspectral Band Processing (RHBP) techniques according to Band SeQuential (BSQ) acquisition format for hyperspectral data.

Recursive tridiagonalization of infinite dimensional Hamiltonians

International Nuclear Information System (INIS)

Haydock, R.; Oregon Univ., Eugene, OR

1989-01-01

Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)

Recursion to food plants by free-ranging Bornean elephant

Directory of Open Access Journals (Sweden)

Megan English

2015-08-01

Full Text Available Plant recovery rates after herbivory are thought to be a key factor driving recursion by herbivores to sites and plants to optimise resource-use but have not been investigated as an explanation for recursion in large herbivores. We investigated the relationship between plant recovery and recursion by elephants (Elephas maximus borneensis in the Lower Kinabatangan Wildlife Sanctuary, Sabah. We identified 182 recently eaten food plants, from 30 species, along 14 × 50 m transects and measured their recovery growth each month over nine months or until they were re-browsed by elephants. The monthly growth in leaf and branch or shoot length for each plant was used to calculate the time required (months for each species to recover to its pre-eaten length. Elephant returned to all but two transects with 10 eaten plants, a further 26 plants died leaving 146 plants that could be re-eaten. Recursion occurred to 58% of all plants and 12 of the 30 species. Seventy-seven percent of the re-eaten plants were grasses. Recovery times to all plants varied from two to twenty months depending on the species. Recursion to all grasses coincided with plant recovery whereas recursion to most browsed plants occurred four to twelve months before they had recovered to their previous length. The small sample size of many browsed plants that received recursion and uneven plant species distribution across transects limits our ability to generalise for most browsed species but a prominent pattern in plant-scale recursion did emerge. Plant recovery time was a good predictor of time to recursion but varied as a function of growth form (grass, ginger, palm, liana and woody and differences between sites. Time to plant recursion coincided with plant recovery time for the elephant’s preferred food, grasses, and perhaps also gingers, but not the other browsed species. Elephants are bulk feeders so it is likely that they time their returns to bulk feed on these grass species when

Recursive regularization step for high-order lattice Boltzmann methods

Science.gov (United States)

Coreixas, Christophe; Wissocq, Gauthier; Puigt, Guillaume; Boussuge, Jean-François; Sagaut, Pierre

2017-09-01

A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from 104 to 106, and where a thorough analysis of the case at Re=3 ×104 is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.

A new recursion operator for Adler's equation in the Viallet form

International Nuclear Information System (INIS)

Mikhailov, A.V.; Wang, J.P.

2011-01-01

For Adler's equation in the Viallet form and Yamilov's discretisation of the Krichever-Novikov equation we present new recursion and Hamiltonian operators. This new recursion operator and the recursion operator found in [A.V. Mikhailov, et al., Theor. Math. Phys. 167 (2011) 421, (arXiv:1004.5346)] satisfy the spectral curve associated with the equation. -- Highlights: → We present new recursion and Hamiltonian operators for the equation. → We establish the relation between this recursion operator and the known one. → The relation is given by the spectral curve associated with the equation.

Recursive Monte Carlo method for deep-penetration problems

International Nuclear Information System (INIS)

Goldstein, M.; Greenspan, E.

1980-01-01

The Recursive Monte Carlo (RMC) method developed for estimating importance function distributions in deep-penetration problems is described. Unique features of the method, including the ability to infer the importance function distribution pertaining to many detectors from, essentially, a single M.C. run and the ability to use the history tape created for a representative region to calculate the importance function in identical regions, are illustrated. The RMC method is applied to the solution of two realistic deep-penetration problems - a concrete shield problem and a Tokamak major penetration problem. It is found that the RMC method can provide the importance function distributions, required for importance sampling, with accuracy that is suitable for an efficient solution of the deep-penetration problems considered. The use of the RMC method improved, by one to three orders of magnitude, the solution efficiency of the two deep-penetration problems considered: a concrete shield problem and a Tokamak major penetration problem. 8 figures, 4 tables

Chain of matrices, loop equations and topological recursion

CERN Document Server

Orantin, Nicolas

2009-01-01

Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. These two definitions, perturbative and non-perturbative, are discussed in this chapter as well as their relation. The so-called loop equations satisfied by integrals over random matrices coupled in chain is discussed as well as their recursive solution in the perturbative case when the matrices are Hermitean.

Optimally eating a stochastic cake. A recursive utility approach

International Nuclear Information System (INIS)

Epaulard, Anne; Pommeret, Aude

2003-01-01

In this short paper, uncertainties on resource stock and on technical progress are introduced into an intertemporal equilibrium model of optimal extraction of a non-renewable resource. The representative consumer maximizes a recursive utility function which disentangles between intertemporal elasticity of substitution and risk aversion. A closed-form solution is derived for both the optimal extraction and price paths. The value of the intertemporal elasticity of substitution relative to unity is then crucial in understanding extraction. Moreover, this model leads to a non-renewable resource price following a geometric Brownian motion

Updating Recursive XML Views of Relations

DEFF Research Database (Denmark)

Choi, Byron; Cong, Gao; Fan, Wenfei

2009-01-01

This paper investigates the view update problem for XML views published from relational data. We consider XML views defined in terms of mappings directed by possibly recursive DTDs compressed into DAGs and stored in relations. We provide new techniques to efficiently support XML view updates...... specified in terms of XPath expressions with recursion and complex filters. The interaction between XPath recursion and DAG compression of XML views makes the analysis of the XML view update problem rather intriguing. Furthermore, many issues are still open even for relational view updates, and need...... to be explored. In response to these, on the XML side, we revise the notion of side effects and update semantics based on the semantics of XML views, and present effecient algorithms to translate XML updates to relational view updates. On the relational side, we propose a mild condition on SPJ views, and show...

Recursion complexity in cognition

CERN Document Server

Roeper, Thomas

2014-01-01

This volume focuses on recursion, highlighting its central role in modern science. It reveals a host of new theoretical arguments, philosophical perspectives, formal representations and empirical evidence from parsing, acquisition and computer models.

Video game for learning and metaphorization of recursive algorithms

Directory of Open Access Journals (Sweden)

Ricardo Inacio Alvares Silva

2013-09-01

Full Text Available The learning of recursive algorithms in computer programming is problematic, because its execution and resolution is not natural to the thinking way people are trained and used to since young. As with other topics in algorithms, we use metaphors to make parallels between the abstract and the concrete to help in understanding the operation of recursive algorithms. However, the classic metaphors employed in this area, such as calculating factorial recursively and Towers of Hanoi game, may just confuse more or be insufficient. In this work, we produced a computer game to assist students in computer courses in learning recursive algorithms. It was designed to have regular video game characteristics, with narrative and classical gameplay elements, commonly found in this kind of product. Aiding to education occurs through metaphorization, or in other words, through experiences provided by game situations that refer to recursive algorithms. To this end, we designed and imbued in the game four valid metaphors related to the theory, and other minor references to the subject.

Syntactic Recursion Facilitates and Working Memory Predicts Recursive Theory of Mind

NARCIS (Netherlands)

Arslan, Burcu; Hohenberger, Annette; Verbrugge, Rineke

2017-01-01

In this study, we focus on the possible roles of second-order syntactic recursion and working memory in terms of simple and complex span tasks in the development of second-order false belief reasoning. We tested 89 Turkish children in two age groups, one younger (4;6-6;5 years) and one older

Inner and Outer Recursive Neural Networks for Chemoinformatics Applications.

Science.gov (United States)

Urban, Gregor; Subrahmanya, Niranjan; Baldi, Pierre

2018-02-26

Deep learning methods applied to problems in chemoinformatics often require the use of recursive neural networks to handle data with graphical structure and variable size. We present a useful classification of recursive neural network approaches into two classes, the inner and outer approach. The inner approach uses recursion inside the underlying graph, to essentially "crawl" the edges of the graph, while the outer approach uses recursion outside the underlying graph, to aggregate information over progressively longer distances in an orthogonal direction. We illustrate the inner and outer approaches on several examples. More importantly, we provide open-source implementations [available at www.github.com/Chemoinformatics/InnerOuterRNN and cdb.ics.uci.edu ] for both approaches in Tensorflow which can be used in combination with training data to produce efficient models for predicting the physical, chemical, and biological properties of small molecules.

Recursive smoothers for hidden discrete-time Markov chains

Directory of Open Access Journals (Sweden)

Lakhdar Aggoun

2005-01-01

Full Text Available We consider a discrete-time Markov chain observed through another Markov chain. The proposed model extends models discussed by Elliott et al. (1995. We propose improved recursive formulae to update smoothed estimates of processes related to the model. These recursive estimates are used to update the parameter of the model via the expectation maximization (EM algorithm.

3. Procedures and Recursion

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 6. Algorithms Procedures and Recursion. R K Shyamasundar. Series Article Volume 1 ... Author Affiliations. R K Shyamasundar1. Computer Science Group, Tata Institute of Fundamental Research, Homi Bhabha Road Mumbai 400 005, India.

Analytic study of the Migdal-Kadanoff recursion formula

International Nuclear Information System (INIS)

Ito, K.R.

1984-01-01

After proposing lattice gauge field models in which the Migdal renormalization group recursion formulas are exact, we study the recursion formulas analytically. If D is less than 4, it is shown that the effective actions of D-dimensional U(1) lattice gauge models are uniformly driven to the high temperature region no matter how low the initial temperature is. If the initial temperature is large enough, this holds for any D and gauge group G. These are also the cases for the recursion formulas of Kadanoff type. It turns out, however, that the string tension for D=3 obtained by these methods is rather big compared with the one already obtained by Mack, Goepfert and by the present author. The reason is clarified. (orig.)

Active control versus recursive backstepping control of a chaotic ...

African Journals Online (AJOL)

... than for the recursive backstepping controllers. However, the flexibility in the choice of the control laws for recursive backstepping design gives room for further improvement in its performance and enables it to achieve the goals of stabilization and tracking. Journal of the Nigerian Association of Mathematical Physics Vol.

Axisymmetric solution with charge in general relativity

International Nuclear Information System (INIS)

Arutyunyan, G.G.; Papoyan, V.V.

1989-01-01

The possibility of generating solutions to the equations of general relativity from known solutions of the generalized theory of gravitation and vice versa is proved. An electrovac solution to Einstein's equations that describes a static axisymmetric gravitational field is found. 14 refs

STATE ESTIMATION IN ALCOHOLIC CONTINUOUS FERMENTATION OF ZYMOMONAS MOBILIS USING RECURSIVE BAYESIAN FILTERING: A SIMULATION APPROACH

Directory of Open Access Journals (Sweden)

Olga Lucia Quintero

2008-05-01

Full Text Available This work presents a state estimator for a continuous bioprocess. To this aim, the Non Linear Filtering theory based on the recursive application of Bayes rule and Monte Carlo techniques is used. Recursive Bayesian Filters Sampling Importance Resampling (SIR is employed, including different kinds of resampling. Generally, bio-processes have strong non-linear and non-Gaussian characteristics, and this tool becomes attractive. The estimator behavior and performance are illustrated with the continuous process of alcoholic fermentation of Zymomonas mobilis. Not too many applications with this tool have been reported in the biotechnological area.

Toward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach

International Nuclear Information System (INIS)

Darmani, G.; Setayeshi, S.; Ramezanpour, H.

2012-01-01

In this paper an efficient computational method based on extending the sensitivity approach (SA) is proposed to find an analytic exact solution of nonlinear differential difference equations. In this manner we avoid solving the nonlinear problem directly. By extension of sensitivity approach for differential difference equations (DDEs), the nonlinear original problem is transformed into infinite linear differential difference equations, which should be solved in a recursive manner. Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained. Numerical examples are employed to show the effectiveness of the proposed approach. (general)

Recursive Algorithm For Linear Regression

Science.gov (United States)

Varanasi, S. V.

1988-01-01

Order of model determined easily. Linear-regression algorithhm includes recursive equations for coefficients of model of increased order. Algorithm eliminates duplicative calculations, facilitates search for minimum order of linear-regression model fitting set of data satisfactory.

On a hierarchical construction of the anisotropic LTSN solution from the isotropic LTSN solution

International Nuclear Information System (INIS)

Foletto, Taline; Segatto, Cynthia F.; Bodmann, Bardo E.; Vilhena, Marco T.

2015-01-01

In this work, we present a recursive scheme targeting the hierarchical construction of anisotropic LTS N solution from the isotropic LTS N solution. The main idea relies in the decomposition of the associated LTS N anisotropic matrix as a sum of two matrices in which one matrix contains the isotropic and the other anisotropic part of the problem. The matrix containing the anisotropic part is considered as the source of the isotropic problem. The solution of this problem is made by the decomposition of the angular flux as a truncated series of intermediate functions and replace in the isotropic equation. After the replacement of these into the split isotropic equation, we construct a set of isotropic recursive problems, that are readily solved by the classic LTS N isotropic method. We apply this methodology to solve problems considering homogeneous and heterogeneous anisotropic regions. Numerical results are presented and compared with the classical LTS N anisotropic solution. (author)

Interacting via the Heap in the Presence of Recursion

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Jurriaan Rot

2012-12-01

Full Text Available Almost all modern imperative programming languages include operations for dynamically manipulating the heap, for example by allocating and deallocating objects, and by updating reference fields. In the presence of recursive procedures and local variables the interactions of a program with the heap can become rather complex, as an unbounded number of objects can be allocated either on the call stack using local variables, or, anonymously, on the heap using reference fields. As such a static analysis is, in general, undecidable. In this paper we study the verification of recursive programs with unbounded allocation of objects, in a simple imperative language for heap manipulation. We present an improved semantics for this language, using an abstraction that is precise. For any program with a bounded visible heap, meaning that the number of objects reachable from variables at any point of execution is bounded, this abstraction is a finitary representation of its behaviour, even though an unbounded number of objects can appear in the state. As a consequence, for such programs model checking is decidable. Finally we introduce a specification language for temporal properties of the heap, and discuss model checking these properties against heap-manipulating programs.

Recursion rules for scattering amplitudes in non-Abelian gauge theories

International Nuclear Information System (INIS)

Kim, C.; Nair, V.P.

1997-01-01

We present a functional derivation of recursion rules for scattering amplitudes in a non-Abelian gauge theory in a form valid to arbitrary loop order. The tree-level and one-loop recursion rules are explicitly displayed. copyright 1997 The American Physical Society

A Proof-Theoretic Account of Primitive Recursion and Primitive Iteration

DEFF Research Database (Denmark)

Cherabini, Luca; Danvy, Olivier

2011-01-01

We revisit both the usual ``going-up'' induction principle and Manna and Waldinger's ``going-down'' induction principle for primitive recursion,`a la Goedel, and primitive iteration, `a la Church. We use 'Kleene's trick' to show that primitive recursion and primitive iiteration are as expressive...

Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain

Energy Technology Data Exchange (ETDEWEB)

Tumelero, Fernanda; Bodmann, Bardo E. J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos Graduacao em Engenharia Mecanica; Lapa, Celso M.F., E-mail: fernanda.tumelero@yahoo.com.br, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: lapa@ien.gov.br [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil)

2017-07-01

In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. (author)

A novel noncommutative KdV-type equation, its recursion operator, and solitons

Science.gov (United States)

Carillo, Sandra; Lo Schiavo, Mauro; Porten, Egmont; Schiebold, Cornelia

2018-04-01

A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived.

A note on the solution of general Falkner-Skan problem by two novel semi-analytical techniques

Directory of Open Access Journals (Sweden)

Ahmed Khidir

2015-12-01

Full Text Available The aim of this paper is to give a presentation of two new iterative methods for solving non-linear differential equations, they are successive linearisation method and spectral homotopy perturbation method. We applied these techniques on the non-linear boundary value problems of Falkner-Skan type. The methods used to find a recursive former for higher order equations that are solved using the Chebyshev spectral method to find solutions that are accurate and converge rapidly to the full numerical solution. The methods are illustrated by progressively applying the technique to the Blasius boundary layer equation, the Falkner-Skan equation and finally, the magnetohydrodynamic (MHD Falkner-Skan equation. The solutions are compared to other methods in the literature such as the homotopy analysis method and the spectral-homotopy analysis method with focus on the accuracy and convergence of this new techniques.

Cross-Validation of Survival Bump Hunting by Recursive Peeling Methods.

Science.gov (United States)

Dazard, Jean-Eudes; Choe, Michael; LeBlanc, Michael; Rao, J Sunil

2014-08-01

We introduce a survival/risk bump hunting framework to build a bump hunting model with a possibly censored time-to-event type of response and to validate model estimates. First, we describe the use of adequate survival peeling criteria to build a survival/risk bump hunting model based on recursive peeling methods. Our method called "Patient Recursive Survival Peeling" is a rule-induction method that makes use of specific peeling criteria such as hazard ratio or log-rank statistics. Second, to validate our model estimates and improve survival prediction accuracy, we describe a resampling-based validation technique specifically designed for the joint task of decision rule making by recursive peeling (i.e. decision-box) and survival estimation. This alternative technique, called "combined" cross-validation is done by combining test samples over the cross-validation loops, a design allowing for bump hunting by recursive peeling in a survival setting. We provide empirical results showing the importance of cross-validation and replication.

General method and exact solutions to a generalized variable-coefficient two-dimensional KdV equation

International Nuclear Information System (INIS)

Chen, Yong; Shanghai Jiao-Tong Univ., Shangai; Chinese Academy of sciences, Beijing

2005-01-01

A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion

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.

Efficient design of two-dimensional recursive digital filters. Final report

International Nuclear Information System (INIS)

Twogood, R.E.; Mitra, S.K.

1980-01-01

This report outlines the research progress during the period August 1978 to July 1979. This work can be divided into seven basic project areas. Project 1 deals with a comparative study of 2-D recursive and nonrecursive digital filters. The second project addresses a new design technique for 2-D half-plane recursive filters, and Projects 3 thru 5 deal with implementation issues. The sixth project presents our recent study of the applicability of array processors to 2-D digital signal processing. The final project involves our investigation into techniques for incorporating symmetry constraints on 2-D recursive filters in order to yield more efficient implementations

General Relativity solutions in modified gravity

Science.gov (United States)

Motohashi, Hayato; Minamitsuji, Masato

2018-06-01

Recent gravitational wave observations of binary black hole mergers and a binary neutron star merger by LIGO and Virgo Collaborations associated with its optical counterpart constrain deviation from General Relativity (GR) both on strong-field regime and cosmological scales with high accuracy, and further strong constraints are expected by near-future observations. Thus, it is important to identify theories of modified gravity that intrinsically possess the same solutions as in GR among a huge number of theories. We clarify the three conditions for theories of modified gravity to allow GR solutions, i.e., solutions with the metric satisfying the Einstein equations in GR and the constant profile of the scalar fields. Our analysis is quite general, as it applies a wide class of single-/multi-field scalar-tensor theories of modified gravity in the presence of matter component, and any spacetime geometry including cosmological background as well as spacetime around black hole and neutron star, for the latter of which these conditions provide a necessary condition for no-hair theorem. The three conditions will be useful for further constraints on modified gravity theories as they classify general theories of modified gravity into three classes, each of which possesses i) unique GR solutions (i.e., no-hair cases), ii) only hairy solutions (except the cases that GR solutions are realized by cancellation between singular coupling functions in the Euler-Lagrange equations), and iii) both GR and hairy solutions, for the last of which one of the two solutions may be selected dynamically.

Parallel Implementation of Riccati Recursion for Solving Linear-Quadratic Control Problems

DEFF Research Database (Denmark)

Frison, Gianluca; Jørgensen, John Bagterp

2013-01-01

In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper...... an alternative version of the Riccati recursion solver for LQ control problems is presented. The performance of both the classical and the alternative version is analyzed from a theoretical as well as a numerical point of view, and the alternative version is found to be approximately 50% faster than...

Approximate Bayesian recursive estimation

Czech Academy of Sciences Publication Activity Database

Kárný, Miroslav

2014-01-01

Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf

Adaptable Iterative and Recursive Kalman Filter Schemes

Science.gov (United States)

Zanetti, Renato

2014-01-01

Nonlinear filters are often very computationally expensive and usually not suitable for real-time applications. Real-time navigation algorithms are typically based on linear estimators, such as the extended Kalman filter (EKF) and, to a much lesser extent, the unscented Kalman filter. The Iterated Kalman filter (IKF) and the Recursive Update Filter (RUF) are two algorithms that reduce the consequences of the linearization assumption of the EKF by performing N updates for each new measurement, where N is the number of recursions, a tuning parameter. This paper introduces an adaptable RUF algorithm to calculate N on the go, a similar technique can be used for the IKF as well.

Time-area efficient multiplier-free recursive filter architectures for FPGA implementation

DEFF Research Database (Denmark)

Shajaan, Mohammad; Sørensen, John Aasted

1996-01-01

Simultaneous design of multiplier-free recursive filters (IIR filters) and their hardware implementation in Xilinx field programmable gate array (XC4000) is presented. The hardware design methodology leads to high performance recursive filters with sampling frequencies in the interval 15-21 MHz (...

Algebraic Optimization of Recursive Database Queries

DEFF Research Database (Denmark)

Hansen, Michael Reichhardt

1988-01-01

Queries are expressed by relational algebra expressions including a fixpoint operation. A condition is presented under which a natural join commutes with a fixpoint operation. This condition is a simple check of attribute sets of sub-expressions of the query. The work may be considered a generali......Queries are expressed by relational algebra expressions including a fixpoint operation. A condition is presented under which a natural join commutes with a fixpoint operation. This condition is a simple check of attribute sets of sub-expressions of the query. The work may be considered...... a generalization of Aho and Ullman, (1979). The result is interpreted in function free logic database terms as a transformation of the recursively defined predicate involving: (a) elimination of an argument, and (b) propagation of selections (instantiations) to the extensionally defined predicates. A collection...

Language, Mind, Practice: Families of Recursive Thinking in Human Reasoning

Science.gov (United States)

Josephson, Marika

2011-01-01

In 2002, Chomsky, Hauser, and Fitch asserted that recursion may be the one aspect of the human language faculty that makes human language unique in the narrow sense--unique to language and unique to human beings. They also argue somewhat more quietly (as do Pinker and Jackendoff 2005) that recursion may be possible outside of language: navigation,…

New compacton solutions and solitary wave solutions of fully nonlinear generalized Camassa-Holm equations

International Nuclear Information System (INIS)

Tian Lixin; Yin Jiuli

2004-01-01

In this paper, we introduce the fully nonlinear generalized Camassa-Holm equation C(m,n,p) and by using four direct ansatzs, we obtain abundant solutions: compactons (solutions with the absence of infinite wings), solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions and obtain kink compacton solutions and nonsymmetry compacton solutions. We also study other forms of fully nonlinear generalized Camassa-Holm equation, and their compacton solutions are governed by linear equations

Recursive B-spline approximation using the Kalman filter

Directory of Open Access Journals (Sweden)

Jens Jauch

2017-02-01

Full Text Available This paper proposes a novel recursive B-spline approximation (RBA algorithm which approximates an unbounded number of data points with a B-spline function and achieves lower computational effort compared with previous algorithms. Conventional recursive algorithms based on the Kalman filter (KF restrict the approximation to a bounded and predefined interval. Conversely RBA includes a novel shift operation that enables to shift estimated B-spline coefficients in the state vector of a KF. This allows to adapt the interval in which the B-spline function can approximate data points during run-time.

Categorical Semantics for Functional Reactive Programming with Temporal Recursion and Corecursion

Directory of Open Access Journals (Sweden)

Wolfgang Jeltsch

2014-06-01

Full Text Available Functional reactive programming (FRP makes it possible to express temporal aspects of computations in a declarative way. Recently we developed two kinds of categorical models of FRP: abstract process categories (APCs and concrete process categories (CPCs. Furthermore we showed that APCs generalize CPCs. In this paper, we extend APCs with additional structure. This structure models recursion and corecursion operators that are related to time. We show that the resulting categorical models generalize those CPCs that impose an additional constraint on time scales. This constraint boils down to ruling out ω-supertasks, which are closely related to Zeno's paradox of Achilles and the tortoise.

Proof Rules for Recursive Procedures

NARCIS (Netherlands)

Hesselink, Wim H.

1993-01-01

Four proof rules for recursive procedures in a Pascal-like language are presented. The main rule deals with total correctness and is based on results of Gries and Martin. The rule is easier to apply than Martin's. It is introduced as an extension of a specification format for Pascal-procedures, with

Nonasymptotic form of the recursion relations of the three-dimensional Ising model

International Nuclear Information System (INIS)

Kozlovskii, M.P.

1989-01-01

Approximate recursion relations for the three-dimensional Ising model are obtained in the form of rapidly converging series. The representation of the recursion relations in the form of nonasymptotic series entails the abandonment of traditional perturbation theory based on a Gaussian measure density. The recursion relations proposed in the paper are used to calculate the critical exponent ν of the correlation length. It is shown that the difference form of the recursion relations leads, when higher non-Gaussian basis measures are used, to disappearance of a dependence of the critical exponent ν on s when s > 2 (s is the parameter of the division of the phase space into layers). The obtained results make it possible to calculate explicit expressions for the thermodynamic functions near the phase transition point

Properties of general relativistic kink solution

International Nuclear Information System (INIS)

Kodama, T.; Oliveira, L.C.S. de; Santos, F.C.

1978-12-01

Properties of the general relativistic kink solution of a nonlinear scalar field recently obtained, are discussed. It has been shown that the kink solution is stable against radical perturbations. Possible applications to Hadron physics from the geometrodynamic point of view are suggested [pt

Recursion theory for metamathematics

CERN Document Server

Smullyan, Raymond M

1993-01-01

This work is a sequel to the author''s Godel''s Incompleteness Theorems, though it can be read independently by anyone familiar with Godel''s incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.

Yang-Mills analogs of general-relativistic solutions

International Nuclear Information System (INIS)

Singlton, D.

1998-01-01

Some solutions of Yang-Mills equations, which can be found with the use of the general relativistic theory and Yang-Mills theory, are discussed. Some notes concerning possible physical sense of these solutions are made. Arguments showing that some of such solutions in the Yang-Mills theory (similar to the general relativistic ones) may be connected with the confinement phenomenon are given in particular. The motion of probe particles located into the phonon potential similar to the Schwarz-Child one is briefly discussed for this purpose [ru

An Integrated Approach for Non-Recursive Formulation of Connection-Coefficients of Orthogonal Functions

Directory of Open Access Journals (Sweden)

Monika GARG

2012-08-01

Full Text Available In this paper, an integrated approach is proposed for non-recursive formulation of connection coefficients of different orthogonal functions in terms of a generic orthogonal function. The application of these coefficients arises when the product of two orthogonal basis functions are to be expressed in terms of single basis functions. Two significant advantages are achieved; one, the non-recursive formulations avoid memory and stack overflows in computer implementations; two, the integrated approach provides for digital hardware once-designed can be used for different functions. Computational savings achieved with the proposed non-recursive formulation vis-à-vis recursive formulation, reported in the literature so far, have been demonstrated using MATLAB PROFILER.

A Revised Piecewise Linear Recursive Convolution FDTD Method for Magnetized Plasmas

International Nuclear Information System (INIS)

Liu Song; Zhong Shuangying; Liu Shaobin

2005-01-01

The piecewise linear recursive convolution (PLRC) finite-different time-domain (FDTD) method improves accuracy over the original recursive convolution (RC) FDTD approach and current density convolution (JEC) but retains their advantages in speed and efficiency. This paper describes a revised piecewise linear recursive convolution PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations of the reflection and transmission coefficients through a magnetized plasma layer. The results show that the revised PLRC-FDTD method has improved the accuracy over the original RC FDTD method and JEC FDTD method

Recursive estimation of the claim rates and sizes in an insurance model

Directory of Open Access Journals (Sweden)

Lakhdar Aggoun

2004-01-01

Full Text Available It is a common fact that for most classes of general insurance, many possible sources of heterogeneity of risk exist. Premium rates based on information from a heterogeneous portfolio might be quite inadequate. One way of reducing this danger is by grouping policies according to the different levels of the various risk factors involved. Using measure change techniques, we derive recursive filters and predictors for the claim rates and claim sizes for the different groups.

A recursion relation for coefficients of fractional parentage in the seniority scheme

International Nuclear Information System (INIS)

Evans, T.

1985-01-01

A recursion relations for coefficients as fractional parentage in the seniority scheme are discussed. Determinated dependence of recursion relations from the particle number permit to evaluate matrix elements of creation and annihilation operators for fermions or bosons. 10 refs. (author)

A Generalized Deduction of the Ideal-Solution Model

Science.gov (United States)

Leo, Teresa J.; Perez-del-Notario, Pedro; Raso, Miguel A.

2006-01-01

A new general procedure for deriving the Gibbs energy of mixing is developed through general thermodynamic considerations, and the ideal-solution model is obtained as a special particular case of the general one. The deduction of the Gibbs energy of mixing for the ideal-solution model is a rational one and viewed suitable for advanced students who…

System Simulation by Recursive Feedback: Coupling a Set of Stand-Alone Subsystem Simulations

Science.gov (United States)

Nixon, D. D.

2001-01-01

Conventional construction of digital dynamic system simulations often involves collecting differential equations that model each subsystem, arran g them to a standard form, and obtaining their numerical gin solution as a single coupled, total-system simultaneous set. Simulation by numerical coupling of independent stand-alone subsimulations is a fundamentally different approach that is attractive because, among other things, the architecture naturally facilitates high fidelity, broad scope, and discipline independence. Recursive feedback is defined and discussed as a candidate approach to multidiscipline dynamic system simulation by numerical coupling of self-contained, single-discipline subsystem simulations. A satellite motion example containing three subsystems (orbit dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Distributed and centralized implementations of coupling have been considered. Numerical results are evaluated by direct comparison with a standard total-system, simultaneous-solution approach.

Recursive Neural Networks in Quark/Gluon Tagging

CERN Multimedia

CERN. Geneva

2018-01-01

Vidyo contribution Based on the natural tree-like structure of jet sequential clustering, the recursive neural networks (RecNNs) embed jet clustering history recursively as in natural language processing. We explore the performance of RecNN in quark/gluon discrimination. The results show that RecNNs work better than the baseline BDT by a few percent in gluon rejection at the working point of 50\\% quark acceptance. We also experimented on some relevant aspects which might influence the performance of networks. It shows that even only particle flow identification as input feature without any extra information on momentum or angular position is already giving a fairly good result, which indicates that most of the information for q/g discrimination is already included in the tree-structure itself.

Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy

International Nuclear Information System (INIS)

Li Nianhua; Li Yuqi

2011-01-01

It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed. A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations (ODEs), which may be gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies. The key is a special form of Lax pair for the AKNS hierarchy. It is proved that under the constraints all equations of the AKNS hierarchy are linearizable. (general)

Lessons in Contingent, Recursive Humility

Science.gov (United States)

Vagle, Mark D.

2011-01-01

In this article, the author argues that critical work in teacher education should begin with teacher educators turning a critical eye on their own practices. The author uses Lesko's conception of contingent, recursive growth and change to analyze a lesson he observed as part of a phenomenological study aimed at understanding more about what it is…

Cosmology in three dimensions: steps towards the general solution

International Nuclear Information System (INIS)

Barrow, John D; Shaw, Douglas J; Tsagas, Christos G

2006-01-01

We use covariant and first-order formalism techniques to study the properties of general relativistic cosmology in three dimensions. The covariant approach provides an irreducible decomposition of the relativistic equations, which allows for a mathematically compact and physically transparent description of the three-dimensional spacetimes. Using this information we review the features of homogeneous and isotropic 3D cosmologies, provide a number of new solutions and study gauge invariant perturbations around them. The first-order formalism is then used to provide a detailed study of the most general 3D spacetimes containing perfect-fluid matter. Assuming the material content to be dust with comoving spatial 2-velocities, we find the general solution of the Einstein equations with a non-zero (and zero) cosmological constant and generalize known solutions of Kriele and the 3D counterparts of the Szekeres solutions. In the case of a non-comoving dust fluid we find the general solution in the case of one non-zero fluid velocity component. We consider the asymptotic behaviour of the families of 3D cosmologies with rotation and shear and analyse their singular structure. We also provide the general solution for cosmologies with one spacelike Killing vector, find solutions for cosmologies containing scalar fields and identify all the PP-wave 2 + 1 spacetimes

On the asymptotic form of the recursion method basis vectors for periodic Hamiltonians

International Nuclear Information System (INIS)

O'Reilly, E.P.; Weaire, D.

1984-01-01

The authors present the first detailed study of the recursion method basis vectors for the case of a periodic Hamiltonian. In the examples chosen, the probability density scales linearly with n as n → infinity, whenever the local density of states is bounded. Whenever it is unbounded and the recursion coefficients diverge, different scaling behaviour is found. These findings are explained and a scaling relationship between the asymptotic forms of the recursion coefficients and basis vectors is proposed. (author)

COMPARISON OF RECURSIVE ESTIMATION TECHNIQUES FOR POSITION TRACKING RADIOACTIVE SOURCES

International Nuclear Information System (INIS)

Muske, K.; Howse, J.

2000-01-01

This paper compares the performance of recursive state estimation techniques for tracking the physical location of a radioactive source within a room based on radiation measurements obtained from a series of detectors at fixed locations. Specifically, the extended Kalman filter, algebraic observer, and nonlinear least squares techniques are investigated. The results of this study indicate that recursive least squares estimation significantly outperforms the other techniques due to the severe model nonlinearity

Recursive Subsystems in Aphasia and Alzheimer's Disease: Case Studies in Syntax and Theory of Mind

Science.gov (United States)

Bánréti, Zoltán; Hoffmann, Ildikó; Vincze, Veronika

2016-01-01

The relationship between recursive sentence embedding and theory-of-mind (ToM) inference is investigated in three persons with Broca's aphasia, two persons with Wernicke's aphasia, and six persons with mild and moderate Alzheimer's disease (AD). We asked questions of four types about photographs of various real-life situations. Type 4 questions asked participants about intentions, thoughts, or utterances of the characters in the pictures (“What may X be thinking/asking Y to do?”). The expected answers typically involved subordinate clauses introduced by conjunctions or direct quotations of the characters' utterances. Broca's aphasics did not produce answers with recursive sentence embedding. Rather, they projected themselves into the characters' mental states and gave direct answers in the first person singular, with relevant ToM content. We call such replies “situative statements.” Where the question concerned the mental state of the character but did not require an answer with sentence embedding (“What does X hate?”), aphasics gave descriptive answers rather than situative statements. Most replies given by persons with AD to Type 4 questions were grammatical instances of recursive sentence embedding. They also gave a few situative statements but the ToM content of these was irrelevant. In more than one third of their well-formed sentence embeddings, too, they conveyed irrelevant ToM contents. Persons with moderate AD were unable to pass secondary false belief tests. The results reveal double dissociation: Broca's aphasics are unable to access recursive sentence embedding but they can make appropriate ToM inferences; moderate AD persons make the wrong ToM inferences but they are able to access recursive sentence embedding. The double dissociation may be relevant for the nature of the relationship between the two recursive capacities. Broca's aphasics compensated for the lack of recursive sentence embedding by recursive ToM reasoning represented in very

On а Recursive-Parallel Algorithm for Solving the Knapsack Problem

Directory of Open Access Journals (Sweden)

Vladimir V. Vasilchikov

2018-01-01

Full Text Available In this paper, we offer an efficient parallel algorithm for solving the NP-complete Knapsack Problem in its basic, so-called 0-1 variant. To find its exact solution, algorithms belonging to the category ”branch and bound methods” have long been used. To speed up the solving with varying degrees of efficiency, various options for parallelizing computations are also used. We propose here an algorithm for solving the problem, based on the paradigm of recursive-parallel computations. We consider it suited well for problems of this kind, when it is difficult to immediately break up the computations into a sufficient number of subtasks that are comparable in complexity, since they appear dynamically at run time. We used the RPM ParLib library, developed by the author, as the main tool to program the algorithm. This library allows us to develop effective applications for parallel computing on a local network in the .NET Framework. Such applications have the ability to generate parallel branches of computation directly during program execution and dynamically redistribute work between computing modules. Any language with support for the .NET Framework can be used as a programming language in conjunction with this library. For our experiments, we developed some C# applications using this library. The main purpose of these experiments was to study the acceleration achieved by recursive-parallel computing. A detailed description of the algorithm and its testing, as well as the results obtained, are also given in the paper.

Compact QED tree-level amplitudes from dressed BCFW recursion relations

International Nuclear Information System (INIS)

Badger, Simon D.; Henn, Johannes M.

2010-05-01

We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and N 2 MHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial. (orig.)

Compact QED tree-level amplitudes from dressed BCFW recursion relations

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon D. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Henn, Johannes M. [Humboldt Univ., Berlin (Germany). Inst. fuer Physik

2010-05-15

We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and N{sup 2}MHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial. (orig.)

Quantum rings and recursion relations in 2D quantum gravity

International Nuclear Information System (INIS)

Kachru, S.

1992-01-01

This paper discusses tachyon condensate perturbations to the action of the two-dimensional string theory corresponding to the c + 1 matrix model. These are shown to deform the action of the ground ring on the tachyon modules, confirming a conjecture of Witten. The ground ring structure is used to derive recursion relations which relate (N + 1) and N tachyon bulk scattering amplitudes. These recursion relations allow one to compute all bulk amplitudes

New solutions of Heun's general equation

International Nuclear Information System (INIS)

Ishkhanyan, Artur; Suominen, Kalle-Antti

2003-01-01

We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)

Exact solution for stresses/displacements in a multilayered hollow cylinder under thermo-mechanical loading

International Nuclear Information System (INIS)

Yeo, W.H.; Purbolaksono, J.; Aliabadi, M.H.; Ramesh, S.; Liew, H.L.

2017-01-01

In this study, a new analytical solution by the recursive method for evaluating stresses/displacements in multilayered hollow cylinder under thermo-mechanical loading was developed. The results for temperature distribution, displacements and stresses obtained by using the proposed solution were shown to be in good agreement with the FEM results. The proposed analytical solution was also found to produce more accurate results than those by the analytical solution reported in literature. - Highlights: • A new analytical solution for evaluating stresses in multilayered hollow cylinder under thermo-mechanical loading. • A simple computational procedure using a recursive method. • A promising technique for evaluating the operating axial and hoop stresses in pressurized composite vessels.

a Recursive Approach to Compute Normal Forms

Science.gov (United States)

HSU, L.; MIN, L. J.; FAVRETTO, L.

2001-06-01

Normal forms are instrumental in the analysis of dynamical systems described by ordinary differential equations, particularly when singularities close to a bifurcation are to be characterized. However, the computation of a normal form up to an arbitrary order is numerically hard. This paper focuses on the computer programming of some recursive formulas developed earlier to compute higher order normal forms. A computer program to reduce the system to its normal form on a center manifold is developed using the Maple symbolic language. However, it should be stressed that the program relies essentially on recursive numerical computations, while symbolic calculations are used only for minor tasks. Some strategies are proposed to save computation time. Examples are presented to illustrate the application of the program to obtain high order normalization or to handle systems with large dimension.

Certified higher-order recursive path ordering

NARCIS (Netherlands)

Koprowski, A.; Pfenning, F.

2006-01-01

The paper reports on a formalization of a proof of wellfoundedness of the higher-order recursive path ordering (HORPO) in the proof checker Coq. The development is axiom-free and fully constructive. Three substantive parts that could be used also in other developments are the formalizations of the

Chiodo formulas for the r-th roots and topological recursion

OpenAIRE

Lewanski, Danilo; Popolitov, Alexandr; Shadrin, Sergey; Zvonkine, Dimitri

2015-01-01

We analyze Chiodo's formulas for the Chern classes related to the r-th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers of these classes with psi-classes are reproduced via the Chekhov-Eynard-Orantin topological recursion. As an application, we prove that the Johnson-Pandharipande-Tseng formula for the orbifold Hurwitz numbers is equivalent to the topological recursion for the orbifold Hurwitz numbers. In particular, t...

Recursive relations for processes with n photons of noncommutative QED

International Nuclear Information System (INIS)

Jafari, Abolfazl

2007-01-01

Recursion relations are derived in the sense of Berends-Giele for the multi-photon processes of noncommutative QED. The relations concern purely photonic processes as well as the processes with two fermions involved, both for arbitrary number of photons at tree level. It is shown that despite of the dependence of noncommutative vertices on momentum, in contrast to momentum-independent color factors of QCD, the recursion relation method can be employed for multi-photon processes of noncommutative QED

Down two steps: Are bilinguals delayed in the acquisition of recursively embedded PPs?

Directory of Open Access Journals (Sweden)

Ana Pérez-Leroux

2017-08-01

Full Text Available The present study examines whether bilingual children are delayed in the ability to produce complex DPs. We elicited production of DPs containing two PP modifiers, in two conditions designed to tease apart the acquisition of an embedding rule from the acquisition of the recursivity of an embedding rule. In the recursive condition, one modifier PP was itself modified by an additional PP. In the non-recursive condition, both PPs sequentially modified the main noun. Participants were 71 English monolingual children and 35 bilinguals between the ages of four and six. The evidence suggested an overall difference between groups, however further analysis revealed that bilinguals differed from monolinguals only insofar as the onset of PP embedding. No specific additional bilingual delay arose from the recursive condition. This suggests that recursive embedding is a resilient domain in language acquisition and supports proposals that link morphosyntactic delays in bilingual children to domains of grammar that are heavily reliant on lexical learning, which would include learning the first instance of PP embedding. --- Original in English.   --- DOI: http://dx.doi.org/10.12957/matraga.2017.28781

A recursive reduction of tensor Feynman integrals

International Nuclear Information System (INIS)

Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.

2009-07-01

We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)

General classical solutions in the noncommutative CPN-1 model

International Nuclear Information System (INIS)

Foda, O.; Jack, I.; Jones, D.R.T.

2002-01-01

We give an explicit construction of general classical solutions for the noncommutative CP N-1 model in two dimensions, showing that they correspond to integer values for the action and topological charge. We also give explicit solutions for the Dirac equation in the background of these general solutions and show that the index theorem is satisfied

The Paradigm Recursion: Is It More Accessible When Introduced in Middle School?

Science.gov (United States)

Gunion, Katherine; Milford, Todd; Stege, Ulrike

2009-01-01

Recursion is a programming paradigm as well as a problem solving strategy thought to be very challenging to grasp for university students. This article outlines a pilot study, which expands the age range of students exposed to the concept of recursion in computer science through instruction in a series of interesting and engaging activities. In…

Solution to Bethe-Salpeter equation via Mellin-Barnes transform

International Nuclear Information System (INIS)

Allendes, Pedro; Kniehl, Bernd; Kondrashuk, Igor; Rojas Medar, Marko; Notte Cuello, Eduardo A.

2012-06-01

We consider Mellin-Barnes transform of triangle ladder-like scalar diagram in d=4 dimensions. It is shown how multi-fold MB transform of the momentum integral corresponding to any number of rungs is reduced to two-fold MB transform. For this purpose we use Belokurov-Usyukina reduction method for four-dimensional scalar integrals in the position space. The result is represented in terms of Euler ψ-function and its derivatives. We derive new formulas for MB two-fold integration in the complex planes of two complex variables. We demonstrate that these formulas solve Bethe-Salpeter equation. We comment on further applications of solution to Bethe-Salpeter equation for vertices in N=4 supersymmetric Yang-Mills theory. We show that the recursive property of MB transforms observed in the present work for that kind of diagrams has nothing to do with quantum field theory, theory of integral transforms, or with theory of polylogarithms in general, but has an origin in a simple recursive property for smooth functions which can be shown by using basic methods of mathematical analysis.

Solution to Bethe-Salpeter equation via Mellin-Barnes transform

Energy Technology Data Exchange (ETDEWEB)

Allendes, Pedro [Concepcion Univ. (Chile). Dept. de Fisica; Kniehl, Bernd [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kondrashuk, Igor; Rojas Medar, Marko [Univ. del Bio-Bio, Chillan (Chile). Dept. de Ciencias Basicas; Notte Cuello, Eduardo A. [Univ. de La Serena (Chile). Facultad de Ciencias

2012-06-15

We consider Mellin-Barnes transform of triangle ladder-like scalar diagram in d=4 dimensions. It is shown how multi-fold MB transform of the momentum integral corresponding to any number of rungs is reduced to two-fold MB transform. For this purpose we use Belokurov-Usyukina reduction method for four-dimensional scalar integrals in the position space. The result is represented in terms of Euler {psi}-function and its derivatives. We derive new formulas for MB two-fold integration in the complex planes of two complex variables. We demonstrate that these formulas solve Bethe-Salpeter equation. We comment on further applications of solution to Bethe-Salpeter equation for vertices in N=4 supersymmetric Yang-Mills theory. We show that the recursive property of MB transforms observed in the present work for that kind of diagrams has nothing to do with quantum field theory, theory of integral transforms, or with theory of polylogarithms in general, but has an origin in a simple recursive property for smooth functions which can be shown by using basic methods of mathematical analysis.

Decidability and Expressiveness of Recursive Weighted Logic

DEFF Research Database (Denmark)

Xue, Bingtian; Larsen, Kim Guldstrand; Mardare, Radu Iulian

2014-01-01

Labelled weighted transition systems (LWSs) are transition systems labelled with actions and real numbers. The numbers represent the costs of the corresponding actions in terms of resources. RecursiveWeighted Logic (RWL) is a multimodal logic that expresses qualitative and quantitative properties...

Wronskians, generalized Wronskians and solutions to the Korteweg-de Vries equation

International Nuclear Information System (INIS)

Ma Wenxiu

2004-01-01

A bridge going from Wronskian solutions to generalized Wronskian solutions of the Korteweg-de Vries (KdV) equation is built. It is then shown that generalized Wronskian solutions can be viewed as Wronskian solutions. The idea is used to generate positons, negatons and their interaction solutions to the KdV equation. Moreover, general positons and negatons are constructed through the Wronskian formulation. A few new exact solutions to the KdV equation are explicitly presented as examples of Wronskian solutions

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

Science.gov (United States)

Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

2017-11-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

International Nuclear Information System (INIS)

Hernandez-Walls, R; Martín-Atienza, B; Salinas-Matus, M; Castillo, J

2017-01-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations. (paper)

The core spline method for solution of quantum-mechanical systems of differential equations for bound states

International Nuclear Information System (INIS)

Aleksandrov, L.; Drenska, M.; Karadzhov, D.

1986-01-01

A generalization of the core spline method is given in the case of solution of the general bound state problem for a system of M linear differential equations with coefficients depending on the spectral parameter. The recursion scheme for construction of basic splines is described. The wave functions are expressed as linear combinations of basic splines, which are approximate partial solutions of the system. The spectral parameter (the eigenvalue) is determined from the condition for existence of a nontrivial solution of a (MxM) linear algebraic system at the last collocation point. The nontrivial solutions of this system determine (M - 1) coefficients of the linear spans, expressing the wave functions. The last unknown coefficient is determined from a boundary (or normalization) condition for the system. The computational aspects of the method are discussed, in particular, its concrete algorithmic realization used in the RODSOL program. The numerical solution of the Dirac system for the bound states of a hydrogen atom is given is an example

On semantics and applications of guarded recursion

DEFF Research Database (Denmark)

Bizjak, Aleš

2016-01-01

denotational model and a logic for reasoning about program equivalence. In the last three chapters we study syntax and semantics of a dependent type theory with a family of later modalities indexed by the set of clocks, and clock quantifiers. In the fourth and fifth chapters we provide two model constructions......In this dissertation we study applications and semantics of guarded recursion, which is a method for ensuring that self-referential descriptions of objects define a unique object. The first two chapters are devoted to applications. We use guarded recursion, first in the form of explicit step......-indexing and then in the form of the internal language of particular sheaf topos, to construct logical relations for reasoning about contextual approximation of probabilistic and nondeterministic programs. These logical relations are sound and complete and useful for showing a range of example equivalences. In the third...

Generalized solutions of nonlinear partial differential equations

CERN Document Server

Rosinger, EE

1987-01-01

During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin

A nested recursive logit model for route choice analysis

DEFF Research Database (Denmark)

Mai, Tien; Frejinger, Emma; Fosgerau, Mogens

2015-01-01

choices and the model does not require any sampling of choice sets. Furthermore, the model can be consistently estimated and efficiently used for prediction.A key challenge lies in the computation of the value functions, i.e. the expected maximum utility from any position in the network to a destination....... The value functions are the solution to a system of non-linear equations. We propose an iterative method with dynamic accuracy that allows to efficiently solve these systems.We report estimation results and a cross-validation study for a real network. The results show that the NRL model yields sensible......We propose a route choice model that relaxes the independence from irrelevant alternatives property of the logit model by allowing scale parameters to be link specific. Similar to the recursive logit (RL) model proposed by Fosgerau et al. (2013), the choice of path is modeled as a sequence of link...

Properties of general classical CPsup(n-1) solutions

International Nuclear Information System (INIS)

Din, A.M.

1980-05-01

The general classical solutions with finite action of the CPsup(n-1) model are displayed. Various properties of the solutions such as topological charge, action, Baecklund like transformations and stability are discussed

Recursion Of Binary Space As A Foundation Of Repeatable Programs

Directory of Open Access Journals (Sweden)

Jeremy Horne

2006-10-01

Full Text Available Every computation, including recursion, is based on natural philosophy. Our world may be expressed in terms of a binary logical space that contains functions that act simultaneously as objects and processes (operands and operators. This paper presents an outline of the results of research about that space and suggests routes for further inquiry. Binary logical space is generated sequentially from an origin in a standard coordinate system. At least one method exists to show that each of the resulting 16 functions repeats itself by repeatedly forward-feeding outputs of a function operating over two others as new operands of the original function until the original function appears as an output, thus behaving as an apparent homeostatic automaton. As any space of any dimension is composed of one or more of these functions, so the space is recursive, as well. Semantics gives meaning to recursive structures, computer programs and fundamental constituents of our universe being two examples. Such thoughts open inquiry into larger philosophical issues as free will and determinism.

General solution of linear vector supersymmetry

International Nuclear Information System (INIS)

Blasi, Alberto; Maggiore, Nicola

2007-01-01

We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such a solution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the cohomology technology, usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example

Theory of Mind Development in Adolescence and Early Adulthood: The Growing Complexity of Recursive Thinking Ability

Science.gov (United States)

Valle, Annalisa; Massaro, Davide; Castelli, Ilaria; Marchetti, Antonella

2015-01-01

This study explores the development of theory of mind, operationalized as recursive thinking ability, from adolescence to early adulthood (N = 110; young adolescents = 47; adolescents = 43; young adults = 20). The construct of theory of mind has been operationalized in two different ways: as the ability to recognize the correct mental state of a character, and as the ability to attribute the correct mental state in order to predict the character’s behaviour. The Imposing Memory Task, with five recursive thinking levels, and a third-order false-belief task with three recursive thinking levels (devised for this study) have been used. The relationship among working memory, executive functions, and linguistic skills are also analysed. Results show that subjects exhibit less understanding of elevated recursive thinking levels (third, fourth, and fifth) compared to the first and second levels. Working memory is correlated with total recursive thinking, whereas performance on the linguistic comprehension task is related to third level recursive thinking in both theory of mind tasks. An effect of age on third-order false-belief task performance was also found. A key finding of the present study is that the third-order false-belief task shows significant age differences in the application of recursive thinking that involves the prediction of others’ behaviour. In contrast, such an age effect is not observed in the Imposing Memory Task. These results may support the extension of the investigation of the third order false belief after childhood. PMID:27247645

A general polynomial solution to convection–dispersion equation ...

Indian Academy of Sciences (India)

Jiao Wang

concentration profiles and optimal solute transport parameters. Furthermore, the general .... requirement; in other words, if Is(t) is cumulated solute added in the column ..... National Natural Science Foundation of China. (Nos. 41530854 and ...

Recursive evaluation of interaction forces of unbounded soil in time domain

International Nuclear Information System (INIS)

Motosaka, M.

1987-01-01

Recursive formulations have hardly been used in the analysis of soil-structure interaction. A notable exception is described in Verbic 1973, which corresponds to the impulse-invariant way discussed in Section 2. Section 3 describes another possibility to derive a recursive relation based on a segment approach using z-transforms. An illustrative example is examined in Section 4, and in Section 5 the number of operations is addressed. This compact paper is based on Wolf and Motosaka 1988. (orig./HP)

A foundation for real recursive function theory

NARCIS (Netherlands)

J.F. Costa; B. S. Loff Barreto (Bruno Serra); J. Mycka

2009-01-01

htmlabstractThe class of recursive functions over the reals, denoted by REC(R), was introduced by Cristopher Moore in his seminal paper written in 1995. Since then many subsequent investigations brought new results: the class REC(R) was put in relation with the class of functions generated by the

Step-indexed Kripke models over recursive worlds

DEFF Research Database (Denmark)

Birkedal, Lars; Reus, Bernhard; Schwinghammer, Jan

2011-01-01

worlds that are recursively defined in a category of metric spaces. In this paper, we broaden the scope of this technique from the original domain-theoretic setting to an elementary, operational one based on step indexing. The resulting method is widely applicable and leads to simple, succinct models...

Testing digital recursive filtering method for radiation measurement channel using pin diode detector

International Nuclear Information System (INIS)

Talpalariu, C. M.; Talpalariu, J.; Popescu, O.; Mocanasu, M.; Lita, I.; Visan, D. A.

2016-01-01

In this work we have studied a software filtering method implemented in a pulse counting computerized measuring channel using PIN diode radiation detector. In case our interest was focalized for low rate decay radiation measurement accuracies improvement and response time optimization. During works for digital mathematical algorithm development, we used a hardware radiation measurement channel configuration based on PIN diode BPW34 detector, preamplifier, filter and programmable counter, computer connected. We report measurement results using two digital recursive methods in statically and dynamically field evolution. Software for graphical input/output real time diagram representation was designed and implemented, facilitating performances evaluation between the response of fixed configuration software recursive filter and dynamically adaptive configuration recursive filter. (authors)

General scalar-tensor cosmology: analytical solutions via noether symmetry

Energy Technology Data Exchange (ETDEWEB)

Massaeli, Erfan; Motaharfar, Meysam; Sepangi, Hamid Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)

2017-02-15

We analyze the cosmology of a general scalar-tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galilean gravity and also the general k-essence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which the dynamics of the system allows a transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the models based on a phantom or quintessence dark energy point of view. Finally, we obtain the condition for stability of a de Sitter solution for which the solution is an attractor of the system. (orig.)

Algorithmic correspondence and completeness in modal logic. V. Recursive extensions of SQEMA

DEFF Research Database (Denmark)

Conradie, Willem; Goranko, Valentin; Vakarelov, Dimiter

2010-01-01

The previously introduced algorithm SQEMA computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend SQEMA with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents...... on the class of ‘recursive formulae’. We also show that a certain version of this algorithm guarantees the canonicity of the formulae on which it succeeds....

On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

Science.gov (United States)

Filimonov, M. Yu.

2017-12-01

The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.

General solution of the Bagley-Torvik equation with fractional-order derivative

Science.gov (United States)

Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.

Analytical Solution of General Bagley-Torvik Equation

Directory of Open Access Journals (Sweden)

William Labecca

2015-01-01

Full Text Available Bagley-Torvik equation appears in viscoelasticity problems where fractional derivatives seem to play an important role concerning empirical data. There are several works treating this equation by using numerical methods and analytic formulations. However, the analytical solutions presented in the literature consider particular cases of boundary and initial conditions, with inhomogeneous term often expressed in polynomial form. Here, by using Laplace transform methodology, the general inhomogeneous case is solved without restrictions in boundary and initial conditions. The generalized Mittag-Leffler functions with three parameters are used and the solutions presented are expressed in terms of Wiman’s functions and their derivatives.

Convolution of second order linear recursive sequences II.

Directory of Open Access Journals (Sweden)

Szakács Tamás

2017-12-01

Full Text Available We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]. In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.

Exploiting fine-grain parallelism in recursive LU factorization

KAUST Repository

Dongarra, Jack; Faverge, Mathieu; Ltaief, Hatem; Luszczek, Piotr R.

2012-01-01

is the panel factorization due to its memory-bound characteristic and the atomicity of selecting the appropriate pivots. We remedy this in our new approach to LU factorization of (narrow and tall) panel submatrices. We use a parallel fine-grained recursive

New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series

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Snezhana Georgieva Gocheva-Ilieva

2013-01-01

Full Text Available There are obtained integral form and recurrence representations for some Fourier series and connected with them Favard constants. The method is based on preliminary integration of Fourier series which permits to establish general recursion formulas for Favard constants. This gives the opportunity for effective summation of infinite series and calculation of some classes of multiple singular integrals by the Favard constants.

Nonlocal integrable PDEs from hierarchies of symmetry laws: The example of Pohlmeyer-Lund-Regge equation and its reflectionless potential solutions

Science.gov (United States)

Demontis, F.; Ortenzi, G.; van der Mee, C.

2018-04-01

By following the ideas presented by Fukumoto and Miyajima in Fukumoto and Miyajima (1996) we derive a generalized method for constructing integrable nonlocal equations starting from any bi-Hamiltonian hierarchy supplied with a recursion operator. This construction provides the right framework for the application of the full machinery of the inverse scattering transform. We pay attention to the Pohlmeyer-Lund-Regge equation coming from the nonlinear Schrödinger hierarchy and construct the formula for the reflectionless potential solutions which are generalizations of multi-solitons. Some explicit examples are discussed.

A new design for SLAM front-end based on recursive SOM

Science.gov (United States)

Yang, Xuesi; Xia, Shengping

2015-12-01

Aiming at the graph optimization-based monocular SLAM, a novel design for the front-end in single camera SLAM is proposed, based on the recursive SOM. Pixel intensities are directly used to achieve image registration and motion estimation, which can save time compared with the current appearance-based frameworks, usually including feature extraction and matching. Once a key-frame is identified, a recursive SOM is used to actualize loop-closure detecting, resulting a more precise location. The experiment on a public dataset validates our method on a computer with a quicker and effective result.

Travelling wave solutions of the generalized Benjamin-Bona-Mahony equation

International Nuclear Information System (INIS)

Estevez, P.G.; Kuru, S.; Negro, J.; Nieto, L.M.

2009-01-01

A class of particular travelling wave solutions of the generalized Benjamin-Bona-Mahony equation is studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and of its modified version, are also recovered.

Predicate Transformers for Recursive Procedures with Local Variables

NARCIS (Netherlands)

Hesselink, Wim H.

1999-01-01

The weakest precondition semantics of recursive procedures with local variables are developed for an imperative language with demonic and angelic operators for unbounded nondeterminate choice. This does not require stacking of local variables. The formalism serves as a foundation for a proof rule

Spherically symmetric solutions of general second-order gravity

International Nuclear Information System (INIS)

Whitt, B.

1988-01-01

The general second-order gravity theory, whose Lagrangian includes higher powers of the curvature, is considered in arbitrary dimensions. It is shown that spherically symmetric solutions are static, except in certain, special, unphysical cases. Spherically symmetric solutions are found and classified. Each theory's solutions fall into a number of distinct branches, which may represent finite space with two singular boundaries, or an asymptotically either flat or (anti--)de Sitter space with one singular boundary. A theory may contain at most one branch of solutions in which all singularities are hidden by event horizons. Such horizons generally emit Hawking radiation, though in certain cases the horizon may have zero temperature. Black holes do not necessarily radiate away all their mass: they may terminate in a zero-temperature black hole, a naked singularity, or a hot black hole in equilibrium with a ''cosmological'' event horizon. The thermodynamics of black-hole solutions is discussed; entropy is found to be an increasing function of horizon area, and the first law is shown to hold

Explicit Solutions for Generalized (2+1)-Dimensional Nonlinear Zakharov-Kuznetsov Equation

International Nuclear Information System (INIS)

Sun Yuhuai; Ma Zhimin; Li Yan

2010-01-01

The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equation are explored by the method of the improved generalized auxiliary differential equation. Many explicit analytic solutions of the Z-K equation are obtained. The methods used to solve the Z-K equation can be employed in further work to establish new solutions for other nonlinear partial differential equations. (general)

Recursive thoughts on the simulation of the flexible multibody dynamics of slender offshore structures

Science.gov (United States)

Schilder, J.; Ellenbroek, M.; de Boer, A.

2017-12-01

In this work, the floating frame of reference formulation is used to create a flexible multibody model of slender offshore structures such as pipelines and risers. It is shown that due to the chain-like topology of the considered structures, the equation of motion can be expressed in terms of absolute interface coordinates. In the presented form, kinematic constraint equations are satisfied explicitly and the Lagrange multipliers are eliminated from the equations. Hence, the structures can be conveniently coupled to finite element or multibody models of for example seabed and vessel. The chain-like topology enables the efficient use of recursive solution procedures for both transient dynamic analysis and equilibrium analysis. For this, the transfer matrix method is used. In order to improve the convergence of the equilibrium analysis, the analytical solution of an ideal catenary is used as an initial configuration, reducing the number of required iterations.

Isotropic extensions of the vacuum solutions in general relativity

Energy Technology Data Exchange (ETDEWEB)

Molina, C. [Universidade de Sao Paulo (USP), SP (Brazil); Martin-Moruno, Prado [Victoria University of Wellington (New Zealand); Gonzalez-Diaz, Pedro F. [Consejo Superior de Investigaciones Cientificas, Madrid (Spain)

2012-07-01

Full text: Spacetimes described by spherically symmetric solutions of Einstein's equations are of paramount importance both in astrophysical applications and theoretical considerations. And among those, black holes are highlighted. In vacuum, Birkhoff's theorem and its generalizations to non-asymptotically flat cases uniquely fix the metric as the Schwarzschild, Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter geometries, the vacuum solutions of the usual general relativity with zero, positive or negative values for the cosmological constant, respectively. In this work we are mainly interested in black holes in a cosmological environment. Of the two main assumptions of the cosmological principle, homogeneity is lost when compact objects are considered. Nevertheless isotropy is still possible, and we enforce this condition. Within this context, we investigate spatially isotropic solutions close - continuously deformable - to the usual vacuum solutions. We obtain isotropic extensions of the usual spherically symmetric vacuum geometries in general relativity. Exact and perturbative solutions are derived. Maximal extensions are constructed and their causal structures are discussed. The classes of geometries obtained include black holes in compact and non-compact universes, wormholes in the interior region of cosmological horizons, and anti-de Sitter geometries with excess/deficit solid angle. The tools developed here are applicable in more general contexts, with extensions subjected to other constraints. (author)

Design and Implementation of Recursive Model Predictive Control for Permanent Magnet Synchronous Motor Drives

Directory of Open Access Journals (Sweden)

Xuan Wu

2015-01-01

Full Text Available In order to control the permanent-magnet synchronous motor system (PMSM with different disturbances and nonlinearity, an improved current control algorithm for the PMSM systems using recursive model predictive control (RMPC is developed in this paper. As the conventional MPC has to be computed online, its iterative computational procedure needs long computing time. To enhance computational speed, a recursive method based on recursive Levenberg-Marquardt algorithm (RLMA and iterative learning control (ILC is introduced to solve the learning issue in MPC. RMPC is able to significantly decrease the computation cost of traditional MPC in the PMSM system. The effectiveness of the proposed algorithm has been verified by simulation and experimental results.

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 ...

Estimation of Mechanical Signals in Induction Motors using the Recursive Prediction Error Method

DEFF Research Database (Denmark)

Børsting, H.; Knudsen, Morten; Rasmussen, Henrik

1993-01-01

Sensor feedback of mechanical quantities for control applications in induction motors is troublesome and relative expensive. In this paper a recursive prediction error (RPE) method has successfully been used to estimate the angular rotor speed ........Sensor feedback of mechanical quantities for control applications in induction motors is troublesome and relative expensive. In this paper a recursive prediction error (RPE) method has successfully been used to estimate the angular rotor speed .....

Parameter Estimation of a Closed Loop Coupled Tank Time Varying System using Recursive Methods

International Nuclear Information System (INIS)

Basir, Siti Nora; Yussof, Hanafiah; Shamsuddin, Syamimi; Selamat, Hazlina; Zahari, Nur Ismarrubie

2013-01-01

This project investigates the direct identification of closed loop plant using discrete-time approach. The uses of Recursive Least Squares (RLS), Recursive Instrumental Variable (RIV) and Recursive Instrumental Variable with Centre-Of-Triangle (RIV + COT) in the parameter estimation of closed loop time varying system have been considered. The algorithms were applied in a coupled tank system that employs covariance resetting technique where the time of parameter changes occur is unknown. The performances of all the parameter estimation methods, RLS, RIV and RIV + COT were compared. The estimation of the system whose output was corrupted with white and coloured noises were investigated. Covariance resetting technique successfully executed when the parameters change. RIV + COT gives better estimates than RLS and RIV in terms of convergence and maximum overshoot

Parametric output-only identification of time-varying structures using a kernel recursive extended least squares TARMA approach

Science.gov (United States)

Ma, Zhi-Sai; Liu, Li; Zhou, Si-Da; Yu, Lei; Naets, Frank; Heylen, Ward; Desmet, Wim

2018-01-01

The problem of parametric output-only identification of time-varying structures in a recursive manner is considered. A kernelized time-dependent autoregressive moving average (TARMA) model is proposed by expanding the time-varying model parameters onto the basis set of kernel functions in a reproducing kernel Hilbert space. An exponentially weighted kernel recursive extended least squares TARMA identification scheme is proposed, and a sliding-window technique is subsequently applied to fix the computational complexity for each consecutive update, allowing the method to operate online in time-varying environments. The proposed sliding-window exponentially weighted kernel recursive extended least squares TARMA method is employed for the identification of a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudo-linear regression TARMA method via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics. Furthermore, the comparisons demonstrate the superior achievable accuracy, lower computational complexity and enhanced online identification capability of the proposed kernel recursive extended least squares TARMA approach.

General classical solutions in the noncommutative CP{sup N-1} model

Energy Technology Data Exchange (ETDEWEB)

Foda, O.; Jack, I.; Jones, D.R.T

2002-10-31

We give an explicit construction of general classical solutions for the noncommutative CP{sup N-1} model in two dimensions, showing that they correspond to integer values for the action and topological charge. We also give explicit solutions for the Dirac equation in the background of these general solutions and show that the index theorem is satisfied.

Topological recursion for Gaussian means and cohomological field theories

Science.gov (United States)

Andersen, J. E.; Chekhov, L. O.; Norbury, P.; Penner, R. C.

2015-12-01

We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich-Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M g,s disc (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M g,1 for all g in three ways: using the refined Harer-Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly.

A theory of general solutions of 3D problems in 1D hexagonal quasicrystals

International Nuclear Information System (INIS)

Gao Yang; Xu Sipeng; Zhao Baosheng

2008-01-01

A theory of general solutions of three-dimensional (3D) problems is developed for the coupled equilibrium equations in 1D hexagonal quasicrystals (QCs), and two new general solutions, which are called generalized Lekhnitskii-Hu-Nowacki (LHN) and Elliott-Lodge (E-L) solutions, respectively, are presented based on three theorems. As a special case, the generalized LHN solution is obtained from our previous general solution by introducing three high-order displacement functions. For further simplification, considering three cases in which three characteristic roots are distinct or possibly equal to each other, the generalized E-L solution shall take different forms, and be expressed in terms of four quasi-harmonic functions which are very simple and useful. It is proved that the general solution presented by Peng and Fan is consistent with one case of the generalized E-L solution, while does not include the other two cases. It is important to note that generalized LHN and E-L solutions are complete in z-convex domains, while incomplete in the usual non-z-convex domains

General solution of string inspired nonlinear equations

International Nuclear Information System (INIS)

Bandos, I.A.; Ivanov, E.; Kapustnikov, A.A.; Ulanov, S.A.

1998-07-01

We present the general solution of the system of coupled nonlinear equations describing dynamics of D-dimensional bosonic string in the geometric (or embedding) approach. The solution is parametrized in terms of two sets of the left- and right-moving Lorentz harmonic variables providing a special coset space realization of the product of two (D-2) dimensional spheres S D-2 = SO(1,D-1)/SO(1,1)xSO(D-2) contained in K D-2 . (author)

Toward the Soundness of Sense Structure Definitions in Thesaurus-Dictionaries. Parsing Problems and Solutions

Directory of Open Access Journals (Sweden)

Neculai Curteanu

2012-10-01

Full Text Available In this paper we point out some difficult problems of thesaurus-dictionary entry parsing, relying on the parsing technology of SCD (Segmentation-Cohesion-Dependency configurations, successfully applied on six largest thesauri -- Romanian (2, French, German (2, and Russian. \\textbf{Challenging Problems:} \\textbf{(a}~Intricate and~/~or recursive structures of the lexicographic segments met in the entries of certain thesauri; \\textbf{(b}~Cyclicity (recursive calls of some sense marker classes on marker sequences; \\textbf{(c}~Establishing the hypergraph-driven dependencies between all the atomic and non-atomic sense definitions. Classical approach to solve these parsing problems is hard mainly because of depth-first search of sense definitions and markers, the substantial complexity of entries, and the sense tree dynamic construction embodied within these parsers. \\textbf{SCD-based Parsing Solutions:} \\textbf{(a}~The SCD parsing method is a procedural tool, completely formal grammar-free, handling the recursive structure of the lexicographic segments by procedural non-recursive calls performed on the SCD parsing configurations of the entry structure. \\textbf{(b}~For dealing with cyclicity (recursive calls between secondary sense markers and the sense enumeration markers, we proposed the Enumeration Closing Condition, sometimes coupled with New{\\_}Paragraphs typographic markers transformed into numeral sense enumeration. \\textbf{(c}~These problems, their lexicographic modeling and parsing solutions are addressed to both dictionary parser programmers to experience the SCD-based parsing method, as well as to lexicographers and thesauri designers for tailoring balanced lexical-semantics granularities and sounder sense tree definitions of the dictionary entries.

All-Pole Recursive Digital Filters Design Based on Ultraspherical Polynomials

Directory of Open Access Journals (Sweden)

N. Stojanovic

2014-09-01

Full Text Available A simple method for approximation of all-pole recursive digital filters, directly in digital domain, is described. Transfer function of these filters, referred to as Ultraspherical filters, is controlled by order of the Ultraspherical polynomial, nu. Parameter nu, restricted to be a nonnegative real number (nu ≥ 0, controls ripple peaks in the passband of the magnitude response and enables a trade-off between the passband loss and the group delay response of the resulting filter. Chebyshev filters of the first and of the second kind, and also Legendre and Butterworth filters are shown to be special cases of these allpole recursive digital filters. Closed form equations for the computation of the filter coefficients are provided. The design technique is illustrated with examples.

Consumption-Portfolio Optimization with Recursive Utility in Incomplete Markets

DEFF Research Database (Denmark)

Kraft, Holger; Seifried, Frank Thomas; Steffensen, Mogens

2013-01-01

In an incomplete market, we study the optimal consumption-portfolio decision of an investor with recursive preferences of Epstein–Zin type. Applying a classical dynamic programming approach, we formulate the associated Hamilton–Jacobi–Bellman equation and provide a suitable verification theorem...

A recursive Formulation of the Inversion of symmetric positive defite matrices in packed storage data format

DEFF Research Database (Denmark)

Andersen, Bjarne Stig; Gunnels, John A.; Gustavson, Fred

2002-01-01

A new Recursive Packed Inverse Calculation Algorithm for symmetric positive definite matrices has been developed. The new Recursive Inverse Calculation algorithm uses minimal storage, \\$n(n+1)/2\\$, and has nearly the same performance as the LAPACK full storage algorithm using \\$n\\^2\\$ memory words...

General solutions of second-order linear difference equations of Euler type

Directory of Open Access Journals (Sweden)

Akane Hongyo

2017-01-01

Full Text Available The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \\(y^{\\prime\\prime}+(\\lambda/t^2y=0\\ or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.

Non-abelian Z-theory: Berends-Giele recursion for the α{sup ′}-expansion of disk integrals

Energy Technology Data Exchange (ETDEWEB)

Mafra, Carlos R. [STAG Research Centre and Mathematical Sciences, University of Southampton,Southampton (United Kingdom); Institute for Advanced Study, School of Natural Sciences,Einstein Drive, Princeton, NJ 08540 (United States); Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Am Mühlenberg 1, 14476 Potsdam (Germany)

2017-01-09

We present a recursive method to calculate the α{sup ′}-expansion of disk integrals arising in tree-level scattering of open strings which resembles the approach of Berends and Giele to gluon amplitudes. Following an earlier interpretation of disk integrals as doubly partial amplitudes of an effective theory of scalars dubbed as Z-theory, we pinpoint the equation of motion of Z-theory from the Berends-Giele recursion for its tree amplitudes. A computer implementation of this method including explicit results for the recursion up to order α{sup ′7} is made available on the website repo.or.cz/BGap.git.

Source localization using recursively applied and projected (RAP) MUSIC

Energy Technology Data Exchange (ETDEWEB)

Mosher, J.C. [Los Alamos National Lab., NM (United States); Leahy, R.M. [Univ. of Southern California, Los Angeles, CA (United States). Signal and Image Processing Inst.

1998-03-01

A new method for source localization is described that is based on a modification of the well known multiple signal classification (MUSIC) algorithm. In classical MUSIC, the array manifold vector is projected onto an estimate of the signal subspace, but errors in the estimate can make location of multiple sources difficult. Recursively applied and projected (RAP) MUSIC uses each successively located source to form an intermediate array gain matrix, and projects both the array manifold and the signal subspace estimate into its orthogonal complement. The MUSIC projection is then performed in this reduced subspace. Using the metric of principal angles, the authors describe a general form of the RAP-MUSIC algorithm for the case of diversely polarized sources. Through a uniform linear array simulation, the authors demonstrate the improved Monte Carlo performance of RAP-MUSIC relative to MUSIC and two other sequential subspace methods, S and IES-MUSIC.

A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation

International Nuclear Information System (INIS)

Sabry, R.; Zahran, M.A.; Fan Engui

2004-01-01

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

Travelling Solitary Wave Solutions for Generalized Time-delayed Burgers-Fisher Equation

International Nuclear Information System (INIS)

Deng Xijun; Han Libo; Li Xi

2009-01-01

In this paper, travelling wave solutions for the generalized time-delayed Burgers-Fisher equation are studied. By using the first-integral method, which is based on the ring theory of commutative algebra, we obtain a class of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation. A minor error in the previous article is clarified. (general)

Supersymmetric solutions of N =(1 ,1 ) general massive supergravity

Science.gov (United States)

Deger, N. S.; Nazari, Z.; Sarıoǧlu, Ö.

2018-05-01

We construct supersymmetric solutions of three-dimensional N =(1 ,1 ) general massive supergravity (GMG). Solutions with a null Killing vector are, in general, pp-waves. We identify those that appear at critical points of the model, some of which do not exist in N =(1 ,1 ) new massive supergravity (NMG). In the timelike case, we find that many solutions are common with NMG, but there is a new class that is genuine to GMG, two members of which are stationary Lifshitz and timelike squashed AdS spacetimes. We also show that in addition to the fully supersymmetric AdS vacuum, there is a second AdS background with a nonzero vector field that preserves 1 /4 supersymmetry.

Recursivity: A Working Paper on Rhetoric and "Mnesis"

Science.gov (United States)

Stormer, Nathan

2013-01-01

This essay proposes the genealogical study of remembering and forgetting as recursive rhetorical capacities that enable discourse to place itself in an ever-changing present. "Mnesis" is a meta-concept for the arrangements of remembering and forgetting that enable rhetoric to function. Most of the essay defines the materiality of "mnesis", first…

Convergence and periodic solutions for the input impedance of a standard ladder network

International Nuclear Information System (INIS)

Ucak, C; Acar, C

2007-01-01

The input impedance of an infinite ladder network is computed by using the recursive relation and by assuming that the input impedance does not change when a new block is added to the network. However, this assumption is not true in general and standard textbooks do not always treat these networks correctly. This paper develops a general solution to obtain the input impedance of a standard ladder network of impedances and admittances for any number of blocks. Then, this result is used to provide the convergence condition for the infinite ladder network. The conditions which lead to periodic input impedance are exploited. It is shown that there are infinite numbers of periodic points and no paradoxical behaviour exists in the standard ladder network

New solutions of Heun's general equation

Energy Technology Data Exchange (ETDEWEB)

Ishkhanyan, Artur [Engineering Center of Armenian National Academy of Sciences, Ashtarak (Armenia); Suominen, Kalle-Antti [Helsinki Institute of Physics, PL 64, Helsinki (Finland)

2003-02-07

We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)

Differential constraints for bounded recursive identification with multivariate splines

NARCIS (Netherlands)

De Visser, C.C.; Chu, Q.P.; Mulder, J.A.

2011-01-01

The ability to perform online model identification for nonlinear systems with unknown dynamics is essential to any adaptive model-based control system. In this paper, a new differential equality constrained recursive least squares estimator for multivariate simplex splines is presented that is able

Minimal solution of general dual fuzzy linear systems

International Nuclear Information System (INIS)

Abbasbandy, S.; Otadi, M.; Mosleh, M.

2008-01-01

Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered

BPSK Receiver Based on Recursive Adaptive Filter with Remodulation

Directory of Open Access Journals (Sweden)

N. Milosevic

2011-12-01

Full Text Available This paper proposes a new binary phase shift keying (BPSK signal receiver intended for reception under conditions of significant carrier frequency offsets. The recursive adaptive filter with least mean squares (LMS adaptation is used. The proposed receiver has a constant, defining the balance between the recursive and the nonrecursive part of the filter, whose proper choice allows a simple construction of the receiver. The correct choice of this parameter could result in unitary length of the filter. The proposed receiver has performance very close to the performance of the BPSK receiver with perfect frequency synchronization, in a wide range of frequency offsets (plus/minus quarter of the signal bandwidth. The results obtained by the software simulation are confirmed by the experimental results measured on the receiver realized with the universal software radio peripheral (USRP, with the baseband signal processing at personal computer (PC.

Mining IP to Domain Name Interactions to Detect DNS Flood Attacks on Recursive DNS Servers

Directory of Open Access Journals (Sweden)

Roberto Alonso

2016-08-01

Full Text Available The Domain Name System (DNS is a critical infrastructure of any network, and, not surprisingly a common target of cybercrime. There are numerous works that analyse higher level DNS traffic to detect anomalies in the DNS or any other network service. By contrast, few efforts have been made to study and protect the recursive DNS level. In this paper, we introduce a novel abstraction of the recursive DNS traffic to detect a flooding attack, a kind of Distributed Denial of Service (DDoS. The crux of our abstraction lies on a simple observation: Recursive DNS queries, from IP addresses to domain names, form social groups; hence, a DDoS attack should result in drastic changes on DNS social structure. We have built an anomaly-based detection mechanism, which, given a time window of DNS usage, makes use of features that attempt to capture the DNS social structure, including a heuristic that estimates group composition. Our detection mechanism has been successfully validated (in a simulated and controlled setting and with it the suitability of our abstraction to detect flooding attacks. To the best of our knowledge, this is the first time that work is successful in using this abstraction to detect these kinds of attacks at the recursive level. Before concluding the paper, we motivate further research directions considering this new abstraction, so we have designed and tested two additional experiments which exhibit promising results to detect other types of anomalies in recursive DNS servers.

Mining IP to Domain Name Interactions to Detect DNS Flood Attacks on Recursive DNS Servers.

Science.gov (United States)

Alonso, Roberto; Monroy, Raúl; Trejo, Luis A

2016-08-17

The Domain Name System (DNS) is a critical infrastructure of any network, and, not surprisingly a common target of cybercrime. There are numerous works that analyse higher level DNS traffic to detect anomalies in the DNS or any other network service. By contrast, few efforts have been made to study and protect the recursive DNS level. In this paper, we introduce a novel abstraction of the recursive DNS traffic to detect a flooding attack, a kind of Distributed Denial of Service (DDoS). The crux of our abstraction lies on a simple observation: Recursive DNS queries, from IP addresses to domain names, form social groups; hence, a DDoS attack should result in drastic changes on DNS social structure. We have built an anomaly-based detection mechanism, which, given a time window of DNS usage, makes use of features that attempt to capture the DNS social structure, including a heuristic that estimates group composition. Our detection mechanism has been successfully validated (in a simulated and controlled setting) and with it the suitability of our abstraction to detect flooding attacks. To the best of our knowledge, this is the first time that work is successful in using this abstraction to detect these kinds of attacks at the recursive level. Before concluding the paper, we motivate further research directions considering this new abstraction, so we have designed and tested two additional experiments which exhibit promising results to detect other types of anomalies in recursive DNS servers.

Exact solutions of the one-dimensional generalized modified complex Ginzburg-Landau equation

International Nuclear Information System (INIS)

Yomba, Emmanuel; Kofane, Timoleon Crepin

2003-01-01

The one-dimensional (1D) generalized modified complex Ginzburg-Landau (MCGL) equation for the traveling wave systems is analytically studied. Exact solutions of this equation are obtained using a method which combines the Painleve test for integrability in the formalism of Weiss-Tabor-Carnevale and Hirota technique of bilinearization. We show that pulses, fronts, periodic unbounded waves, sources, sinks and solution as collision between two fronts are the important coherent structures that organize much of the dynamical properties of these traveling wave systems. The degeneracies of the 1D generalized MCGL equation are examined as well as several of their solutions. These degeneracies include two important equations: the 1D generalized modified Schroedinger equation and the 1D generalized real modified Ginzburg-Landau equation. We obtain that the one parameter family of traveling localized source solutions called 'Nozaki-Bekki holes' become a subfamily of the dark soliton solutions in the 1D generalized modified Schroedinger limit

Solution for state constrained optimal control problems applied to power split control for hybrid vehicles

NARCIS (Netherlands)

Keulen, van T.A.C.; Gillot, J.; Jager, de A.G.; Steinbuch, M.

2014-01-01

This paper presents a numerical solution for scalar state constrained optimal control problems. The algorithm rewrites the constrained optimal control problem as a sequence of unconstrained optimal control problems which can be solved recursively as a two point boundary value problem. The solution

Charged Analogues of Henning Knutsen Type Solutions in General Relativity

Science.gov (United States)

Gupta, Y. K.; Kumar, Sachin; Pratibha

2011-11-01

In the present article, we have found charged analogues of Henning Knutsen's interior solutions which join smoothly to the Reissner-Nordstrom metric at the pressure free interface. The solutions are singularity free and analyzed numerically with respect to pressure, energy-density and charge-density in details. The solutions so obtained also present the generalization of A.L. Mehra's solutions.

Theory of Mind, linguistic recursion and autism spectrum disorder

DEFF Research Database (Denmark)

Polyanskaya, Irina; Blackburn, Patrick Rowan; Braüner, Torben

2017-01-01

In this paper we give the motivation for and discuss the design of an experiment investigating whether the acquisition of linguistic recur-sion helps children with Autism Spectrum Disorder (ASD) develop second-order false belief skills. We first present the relevant psycho-logical concepts (in...

Algebraic computability and enumeration models recursion theory and descriptive complexity

CERN Document Server

Nourani, Cyrus F

2016-01-01

This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic type...

Model-based Recursive Partitioning for Subgroup Analyses

OpenAIRE

Seibold, Heidi; Zeileis, Achim; Hothorn, Torsten

2016-01-01

The identification of patient subgroups with differential treatment effects is the first step towards individualised treatments. A current draft guideline by the EMA discusses potentials and problems in subgroup analyses and formulated challenges to the development of appropriate statistical procedures for the data-driven identification of patient subgroups. We introduce model-based recursive partitioning as a procedure for the automated detection of patient subgroups that are identifiable by...

Recursive prediction error methods for online estimation in nonlinear state-space models

Directory of Open Access Journals (Sweden)

Dag Ljungquist

1994-04-01

Full Text Available Several recursive algorithms for online, combined state and parameter estimation in nonlinear state-space models are discussed in this paper. Well-known algorithms such as the extended Kalman filter and alternative formulations of the recursive prediction error method are included, as well as a new method based on a line-search strategy. A comparison of the algorithms illustrates that they are very similar although the differences can be important for the online tracking capabilities and robustness. Simulation experiments on a simple nonlinear process show that the performance under certain conditions can be improved by including a line-search strategy.

Evaluation of the Kubo formula for the conductivity using the recursion method

International Nuclear Information System (INIS)

Yeyati, A.L.; Weissmann, M.; Anda, E.

1988-09-01

We propose a numerical algorithm based on the recursion method to calculate the conductivity of a disordered system described by a tight-binding Hamiltonian. It has the advantage that the density of states and the conductivity can be obtained in a single recursion calculation. The method is applied to simple one and two-dimensional incommensurate systems in order to check the validity of the assumptions made and the numerical efficiency. The calculated conductivity shows a clear drop when the Fermi energy crosses a mobility edge. Potential applications of this work to other systems are discussed. (author). 13 refs, 9 figs

Recursive estimation techniques for detection of small objects in infrared image data

Science.gov (United States)

Zeidler, J. R.; Soni, T.; Ku, W. H.

1992-04-01

This paper describes a recursive detection scheme for point targets in infrared (IR) images. Estimation of the background noise is done using a weighted autocorrelation matrix update method and the detection statistic is calculated using a recursive technique. A weighting factor allows the algorithm to have finite memory and deal with nonstationary noise characteristics. The detection statistic is created by using a matched filter for colored noise, using the estimated noise autocorrelation matrix. The relationship between the weighting factor, the nonstationarity of the noise and the probability of detection is described. Some results on one- and two-dimensional infrared images are presented.

Positive solution of a time and energy dependent neutron transport problem

International Nuclear Information System (INIS)

Pao, C.V.

1975-01-01

A constructive method is given for the determination of a solution and an existence--uniqueness theorem for some nonlinear time and energy dependent neutron transport problems, including the linear transport system. The geometry of the medium under consideration is allowed to be either bounded or unbounded which includes the geometry of a finite or infinite cylinder, a half-space and the whole space R/subm/ (m=1,2,center-dotcenter-dotcenter-dot). Our approach to the problem is by successive approximation which leads to various recursion formulas for the approximations in terms of explicit integrations. It is shown under some Lipschitz conditions on the nonlinear functions, which describe the process of neutrons absorption, fission, and scattering, that the sequence of approximations converges to a unique positive solution. Since these conditions are satisfied by the linear transport equation, all the results for the nonlinear system are valid for the linear transport problem. In the general nonlinear problem, the existence of both local and global solutions are discussed, and an iterative process for the construction of the solution is given

Analysis of litter size and average litter weight in pigs using a recursive model

DEFF Research Database (Denmark)

Varona, Luis; Sorensen, Daniel; Thompson, Robin

2007-01-01

An analysis of litter size and average piglet weight at birth in Landrace and Yorkshire using a standard two-trait mixed model (SMM) and a recursive mixed model (RMM) is presented. The RMM establishes a one-way link from litter size to average piglet weight. It is shown that there is a one......-to-one correspondence between the parameters of SMM and RMM and that they generate equivalent likelihoods. As parameterized in this work, the RMM tests for the presence of a recursive relationship between additive genetic values, permanent environmental effects, and specific environmental effects of litter size......, on average piglet weight. The equivalent standard mixed model tests whether or not the covariance matrices of the random effects have a diagonal structure. In Landrace, posterior predictive model checking supports a model without any form of recursion or, alternatively, a SMM with diagonal covariance...

Explicit flow equations and recursion operator of the ncKP hierarchy

International Nuclear Information System (INIS)

He, Jingsong; Wang, Lihong; Tu, Junyi; Li, Xiaodong

2011-01-01

The explicit expression of the flow equations of the noncommutative Kadomtsev–Petviashvili (ncKP) hierarchy is derived. Compared with the flow equations of the KP hierarchy, our result shows that the additional terms in the flow equations of the ncKP hierarchy indeed consist of commutators of dynamical coordinates {u i }. The recursion operator for the flow equations under n-reduction is presented. Further, under 2-reduction, we calculate a nonlocal recursion operator Φ(2) of the noncommutative Korteweg–de Vries(ncKdV) hierarchy, which generates a hierarchy of local, higher-order flows. Thus we solve the open problem proposed by Olver and Sokolov (1998 Commun. Math. Phys. 193 245–68)

Berends-Giele recursions and the BCJ duality in superspace and components

Energy Technology Data Exchange (ETDEWEB)

Mafra, Carlos R. [Institute for Advanced Study, School of Natural Sciences,Einstein Drive, Princeton, NJ 08540 (United States); DAMTP, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Am Muehlenberg, 14476 Potsdam (Germany)

2016-03-15

The recursive method of Berends and Giele to compute tree-level gluon amplitudes is revisited using the framework of ten-dimensional super Yang-Mills. First, we prove that the pure spinor formula to compute SYM tree amplitudes derived in 2010 reduces to the standard Berends-Giele formula from the 80s when restricted to gluon amplitudes and additionally determine the fermionic completion. Second, using BRST cohomology manipulations in superspace, alternative representations of the component amplitudes are explored and the Bern-Carrasco-Johansson relations among partial tree amplitudes are derived in a novel way. Finally, it is shown how the supersymmetric components of manifestly local BCJ-satisfying tree-level numerators can be computed in a recursive fashion.

Berends-Giele recursions and the BCJ duality in superspace and components

International Nuclear Information System (INIS)

Mafra, Carlos R.; Schlotterer, Oliver

2016-01-01

The recursive method of Berends and Giele to compute tree-level gluon amplitudes is revisited using the framework of ten-dimensional super Yang-Mills. First, we prove that the pure spinor formula to compute SYM tree amplitudes derived in 2010 reduces to the standard Berends-Giele formula from the 80s when restricted to gluon amplitudes and additionally determine the fermionic completion. Second, using BRST cohomology manipulations in superspace, alternative representations of the component amplitudes are explored and the Bern-Carrasco-Johansson relations among partial tree amplitudes are derived in a novel way. Finally, it is shown how the supersymmetric components of manifestly local BCJ-satisfying tree-level numerators can be computed in a recursive fashion.

Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem

Science.gov (United States)

Badia, Santiago; Martín, Alberto F.; Planas, Ramon

2014-10-01

The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 × 2 block matrix, and consider an LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknowns, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.

Exact solutions of generalized Zakharov and Ginzburg-Landau equations

International Nuclear Information System (INIS)

Zhang Jinliang; Wang Mingliang; Gao Kequan

2007-01-01

By using the homogeneous balance principle, the exact solutions of the generalized Zakharov equations and generalized Ginzburg-Landau equation are obtained with the aid of a set of subsidiary higher-order ordinary differential equations (sub-equations for short)

Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation

International Nuclear Information System (INIS)

Pandir, Yusuf; Gurefe, Yusuf; Misirli, Emine

2013-01-01

In this paper, we study the Kadomtsev-Petviashvili equation with generalized evolution and derive some new results using the approach called the trial equation method. The obtained results can be expressed by the soliton solutions, rational function solutions, elliptic function solutions and Jacobi elliptic function solutions. In the discussion, we give a new version of the trial equation method for nonlinear differential equations.

Recursive Ultrasound Imaging

DEFF Research Database (Denmark)

Nikolov, Svetoslav; Gammelmark, Kim; Jensen, Jørgen Arendt

1999-01-01

This paper presents a new imaging method, applicable for both 2D and 3D imaging. It is based on Synthetic Transmit Aperture Focusing, but unlike previous approaches a new frame is created after every pulse emission. The elements from a linear transducer array emit pulses one after another. The same...... transducer element is used after N-xmt emissions. For each emission the signals from the individual elements are beam-formed in parallel for all directions in the image. A new frame is created by adding the new RF lines to the RF lines from the previous frame. The RF data recorded at the previous emission...... with the same element are subtracted. This yields a new image after each pulse emission and can give a frame rate of e.g. 5000 images/sec. The paper gives a derivation of the recursive imaging technique and compares simulations for fast B-mode imaging with measurements. A low value of N-xmt is necessary...

Recursive ultrasound imaging

DEFF Research Database (Denmark)

2000-01-01

A method and an apparatus for recursive ultrasound imaging is presented. The method uses a Synthetic Transmit Aperture, but unlike previous approaches a new frame is created at every pulse emission. In receive, parallel beam forming is implemented. The beam formed RF data is added to the previously...... created RF lines. To keep the level of the signal, the RF data obtained previously, when emitting with the same element is subtracted from the RF lines. Up to 5000 frames/sec can be achieved for a tissue depth of 15 cm with a speed of sound of c = 1540 m/s. The high frame rate makes continuous imaging...... data possible, which can significantly enhance flow imaging. A point spread function 2° wide at -6 dB and grating lobes of $m(F) -50 dB is obtained with a 64 elements phased array with a central frequency ƒ¿0? = 3 MHz using a sparse transmit aperture using only 10 elements (N¿xmt? = 10) during pulse...

The Free Energy in the Derrida-Retaux Recursive Model

Science.gov (United States)

Hu, Yueyun; Shi, Zhan

2018-05-01

We are interested in a simple max-type recursive model studied by Derrida and Retaux (J Stat Phys 156:268-290, 2014) in the context of a physics problem, and find a wide range for the exponent in the free energy in the nearly supercritical regime.

A metric model of lambda calculus with guarded recursion

DEFF Research Database (Denmark)

Birkedal, Lars; Schwinghammer, Jan; Støvring, Kristian

2010-01-01

We give a model for Nakano’s typed lambda calculus with guarded recursive definitions in a category of metric spaces. By proving a computational adequacy result that relates the interpretation with the operational semantics, we show that the model can be used to reason about contextual equivalence....

Symbolic Reachability for Process Algebras with Recursive Data Types

NARCIS (Netherlands)

Blom, Stefan; van de Pol, Jan Cornelis; Fitzgerald, J.S.; Haxthausen, A.E.; Yenigun, H.

2008-01-01

In this paper, we present a symbolic reachability algorithm for process algebras with recursive data types. Like the various saturation based algorithms of Ciardo et al, the algorithm is based on partitioning of the transition relation into events whose influence is local. As new features, our

General solution of the Dirac equation for quasi-two-dimensional electrons

Energy Technology Data Exchange (ETDEWEB)

Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)

2016-06-15

The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.

Functional Dual Adaptive Control with Recursive Gaussian Process Model

International Nuclear Information System (INIS)

Prüher, Jakub; Král, Ladislav

2015-01-01

The paper deals with dual adaptive control problem, where the functional uncertainties in the system description are modelled by a non-parametric Gaussian process regression model. Current approaches to adaptive control based on Gaussian process models are severely limited in their practical applicability, because the model is re-adjusted using all the currently available data, which keeps growing with every time step. We propose the use of recursive Gaussian process regression algorithm for significant reduction in computational requirements, thus bringing the Gaussian process-based adaptive controllers closer to their practical applicability. In this work, we design a bi-criterial dual controller based on recursive Gaussian process model for discrete-time stochastic dynamic systems given in an affine-in-control form. Using Monte Carlo simulations, we show that the proposed controller achieves comparable performance with the full Gaussian process-based controller in terms of control quality while keeping the computational demands bounded. (paper)

Study of recursive model for pole-zero cancellation circuit

International Nuclear Information System (INIS)

Zhou Jianbin; Zhou Wei; Hong Xu; Hu Yunchuan; Wan Xinfeng; Du Xin; Wang Renbo

2014-01-01

The output of charge sensitive amplifier (CSA) is a negative exponential signal with long decay time which will result in undershoot after C-R differentiator. Pole-zero cancellation (PZC) circuit is often applied to eliminate undershoot in many radiation detectors. However, it is difficult to use a zero created by PZC circuit to cancel a pole in CSA output signal accurately because of the influences of electronic components inherent error and environmental factors. A novel recursive model for PZC circuit is presented based on Kirchhoff's Current Law (KCL) in this paper. The model is established by numerical differentiation algorithm between the input and the output signal. Some simulation experiments for a negative exponential signal are carried out using Visual Basic for Application (VBA) program and a real x-ray signal is also tested. Simulated results show that the recursive model can reduce the time constant of input signal and eliminate undershoot. (authors)

Exact solutions of nonlinear generalizations of the Klein Gordon and Schrodinger equations

International Nuclear Information System (INIS)

Burt, P.B.

1978-01-01

Exact solutions of sine Gordon and multiple sine Gordon equations are constructed in terms of solutions of a linear base equation, the Klein Gordon equation and also in terms of nonlinear base equations where the nonlinearity is polynomial in the dependent variable. Further, exact solutions of nonlinear generalizations of the Schrodinger equation and of additional nonlinear generalizations of the Klein Gordon equation are constructed in terms of solutions of linear base equations. Finally, solutions with spherical symmetry, of nonlinear Klein Gordon equations are given. 14 references

Solution of generalized control system equations at steady state

International Nuclear Information System (INIS)

Vilim, R.B.

1987-01-01

Although a number of reactor systems codes feature generalized control system models, none of the models offer a steady-state solution finder. Indeed, if a transient is to begin from steady-state conditions, the user must provide estimates for the control system initial conditions and run a null transient until the plant converges to steady state. Several such transients may have to be run before values for control system demand signals are found that produce the desired plant steady state. The intent of this paper is (a) to present the control system equations assumed in the SASSYS reactor systems code and to identify the appropriate set of initial conditions, (b) to describe the generalized block diagram approach used to represent these equations, and (c) to describe a solution method and algorithm for computing these initial conditions from the block diagram. The algorithm has been installed in the SASSYS code for use with the code's generalized control system model. The solution finder greatly enhances the effectiveness of the code and the efficiency of the user in running it

General analytical shakedown solution for structures with kinematic hardening materials

Science.gov (United States)

Guo, Baofeng; Zou, Zongyuan; Jin, Miao

2016-09-01

The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems: a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.

A database for extract solutions in general relativity

International Nuclear Information System (INIS)

Horvath, I.; Horvath, Zs.; Lukacs, B.

1993-07-01

The field of equations of General Relativity are coupled second order partial differential equations. Therefore no general method is known to generate solutions for prescribed initial and boundary conditions. In addition, the meaning of the particular coordinates cannot be known until the metric is not found. Therefore the result must permit arbitrary coordinate transformations, i.e. most kinds of approximating methods are improper. So exact solutions are necessary and each one is an individual product. For storage, retrieval and comparison database handling techniques are needed. A database of 1359 articles is shown (cross-referred at least once) published in 156 more important journals. It can be handled by dBase III plus on IBM PC's. (author) 5 refs.; 5 tabs

Recursive deconvolution of combinatorial chemical libraries.

OpenAIRE

Erb, E; Janda, K D; Brenner, S

1994-01-01

A recursive strategy that solves for the active members of a chemical library is presented. A pentapeptide library with an alphabet of Gly, Leu, Phe, and Tyr (1024 members) was constructed on a solid support by the method of split synthesis. One member of this library (NH2-Tyr-Gly-Gly-Phe-Leu) is a native binder to a beta-endorphin antibody. A variation of the split synthesis approach is used to build the combinatorial library. In four vials, a member of the library's alphabet is coupled to a...

Travelling wave solutions in delayed cooperative systems

International Nuclear Information System (INIS)

Li, Bingtuan; Zhang, Liang

2011-01-01

We establish the existence of travelling wave solutions for delayed cooperative recursions that are allowed to have more than two equilibria. We define an important extended real number that is used to determine the speeds of travelling wave solutions. The results can be applied to a large class of delayed cooperative reaction–diffusion models. We show that for a delayed Lotka–Volterra reaction–diffusion competition model, there exists a finite positive number c * + that can be characterized as the slowest speed of travelling wave solutions connecting two mono-culture equilibria or connecting a mono-culture with the coexistence equilibrium

Recursive Estimation for Dynamical Systems with Different Delay Rates Sensor Network and Autocorrelated Process Noises

Directory of Open Access Journals (Sweden)

Jianxin Feng

2014-01-01

Full Text Available The recursive estimation problem is studied for a class of uncertain dynamical systems with different delay rates sensor network and autocorrelated process noises. The process noises are assumed to be autocorrelated across time and the autocorrelation property is described by the covariances between different time instants. The system model under consideration is subject to multiplicative noises or stochastic uncertainties. The sensor delay phenomenon occurs in a random way and each sensor in the sensor network has an individual delay rate which is characterized by a binary switching sequence obeying a conditional probability distribution. By using the orthogonal projection theorem and an innovation analysis approach, the desired recursive robust estimators including recursive robust filter, predictor, and smoother are obtained. Simulation results are provided to demonstrate the effectiveness of the proposed approaches.

EEG and MEG source localization using recursively applied (RAP) MUSIC

Energy Technology Data Exchange (ETDEWEB)

Mosher, J.C. [Los Alamos National Lab., NM (United States); Leahy, R.M. [University of Southern California, Los Angeles, CA (United States). Signal and Image Processing Inst.

1996-12-31

The multiple signal characterization (MUSIC) algorithm locates multiple asynchronous dipolar sources from electroencephalography (EEG) and magnetoencephalography (MEG) data. A signal subspace is estimated from the data, then the algorithm scans a single dipole model through a three-dimensional head volume and computes projections onto this subspace. To locate the sources, the user must search the head volume for local peaks in the projection metric. Here we describe a novel extension of this approach which we refer to as RAP (Recursively APplied) MUSIC. This new procedure automatically extracts the locations of the sources through a recursive use of subspace projections, which uses the metric of principal correlations as a multidimensional form of correlation analysis between the model subspace and the data subspace. The dipolar orientations, a form of `diverse polarization,` are easily extracted using the associated principal vectors.

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Rasmussen, Kim; Henning, D.; Gabriel, H.

1996-01-01

We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interes...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.......We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...

Computational Error Estimate for the Power Series Solution of Odes ...

African Journals Online (AJOL)

This paper compares the error estimation of power series solution with recursive Tau method for solving ordinary differential equations. From the computational viewpoint, the power series using zeros of Chebyshevpolunomial is effective, accurate and easy to use. Keywords: Lanczos Tau method, Chebyshev polynomial, ...

QCD amplitudes with 2 initial spacelike legs via generalised BCFW recursion

Energy Technology Data Exchange (ETDEWEB)

Kutak, Krzysztof; Hameren, Andreas van; Serino, Mirko [The H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152, 31-342, Cracow (Poland)

2017-02-02

We complete the generalisation of the BCFW recursion relation to the off-shell case, allowing for the computation of tree level scattering amplitudes for full High Energy Factorisation (HEF), i.e. with both incoming partons having a non-vanishing transverse momentum. We provide explicit results for color-ordered amplitudes with two off-shell legs in massless QCD up to 4 point, continuing the program begun in two previous papers. For the 4-fermion amplitudes, which are not BCFW-recursible, we perform a diagrammatic computation, so as to offer a complete set of expressions. We explicitly show and discuss some plots of the squared 2→2 matrix elements as functions of the differences in rapidity and azimuthal angle of the final state particles.

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

International Nuclear Information System (INIS)

Ugurlu, Yavuz; Kaya, Dogan

2008-01-01

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

Smooth Gowdy-symmetric generalized Taub–NUT solutions

International Nuclear Information System (INIS)

Beyer, Florian; Hennig, Jörg

2012-01-01

We study a class of S 3 -Gowdy vacuum models with a regular past Cauchy horizon which we call smooth Gowdy-symmetric generalized Taub–NUT solutions. In particular, we prove the existence of such solutions by formulating a singular initial value problem with asymptotic data on the past Cauchy horizon. We prove that also a future Cauchy horizon exists for generic asymptotic data, and derive an explicit expression for the metric on the future Cauchy horizon in terms of the asymptotic data on the past horizon. This complements earlier results about S 1 ×S 2 -Gowdy models. (paper)

Active control versus recursive backstepping control of a chaotic ...

African Journals Online (AJOL)

In this paper active controllers and recursive backstepping controllers are designed for a third order chaotic system. The performances of these controllers in the control of the dynamics of the chaotic system are investigated numerically and are found to be effective. Comparison of their transient performances show that the ...

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

Energy Technology Data Exchange (ETDEWEB)

Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya36@yahoo.com

2008-04-14

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

A recursive algorithm for trees and forests

OpenAIRE

Guo, Song; Guo, Victor J. W.

2017-01-01

Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on $\\{1,2,\\ldots,n\\}$. Classical formulas for counting various trees such as rooted trees, bipartite trees, tripartite trees, plane trees, $k$-ary plane trees, $k$-edge colored trees follow immediately from our recursive relations.

Using Visualization to Generalize on Quadratic Patterning Tasks

Science.gov (United States)

Kirwan, J. Vince

2017-01-01

Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…

Particular solutions of generalized Euler-Poisson-Darboux equation

Directory of Open Access Journals (Sweden)

Rakhila B. Seilkhanova

2015-01-01

Full Text Available In this article we consider the generalized Euler-Poisson-Darboux equation $$ {u}_{tt}+\\frac{2\\gamma }{t}{{u}_{t}}={u}_{xx}+{u}_{yy} +\\frac{2\\alpha }{x}{{u}_{x}}+\\frac{2\\beta }{y}{{u}_y},\\quad x>0,\\;y>0,\\;t>0. $$ We construct particular solutions in an explicit form expressed by the Lauricella hypergeometric function of three variables. Properties of each constructed solutions have been investigated in sections of surfaces of the characteristic cone. Precisely, we prove that found solutions have singularity $1/r$ at $r\\to 0$, where ${{r}^2}={{( x-{{x}_0}}^2}+{{( y-{{y}_0}}^2}-{{( t-{{t}_0}}^2}$.

Output-Only Modal Parameter Recursive Estimation of Time-Varying Structures via a Kernel Ridge Regression FS-TARMA Approach

Directory of Open Access Journals (Sweden)

Zhi-Sai Ma

2017-01-01

Full Text Available Modal parameter estimation plays an important role in vibration-based damage detection and is worth more attention and investigation, as changes in modal parameters are usually being used as damage indicators. This paper focuses on the problem of output-only modal parameter recursive estimation of time-varying structures based upon parameterized representations of the time-dependent autoregressive moving average (TARMA. A kernel ridge regression functional series TARMA (FS-TARMA recursive identification scheme is proposed and subsequently employed for the modal parameter estimation of a numerical three-degree-of-freedom time-varying structural system and a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudolinear regression FS-TARMA approach via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics in a recursive manner.

Recursive representation of the torus 1-point conformal block

Science.gov (United States)

Hadasz, Leszek; Jaskólski, Zbigniew; Suchanek, Paulina

2010-01-01

The recursive relation for the 1-point conformal block on a torus is derived and used to prove the identities between conformal blocks recently conjectured by Poghossian in [1]. As an illustration of the efficiency of the recurrence method the modular invariance of the 1-point Liouville correlation function is numerically analyzed.

A bijection between phylogenetic trees and plane oriented recursive trees

OpenAIRE

Prodinger, Helmut

2017-01-01

Phylogenetic trees are binary nonplanar trees with labelled leaves, and plane oriented recursive trees are planar trees with an increasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the respective representations a 2-partitions and trapezoidal words.

Recursive subspace identification for in flight modal analysis of airplanes

OpenAIRE

De Cock , Katrien; Mercère , Guillaume; De Moor , Bart

2006-01-01

International audience; In this paper recursive subspace identification algorithms are applied to track the modal parameters of airplanes on-line during test flights. The ability to track changes in the damping ratios and the influence of the forgetting factor are studied through simulations.

A self-applicable online partial evaluator for recursive flowchart languages

DEFF Research Database (Denmark)

Glück, Robert

2012-01-01

This paper describes a self-applicable online partial evaluator for a ¿owchart language with recursive calls. Self-application of the partial evaluator yields generating extensions that are as ef¿cient as those reported in the literature for of¿ine partial evaluation. This result is remarkable...... because it has been assumed that online partial evaluation techniques unavoidably lead to inef¿cient and overgeneralized generating extensions. The purpose of this paper is not to determine which kind of partial evaluation is better, but to show how the problem can be solved by recursive polyvariant...... specialization. The design of the self-applicable online partial evaluator is based on a number of known techniques, but by combining them in a new way this result can be produced. The partial evaluator, its techniques, and its implementation are presented in full. Self-application according to all three...

The Generalized Wronskian Solution to a Negative KdV-mKdV Equation

International Nuclear Information System (INIS)

Liu Yu-Qing; Chen Deng-Yuan; Hu Chao

2012-01-01

A negative KdV-mKdV hierarchy is presented through the KdV-mKdV operator. The generalized Wronskian solution to the negative KdV-mKdV equation is obtained. Some soliton-like solutions and a complexiton solution are presented explicitly as examples. (general)

On global structure of general solution of the Chew-Sow equations

International Nuclear Information System (INIS)

Gerdt, V.P.

1981-01-01

The Chew-Low equations for static p-wave πN-scattering are considered. The equations are formulated in the form of a system of three nonlinear difference equations of the first order which have the general solution depending on three arbitrary periodic functions. An approach to the global construction of the general solution is suggested which is based on the series expansion in powers of one of the arbitrary functions C(ω) determining the structure of the invariant curve for the Chew-Low equations. It is shown that the initial nonlinear problem is reduced to the linear one in every order in C(ω). By means of solving the linear problem the general solution is found in the first-order approximation in C(ω) [ru

A solution for tensor reduction of one-loop N-point functions with N{>=}6

Energy Technology Data Exchange (ETDEWEB)

Fleischer, J. [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2011-11-15

Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop N-point corrections are needed. We study here the tensor reduction for Feynman integrals with N{>=}6. A general, recursive solution by Binoth et al. expresses N-point Feynman integrals of rank R in terms of (N-1)-point Feynman integrals of rank (R-1) (for N{>=}6). We show that the coefficients can be obtained analytically from suitable representations of the metric tensor. Contractions of the tensor integrals with external momenta can be efficiently expressed as well. We consider our approach particularly well suited for automatization. (orig.)

Generalized Sturmian Solutions for Many-Particle Schrödinger Equations

DEFF Research Database (Denmark)

Avery, John; Avery, James Emil

2004-01-01

The generalized Sturmian method for obtaining solutions to the many-particle Schrodinger equation is reviewed. The method makes use of basis functions that are solutions of an approximate Schrodinger equation with a weighted zeroth-order potential. The weighting factors are especially chosen so...

Denotational semantics of recursive types in synthetic guarded domain theory

DEFF Research Database (Denmark)

Møgelberg, Rasmus Ejlers; Paviotti, Marco

2016-01-01

typed lambda calculus with fixed points). This model was intensional in that it could distinguish between computations computing the same result using a different number of fixed point unfoldings. In this work we show how also programming languages with recursive types can be given denotational...

Pedestrian Path Prediction with Recursive Bayesian Filters: A Comparative Study

NARCIS (Netherlands)

Schneider, N.; Gavrila, D.M.

2013-01-01

In the context of intelligent vehicles, we perform a comparative study on recursive Bayesian filters for pedestrian path prediction at short time horizons (< 2s). We consider Extended Kalman Filters (EKF) based on single dynamical models and Interacting Multiple Models (IMM) combining several such

Hybrid recursive active filters for duplexing in RF transmitter front-ends

Science.gov (United States)

Gottardo, Giuseppe; Donati, Giovanni; Musolff, Christian; Fischer, Georg; Felgentreff, Tilman

2016-08-01

Duplex filters in modern base transceiver stations shape the channel in order to perform common frequency division duplex operations. Usually, they are designed as cavity filters, which are expensive and have large dimensions. Thanks to the emerging digital technology and fast digital converters, it is possible to transfer the efforts of designing analog duplex filters into digital numeric algorithms applied to feedback structures, operating on power. This solution provides the shaping of the signal spectrum directly at the output of the radio frequency (RF) power amplifiers (PAs) relaxing the transmitter design especially in the duplexer and in the antenna sections. The design of a digital baseband feedback applied to the analog power RF amplifiers (hybrid filter) is presented and verified by measurements. A model to describe the hybrid system is investigated, and the relation between phase and resonance peaks of the resulting periodic band-pass transfer function is described. The stability condition of the system is analyzed using Nyquist criterion. A solution involving a number of digital feedback and forward branches is investigated defining the parameters of the recursive structure. This solution allows the closed loop system to show a periodic band pass with up to 500 kHz bandwidth at the output of the RF amplifier. The band-pass magnitude reaches up to 17 dB selectivity. The rejection of the PA noise in the out-of-band frequencies is verified by measurements. The filter is tested with a modulated LTE (Long Term Evolution) signal showing an ACPR (Adjacent Channel Power Ratio) enhancement of 10 dB of the transmitted signal.

Computer local construction of a general solution for the Chew-Low equations

International Nuclear Information System (INIS)

Gerdt, V.P.

1980-01-01

General solution of the dynamic form of the Chew-Low equations in the vicinity of the restpoint is considered. A method for calculating coefficients of series being members of such solution is suggested. The results of calculations, coefficients of power series and expansions carried out by means of the SCHOONSCHIP and SYMBAL systems are given. It is noted that the suggested procedure of the Chew-Low equation solutions basing on using an electronic computer as an instrument for analytical calculations permits to obtain detail information on the local structure of general solution

Hierarchical Recursive Organization and the Free Energy Principle: From Biological Self-Organization to the Psychoanalytic Mind

Directory of Open Access Journals (Sweden)

Patrick Connolly

2017-09-01

Full Text Available The present paper argues that a systems theory epistemology (and particularly the notion of hierarchical recursive organization provides the critical theoretical context within which the significance of Friston's (2010a Free Energy Principle (FEP for both evolution and psychoanalysis is best understood. Within this perspective, the FEP occupies a particular level of the hierarchical organization of the organism, which is the level of biological self-organization. This form of biological self-organization is in turn understood as foundational and pervasive to the higher levels of organization of the human organism that are of interest to both neuroscience as well as psychoanalysis. Consequently, central psychoanalytic claims should be restated, in order to be located in their proper place within a hierarchical recursive organization of the (situated organism. In light of the FEP the realization of the psychoanalytic mind by the brain should be seen in terms of the evolution of different levels of systematic organization where the concepts of psychoanalysis describe a level of hierarchical recursive organization superordinate to that of biological self-organization and the FEP. The implication of this formulation is that while “psychoanalytic” mental processes are fundamentally subject to the FEP, they nonetheless also add their own principles of process over and above that of the FEP. A model found in Grobbelaar (1989 offers a recursive bottom-up description of the self-organization of the psychoanalytic ego as dependent on the organization of language (and affect, which is itself founded upon the tendency toward autopoiesis (self-making within the organism, which is in turn described as formally similar to the FEP. Meaningful consilience between Grobbelaar's model and the hierarchical recursive description available in Friston's (2010a theory is described. The paper concludes that the valuable contribution of the FEP to psychoanalysis

The general solution of a Nim-heap game

Institute of Scientific and Technical Information of China (English)

宋林森; 卢澎涛

2010-01-01

As a combinatorial one,the game Nim turns out to be extremely useful in certain types of combinatorial game analysis.It has given the general solution of the game a Nim-heap game and the result has proved true.

New explicit spike solutions-non-local component of the generalized Mixmaster attractor

International Nuclear Information System (INIS)

Lim, Woei Chet

2008-01-01

By applying a standard solution-generating transformation to an arbitrary vacuum Bianchi type II solution, one generates a new solution with spikes commonly observed in numerical simulations. It is conjectured that the spike solutions are part of the generalized Mixmaster attractor

LAGRANGE SOLUTIONS TO THE DISCRETE-TIME GENERAL THREE-BODY PROBLEM

International Nuclear Information System (INIS)

Minesaki, Yukitaka

2013-01-01

There is no known integrator that yields exact orbits for the general three-body problem (G3BP). It is difficult to verify whether a numerical procedure yields the correct solutions to the G3BP because doing so requires knowledge of all 11 conserved quantities, whereas only six are known. Without tracking all of the conserved quantities, it is possible to show that the discrete general three-body problem (d-G3BP) yields the correct orbits corresponding to Lagrange solutions of the G3BP. We show that the d-G3BP yields the correct solutions to the G3BP for two special cases: the equilateral triangle and collinear configurations. For the triangular solution, we use the fact that the solution to the three-body case is a superposition of the solutions to the three two-body cases, and we show that the three bodies maintain the same relative distances at all times. To obtain the collinear solution, we assume a specific permutation of the three bodies arranged along a straight rotating line, and we show that the d-G3BP maintains the same distance ratio between two bodies as in the G3BP. Proving that the d-G3BP solutions for these cases are equivalent to those of the G3BP makes it likely that the d-G3BP and G3BP solutions are equivalent in other cases. To our knowledge, this is the first work that proves the equivalence of the discrete solutions and the Lagrange orbits.

On the structure of generalized monopole solutions in gauge-theories

International Nuclear Information System (INIS)

Horvath, Z.; Palla, L.

1976-01-01

A method is presented for constructing generalized 't Hooft monopole solutions in a gauge theory with an arbitrary gauge group. Restrictions arising from the condition of finite energy are derived. The radial oscillation of the solution is discussed. Using this method all the SU(3) solutions known in the literature are reproduced. Finite energy monopoles possessing magnetic charge in the range g 0 0 0 are found in SU(N) gauge theories. Different charge quantization conditions are analyzed to understand the structure of the solutions. (Auth.)

Recursive and non-linear logistic regression: moving on from the original EuroSCORE and EuroSCORE II methodologies.

Science.gov (United States)

Poullis, Michael

2014-11-01

EuroSCORE II, despite improving on the original EuroSCORE system, has not solved all the calibration and predictability issues. Recursive, non-linear and mixed recursive and non-linear regression analysis were assessed with regard to sensitivity, specificity and predictability of the original EuroSCORE and EuroSCORE II systems. The original logistic EuroSCORE, EuroSCORE II and recursive, non-linear and mixed recursive and non-linear regression analyses of these risk models were assessed via receiver operator characteristic curves (ROC) and Hosmer-Lemeshow statistic analysis with regard to the accuracy of predicting in-hospital mortality. Analysis was performed for isolated coronary artery bypass grafts (CABGs) (n = 2913), aortic valve replacement (AVR) (n = 814), mitral valve surgery (n = 340), combined AVR and CABG (n = 517), aortic (n = 350), miscellaneous cases (n = 642), and combinations of the above cases (n = 5576). The original EuroSCORE had an ROC below 0.7 for isolated AVR and combined AVR and CABG. None of the methods described increased the ROC above 0.7. The EuroSCORE II risk model had an ROC below 0.7 for isolated AVR only. Recursive regression, non-linear regression, and mixed recursive and non-linear regression all increased the ROC above 0.7 for isolated AVR. The original EuroSCORE had a Hosmer-Lemeshow statistic that was above 0.05 for all patients and the subgroups analysed. All of the techniques markedly increased the Hosmer-Lemeshow statistic. The EuroSCORE II risk model had a Hosmer-Lemeshow statistic that was significant for all patients (P linear regression failed to improve on the original Hosmer-Lemeshow statistic. The mixed recursive and non-linear regression using the EuroSCORE II risk model was the only model that produced an ROC of 0.7 or above for all patients and procedures and had a Hosmer-Lemeshow statistic that was highly non-significant. The original EuroSCORE and the EuroSCORE II risk models do not have adequate ROC and Hosmer

Travelling wave solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations

Directory of Open Access Journals (Sweden)

M. Arshad

Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method

Recursive construction of (J,L (J,L QC LDPC codes with girth 6

Directory of Open Access Journals (Sweden)

Mohammad Gholami

2016-06-01

Full Text Available ‎In this paper‎, ‎a recursive algorithm is presented to generate some exponent matrices which correspond to Tanner graphs with girth at least 6‎. ‎For a J×L J×L exponent matrix E E‎, ‎the lower bound Q(E Q(E is obtained explicitly such that (J,L (J,L QC LDPC codes with girth at least 6 exist for any circulant permutation matrix (CPM size m≥Q(E m≥Q(E‎. ‎The results show that the exponent matrices constructed with our recursive algorithm have smaller lower-bound than the ones proposed recently with girth 6‎

The Lehmer Matrix and Its Recursive Analogue

Science.gov (United States)

2010-01-01

LU factorization of matrix A by considering det A = det U = ∏n i=1 2i−1 i2 . The nth Catalan number is given in terms of binomial coefficients by Cn...for failing to comply with a collection of information if it does not display a currently valid OMB control number . 1. REPORT DATE 2010 2. REPORT...TYPE 3. DATES COVERED 00-00-2010 to 00-00-2010 4. TITLE AND SUBTITLE The Lehmer matrix and its recursive analogue 5a. CONTRACT NUMBER 5b

Exact solutions of (3 + 1-dimensional generalized KP equation arising in physics

Directory of Open Access Journals (Sweden)

Syed Tauseef Mohyud-Din

Full Text Available In this work, we have obtained some exact solutions to (3 + 1-dimensional generalized KP Equation. The improved tanϕ(ξ2-expansion method has been introduced to construct the exact solutions of nonlinear evolution equations. The obtained solutions include hyperbolic function solutions, trigonometric function solutions, exponential solutions, and rational solutions. Our study has added some new varieties of solutions to already available solutions. It is also worth mentioning that the computational work has been reduced significantly. Keywords: Improved tanϕ(ξ2-expansion method, Hyperbolic function solution, Trigonometric function solution, Rational solution, (3 + 1-dimensional generalized KP equation

Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Sun Chengfeng; Gao Hongjun

2009-01-01

The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.

The general supersymmetric solution of topologically massive supergravity

International Nuclear Information System (INIS)

Gibbons, G W; Pope, C N; Sezgin, E

2008-01-01

We find the general fully nonlinear solution of topologically massive supergravity admitting a Killing spinor. It is of plane-wave type, with a null Killing vector field. Conversely, we show that all solutions with a null Killing vector are supersymmetric for one or the other choice of sign for the Chern-Simons coupling constant μ. If μ does not take the critical value, μ = ±1, these solutions are asymptotically regular on a Poincare patch, but do not admit a smooth global compactification with boundary S 1 x R. In the critical case, the solutions have a logarithmic singularity on the boundary of the Poincare patch. We derive a Nester-Witten identity, which allows us to identify the associated charges, but we conclude that the presence of the Chern-Simons term prevents us from making a statement about their positivity. The Nester-Witten procedure is applied to the BTZ black hole

Symmetries and recursion operators of variable coefficient Korteweg-de Vries equations

International Nuclear Information System (INIS)

Baby, B.V.

1987-01-01

The infinitely many symmetries and recursion operators are constructed for two recently introduced variable coefficient Korteweg-de Vries equations, u t +αt n uu x +βt 2n+1 u xxx =0 and v t +βt 2n+1 (v 3 -6vv x )+(n+1)/t(xv x +2v)=0. The recursion operators are developed from Lax-pairs and this method is extended to nonisospectral problems. Olver's method of finding the existence of infinitely many symmetries for an evolution equation is found to be true for the nonisospectral case. It is found that the minimum number of different infinite sets of symmetries is the same as the number of independent similarity transformation groups associated with the given evolution equation. The relation between Painleve property and symmetries is also discussed in this paper. (author). 29 refs

Recursive parameter estimation for Hammerstein-Wiener systems using modified EKF algorithm.

Science.gov (United States)

Yu, Feng; Mao, Zhizhong; Yuan, Ping; He, Dakuo; Jia, Mingxing

2017-09-01

This paper focuses on the recursive parameter estimation for the single input single output Hammerstein-Wiener system model, and the study is then extended to a rarely mentioned multiple input single output Hammerstein-Wiener system. Inspired by the extended Kalman filter algorithm, two basic recursive algorithms are derived from the first and the second order Taylor approximation. Based on the form of the first order approximation algorithm, a modified algorithm with larger parameter convergence domain is proposed to cope with the problem of small parameter convergence domain of the first order one and the application limit of the second order one. The validity of the modification on the expansion of convergence domain is shown from the convergence analysis and is demonstrated with two simulation cases. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Solving the AKNS Hierarchy by Its Bilinear Form: Generalized Double Wronskian Solutions

International Nuclear Information System (INIS)

Yin Fumei; Sun Yepeng; Cai Fuqing; Chen Dengyuan

2008-01-01

Through the Wronskian technique, a simple and direct proof is presented that the AKNS hierarchy in the bilinear form has generalized double Wronskian solutions. Moreover, by using a unified way, soliton solutions, rational solutions, Matveev solutions and complexitons in double Wronskian form for it are constructed.

A Decidable Recursive Logic for Weighted Transition Systems

DEFF Research Database (Denmark)

Xue, Bingtian; Larsen, Kim Guldstrand; Mardare, Radu Iulian

2014-01-01

In this paper we develop and study the Recursive Weighted Logic (RWL), a multi-modal logic that expresses qualitative and quantitative properties of labelled weighted transition systems (LWSs). LWSs are transition systems labelled with actions and real-valued quantities representing the costs of ...... extends previous results that we have demonstrated for a similar but much more restrictive logic that can only use one variable for each type of resource to encode logical properties....

Using metrics for proof rules for recursively defined delay-insensitive specifications

NARCIS (Netherlands)

Mallon, WC; Udding, JT

1997-01-01

An advantage of algebraic specifications of delay insensitive asynchronous processes over most other formalisms is that it allows the recursive definition of processes, and correctness proofs of an implementation through fixpoint induction. On the other hand, proofs by fixpoint induction are

New exact travelling wave solutions for the generalized nonlinear Schroedinger equation with a source

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

Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation

International Nuclear Information System (INIS)

Ma Zhi-Min; Sun Yu-Huai; Liu Fu-Sheng

2013-01-01

In this paper, the generalized Boussinesq wave equation u tt — u xx + a(u m ) xx + bu xxxx = 0 is investigated by using the bifurcation theory and the method of phase portraits analysis. Under the different parameter conditions, the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained. (general)

Chiodo formulas for the r-th roots and topological recursion

NARCIS (Netherlands)

Lewanski, D.; Popolitov, A.; Shadrin, S.; Zvonkine, D.

We analyze Chiodo’s formulas for the Chern classes related to the r-th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers of these classes with ψ-classes are reproduced via the Chekhov–Eynard–Orantin topological recursion. As

Algebraic solutions of anti-self-dual gravity

International Nuclear Information System (INIS)

Sheftel, M.B.

2011-01-01

Full text: (author)It is considered a four-dimensional PDE: complex Monge-Amp'ere equation (CMA), solutions of which govern anti-self-dual gravity, i.e. determine anti-self-dual Ricci-flat Kahler metrics, solutions of the vacuum Einstein equations with the Euclidean signature. It is used simultaneously two mutually complex conjugate pairs of partner symmetries of CMA related by a recursion relation. For both pairs of partner symmetries, using Lie equations, it is introduced explicitly group parameters as additional variables, replacing symmetry characteristics and their complex conjugates by derivatives of the unknown with respect to group parameters. It is studied the resulting system of six equations in the eight-dimensional space, that includes CMA, four equations of the recursion between partner symmetries and one integrability condition of this system. It is used point symmetries of this extended system for performing its symmetry reduction with respect to group parameters that facilitates solving the extended system. This procedure does not imply a reduction in the number of physical variables and hence it is ended up with orbits of non-invariant solutions of CMA, generated by one partner symmetry, not used in the reduction. These solutions are determined by six linear equations with constant coefficients in the five-dimensional space which are obtained by a three-dimensional Legendre transformation of the reduced extended system. It is presented an example of algebraic solutions that govern Legendre-transformed Ricci-flat Kahler metrics with no Killing vectors. It is defined as a set of roots of a homogeneous polynomial of degree 6 in the six complex variables which determines a four-dimensional compact manifold in a five-dimensional complex projective space

General solution of Bateman equations for nuclear transmutations

International Nuclear Information System (INIS)

Cetnar, Jerzy

2006-01-01

The paper concerns the linear chain method of solving Bateman equations for nuclear transmutation in derivation of the general solution for linear chain with repeated transitions and thus elimination of existing numerical problems. In addition, applications of derived equations for transmutation trajectory analysis method is presented

Analytical Solution of General Bagley-Torvik Equation

OpenAIRE

William Labecca; Osvaldo Guimarães; José Roberto C. Piqueira

2015-01-01

Bagley-Torvik equation appears in viscoelasticity problems where fractional derivatives seem to play an important role concerning empirical data. There are several works treating this equation by using numerical methods and analytic formulations. However, the analytical solutions presented in the literature consider particular cases of boundary and initial conditions, with inhomogeneous term often expressed in polynomial form. Here, by using Laplace transform methodology, the general inhomoge...

Towards the general solution of the Yang-Mills equations

International Nuclear Information System (INIS)

Helfer, A.D.

1985-01-01

The author presents a new non-perturbative technique for finding arbitrary self-dual solutions to the Yang-Mills equations, and of describing massless fields minimally coupled to them. The approach uses techniques of complex analysis in several variables, and is complementary to Ward's: it is expected that a combination of the two techniques will yield general, non-self-dual solutions to the Yang-Mills equations. This has been verified to first order in perturbation theory

Features and Recursive Structure

Directory of Open Access Journals (Sweden)

Kuniya Nasukawa

2015-01-01

Full Text Available Based on the cross-linguistic tendency that weak vowels are realized with a central quality such as ə, ɨ, or ɯ, this paper attempts to account for this choice by proposing that the nucleus itself is one of the three monovalent vowel elements |A|, |I| and |U| which function as the building blocks of melodic structure. I claim that individual languages make a parametric choice to determine which of the three elements functions as the head of a nuclear expression. In addition, I show that elements can be freely concatenated to create melodic compounds. The resulting phonetic value of an element compound is determined by the specific elements it contains and by the head-dependency relations between those elements. This concatenation-based recursive mechanism of melodic structure can also be extended to levels above the segment, thus ultimately eliminating the need for syllabic constituents. This approach reinterprets the notion of minimalism in phonology by opposing the string-based flat structure.

Attitude determination and calibration using a recursive maximum likelihood-based adaptive Kalman filter

Science.gov (United States)

Kelly, D. A.; Fermelia, A.; Lee, G. K. F.

1990-01-01

An adaptive Kalman filter design that utilizes recursive maximum likelihood parameter identification is discussed. At the center of this design is the Kalman filter itself, which has the responsibility for attitude determination. At the same time, the identification algorithm is continually identifying the system parameters. The approach is applicable to nonlinear, as well as linear systems. This adaptive Kalman filter design has much potential for real time implementation, especially considering the fast clock speeds, cache memory and internal RAM available today. The recursive maximum likelihood algorithm is discussed in detail, with special attention directed towards its unique matrix formulation. The procedure for using the algorithm is described along with comments on how this algorithm interacts with the Kalman filter.

A recursive field-normalized bibliometric performance indicator: an application to the field of library and information science.

Science.gov (United States)

Waltman, Ludo; Yan, Erjia; van Eck, Nees Jan

2011-10-01

Two commonly used ideas in the development of citation-based research performance indicators are the idea of normalizing citation counts based on a field classification scheme and the idea of recursive citation weighing (like in PageRank-inspired indicators). We combine these two ideas in a single indicator, referred to as the recursive mean normalized citation score indicator, and we study the validity of this indicator. Our empirical analysis shows that the proposed indicator is highly sensitive to the field classification scheme that is used. The indicator also has a strong tendency to reinforce biases caused by the classification scheme. Based on these observations, we advise against the use of indicators in which the idea of normalization based on a field classification scheme and the idea of recursive citation weighing are combined.

Classification and Recursion Operators of Dark Burgers' Equation

Science.gov (United States)

Chen, Mei-Dan; Li, Biao

2018-01-01

With the help of symbolic computation, two types of complete scalar classification for dark Burgers' equations are derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every class of dark Burgers' systems; so some special equations including symmetry equation and dual symmetry equation are obtained by selecting the free parameter. Furthermore, two kinds of recursion operators for these dark Burgers' equations are constructed by two direct assumption methods.

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

Directory of Open Access Journals (Sweden)

G. M. N’Guérékata

2018-01-01

Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.

On the stability of soliton solution in NLS-type general field model

International Nuclear Information System (INIS)

Chakrabarti, S.; Nayyar, A.H.

1982-08-01

A model incorporating the nonlinear Schroedinger equation and its generalizations is considered and the stability of its periodic-in-time solutions under the restriction of a fixed charge Q is analysed. It is shown that the necessary condition for the stability is given by the inequality deltaQ/deltaν<0, where ν is the parameter of periodicity of the solution in time. In particular, one specific class of Lagrangians is considered and, in addition, the sufficient conditions for the stability of the soliton solutions are also determined. This study thus examines both the necessary and the sufficient conditions for the stability of the solutions of nonlinear Schroedinger equation and some of its generalizations. (author)

Conditional Stability of Solitary-Wave Solutions for Generalized Compound KdV Equation and Generalized Compound KdV-Burgers Equation

International Nuclear Information System (INIS)

Zhang Weiguo; Dong Chunyan; Fan Engui

2006-01-01

In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.

Exploiting fine-grain parallelism in recursive LU factorization

KAUST Repository

Dongarra, Jack

2012-01-01

The LU factorization is an important numerical algorithm for solving system of linear equations. This paper proposes a novel approach for computing the LU factorization in parallel on multicore architectures. It improves the overall performance and also achieves the numerical quality of the standard LU factorization with partial pivoting. While the update of the trailing submatrix is computationally intensive and highly parallel, the inherently problematic portion of the LU factorization is the panel factorization due to its memory-bound characteristic and the atomicity of selecting the appropriate pivots. We remedy this in our new approach to LU factorization of (narrow and tall) panel submatrices. We use a parallel fine-grained recursive formulation of the factorization. It is based on conflict-free partitioning of the data and lock-less synchronization mechanisms. Our implementation lets the overall computation naturally flow with limited contention. Our recursive panel factorization provides the necessary performance increase for the inherently problematic portion of the LU factorization of square matrices. A large panel width results in larger Amdahl\\'s fraction as our experiments have revealed which is consistent with related efforts. The performance results of our implementation reveal superlinear speedup and far exceed what can be achieved with equivalent MKL and/or LAPACK routines. © 2012 The authors and IOS Press. All rights reserved.

Bouncing solutions from generalized EoS

Energy Technology Data Exchange (ETDEWEB)

Contreras, F. [Universidad de Santiago de Chile, Departamento de Matematicas, Santiago (Chile); Cruz, N.; Palma, G. [Universidad de Santiago, Departamento de Fisica, Santiago (Chile)

2017-12-15

We present an exact analytical bouncing solution for a closed universe filled with only one exotic fluid with negative pressure, obeying a generalized equation of state (GEoS) of the form p(ρ) = Aρ+Bρ{sup λ}, where A, B and λ are constants. In our solution A = -1/3, λ = 1/2, and B < 0 is kept as a free parameter. For particular values of the initial conditions, we find that our solution obeys the null energy condition (NEC), which allows us to reinterpret the matter source as that of a real scalar field, φ, with a positive kinetic energy and a potential V(φ). We numerically compute the scalar field as a function of time as well as its potential V(φ), and we find an analytical function for the potential that fits very accurately with the numerical data obtained. The shape of this potential can be well described by a Gaussian-type of function, and hence there is no spontaneous symmetry minimum of V(φ). We show numerically that the bouncing scenario is structurally stable in a small vicinity of the value A = -1/3. We also include the study of the evolution of the linear fluctuations due to linear perturbations in the metric. These perturbations show an oscillatory behavior near the bouncing and approach a constant at large scales. (orig.)

A Note about the General Meromorphic Solutions of the Fisher Equation

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Jian-ming Qi

2014-01-01

Full Text Available We employ the complex method to obtain the general meromorphic solutions of the Fisher equation, which improves the corresponding results obtained by Ablowitz and Zeppetella and other authors (Ablowitz and Zeppetella, 1979; Feng and Li, 2006; Guo and Chen, 1991, and wg,i(z are new general meromorphic solutions of the Fisher equation for c=±5i/6. Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics.

A RECURSIVE ALGORITHM SUITABLE FOR REAL-TIME MEASUREMENT

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Giovanni Bucci

1995-12-01

Full Text Available This paper deals with a recursive algorithm suitable for realtime measurement applications, based on an indirect technique, useful in those applications where the required quantities cannot be measured in a straightforward way. To cope with time constraints a parallel formulation of it, suitable to be implemented on multiprocessor systems, is presented. The adopted concurrent implementation is based on factorization techniques. Some experimental results related to the application of the system for carrying out measurements on synchronous motors are included.

A Study for Obtaining New and More General Solutions of Special-Type Nonlinear Equation

International Nuclear Information System (INIS)

Zhao Hong

2007-01-01

The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions.

New solutions of the generalized ellipsoidal wave equation

Directory of Open Access Journals (Sweden)

Harold Exton

1999-10-01

Full Text Available Certain aspects and a contribution to the theory of new forms of solutions of an algebraic form of the generalized ellipsoidal wave equation are deduced by considering the Laplace transform of a soluble system of linear differential equations. An ensuing system of non-linear algebraic equations is shown to be consistent and is numerically implemented by means of the computer algebra package MAPLE V. The main results are presented as series of hypergeometric type of there and four variables which readily lend themselves to numerical handling although this does not indicate all of the detailedanalytic properties of the solutions under consideration.

A general solution strategy of modified power method for higher mode solutions

International Nuclear Information System (INIS)

Zhang, Peng; Lee, Hyunsuk; Lee, Deokjung

2016-01-01

A general solution strategy of the modified power iteration method for calculating higher eigenmodes has been developed and applied in continuous energy Monte Carlo simulation. The new approach adopts four features: 1) the eigen decomposition of transfer matrix, 2) weight cancellation for higher modes, 3) population control with higher mode weights, and 4) stabilization technique of statistical fluctuations using multi-cycle accumulations. The numerical tests of neutron transport eigenvalue problems successfully demonstrate that the new strategy can significantly accelerate the fission source convergence with stable convergence behavior while obtaining multiple higher eigenmodes at the same time. The advantages of the new strategy can be summarized as 1) the replacement of the cumbersome solution step of high order polynomial equations required by Booth's original method with the simple matrix eigen decomposition, 2) faster fission source convergence in inactive cycles, 3) more stable behaviors in both inactive and active cycles, and 4) smaller variances in active cycles. Advantages 3 and 4 can be attributed to the lower sensitivity of the new strategy to statistical fluctuations due to the multi-cycle accumulations. The application of the modified power method to continuous energy Monte Carlo simulation and the higher eigenmodes up to 4th order are reported for the first time in this paper. -- Graphical abstract: -- Highlights: •Modified power method is applied to continuous energy Monte Carlo simulation. •Transfer matrix is introduced to generalize the modified power method. •All mode based population control is applied to get the higher eigenmodes. •Statistic fluctuation can be greatly reduced using accumulated tally results. •Fission source convergence is accelerated with higher mode solutions.

Generalized dynamics of soft-matter quasicrystals mathematical models and solutions

CERN Document Server

Fan, Tian-You

2017-01-01

The book systematically introduces the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (SMQ). It provides methods for solving the initial-boundary value problems in these systems. The solutions obtained demonstrate the distribution, deformation and motion of the soft-matter quasicrystals, and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. Mathematical solutions for solid and soft-matter quasicrystals are compared, to help readers to better understand the featured properties of SMQ.

Joint Analysis of Binomial and Continuous Traits with a Recursive Model

DEFF Research Database (Denmark)

Varona, Louis; Sorensen, Daniel

2014-01-01

This work presents a model for the joint analysis of a binomial and a Gaussian trait using a recursive parametrization that leads to a computationally efficient implementation. The model is illustrated in an analysis of mortality and litter size in two breeds of Danish pigs, Landrace and Yorkshir...

Recursion relations for the overlap of a Morse continuum state with a Lanczos basis state

International Nuclear Information System (INIS)

Lutrus, C.K.; Suck Salk, S.H.

1988-01-01

In the resonant reactive scattering theory of Mundel, Berman, and Domcke [Phys. Rev. A 32, 181 (1985)], the overlap of a Morse continuum state and a Lanczos basis state appears in the expression of transition amplitude. In their study, recursion relations for Green's functions in the Lanczos basis were used for computational efficiency. In this paper we derive new recursion relations specifically for the evaluation of overlap between the Morse continuum wave and Lanczos basis state that appears in the transition amplitude of resonant scattering. They are found to be simple to use with great accuracy

Recursive estimation of the parts production process quality indicator

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Filipovich Oleg

2017-01-01

Full Text Available Consideration is given to a mathematical representation for manufacturing of batch parts on a metal-cutting machine tool. Linear dimensions of machined parts are assumed to be the major quality indicator, deviation from these dimensions is determined by size setting of machine tool and ensemble of random factors. It is allowed to have absolutely precise pre-setting of machine tool, effects from setup level offsetting due to deformation in process equipment on the specified indicator are disregarded. Consideration is given to factors which affect the tool wear, with two definitions of tool wear being provided. Reasons for development of random error in processing, dependence of measurement results on error as well as distribution laws and some parameters of random values are provided. To evaluate deviation of size setting value in each cycle, it is proposed to apply a recursive algorithm in description of investigated dynamic discrete process in the space state. Kalman filter equations are used in description of process model by means of first-order difference equations. The algorithm of recursive estimation is implemented in the mathematical software Maple. Simulation results which prove effectiveness of algorithm application to investigate the given dynamic system are provided. Variants of algorithm application and opportunities of further research are proposed.

On the exact solution for the multi-group kinetic neutron diffusion equation in a rectangle

International Nuclear Information System (INIS)

Petersen, C.Z.; Vilhena, M.T.M.B. de; Bodmann, B.E.J.

2011-01-01

In this work we consider the two-group bi-dimensional kinetic neutron diffusion equation. The solution procedure formalism is general with respect to the number of energy groups, neutron precursor families and regions with different chemical compositions. The fast and thermal flux and the delayed neutron precursor yields are expanded in a truncated double series in terms of eigenfunctions that, upon insertion into the kinetic equation and upon taking moments, results in a first order linear differential matrix equation with source terms. We split the matrix appearing in the transformed problem into a sum of a diagonal matrix plus the matrix containing the remaining terms and recast the transformed problem into a form that can be solved in the spirit of Adomian's recursive decomposition formalism. Convergence of the solution is guaranteed by the Cardinal Interpolation Theorem. We give numerical simulations and comparisons with available results in the literature. (author)

New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

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Yusuf Pandir

2013-01-01

Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

CP-recursion and the derivation of verb second in Germanic main and embedded clauses

DEFF Research Database (Denmark)

Vikner, Sten

2017-01-01

, this is normally not the case for all types of embedded clauses, as e. g. embedded questions (almost) never allow V2 (Julien 2007, Vikner 2001, though see McCloskey 2006 and Biberauer 2015). As in Nyvad et al. (2016), I will explore a particular derivation of (embedded) V2, in terms of a cP/CP-distinction, which...... may be seen as a version of the CP-recursion analysis (deHaan & Weerman 1986, Vikner 1995 and many others). The idea is that because embedded V2 clauses do not allow extraction, whereas other types of CP-recursion clauses do (Christensen et al. 2013a; Christensen et al. 2013b; Christensen & Nyvad 2014...

Inversion of General Cyclic Heptadiagonal Matrices

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A. A. Karawia

2013-01-01

Full Text Available We describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The computational cost of it is operations. The algorithm is implementable to the Computer Algebra System (CAS such as MAPLE, MATLAB, and MATHEMATICA. Two examples are presented for the sake of illustration.

Analysis and application of two recursive parametric estimation algorithms for an asynchronous machine

International Nuclear Information System (INIS)

Damek, Nawel; Kamoun, Samira

2011-01-01

In this communication, two recursive parametric estimation algorithms are analyzed and applied to an squirrelcage asynchronous machine located at the research ''Unit of Automatic Control'' (UCA) at ENIS. The first algorithm which, use the transfer matrix mathematical model, is based on the gradient principle. The second algorithm, which use the state-space mathematical model, is based on the minimization of the estimation error. These algorithms are applied as a key technique to estimate asynchronous machine with unknown, but constant or timevarying parameters. Stator voltage and current are used as measured data. The proposed recursive parametric estimation algorithms are validated on the experimental data of an asynchronous machine under normal operating condition as full load. The results show that these algorithms can estimate effectively the machine parameters with reliability.

A new Bayesian recursive technique for parameter estimation

Science.gov (United States)

Kaheil, Yasir H.; Gill, M. Kashif; McKee, Mac; Bastidas, Luis

2006-08-01

The performance of any model depends on how well its associated parameters are estimated. In the current application, a localized Bayesian recursive estimation (LOBARE) approach is devised for parameter estimation. The LOBARE methodology is an extension of the Bayesian recursive estimation (BARE) method. It is applied in this paper on two different types of models: an artificial intelligence (AI) model in the form of a support vector machine (SVM) application for forecasting soil moisture and a conceptual rainfall-runoff (CRR) model represented by the Sacramento soil moisture accounting (SAC-SMA) model. Support vector machines, based on statistical learning theory (SLT), represent the modeling task as a quadratic optimization problem and have already been used in various applications in hydrology. They require estimation of three parameters. SAC-SMA is a very well known model that estimates runoff. It has a 13-dimensional parameter space. In the LOBARE approach presented here, Bayesian inference is used in an iterative fashion to estimate the parameter space that will most likely enclose a best parameter set. This is done by narrowing the sampling space through updating the "parent" bounds based on their fitness. These bounds are actually the parameter sets that were selected by BARE runs on subspaces of the initial parameter space. The new approach results in faster convergence toward the optimal parameter set using minimum training/calibration data and fewer sets of parameter values. The efficacy of the localized methodology is also compared with the previously used BARE algorithm.

Online Solution of Two-Player Zero-Sum Games for Continuous-Time Nonlinear Systems With Completely Unknown Dynamics.

Science.gov (United States)

Fu, Yue; Chai, Tianyou

2016-12-01

Regarding two-player zero-sum games of continuous-time nonlinear systems with completely unknown dynamics, this paper presents an online adaptive algorithm for learning the Nash equilibrium solution, i.e., the optimal policy pair. First, for known systems, the simultaneous policy updating algorithm (SPUA) is reviewed. A new analytical method to prove the convergence is presented. Then, based on the SPUA, without using a priori knowledge of any system dynamics, an online algorithm is proposed to simultaneously learn in real time either the minimal nonnegative solution of the Hamilton-Jacobi-Isaacs (HJI) equation or the generalized algebraic Riccati equation for linear systems as a special case, along with the optimal policy pair. The approximate solution to the HJI equation and the admissible policy pair is reexpressed by the approximation theorem. The unknown constants or weights of each are identified simultaneously by resorting to the recursive least square method. The convergence of the online algorithm to the optimal solutions is provided. A practical online algorithm is also developed. Simulation results illustrate the effectiveness of the proposed method.

Recursive recovery of Markov transition probabilities from boundary value data

Energy Technology Data Exchange (ETDEWEB)

Patch, Sarah Kathyrn [Univ. of California, Berkeley, CA (United States)

1994-04-01

In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requires finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.

Layer-splitting technique for testing the recursive scheme for multilayer shields gamma ray buildup factors

International Nuclear Information System (INIS)

Alkhatib, Sari F.; Park, Chang Je; Jeong, Hae Yong; Lee, Yongdeok

2016-01-01

Highlights: • A simple formalism is suggested for the recursive approach and then it is used to produce buildup factors for certain multilayer shields. • The newly layer-splitting technique is implemented on the studied cases for testing the suggested formalism performance. • The buildup factors are generated using cubic polynomial fitting functions that are produced based on previous well-acknowledge data. - Abstract: This study illustrates the implementation of the newly suggested layer-splitting testing technique. This technique is introduced in order to be implemented in examining suggested formalisms for the recursive scheme (or iterative scheme). The recursive scheme is a concept used in treating and producing the gamma ray buildup factors in the case of multilayer shields. The layer-splitting technique simply enforces the scheme to treat a single layer of one material as two separated layers with similar characteristics. Thus it subjects the scheme to an abnormal definition of the multilayer shield that will test its performance in treating the successive layers. Thus, it will act as a method of verification for the approximations and assumptions taken in consideration. A simple formalism was suggested for the recursive scheme then the splitting technique was implemented on it. The results of implementing both the suggested formalism and the splitting technique are then illustrated and discussed. Throughout this study, cubic polynomial fitting functions were used to generate the data of buildup factors for the basic single-media that constitute the multilayer shields understudy. This study is limited to the cases of multiple shields consisting of repeated consecutive thin layers of lead–water and iron–water shields for 1 MeV gamma rays. The produced results of the buildup factor values through the implementation of the suggested formalism showed good consistency with the Monte Carlo simulation results of Lin and Jiang work. In the implementation of

Generalized Truncated Methods for an Efficient Solution of Retrial Systems

Directory of Open Access Journals (Sweden)

Ma Jose Domenech-Benlloch

2008-01-01

Full Text Available We are concerned with the analytic solution of multiserver retrial queues including the impatience phenomenon. As there are not closed-form solutions to these systems, approximate methods are required. We propose two different generalized truncated methods to effectively solve this type of systems. The methods proposed are based on the homogenization of the state space beyond a given number of users in the retrial orbit. We compare the proposed methods with the most well-known methods appeared in the literature in a wide range of scenarios. We conclude that the proposed methods generally outperform previous proposals in terms of accuracy for the most common performance parameters used in retrial systems with a moderated growth in the computational cost.

Abundant general solitary wave solutions to the family of KdV type equations

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Md. Azmol Huda

2017-03-01

Full Text Available This work explores the construction of more general exact traveling wave solutions of some nonlinear evolution equations (NLEEs through the application of the (G′/G, 1/G-expansion method. This method is allied to the widely used (G′/G-method initiated by Wang et al. and can be considered as an extension of the (G′/G-expansion method. For effectiveness, the method is applied to the family of KdV type equations. Abundant general form solitary wave solutions as well as periodic solutions are successfully obtained through this method. Moreover, in the obtained wider set of solutions, if we set special values of the parameters, some previously known solutions are revived. The approach of this method is simple and elegantly standard. Having been computerized it is also powerful, reliable and effective.

Stability of oscillatory solutions of differential equations with a general piecewise constant argument

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Kuo-Shou Chiu

2011-11-01

Full Text Available We examine scalar differential equations with a general piecewise constant argument, in short DEPCAG, that is, the argument is a general step function. Criteria of existence of the oscillatory and nonoscillatory solutions of such equations are proposed. Necessary and sufficient conditions for stability of the zero solution are obtained. Appropriate examples are given to show our results.

Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems. An algorithm

Energy Technology Data Exchange (ETDEWEB)

Thirukkanesh, S. [Eastern University, Department of Mathematics, Chenkalady (Sri Lanka); Ragel, F.C. [Eastern University, Department of Physics, Chenkalady (Sri Lanka); Sharma, Ranjan; Das, Shyam [P.D. Women' s College, Department of Physics, Jalpaiguri (India)

2018-01-15

We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as an anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular solution is taken up to show its physical acceptability. Making use of the current estimate of mass and radius of a known pulsar, the effects of anisotropic stress on the gross physical behaviour of a relativistic compact star is also highlighted. (orig.)

On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid

Science.gov (United States)

Khan, M.; Anjum, Asia; Qi, Haitao; Fetecau, C.

2010-02-01

This paper deals with exact solutions for some oscillating motions of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of fluid model. Analytical expressions for the velocity field and the corresponding shear stress for flows due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient are determined using Fourier sine and Laplace transforms. The obtained solutions are presented under integral and series forms in terms of the Mittag-Leffler functions. For α = β = 1, our solutions tend to the similar solutions for ordinary Oldroyd-B fluid. A comparison between generalized and ordinary Oldroyd-B fluids is shown by means of graphical illustrations.

A New Solution for Einstein Field Equation in General Relativity

Science.gov (United States)

Mousavi, Sadegh

2006-05-01

There are different solutions for Einstein field equation in general relativity that they have been proposed by different people the most important solutions are Schwarzchild, Reissner Nordstrom, Kerr and Kerr Newmam. However, each one of these solutions limited to special case. I've found a new solution for Einstein field equation which is more complete than all previous ones and this solution contains the previous solutions as its special forms. In this talk I will present my new metric for Einstein field equation and the Christofel symbols and Richi and Rieman tensor components for the new metric that I have calculated them by GR TENSOR software. As a result I will determine the actual movement of black holes which is different From Kerr black hole's movement. Finally this new solution predicts, existence of a new and constant field in the nature (that nobody can found it up to now), so in this talk I will introduce this new field and even I will calculate the amount of this field. SADEGH MOUSAVI, Amirkabir University of Technology.

Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

International Nuclear Information System (INIS)

Fischer, E.

1977-01-01

Various families of exact solutions to the Einstein and Einstein--Maxwell field equations of general relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations. The physical situations in which such equations arise include: the external gravitational field of an axisymmetric, uncharged steadily rotating body, cylindrical gravitational waves with two degrees of freedom, colliding plane gravitational waves, the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein--Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa. The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables

Stability of recursive out-of-sequence measurement filters: an open problem

Science.gov (United States)

Chen, Lingji; Moshtagh, Nima; Mehra, Raman K.

2011-06-01

In many applications where communication delays are present, measurements with earlier time stamps can arrive out-of-sequence, i.e., after state estimates have been obtained for the current time instant. To incorporate such an Out-Of-Sequence Measurement (OOSM), many algorithms have been proposed in the literature to obtain or approximate the optimal estimate that would have been obtained if the OOSM had arrived in-sequence. When OOSM occurs repeatedly, approximate estimations as a result of incorporating one OOSM have to serve as the basis for incorporating yet another OOSM. The question of whether the "approximation of approximation" is well behaved, i.e., whether approximation errors accumulate in a recursive setting, has not been adequately addressed in the literature. This paper draws attention to the stability question of recursive OOSM processing filters, formulates the problem in a specific setting, and presents some simulation results that suggest that such filters are indeed well-behaved. Our hope is that more research will be conducted in the future to rigorously establish stability properties of these filters.

A general solution of the plane problem thermoelasticity in polar coordinates

International Nuclear Information System (INIS)

Tabakman, H.D.; Lin, Y.J.

1977-01-01

A general solution, in polar coordinates, of the plane problem in thermoelasticity is obtained in terms of a stress and displacement function. The solution is valid for arbitrary temperature distribution T(r, theta). The characteristic feature of the paper is the forthright determination of the displacement components brought about by the introduction of a displacement function

Particular transcendent solution of the Ernst system generalized on n fields

International Nuclear Information System (INIS)

Leaute, B.; Marcilhacy, G.

1986-01-01

A particular solution, a function of a particular form of the fifth Painleve transcendent, of the Ernst system generalized to n fields is determined, which characterizes both the stationary axially symmetric fields, the solution of the Einstein (n-1) Maxwell equations, and one class of axially symmetric static self-dual SU(n+1) Yang--Mills fields

Peakons, solitary patterns and periodic solutions for generalized Camassa-Holm equations

International Nuclear Information System (INIS)

Zheng Yin; Lai Shaoyong

2008-01-01

This Letter deals with a generalized Camassa-Holm equation and a nonlinear dispersive equation by making use of a mathematical technique based on using integral factors for solving differential equations. The peakons, solitary patterns and periodic solutions are expressed analytically under various circumstances. The conditions that cause the qualitative change in the physical structures of the solutions are highlighted

Magnetotail equilibrium theory - The general three-dimensional solution

Science.gov (United States)

Birn, J.

1987-01-01

The general magnetostatic equilibrium problem for the geomagnetic tail is reduced to the solution of ordinary differential equations and ordinary integrals. The theory allows the integration of the self-consistent magnetotail equilibrium field from the knowledge of four functions of two space variables: the neutral sheet location, the total pressure, the magnetic field strength, and the z component of the magnetic field at the neutral sheet.

On the Painleve integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Xu Guiqiong; Li Zhibin

2005-01-01

It is proven that generalized coupled higher-order nonlinear Schroedinger equations possess the Painleve property for two particular choices of parameters, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests

Automatic computation and solution of generalized harmonic balance equations

Science.gov (United States)

Peyton Jones, J. C.; Yaser, K. S. A.; Stevenson, J.

2018-02-01

Generalized methods are presented for generating and solving the harmonic balance equations for a broad class of nonlinear differential or difference equations and for a general set of harmonics chosen by the user. In particular, a new algorithm for automatically generating the Jacobian of the balance equations enables efficient solution of these equations using continuation methods. Efficient numeric validation techniques are also presented, and the combined algorithm is applied to the analysis of dc, fundamental, second and third harmonic response of a nonlinear automotive damper.

Real-time recursive motion segmentation of video data on a programmable device

NARCIS (Netherlands)

Wittebrood, R.B; Haan, de G.

2001-01-01

We previously reported on a recursive algorithm enabling real-time object-based motion estimation (OME) of standard definition video on a digital signal processor (DSP). The algorithm approximates the motion of the objects in the image with parametric motion models and creates a segmentation mask by

The Exact Solution for Linear Thermoelastic Axisymmetric Deformations of Generally Laminated Circular Cylindrical Shells

Science.gov (United States)

Nemeth, Michael P.; Schultz, Marc R.

2012-01-01

A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.

A recursive framework for time-dependent characteristics of tested and maintained standby units with arbitrary distributions for failures and repairs

International Nuclear Information System (INIS)

Vaurio, Jussi K.

2015-01-01

The time-dependent unavailability and the failure and repair intensities of periodically tested aging standby system components are solved with recursive equations under three categories of testing and repair policies. In these policies, tests or repairs or both can be minimal or perfect renewals. Arbitrary distributions are allowed to times to failure as well as to repair and renewal durations. Major preventive maintenance is done periodically or at random times, e.g. when a true demand occurs. In the third option process renewal is done if a true demand occurs or when a certain mission time has expired since the previous maintenance, whichever occurs first. A practical feature is that even if a repair can renew the unit, it does not generally renew the alternating process. The formalism updates and extends earlier results by using a special backward-renewal equation method, by allowing scheduled tests not limited to equal intervals and accepting arbitrary distributions and multiple failure types and causes, including failures caused by tests, human errors and true demands. Explicit solutions are produced to integral equations associated with an age-renewal maintenance policy. - Highlights: • Time-dependent unavailability, failure count and repair count for a standby system. • Free testing schedule and distributions for times to failure, repair and maintenance. • Multiple failure modes; tests or repairs or both can be minimal or perfect renewals. • Process renewals periodically, randomly or based on the process age or an initiator. • Backward renewal equations as explicit solutions to Volterra-type integral equations

The General Traveling Wave Solutions of the Fisher Equation with Degree Three

Directory of Open Access Journals (Sweden)

Wenjun Yuan

2013-01-01

degree three and the general meromorphic solutions of the integrable Fisher equations with degree three, which improves the corresponding results obtained by Feng and Li (2006, Guo and Chen (1991, and Ağırseven and Öziş (2010. Moreover, all wg,1(z are new general meromorphic solutions of the Fisher equations with degree three for c=±3/2. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.

The recursive combination filter approach of pre-processing for the estimation of standard deviation of RR series.

Science.gov (United States)

Mishra, Alok; Swati, D

2015-09-01

Variation in the interval between the R-R peaks of the electrocardiogram represents the modulation of the cardiac oscillations by the autonomic nervous system. This variation is contaminated by anomalous signals called ectopic beats, artefacts or noise which mask the true behaviour of heart rate variability. In this paper, we have proposed a combination filter of recursive impulse rejection filter and recursive 20% filter, with recursive application and preference of replacement over removal of abnormal beats to improve the pre-processing of the inter-beat intervals. We have tested this novel recursive combinational method with median method replacement to estimate the standard deviation of normal to normal (SDNN) beat intervals of congestive heart failure (CHF) and normal sinus rhythm subjects. This work discusses the improvement in pre-processing over single use of impulse rejection filter and removal of abnormal beats for heart rate variability for the estimation of SDNN and Poncaré plot descriptors (SD1, SD2, and SD1/SD2) in detail. We have found the 22 ms value of SDNN and 36 ms value of SD2 descriptor of Poincaré plot as clinical indicators in discriminating the normal cases from CHF cases. The pre-processing is also useful in calculation of Lyapunov exponent which is a nonlinear index as Lyapunov exponents calculated after proposed pre-processing modified in a way that it start following the notion of less complex behaviour of diseased states.

Spinning solutions in general relativity with infinite central density

Science.gov (United States)

Flammer, P. D.

2018-05-01

This paper presents general relativistic numerical simulations of uniformly rotating polytropes. Equations are developed using MSQI coordinates, but taking a logarithm of the radial coordinate. The result is relatively simple elliptical differential equations. Due to the logarithmic scale, we can resolve solutions with near-singular mass distributions near their center, while the solution domain extends many orders of magnitude larger than the radius of the distribution (to connect with flat space-time). Rotating solutions are found with very high central energy densities for a range of adiabatic exponents. Analytically, assuming the pressure is proportional to the energy density (which is true for polytropes in the limit of large energy density), we determine the small radius behavior of the metric potentials and energy density. This small radius behavior agrees well with the small radius behavior of large central density numerical results, lending confidence to our numerical approach. We compare results with rotating solutions available in the literature, which show good agreement. We study the stability of spherical solutions: instability sets in at the first maximum in mass versus central energy density; this is also consistent with results in the literature, and further lends confidence to the numerical approach.

Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems

Directory of Open Access Journals (Sweden)

Misha V. Feigin

2009-09-01

Full Text Available We consider trigonometric solutions of WDVV equations and derive geometric conditions when a collection of vectors with multiplicities determines such a solution. We incorporate these conditions into the notion of trigonometric Veselov system (v-system and we determine all trigonometric v-systems with up to five vectors. We show that generalized Calogero-Moser-Sutherland operator admits a factorized eigenfunction if and only if it corresponds to the trigonometric v-system; this inverts a one-way implication observed by Veselov for the rational solutions.

Bounded queries in recursion theory

CERN Document Server

Gasarch, William I

1999-01-01

One of the major concerns of theoretical computer science is the classifi­ cation of problems in terms of how hard they are. The natural measure of difficulty of a function is the amount of time needed to compute it (as a function of the length of the input). Other resources, such as space, have also been considered. In recursion theory, by contrast, a function is considered to be easy to compute if there exists some algorithm that computes it. We wish to classify functions that are hard, i.e., not computable, in a quantitative way. We cannot use time or space, since the functions are not even computable. We cannot use Turing degree, since this notion is not quantitative. Hence we need a new notion of complexity-much like time or spac~that is quantitative and yet in some way captures the level of difficulty (such as the Turing degree) of a function.

Exact solution of the N-dimensional generalized Dirac-Coulomb equation

International Nuclear Information System (INIS)

Tutik, R.S.

1992-01-01

An exact solution to the bound state problem for the N-dimensional generalized Dirac-Coulomb equation, whose potential contains both the Lorentz-vector and Lorentz-scalar terms of the Coulomb form, is obtained. 24 refs. (author)

Hurwitz numbers, moduli of curves, topological recursion, Givental's theory and their relations

NARCIS (Netherlands)

Spitz, L.

2014-01-01

The study of curves is an important area of research in algebraic geometry and mathematical physics. In my thesis I study so-called moduli spaces of curves; these are spaces that parametrize all curves with some specified properties. In particular, I study maps from curves to other spaces, recursive

New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

International Nuclear Information System (INIS)

Chen Huaitang; Zhang Hongqing

2004-01-01

A generalized tanh function method is 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 Riccati equation which has more new solutions. More new multiple soliton solutions are obtained for the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

General solution for first order elliptic systems in the plane

International Nuclear Information System (INIS)

Mshimba, A.S.

1990-01-01

It is shown that a system of 2n real-valued partial differential equations of first order, which under certain assumptions can be transformed to the so-called 'complex normal form', admits a general solution. 15 refs

Analytical approximate solutions for a general class of nonlinear delay differential equations.

Science.gov (United States)

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

The generalized tanh method to obtain exact solutions of nonlinear partial differential equation

OpenAIRE

Gómez, César

2007-01-01

In this paper, we present the generalized tanh method to obtain exact solutions of nonlinear partial differential equations, and we obtain solitons and exact solutions of some important equations of the mathematical physics.

Recursive Cluster Elimination (RCE for classification and feature selection from gene expression data

Directory of Open Access Journals (Sweden)

Showe Louise C

2007-05-01

Full Text Available Abstract Background Classification studies using gene expression datasets are usually based on small numbers of samples and tens of thousands of genes. The selection of those genes that are important for distinguishing the different sample classes being compared, poses a challenging problem in high dimensional data analysis. We describe a new procedure for selecting significant genes as recursive cluster elimination (RCE rather than recursive feature elimination (RFE. We have tested this algorithm on six datasets and compared its performance with that of two related classification procedures with RFE. Results We have developed a novel method for selecting significant genes in comparative gene expression studies. This method, which we refer to as SVM-RCE, combines K-means, a clustering method, to identify correlated gene clusters, and Support Vector Machines (SVMs, a supervised machine learning classification method, to identify and score (rank those gene clusters for the purpose of classification. K-means is used initially to group genes into clusters. Recursive cluster elimination (RCE is then applied to iteratively remove those clusters of genes that contribute the least to the classification performance. SVM-RCE identifies the clusters of correlated genes that are most significantly differentially expressed between the sample classes. Utilization of gene clusters, rather than individual genes, enhances the supervised classification accuracy of the same data as compared to the accuracy when either SVM or Penalized Discriminant Analysis (PDA with recursive feature elimination (SVM-RFE and PDA-RFE are used to remove genes based on their individual discriminant weights. Conclusion SVM-RCE provides improved classification accuracy with complex microarray data sets when it is compared to the classification accuracy of the same datasets using either SVM-RFE or PDA-RFE. SVM-RCE identifies clusters of correlated genes that when considered together

Recursion-transform method for computing resistance of the complex resistor network with three arbitrary boundaries.

Science.gov (United States)

Tan, Zhi-Zhong

2015-05-01

We develop a general recursion-transform (R-T) method for a two-dimensional resistor network with a zero resistor boundary. As applications of the R-T method, we consider a significant example to illuminate the usefulness for calculating resistance of a rectangular m×n resistor network with a null resistor and three arbitrary boundaries, a problem never solved before, since Green's function techniques and Laplacian matrix approaches are invalid in this case. Looking for the exact calculation of the resistance of a binary resistor network is important but difficult in the case of an arbitrary boundary since the boundary is like a wall or trap which affects the behavior of finite network. In this paper we obtain several general formulas of resistance between any two nodes in a nonregular m×n resistor network in both finite and infinite cases. In particular, 12 special cases are given by reducing one of the general formulas to understand its applications and meanings, and an integral identity is found when we compare the equivalent resistance of two different structures of the same problem in a resistor network.

Nonlinear Disturbance Attenuation Controller for Turbo-Generators in Power Systems via Recursive Design

NARCIS (Netherlands)

Cao, M.; Shen, T.L.; Song, Y.H.; Mei, S.W.

2002-01-01

The paper proposes a nonlinear robust controller for steam governor control in power systems. Based on dissipation theory, an innovative recursive design method is presented to construct the storage function of single machine infinite bus (SMIB) and multi-machine power systems. Furthermore, the

Parameter Estimation of Permanent Magnet Synchronous Motor Using Orthogonal Projection and Recursive Least Squares Combinatorial Algorithm

Directory of Open Access Journals (Sweden)

Iman Yousefi

2015-01-01

Full Text Available This paper presents parameter estimation of Permanent Magnet Synchronous Motor (PMSM using a combinatorial algorithm. Nonlinear fourth-order space state model of PMSM is selected. This model is rewritten to the linear regression form without linearization. Noise is imposed to the system in order to provide a real condition, and then combinatorial Orthogonal Projection Algorithm and Recursive Least Squares (OPA&RLS method is applied in the linear regression form to the system. Results of this method are compared to the Orthogonal Projection Algorithm (OPA and Recursive Least Squares (RLS methods to validate the feasibility of the proposed method. Simulation results validate the efficacy of the proposed algorithm.

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

Science.gov (United States)

Daly, Edoardo; Basser, Hossein; Rudman, Murray

2018-05-01

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

Recursive inter-generational utility in global climate risk modeling

Energy Technology Data Exchange (ETDEWEB)

Minh, Ha-Duong [Centre International de Recherche sur l' Environnement et le Developpement (CIRED-CNRS), 75 - Paris (France); Treich, N. [Institut National de Recherches Agronomiques (INRA-LEERNA), 31 - Toulouse (France)

2003-07-01

This paper distinguishes relative risk aversion and resistance to inter-temporal substitution in climate risk modeling. Stochastic recursive preferences are introduced in a stylized numeric climate-economy model using preliminary IPCC 1998 scenarios. It shows that higher risk aversion increases the optimal carbon tax. Higher resistance to inter-temporal substitution alone has the same effect as increasing the discount rate, provided that the risk is not too large. We discuss implications of these findings for the debate upon discounting and sustainability under uncertainty. (author)

Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy's law

International Nuclear Information System (INIS)

Khan, M.; Hayat, T.; Asghar, S.

2005-12-01

This paper deals with an exact solution for the magnetohydrodynamic (MHD) flow of a generalized Oldroyd-B fluid in a circular pipe. For the description of such a fluid, the fractional calculus approach has been used throughout the analysis. Based on modified Darcy's law for generalized Oldroyd-B fluid, the velocity field is calculated analytically. Several known solutions can be recovered as the limiting cases of our solution. (author)

The Monge-Ampère equation: Hamiltonian and symplectic structures, recursions, and hierarchies

NARCIS (Netherlands)

Kersten, P.H.M.; Krasil'shchik, I.; Verbovetsky, A.V.

2004-01-01

Using methods of geometry and cohomology developed recently, we study the Monge-Ampère equation, arising as the first nontrivial equation in the associativity equations, or WDVV equations. We describe Hamiltonian and symplectic structures as well as recursion operators for this equation in its

Quantum solutions for Prisoner's Dilemma game with general parameters

International Nuclear Information System (INIS)

Sun, Z.W.; Jin, H.; Zhao, H.

2008-01-01

The quantum game of the Prisoner's Dilemma with general payoff matrix was studied in L. Marinatto and T. Weber's scheme presented in [Phys. Lett. A 272 (2000) 291, so that the results of two schemes of the quantum game can be compared. The Nash equilibria and the solutions of the game are obtained. They are related to initial state, matrix parameters and the intervals among the parameters. It can be concluded from the results that the quantum PD game in Marinatto and Weber's scheme matches the one in Eisert et al.'s scheme, one with general unitary operations.

Efficient O(N) recursive computation of the operational space inertial matrix

International Nuclear Information System (INIS)

Lilly, K.W.; Orin, D.E.

1993-01-01

The operational space inertia matrix Λ reflects the dynamic properties of a robot manipulator to its tip. In the control domain, it may be used to decouple force and/or motion control about the manipulator workspace axes. The matrix Λ also plays an important role in the development of efficient algorithms for the dynamic simulation of closed-chain robotic mechanisms, including simple closed-chain mechanisms such as multiple manipulator systems and walking machines. The traditional approach used to compute Λ has a computational complexity of O(N 3 ) for an N degree-of-freedom manipulator. This paper presents the development of a recursive algorithm for computing the operational space inertia matrix (OSIM) that reduces the computational complexity to O(N). This algorithm, the inertia propagation method, is based on a single recursion that begins at the base of the manipulator and progresses out to the last link. Also applicable to redundant systems and mechanisms with multiple-degree-of-freedom joints, the inertia propagation method is the most efficient method known for computing Λ for N ≥ 6. The numerical accuracy of the algorithm is discussed for a PUMA 560 robot with a fixed base

General solution of Poisson equation in three dimensions for disk-like galaxies

International Nuclear Information System (INIS)

Tong, Y.; Zheng, X.; Peng, O.

1982-01-01

The general solution of the Poisson equation is solved by means of integral transformations for Vertical BarkVertical Barr>>1 provided that the perturbed density of disk-like galaxies distributes along the radial direction according to the Hankel function. This solution can more accurately represent the outer spiral arms of disk-like galaxies

On the General Analytical Solution of the Kinematic Cosserat Equations

KAUST Repository

Michels, Dominik L.

2016-09-01

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.

On the General Analytical Solution of the Kinematic Cosserat Equations

KAUST Repository

Michels, Dominik L.; Lyakhov, Dmitry; Gerdt, Vladimir P.; Hossain, Zahid; Riedel-Kruse, Ingmar H.; Weber, Andreas G.

2016-01-01

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.

Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach

Science.gov (United States)

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…

Chirped self-similar solutions of a generalized nonlinear Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Fei Jin-Xi [Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Zheng Chun-Long [Shaoguan Univ., Guangdong (China). School of Physics and Electromechanical Engineering; Shanghai Univ. (China). Shanghai Inst. of Applied Mathematics and Mechanics

2011-01-15

An improved homogeneous balance principle and an F-expansion technique are used to construct exact chirped self-similar solutions to the generalized nonlinear Schroedinger equation with distributed dispersion, nonlinearity, and gain coefficients. Such solutions exist under certain conditions and impose constraints on the functions describing dispersion, nonlinearity, and distributed gain function. The results show that the chirp function is related only to the dispersion coefficient, however, it affects all of the system parameters, which influence the form of the wave amplitude. As few characteristic examples and some simple chirped self-similar waves are presented. (orig.)

Analytical representation for solution of the neutron point kinetics equation with time-dependent reactivity and free of the stiffness character

International Nuclear Information System (INIS)

Silva, Milena Wollmann da

2013-01-01

In this work, we report a genuine analytical representation for the solution of the neutron point kinetics equation free of the stiffness character, assuming that the reactivity is a continuous and sectionally continuous function of time. To this end, we initially cast the point kinetics equation in a first order linear differential equation. Next, we split the corresponding matrix as a sum of a diagonal matrix with a matrix, whose components contain the off-diagonal elements. Next, expanding the neutron density and the delayed neutron precursors concentrations in a truncated series, and replacing these expansions in the matrix equation, we come out with an equation, which allows to construct a recursive system, a first order matrix differential equation with source. The fundamental characteristic of this system relies on the fact that the corresponding matrix is diagonal, meanwhile the source term is written in terms of the matrix with the off-diagonal components. Further, the first equation of the recursive system has no source and satisfies the initial conditions. On the other hand, the remaining equations satisfy the null initial condition. Due to the diagonal feature of the matrix, we attain analytical solutions for these recursive equations. We also mention that we evaluate the results for any time value, without the analytical continuity because the purposed solution is free on the stiffness character. Finally, we present numerical simulations and comparisons against literature results, considering specific the applications for the following reactivity functions: constant, step, ramp, and sine. (author)

A general solution to the material performance index for bending strength design

International Nuclear Information System (INIS)

Burgess, S.C.; Pasini, D.; Smith, D.J.; Alemzadeh, K.

2006-01-01

This paper presents a general solution to the material performance index for the bending strength design of beams. In general, the performance index for strength design is ρ f q /ρ where σ f is the material strength, ρ is the material density and q is a function of the direction of scaling. Previous studies have only solved q for three particular cases: proportional scaling of width and height (q=2/3), constrained height (q=1) and constrained width (q=1/2). This paper presents a general solution to the exponent q for any arbitrary direction of scaling. The index is used to produce performance maps that rank relative material performance for particular design cases. The performance index and the performance maps are applied to a design case study

Recursive estimation of high-order Markov chains: Approximation by finite mixtures

Czech Academy of Sciences Publication Activity Database

Kárný, Miroslav

2016-01-01

Roč. 326, č. 1 (2016), s. 188-201 ISSN 0020-0255 R&D Projects : GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Markov chain * Approximate parameter estimation * Bayesian recursive estimation * Adaptive systems * Kullback–Leibler divergence * Forgetting Subject RIV: BC - Control Systems Theory Impact factor: 4.832, year: 2016 http://library.utia.cas.cz/separaty/2015/AS/karny-0447119.pdf

Separating the Classes of Recursively Enumerable Languages Based on Machine Size

Czech Academy of Sciences Publication Activity Database

van Leeuwen, J.; Wiedermann, Jiří

2015-01-01

Roč. 26, č. 6 (2015), s. 677-695 ISSN 0129-0541 R&D Projects: GA ČR GAP202/10/1333 Grant - others:GA ČR(CZ) GA15-04960S Institutional support: RVO:67985807 Keywords : recursively enumerable languages * RE hierarchy * finite languages * machine size * descriptional complexity * Turing machines with advice Subject RIV: IN - Informatics, Computer Science Impact factor: 0.467, year: 2015

Tables of generalized Airy functions for the asymptotic solution of the differential equation

CERN Document Server

Nosova, L N

1965-01-01

Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations contains tables of the special functions, namely, the generalized Airy functions, and their first derivatives, for real and pure imaginary values. The tables are useful for calculations on toroidal shells, laminae, rode, and for the solution of certain other problems of mathematical physics. The values of the functions were computed on the ""Strela"" highspeed electronic computer.This book will be of great value to mathematicians, researchers, and students.

Locating one pairwise interaction: Three recursive constructions

Directory of Open Access Journals (Sweden)

Charles J. Colbourn

2016-09-01

Full Text Available In a complex component-based system, choices (levels for components (factors may interact tocause faults in the system behaviour. When faults may be caused by interactions among few factorsat specific levels, covering arrays provide a combinatorial test suite for discovering the presence offaults. While well studied, covering arrays do not enable one to determine the specific levels of factorscausing the faults; locating arrays ensure that the results from test suite execution suffice to determinethe precise levels and factors causing faults, when the number of such causes is small. Constructionsfor locating arrays are at present limited to heuristic computational methods and quite specific directconstructions. In this paper three recursive constructions are developed for locating arrays to locateone pairwise interaction causing a fault.

Solution of the neutron transport problem with anisotropic scattering in cylindrical geometry by the decomposition method

International Nuclear Information System (INIS)

Goncalves, G.A.; Bogado Leite, S.Q.; Vilhena, M.T. de

2009-01-01

An analytical solution has been obtained for the one-speed stationary neutron transport problem, in an infinitely long cylinder with anisotropic scattering by the decomposition method. Series expansions of the angular flux distribution are proposed in terms of suitably constructed functions, recursively obtainable from the isotropic solution, to take into account anisotropy. As for the isotropic problem, an accurate closed-form solution was chosen for the problem with internal source and constant incident radiation, obtained from an integral transformation technique and the F N method

A novel intrusion detection method based on OCSVM and K-means recursive clustering

Directory of Open Access Journals (Sweden)

Leandros A. Maglaras

2015-01-01

Full Text Available In this paper we present an intrusion detection module capable of detecting malicious network traffic in a SCADA (Supervisory Control and Data Acquisition system, based on the combination of One-Class Support Vector Machine (OCSVM with RBF kernel and recursive k-means clustering. Important parameters of OCSVM, such as Gaussian width o and parameter v affect the performance of the classifier. Tuning of these parameters is of great importance in order to avoid false positives and over fitting. The combination of OCSVM with recursive k- means clustering leads the proposed intrusion detection module to distinguish real alarms from possible attacks regardless of the values of parameters o and v, making it ideal for real-time intrusion detection mechanisms for SCADA systems. Extensive simulations have been conducted with datasets extracted from small and medium sized HTB SCADA testbeds, in order to compare the accuracy, false alarm rate and execution time against the base line OCSVM method.

All-Pole Recursive Digital Filters Design Based on Ultraspherical Polynomials

OpenAIRE

N. Stojanovic; N. Stamenkovic; V. Stojanovic

2014-01-01

A simple method for approximation of all-pole recursive digital filters, directly in digital domain, is described. Transfer function of these filters, referred to as Ultraspherical filters, is controlled by order of the Ultraspherical polynomial, nu. Parameter nu, restricted to be a nonnegative real number (nu ≥ 0), controls ripple peaks in the passband of the magnitude response and enables a trade-off between the passband loss and the group delay response of the resulting filter. Chebyshev f...

A general solution of the plane problem in thermoelasticity in polar coordinates

International Nuclear Information System (INIS)

Tabakman, H.D.; Lin, Y.J.

1977-01-01

A general solution, in polar coordinates, of the plane problem in thermoelasticity is obtained in terms of a stress and displacement function. The solution is valid for arbitrary temperature distribution T(r,theta). The characteristic feature of the paper is the forthright determination of the displacement components brought about by the introduction of a displacement function. (Auth.)

New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks.

Science.gov (United States)

Bouchard, M

2001-01-01

In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

Recursive wind speed forecasting based on Hammerstein Auto-Regressive model

International Nuclear Information System (INIS)

Ait Maatallah, Othman; Achuthan, Ajit; Janoyan, Kerop; Marzocca, Pier

2015-01-01

Highlights: • Developed a new recursive WSF model for 1–24 h horizon based on Hammerstein model. • Nonlinear HAR model successfully captured chaotic dynamics of wind speed time series. • Recursive WSF intrinsic error accumulation corrected by applying rotation. • Model verified for real wind speed data from two sites with different characteristics. • HAR model outperformed both ARIMA and ANN models in terms of accuracy of prediction. - Abstract: A new Wind Speed Forecasting (WSF) model, suitable for a short term 1–24 h forecast horizon, is developed by adapting Hammerstein model to an Autoregressive approach. The model is applied to real data collected for a period of three years (2004–2006) from two different sites. The performance of HAR model is evaluated by comparing its prediction with the classical Autoregressive Integrated Moving Average (ARIMA) model and a multi-layer perceptron Artificial Neural Network (ANN). Results show that the HAR model outperforms both the ARIMA model and ANN model in terms of root mean square error (RMSE), mean absolute error (MAE), and Mean Absolute Percentage Error (MAPE). When compared to the conventional models, the new HAR model can better capture various wind speed characteristics, including asymmetric (non-gaussian) wind speed distribution, non-stationary time series profile, and the chaotic dynamics. The new model is beneficial for various applications in the renewable energy area, particularly for power scheduling

The DART general equilibrium model: A technical description

OpenAIRE

Springer, Katrin

1998-01-01

This paper provides a technical description of the Dynamic Applied Regional Trade (DART) General Equilibrium Model. The DART model is a recursive dynamic, multi-region, multi-sector computable general equilibrium model. All regions are fully specified and linked by bilateral trade flows. The DART model can be used to project economic activities, energy use and trade flows for each of the specified regions to simulate various trade policy as well as environmental policy scenarios, and to analy...

Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient

International Nuclear Information System (INIS)

Cao Rui; Zhang Jian

2013-01-01

In this paper, the trial function method is extended to study the generalized nonlinear Schrödinger equation with time-dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrödinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrödinger equation with time-dependent coefficients under constraint conditions. (general)

Recursive nearest neighbor search in a sparse and multiscale domain for comparing audio signals

DEFF Research Database (Denmark)

Sturm, Bob L.; Daudet, Laurent

2011-01-01

We investigate recursive nearest neighbor search in a sparse domain at the scale of audio signals. Essentially, to approximate the cosine distance between the signals we make pairwise comparisons between the elements of localized sparse models built from large and redundant multiscale dictionaries...

Transmittivity and wavefunctions in one-dimensional generalized Aubry models

International Nuclear Information System (INIS)

Basu, C.; Mookerjee, A.; Sen, A.K.; Thakur, P.K.

1990-07-01

We use the vector recursion method of Haydock to obtain the transmittance of a class of generalized Aubry models in one-dimension. We also study the phase change of the wavefunctions as they travel through the chain and also the behaviour of the conductance with changes in size. (author). 10 refs, 9 figs

Analytical Solution of a Generalized Hirota-Satsuma Equation

Science.gov (United States)

Kassem, M.; Mabrouk, S.; Abd-el-Malek, M.

A modified version of generalized Hirota-Satsuma is here solved using a two parameter group transformation method. This problem in three dimensions was reduced by Estevez [1] to a two dimensional one through a Lie transformation method and left unsolved. In the present paper, through application of symmetry transformation the Lax pair has been reduced to a system of ordinary equations. Three transformations cases are investigated. The obtained analytical solutions are plotted and show a profile proper to deflagration processes, well described by Degasperis-Procesi equation.

General-purpose chemical analyzer for on-line analyses of radioactive solutions

International Nuclear Information System (INIS)

Spencer, W.A.; Kronberg, J.W.

1983-01-01

An automated analyzer is being developed to perform analytical measurements on radioactive solutions on-line in a hostile environment. This General Purpose Chemical Analyzer (GPCA) samples a process stream, adds reagents, measures solution absorbances or electrode potentials, and automatically calculates the results. The use of modular components, under microprocessor control, permits a single analyzer design to carry out many types of analyses. This paper discusses the more important design criteria for the GPCA, and describes the equipment being tested in a prototype unit

An approximate JKR solution for a general contact, including rough contacts

Science.gov (United States)

Ciavarella, M.

2018-05-01

In the present note, we suggest a simple closed form approximate solution to the adhesive contact problem under the so-called JKR regime. The derivation is based on generalizing the original JKR energetic derivation assuming calculation of the strain energy in adhesiveless contact, and unloading at constant contact area. The underlying assumption is that the contact area distributions are the same as under adhesiveless conditions (for an appropriately increased normal load), so that in general the stress intensity factors will not be exactly equal at all contact edges. The solution is simply that the indentation is δ =δ1 -√{ 2 wA‧ /P″ } where w is surface energy, δ1 is the adhesiveless indentation, A‧ is the first derivative of contact area and P‧‧ the second derivative of the load with respect to δ1. The solution only requires macroscopic quantities, and not very elaborate local distributions, and is exact in many configurations like axisymmetric contacts, but also sinusoidal waves contact and correctly predicts some features of an ideal asperity model used as a test case and not as a real description of a rough contact problem. The solution permits therefore an estimate of the full solution for elastic rough solids with Gaussian multiple scales of roughness, which so far was lacking, using known adhesiveless simple results. The result turns out to depend only on rms amplitude and slopes of the surface, and as in the fractal limit, slopes would grow without limit, tends to the adhesiveless result - although in this limit the JKR model is inappropriate. The solution would also go to adhesiveless result for large rms amplitude of roughness hrms, irrespective of the small scale details, and in agreement with common sense, well known experiments and previous models by the author.

Lane-Emden equation with inertial force and general polytropic dynamic model for molecular cloud cores

Science.gov (United States)

Li, DaLei; Lou, Yu-Qing; Esimbek, Jarken

2018-01-01

We study self-similar hydrodynamics of spherical symmetry using a general polytropic (GP) equation of state and derive the GP dynamic Lane-Emden equation (LEE) with a radial inertial force. In reference to Lou & Cao, we solve the GP dynamic LEE for both polytropic index γ = 1 + 1/n and the isothermal case n → +∞; our formalism is more general than the conventional polytropic model with n = 3 or γ = 4/3 of Goldreich & Weber. For proper boundary conditions, we obtain an exact constant solution for arbitrary n and analytic variable solutions for n = 0 and n = 1, respectively. Series expansion solutions are derived near the origin with the explicit recursion formulae for the series coefficients for both the GP and isothermal cases. By extensive numerical explorations, we find that there is no zero density at a finite radius for n ≥ 5. For 0 ≤ n 0 for monotonically decreasing density from the origin and vanishing at a finite radius for c being less than a critical value Ccr. As astrophysical applications, we invoke our solutions of the GP dynamic LEE with central finite boundary conditions to fit the molecular cloud core Barnard 68 in contrast to the static isothermal Bonnor-Ebert sphere by Alves et al. Our GP dynamic model fits appear to be sensibly consistent with several more observations and diagnostics for density, temperature and gas pressure profiles.

Global existence of a generalized solution for the radiative transfer equations

International Nuclear Information System (INIS)

Golse, F.; Perthame, B.

1984-01-01

We prove global existence of a generalized solution of the radiative transfer equations, extending Mercier's result to the case of a layer with an initially cold area. Our Theorem relies on the results of Crandall and Ligett [fr

Assessing the relative importance of correlates of loneliness in later life: Gaining insight using recursive partitioning

DEFF Research Database (Denmark)

Ejlskov, Linda; Wulff, Jesper; Bøggild, Henrik

2017-01-01

and demographic correlates were poor identifiers of loneliness. The regression tree suggested that loneliness was not raised among those with poor mental wellbeing if they identified their partner as closest confidante and had frequent social contact. CONCLUSION: Recursive partitioning can identify which......OBJECTIVES: Improving the design and targeting of interventions is important for alleviating loneliness among older adults. This requires identifying which correlates are the most important predictors of loneliness. This study demonstrates the use of recursive partitioning in exploring...... the characteristics and assessing the relative importance of correlates of loneliness in older adults. METHOD: Using exploratory regression trees and random forests, we examined combinations and the relative importance of 42 correlates in relation to loneliness at age 68 among 2453 participants from the birth cohort...

Fundamental solutions for Schrödinger operators with general inverse square potentials

KAUST Repository

Chen, Huyuan; Alhomedan, Suad; Hajaiej, Hichem; Markowich, Peter A.

2017-01-01

In this paper, we clarify the fundamental solutions for Schrödinger operators given as (Formula presented.), where the potential V is a general inverse square potential in (Formula presented.) with (Formula presented.). In particular, letting (Formula presented.),(Formula presented.) where (Formula presented.), we discuss the existence and nonexistence of positive fundamental solutions for Hardy operator (Formula presented.), which depend on the parameter t.

Fundamental solutions for Schrödinger operators with general inverse square potentials

KAUST Repository

Chen, Huyuan

2017-03-17

In this paper, we clarify the fundamental solutions for Schrödinger operators given as (Formula presented.), where the potential V is a general inverse square potential in (Formula presented.) with (Formula presented.). In particular, letting (Formula presented.),(Formula presented.) where (Formula presented.), we discuss the existence and nonexistence of positive fundamental solutions for Hardy operator (Formula presented.), which depend on the parameter t.

General thermo-elastic solution of radially heterogeneous, spherically isotropic rotating sphere

Energy Technology Data Exchange (ETDEWEB)

Bayat, Yahya; EkhteraeiToussi, THamid [Ferdowsi University of Mashhad, Mashhad (Iran, Islamic Republic of)

2015-06-15

A thick walled rotating spherical object made of transversely isotropic functionally graded materials (FGMs) with general types of thermo-mechanical boundary conditions is studied. The thermo-mechanical governing equations consisting of decoupled thermal and mechanical equations are represented. The centrifugal body forces of the rotation are considered in the modeling phase. The unsymmetrical thermo-mechanical boundary conditions and rotational body forces are expressed in terms of the Legendre series. The series method is also implemented in the solution of the resulting equations. The solutions are checked with the known literature and FEM based solutions of ABAQUS software. The effects of anisotropy and heterogeneity are studied through the case studies and the results are represented in different figures. The newly developed series form solution is applicable to the rotating FGM spherical transversely isotropic vessels having nonsymmetrical thermo-mechanical boundary condition.

A model of guarded recursion with clock synchronisation

DEFF Research Database (Denmark)

Bizjak, Aleš; Møgelberg, Rasmus Ejlers

2015-01-01

productivity to be captured in types. The calculus uses clocks representing time streams and clock quantifiers which allow limited and controlled elimination of modalities. The calculus has since been extended to dependent types by Møgelberg. Both works give denotational semantics but no rewrite semantics....... In previous versions of this calculus, different clocks represented separate time streams and clock synchronisation was prohibited. In this paper we show that allowing clock synchronisation is safe by constructing a new model of guarded recursion and clocks. This result will greatly simplify the type theory...... by removing freshness restrictions from typing rules, and is a necessary step towards defining rewrite semantics, and ultimately implementing the calculus....

Nonparametric bootstrap procedures for predictive inference based on recursive estimation schemes

OpenAIRE

Corradi, Valentina; Swanson, Norman R.

2005-01-01

Our objectives in this paper are twofold. First, we introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. Thereafter, we present two examples where predictive accuracy tests are made operational using our new bootstrap procedures. In one application, we outline a consistent test for out-of-sample nonlinear Granger causality, and in the other we outline a test for selecting amongst multiple alternative forecasting models, all of which are possibl...

Projection-based Bayesian recursive estimation of ARX model with uniform innovations

Czech Academy of Sciences Publication Activity Database

Kárný, Miroslav; Pavelková, Lenka

2007-01-01

Roč. 56, 9/10 (2007), s. 646-655 ISSN 0167-6911 R&D Projects: GA AV ČR 1ET100750401; GA MŠk 2C06001; GA MDS 1F43A/003/120 Institutional research plan: CEZ:AV0Z10750506 Keywords : ARX model * Bayesian recursive estimation * Uniform distribution Subject RIV: BC - Control Systems Theory Impact factor: 1.634, year: 2007 http://dx.doi.org/10.1016/j.sysconle.2007.03.005

Nonlinear dynamics for charges particle beams with a curved axis in the matrix - recursive model

Energy Technology Data Exchange (ETDEWEB)

Dymnikov, A D [University of St Petersburg, (Russian Federation). Institute of Computational Mathematics and Control Process

1994-12-31

In this paper a new matrix and recursive approach has been outlined for treating nonlinear optics of charged particle beams. This approach is a new analytical and computational tool for designers of optimal beam control systems. 9 refs.

Recursive least squares method of regression coefficients estimation as a special case of Kalman filter

Science.gov (United States)

Borodachev, S. M.

2016-06-01

The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.

Nonlinear dynamics for charges particle beams with a curved axis in the matrix - recursive model

Energy Technology Data Exchange (ETDEWEB)

Dymnikov, A.D. [University of St Petersburg, (Russian Federation). Institute of Computational Mathematics and Control Process

1993-12-31

In this paper a new matrix and recursive approach has been outlined for treating nonlinear optics of charged particle beams. This approach is a new analytical and computational tool for designers of optimal beam control systems. 9 refs.

Nonlinear dynamics for charges particle beams with a curved axis in the matrix - recursive model

International Nuclear Information System (INIS)

Dymnikov, A.D.

1993-01-01

In this paper a new matrix and recursive approach has been outlined for treating nonlinear optics of charged particle beams. This approach is a new analytical and computational tool for designers of optimal beam control systems. 9 refs

Exact solution of the generalized Peierls equation for arbitrary n-fold screw dislocation

Science.gov (United States)

Wang, Shaofeng; Hu, Xiangsheng

2018-05-01

The exact solution of the generalized Peierls equation is presented and proved for arbitrary n-fold screw dislocation. The displacement field, stress field and the energy of the n-fold dislocation are also evaluated explicitly. It is found that the solution defined on each individual fold is given by the tail cut from the original Peierls solution. In viewpoint of energetics, a screw dislocation has a tendency to spread the distribution on all possible slip planes which are contained in the dislocation line zone. Based on the exact solution, the approximated solution of the improved Peierls equation is proposed for the modified γ-surface.

Multicritical phase diagrams of the spin-((3)/(2)) Blume-Emery-Griffiths model on the Bethe lattice using the recursion method

International Nuclear Information System (INIS)

Ekiz, Cesur; Albayrak, Erhan; Keskin, Mustafa.

2003-01-01

The multicritical behaviour of the spin-((3)/(2)) Blume-Emery-Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field is studied on the Bethe lattice by introducing two-sublattices A and B within the exact recursion equations. Exact expressions for the free energy, the Curie or second-order phase transition temperatures, as well as for the magnetization and quadrupolar moment order parameters are obtained. The general procedure of investigation of critical properties is discussed and phase diagrams are obtained, in particular, for negative biquadratic couplings. The phase diagram of the model exhibits a rich variety of behaviours. Results are compared with other approximate methods

Using Recursive Regression to Explore Nonlinear Relationships and Interactions: A Tutorial Applied to a Multicultural Education Study

Directory of Open Access Journals (Sweden)

Kenneth David Strang

2009-03-01

Full Text Available This paper discusses how a seldom-used statistical procedure, recursive regression (RR, can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and multiple linear regression for method triangulation. By comparison, nonlinear cluster analysis also generates graphical dendrograms to visually depict relationships, but RR (as implemented here uses multiple combinations of nominal and interval predictors regressed on a categorical or ratio dependent variable. In similar fashion, multidimensional scaling, multiple discriminant analysis and conjoint analysis are constrained at best to predicting an ordinal dependent variable (as currently implemented in popular software. A flexible capability of RR (again as implemented here is the transformation of factor data (for substituting codes. One powerful RR feature is the ability to treat missing data as a theoretically important predictor value (useful for survey questions that respondents do not wish to answer. For practitioners, the paper summarizes how this technique fits within the generally-accepted statistical methods. Popular software such as SPSS, SAS or LISREL can be used, while sample data can be imported in common formats including ASCII text, comma delimited, Excel XLS, and SPSS SAV. A tutorial approach is applied here using RR in LISREL. The tutorial leverages a partial sample from a study that used recursive regression to predict grades from international student learning styles. Some tutorial portions are technical, to improve the ambiguous RR literature.

Predictive Sampling of Rare Conformational Events in Aqueous Solution: Designing a Generalized Orthogonal Space Tempering Method.

Science.gov (United States)

Lu, Chao; Li, Xubin; Wu, Dongsheng; Zheng, Lianqing; Yang, Wei

2016-01-12

In aqueous solution, solute conformational transitions are governed by intimate interplays of the fluctuations of solute-solute, solute-water, and water-water interactions. To promote molecular fluctuations to enhance sampling of essential conformational changes, a common strategy is to construct an expanded Hamiltonian through a series of Hamiltonian perturbations and thereby broaden the distribution of certain interactions of focus. Due to a lack of active sampling of configuration response to Hamiltonian transitions, it is challenging for common expanded Hamiltonian methods to robustly explore solvent mediated rare conformational events. The orthogonal space sampling (OSS) scheme, as exemplified by the orthogonal space random walk and orthogonal space tempering methods, provides a general framework for synchronous acceleration of slow configuration responses. To more effectively sample conformational transitions in aqueous solution, in this work, we devised a generalized orthogonal space tempering (gOST) algorithm. Specifically, in the Hamiltonian perturbation part, a solvent-accessible-surface-area-dependent term is introduced to implicitly perturb near-solute water-water fluctuations; more importantly in the orthogonal space response part, the generalized force order parameter is generalized as a two-dimension order parameter set, in which essential solute-solvent and solute-solute components are separately treated. The gOST algorithm is evaluated through a molecular dynamics simulation study on the explicitly solvated deca-alanine (Ala10) peptide. On the basis of a fully automated sampling protocol, the gOST simulation enabled repetitive folding and unfolding of the solvated peptide within a single continuous trajectory and allowed for detailed constructions of Ala10 folding/unfolding free energy surfaces. The gOST result reveals that solvent cooperative fluctuations play a pivotal role in Ala10 folding/unfolding transitions. In addition, our assessment

Approximate solution of generalized Ginzburg-Landau-Higgs system via homotopy perturbation method

Energy Technology Data Exchange (ETDEWEB)

Lu Juhong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Dept. of Information Engineering, Coll. of Lishui Professional Tech., Zhejiang (China); Zheng Chunlong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Shanghai Inst. of Applied Mathematics and Mechanics, Shanghai Univ., SH (China)

2010-04-15

Using the homotopy perturbation method, a class of nonlinear generalized Ginzburg-Landau-Higgs systems (GGLH) is considered. Firstly, by introducing a homotopic transformation, the nonlinear problem is changed into a system of linear equations. Secondly, by selecting a suitable initial approximation, the approximate solution with arbitrary degree accuracy to the generalized Ginzburg-Landau-Higgs system is derived. Finally, another type of homotopic transformation to the generalized Ginzburg-Landau-Higgs system reported in previous literature is briefly discussed. (orig.)

Soft sensor modelling by time difference, recursive partial least squares and adaptive model updating

International Nuclear Information System (INIS)

Fu, Y; Xu, O; Yang, W; Zhou, L; Wang, J

2017-01-01

To investigate time-variant and nonlinear characteristics in industrial processes, a soft sensor modelling method based on time difference, moving-window recursive partial least square (PLS) and adaptive model updating is proposed. In this method, time difference values of input and output variables are used as training samples to construct the model, which can reduce the effects of the nonlinear characteristic on modelling accuracy and retain the advantages of recursive PLS algorithm. To solve the high updating frequency of the model, a confidence value is introduced, which can be updated adaptively according to the results of the model performance assessment. Once the confidence value is updated, the model can be updated. The proposed method has been used to predict the 4-carboxy-benz-aldehyde (CBA) content in the purified terephthalic acid (PTA) oxidation reaction process. The results show that the proposed soft sensor modelling method can reduce computation effectively, improve prediction accuracy by making use of process information and reflect the process characteristics accurately. (paper)

Shock-jump conditions in a general medium: weak-solution approach

Science.gov (United States)

Forbes, L. K.; Krzysik, O. A.

2017-05-01

General conservation laws are considered, and the concept of a weak solution is extended to the case of an equation involving three space variables and time. Four-dimensional vector calculus is used to develop general jump conditions at a shock wave in the material. To illustrate the use of this result, jump conditions at a shock in unsteady three-dimensional compressible gas flow are presented. It is then proved rigorously that these reduce to the commonly assumed conditions in coordinates normal and tangential to the shock face. A similar calculation is also outlined for an unsteady three-dimensional shock in magnetohydrodynamics, and in a chemically reactive fluid. The technique is available for determining shock-jump conditions in quite general continuous media.

Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation

International Nuclear Information System (INIS)

Zhang Liang; Zhang Lifeng; Li Chongyin

2008-01-01

By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions

Black holes in the Universe: Generalized Lemaitre-Tolman-Bondi solutions

International Nuclear Information System (INIS)

Gao Changjun; Chen Xuelei; Shen Yougen; Faraoni, Valerio

2011-01-01

We present new exact solutions which presumably describe black holes in the background of a spatially flat, pressureless dark-matter- or dark matter plus dark energy (DM+DE)- or quintom-dominated Universe. These solutions generalize Lemaitre-Tolman-Bondi metrics. For a dark-matter- or (DM+DE)-dominated universe, the area of the black hole apparent horizon (AH) decreases with the expansion of the Universe while that of the cosmic AH increases. However, for a quintom-dominated universe, the black hole AH first shrinks and then expands, while the cosmic AH first expands and then shrinks. A (DM+DE)-dominated universe containing a black hole will evolve to the Schwarzschild-de Sitter solution with both AHs approaching constant size. In a quintom-dominated universe, the black hole and cosmic AHs will coincide at a certain time, after which the singularity becomes naked, violating cosmic censorship.

Path integral solution of linear second order partial differential equations I: the general construction

International Nuclear Information System (INIS)

LaChapelle, J.

2004-01-01

A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette

Semiclassical series solution of the generalized phase shift atom--diatom scattering equations

International Nuclear Information System (INIS)

Squire, K.R.; Curtiss, C.F.

1980-01-01

A semiclassical series solution of the previously developed operator form of the generalized phase shift equations describing atom--diatom scattering is presented. This development is based on earlier work which led to a double series in powers of Planck's constant and a scaling parameter of the anisotropic portion of the intermolecular potential. The present solution is similar in that it is a double power series in Planck's constant and in the difference between the spherical radial momentum and a first order approximation. The present series solution avoids difficulties of the previous series associated with the classical turning point

A general method for enclosing solutions of interval linear equations

Czech Academy of Sciences Publication Activity Database

Rohn, Jiří

2012-01-01

Roč. 6, č. 4 (2012), s. 709-717 ISSN 1862-4472 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * enclosure * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 1.654, year: 2012

Solutions to the maximal spacelike hypersurface equation in generalized Robertson-Walker spacetimes

Directory of Open Access Journals (Sweden)

Henrique F. de Lima

2018-03-01

Full Text Available We apply some generalized maximum principles for establishing uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker (GRW spacetime, which is supposed to obey the so-called timelike convergence condition (TCC. As application, we study the uniqueness and nonexistence of entire solutions of a suitable maximal spacelike hypersurface equation in GRW spacetimes obeying the TCC.

Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation

KAUST Repository

Said-Houari, Belkacem

2014-01-01

In this paper, we study the decay rates of solutions for the generalized Benjamin-Bona-Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314-340 and Nonlinear Anal. 75(7) (2012), 3385-3392. © 2014-IOS Press.

Unified semiclassical theory for the two-state system: an analytical solution for general nonadiabatic tunneling.

Science.gov (United States)

Zhu, Chaoyuan; Lin, Sheng Hsien

2006-07-28

Unified semiclasical solution for general nonadiabatic tunneling between two adiabatic potential energy surfaces is established by employing unified semiclassical solution for pure nonadiabatic transition [C. Zhu, J. Chem. Phys. 105, 4159 (1996)] with the certain symmetry transformation. This symmetry comes from a detailed analysis of the reduced scattering matrix for Landau-Zener type of crossing as a special case of nonadiabatic transition and nonadiabatic tunneling. Traditional classification of crossing and noncrossing types of nonadiabatic transition can be quantitatively defined by the rotation angle of adiabatic-to-diabatic transformation, and this rotational angle enters the analytical solution for general nonadiabatic tunneling. The certain two-state exponential potential models are employed for numerical tests, and the calculations from the present general nonadiabatic tunneling formula are demonstrated in very good agreement with the results from exact quantum mechanical calculations. The present general nonadiabatic tunneling formula can be incorporated with various mixed quantum-classical methods for modeling electronically nonadiabatic processes in photochemistry.

Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

Science.gov (United States)

Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei

2018-03-01

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.

General-base catalysed hydrolysis and nucleophilic substitution of activated amides in aqueous solutions

NARCIS (Netherlands)

Buurma, NJ; Blandamer, MJ; Engberts, JBFN; Buurma, Niklaas J.

The reactivity of 1-benzoyl-3-phenyl-1,2,4-triazole (1a) was studied in the presence of a range of weak bases in aqueous solution. A change in mechanism is observed from general-base catalysed hydrolysis to nucleophilic substitution and general-base catalysed nucleophilic substitution. A slight

Optimal hydrograph separation using a recursive digital filter constrained by chemical mass balance, with application to selected Chesapeake Bay watersheds

Science.gov (United States)

Raffensperger, Jeff P.; Baker, Anna C.; Blomquist, Joel D.; Hopple, Jessica A.

2017-06-26

Quantitative estimates of base flow are necessary to address questions concerning the vulnerability and response of the Nation’s water supply to natural and human-induced change in environmental conditions. An objective of the U.S. Geological Survey National Water-Quality Assessment Project is to determine how hydrologic systems are affected by watershed characteristics, including land use, land cover, water use, climate, and natural characteristics (geology, soil type, and topography). An important component of any hydrologic system is base flow, generally described as the part of streamflow that is sustained between precipitation events, fed to stream channels by delayed (usually subsurface) pathways, and more specifically as the volumetric discharge of water, estimated at a measurement site or gage at the watershed scale, which represents groundwater that discharges directly or indirectly to stream reaches and is then routed to the measurement point.Hydrograph separation using a recursive digital filter was applied to 225 sites in the Chesapeake Bay watershed. The recursive digital filter was chosen for the following reasons: it is based in part on the assumption that groundwater acts as a linear reservoir, and so has a physical basis; it has only two adjustable parameters (alpha, obtained directly from recession analysis, and beta, the maximum value of the base-flow index that can be modeled by the filter), which can be determined objectively and with the same physical basis of groundwater reservoir linearity, or that can be optimized by applying a chemical-mass-balance constraint. Base-flow estimates from the recursive digital filter were compared with those from five other hydrograph-separation methods with respect to two metrics: the long-term average fraction of streamflow that is base flow, or base-flow index, and the fraction of days where streamflow is entirely base flow. There was generally good correlation between the methods, with some biased

Existence of solution for a general fractional advection-dispersion equation

Science.gov (United States)

Torres Ledesma, César E.

2018-05-01

In this work, we consider the existence of solution to the following fractional advection-dispersion equation -d/dt ( p {_{-∞}}It^{β }(u'(t)) + q {t}I_{∞}^{β }(u'(t))) + b(t)u = f(t, u(t)),t\\in R where β \\in (0,1) , _{-∞}It^{β } and tI_{∞}^{β } denote left and right Liouville-Weyl fractional integrals of order β respectively, 0continuous functions. Due to the general assumption on the constant p and q, the problem (0.1) does not have a variational structure. Despite that, here we study it performing variational methods, combining with an iterative technique, and give an existence criteria of solution for the problem (0.1) under suitable assumptions.

Numerical solution of pipe flow problems for generalized Newtonian fluids

International Nuclear Information System (INIS)

Samuelsson, K.

1993-01-01

In this work we study the stationary laminar flow of incompressible generalized Newtonian fluids in a pipe with constant arbitrary cross-section. The resulting nonlinear boundary value problems can be written in a variational formulation and solved using finite elements and the augmented Lagrangian method. The solution of the boundary value problem is obtained by finding a saddle point of the augmented Lagrangian. In the algorithm the nonlinear part of the equations is treated locally and the solution is obtained by iteration between this nonlinear problem and a global linear problem. For the solution of the linear problem we use the SSOR preconditioned conjugate gradient method. The approximating problem is solved on a sequence of adaptively refined grids. A scheme for adjusting the value of the crucial penalization parameter of the augmented Lagrangian is proposed. Applications to pipe flow and a problem from the theory of capacities are given. (author) (34 refs.)

Recursive Neural Networks Based on PSO for Image Parsing

Directory of Open Access Journals (Sweden)

Guo-Rong Cai

2013-01-01

Full Text Available This paper presents an image parsing algorithm which is based on Particle Swarm Optimization (PSO and Recursive Neural Networks (RNNs. State-of-the-art method such as traditional RNN-based parsing strategy uses L-BFGS over the complete data for learning the parameters. However, this could cause problems due to the nondifferentiable objective function. In order to solve this problem, the PSO algorithm has been employed to tune the weights of RNN for minimizing the objective. Experimental results obtained on the Stanford background dataset show that our PSO-based training algorithm outperforms traditional RNN, Pixel CRF, region-based energy, simultaneous MRF, and superpixel MRF.

Structural properties of recursively partitionable graphs with connectivity 2

DEFF Research Database (Denmark)

Baudon, Olivier; Bensmail, Julien; Foucaud, Florent

2017-01-01

, namely the ones of being online arbitrarily partitionable and recursively arbitrarily partitionable (OL-AP and R-AP for short, respectively), in which the subgraphs induced by a partition of G must not only be con-nected but also ful_l additional conditions. In this paper, we point out some structural...... properties of OL-AP and R-AP graphs with connectivity 2. In particular, we show that deleting a cut pair of these graphs results in a graph with a bounded number of components, some of whom have a small number of vertices. We obtain these results by studying a simple class of 2-connected graphs called...

Generalized Stokes eignefunctions: a new trial basis for the solution of incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Batcho, P.F.; Karniadakis, G.E.

1994-01-01

The present study focuses on the solution of the incompressible Navier-Stokes equations in general, non-separable domains, and employs a Galerkin projection of divergence-free vector functions as a trail basis. This basis is obtained from the solution of a generalized constrained Stokes eigen-problem in the domain of interest. Faster convergence can be achieved by constructing a singular Stokes eigen-problem in which the Stokes operator is modified to include a variable coefficient which vanishes at the domain boundaries. The convergence properties of such functions are advantageous in a least squares sense and are shown to produce significantly better approximations to the solution of the Navier-Stokes equations in post-critical states where unsteadiness characterizes the flowfield. Solutions for the eigen-systems are efficiently accomplished using a combined Lanczos-Uzawa algorithm and spectral element discretizations. Results are presented for different simulations using these global spectral trial basis on non-separable and multiply-connected domains. It is confirmed that faster convergence is obtained using the singular eigen-expansions in approximating stationary Navier-Stokes solutions in general domains. It is also shown that 100-mode expansions of time-dependent solutions based on the singular Stokes eigenfunctions are sufficient to accurately predict the dynamics of flows in such domains, including Hopf bifurcations, intermittency, and details of flow structures

A non-local theory of generalized entropy solutions of the Cauchy problem for a class of hyperbolic systems of conservation laws

International Nuclear Information System (INIS)

Panov, E Yu

1999-01-01

We consider a hyperbolic system of conservation laws on the space of symmetric second-order matrices. The right-hand side of this system contains the functional calculus operator f-bar(U) generated in the general case only by a continuous scalar function f(u). For these systems we define and describe the set of singular entropies, introduce the concept of generalized entropy solutions of the corresponding Cauchy problem, and investigate the properties of generalized entropy solutions. We define the class of strong generalized entropy solutions, in which the Cauchy problem has precisely one solution. We suggest a condition on the initial data under which any generalized entropy solution is strong, which implies its uniqueness. Under this condition we establish that the 'vanishing viscosity' method converges. An example shows that in the general case there can be more than one generalized entropy solution

General exact solution for homogeneous time-dependent self-gravitating perfect fluids

International Nuclear Information System (INIS)

Gaete, P.; Hojman, R.

1988-01-01

A procedure to obtain the general exact solution of Einstein equations for a self-gravitating spherically-symmetric static perfect fluid obeying an arbitrary equation of state, is applied to time-dependent Kantowsky-Sachs line elements (with spherical, planar and hyperbolic symmetry). As in the static case, the solution is generated by an arbitrary function of the independent variable and its first derivative. To illustrate the results, the whole family of (plane-symmetric) solutions with a ''gamma-law'' equation of state is explicity obtained in terms of simple known functions. It is also shown that, while in the static plane-symmtric line elements, every metric is in one to one correspondence with a ''partner-metric'' (both originated from the same generatrix function), in this case every generatrix function univocally determines one metric. (author) [pt

Centennial of General Relativity (1915-2015); The Schwarzschild Solution and Black Holes

OpenAIRE

Blinder, S. M.

2015-01-01

This year marks the 100th anniversary of Einstein's General Theory of Relativity (1915-2015). The first nontrivial solution of the Einstein field equations was derived by Karl Schwarzschild in 1916. This Note will focus mainly on the Schwarzschild solution and the remarkable developments which it inspired, the most dramatic being the prediction of black holes. Later extensions of Schwarzschild's spacetime structure has led to even wilder conjectures, such as white holes and passages to other ...

Reliability evaluation of non-reparable three-state systems using Markov model and its comparison with the UGF and the recursive methods

International Nuclear Information System (INIS)

Pourkarim Guilani, Pedram; Sharifi, Mani; Niaki, S.T.A.; Zaretalab, Arash

2014-01-01

In multi-state systems (MSS) reliability problems, it is assumed that the components of each subsystem have different performance rates with certain probabilities. This leads into extensive computational efforts involved in using the commonly employed universal generation function (UGF) and the recursive algorithm to obtain reliability of systems consisting of a large number of components. This research deals with evaluating non-repairable three-state systems reliability and proposes a novel method based on a Markov process for which an appropriate state definition is provided. It is shown that solving the derived differential equations significantly reduces the computational time compared to the UGF and the recursive algorithm. - Highlights: • Reliability evaluation of a non-repairable three-state systems is aimed. • A novel method based on a Markov process is proposed. • An appropriate state definition is provided. • Computational time is significantly less compared to the ones in the UGF and the recursive methods

Speed control of induction motor using fuzzy recursive least squares technique

OpenAIRE

Santiago Sánchez; Eduardo Giraldo

2008-01-01

A simple adaptive controller design is presented in this paper, the control system uses the adaptive fuzzy logic, sliding modes and is trained with the recursive least squares technique. The problem of parameter variation is solved with the adaptive controller; the use of an internal PI regulator produces that the speed control of the induction motor be achieved by the stator currents instead the input voltage. The rotor-flux oriented coordinated system model is used to develop and test the c...

Orthogonal functions, discrete variable representation, and generalized gauss quadratures

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2002-01-01

in the original representation. This has been exploited in bound-state, scattering, and time-dependent problems using the so-called, discrete variable representation (DVR). At the core of this approach is the mathematical three-term recursion relationship satisfied by the classical orthogonal functions...... functions, this is not the case. However, they may be computed in a stable numerical fashion, via the recursion. In essence, this is an application of the well-known Lanczos recursion approach. Once the recursion coefficients are known, it is possible to compute the points and weights of quadratures on...

On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

International Nuclear Information System (INIS)

Liu Hongzhun; Pan Zuliang; Li Peng

2006-01-01

In this article, we will derive an equality, where the Taylor series expansion around ε = 0 for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Baecklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Baecklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.

Do we represent intentional action as recursively embedded? The answer must be empirical. A comment on Vicari and Adenzato (2014).

Science.gov (United States)

Martins, Mauricio D; Fitch, W Tecumseh

2015-12-15

The relationship between linguistic syntax and action planning is of considerable interest in cognitive science because many researchers suggest that "motor syntax" shares certain key traits with language. In a recent manuscript in this journal, Vicari and Adenzato (henceforth VA) critiqued Hauser, Chomsky and Fitch's 2002 (henceforth HCF's) hypothesis that recursion is language-specific, and that its usage in other domains is parasitic on language resources. VA's main argument is that HCF's hypothesis is falsified by the fact that recursion typifies the structure of intentional action, and recursion in the domain of action is independent of language. Here, we argue that VA's argument is incomplete, and that their formalism can be contrasted with alternative frameworks that are equally consistent with existing data. Therefore their conclusions are premature without further empirical testing and support. In particular, to accept VA's argument it would be necessary to demonstrate both that humans in fact represent self-embedding in the structure of intentional action, and that language is not used to construct these representations. Copyright © 2015 Elsevier Inc. All rights reserved.

Exact periodic solutions of the sixth-order generalized Boussinesq equation

International Nuclear Information System (INIS)

Kamenov, O Y

2009-01-01

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u tt = u xx + 3(u 2 ) xx + u xxxx + αu xxxxxx , α in R, depending on the positive parameter α. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

Structural damage diagnosis based on on-line recursive stochastic subspace identification

International Nuclear Information System (INIS)

Loh, Chin-Hsiung; Weng, Jian-Huang; Liu, Yi-Cheng; Lin, Pei-Yang; Huang, Shieh-Kung

2011-01-01

This paper presents a recursive stochastic subspace identification (RSSI) technique for on-line and almost real-time structural damage diagnosis using output-only measurements. Through RSSI the time-varying natural frequencies of a system can be identified. To reduce the computation time in conducting LQ decomposition in RSSI, the Givens rotation as well as the matrix operation appending a new data set are derived. The relationship between the size of the Hankel matrix and the data length in each shifting moving window is examined so as to extract the time-varying features of the system without loss of generality and to establish on-line and almost real-time system identification. The result from the RSSI technique can also be applied to structural damage diagnosis. Off-line data-driven stochastic subspace identification was used first to establish the system matrix from the measurements of an undamaged (reference) case. Then the RSSI technique incorporating a Kalman estimator is used to extract the dynamic characteristics of the system through continuous monitoring data. The predicted residual error is defined as a damage feature and through the outlier statistics provides an indicator of damage. Verification of the proposed identification algorithm by using the bridge scouring test data and white noise response data of a reinforced concrete frame structure is conducted

Travelling wave solutions in a class of generalized Korteweg-de Vries equation

International Nuclear Information System (INIS)

Shen Jianwei; Xu Wei

2007-01-01

In this paper, we consider a new generalization of KdV equation u t = u x u l-2 + α[2u xxx u p + 4pu p-1 u x u xx + p(p - 1)u p-2 (u x ) 3 ] and investigate its bifurcation of travelling wave solutions. From the above analysis, we know that there exists compacton and cusp waves in the system. We explain the reason that these non-smooth travelling wave solution arise by using the bifurcation theory

The understanding of the students about the nature of light in recursive curriculum

Directory of Open Access Journals (Sweden)

Geide Rosa Coelho

2010-01-01

Full Text Available We report an inquiry on the development of students' understanding about the nature of light. The study happened in a learning environment with a recursive and spiral Physics syllabus. We investigated the change in students' understanding about the nature of light during their 3rd year in High School, and the level of understanding about this subject achieved by students at the end of this year. To assess the students' understanding, we developed an open questionnaire form and a set of hierarchical categories, consisting of five different models about the nature of light. The questionnaire was used to access the students´ understanding at the beginning and at the end of the third level of the recursive curriculum. The results showed that students have a high level of prior knowledge, and also that the Physics learning they experienced had enhanced their understanding, despite the effects are not verified in all the Physics classes. By the end of the third year, most of the students explain the nature of light using or a corpuscular electromagnetic model or a dual electromagnetic model, but some students use these models with inconsistencies in their explanations.

Local Stability Conditions for Two Types of Monetary Models with Recursive Utility

OpenAIRE

Miyazaki, Kenji; Utsunomiya, Hitoshi

2009-01-01

This paper explores local stability conditions for money-in-utility-function (MIUF) and transaction-costs (TC) models with recursive utility.A monetary variant of the Brock-Gale condition provides a theoretical justification of the comparative statics analysis. One of sufficient conditions for local stability is increasing marginal impatience (IMI) in consumption and money. However, this does not deny the possibility of decreasing marginal impatience (DMI). The local stability with DMI is mor...

A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems.

Science.gov (United States)

Kazemi, Mahdi; Arefi, Mohammad Mehdi

2017-03-01

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Recursive Utility and the Superneutrality of Money on the Transition Path

OpenAIRE

Miyazaki, Kenji

2010-01-01

this paper investigates whether a change in the growth rate of the money supply enhances the rate of capital accumulation in a cash-in-advance monetary model with recursive utility. Although money is superneutral in the steady state, the effect of the growth rate of money on the speed of capital accumulation depends not only on the curvature of the felicity but also on the slope and curvature of the discount rate function. We find that when the discount rate decreases with consumption and the...

Speed control of induction motor using fuzzy recursive least squares technique

Directory of Open Access Journals (Sweden)

Santiago Sánchez

2008-12-01

Full Text Available A simple adaptive controller design is presented in this paper, the control system uses the adaptive fuzzy logic, sliding modes and is trained with the recursive least squares technique. The problem of parameter variation is solved with the adaptive controller; the use of an internal PI regulator produces that the speed control of the induction motor be achieved by the stator currents instead the input voltage. The rotor-flux oriented coordinated system model is used to develop and test the control system.

On generalized Melvin solution for the Lie algebra E6

International Nuclear Information System (INIS)

Bolokhov, S.V.; Ivashchuk, V.D.

2017-01-01

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model in D dimensions, D ≥ 4, contains n 2-forms and l ≥ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions H s (z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials H s (z), s = 1,.., 6, for the Lie algebra E 6 are obtained and a corresponding solution for l = n = 6 is presented. The polynomials depend upon integration constants Q s , s = 1,.., 6. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for E 6 -polynomials at large z are governed by the integer-valued matrix ν = A -1 (I + P), where A -1 is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the Z 2 -group of symmetry of the Dynkin diagram. The 2-form fluxes Φ s , s = 1,.., 6, are calculated. (orig.)

Accounting Fundamentals and Variations of Stock Price: Methodological Refinement with Recursive Simultaneous Model

OpenAIRE

Sumiyana, Sumiyana; Baridwan, Zaki

2013-01-01

This study investigates association between accounting fundamentals and variations of stock prices using recursive simultaneous equation model. The accounting fundamentalsconsist of earnings yield, book value, profitability, growth opportunities and discount rate. The prior single relationships model has been investigated by Chen and Zhang (2007),Sumiyana (2011) and Sumiyana et al. (2010). They assume that all accounting fundamentals associate direct-linearly to the stock returns. This study ...

Binary recursive partitioning: background, methods, and application to psychology.

Science.gov (United States)

Merkle, Edgar C; Shaffer, Victoria A

2011-02-01

Binary recursive partitioning (BRP) is a computationally intensive statistical method that can be used in situations where linear models are often used. Instead of imposing many assumptions to arrive at a tractable statistical model, BRP simply seeks to accurately predict a response variable based on values of predictor variables. The method outputs a decision tree depicting the predictor variables that were related to the response variable, along with the nature of the variables' relationships. No significance tests are involved, and the tree's 'goodness' is judged based on its predictive accuracy. In this paper, we describe BRP methods in a detailed manner and illustrate their use in psychological research. We also provide R code for carrying out the methods.

The gravitational polarization in general relativity: solution to Szekeres' model of quadrupole polarization

International Nuclear Information System (INIS)

Montani, Giovanni; Ruffini, Remo; Zalaletdinov, Roustam

2003-01-01

A model for the static weak-field macroscopic medium is analysed and the equation for the macroscopic gravitational potential is derived. This is a biharmonic equation which is a non-trivial generalization of the Poisson equation of Newtonian gravity. In the case of strong gravitational quadrupole polarization, it essentially holds inside a macroscopic matter source. Outside the source the gravitational potential fades away exponentially. The equation is equivalent to a system of the Poisson equation and the non-homogeneous modified Helmholtz equations. The general solution to this system is obtained by using the Green function method and it is not limited to Newtonian gravity. In the case of insignificant gravitational quadrupole polarization, the equation for macroscopic gravitational potential becomes the Poisson equation with the matter density renormalized by a factor including the value of the quadrupole gravitational polarization of the source. The general solution to this equation obtained by using the Green function method is limited to Newtonian gravity

Cusping, transport and variance of solutions to generalized Fokker-Planck equations

Science.gov (United States)

Carnaffan, Sean; Kawai, Reiichiro

2017-06-01

We study properties of solutions to generalized Fokker-Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker-Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.

Determinable solutions for one-dimensional quantum potentials: scattering, quasi-bound and bound-state problems

International Nuclear Information System (INIS)

Lee, Hwasung; Lee, Y J

2007-01-01

We derive analytic expressions of the recursive solutions to Schroedinger's equation by means of a cutoff-potential technique for one-dimensional piecewise-constant potentials. These solutions provide a method for accurately determining the transmission probabilities as well as the wavefunction in both classically accessible regions and inaccessible regions for any barrier potentials. It is also shown that the energy eigenvalues and the wavefunctions of bound states can be obtained for potential-well structures by exploiting this method. Calculational results of illustrative examples are shown in order to verify this method for treating barrier and potential-well problems

Recursive stochastic effects in valley hybrid inflation

Science.gov (United States)

Levasseur, Laurence Perreault; Vennin, Vincent; Brandenberger, Robert

2013-10-01

Hybrid inflation is a two-field model where inflation ends because of a tachyonic instability, the duration of which is determined by stochastic effects and has important observational implications. Making use of the recursive approach to the stochastic formalism presented in [L. P. Levasseur, preceding article, Phys. Rev. D 88, 083537 (2013)], these effects are consistently computed. Through an analysis of backreaction, this method is shown to converge in the valley but points toward an (expected) instability in the waterfall. It is further shown that the quasistationarity of the auxiliary field distribution breaks down in the case of a short-lived waterfall. We find that the typical dispersion of the waterfall field at the critical point is then diminished, thus increasing the duration of the waterfall phase and jeopardizing the possibility of a short transition. Finally, we find that stochastic effects worsen the blue tilt of the curvature perturbations by an O(1) factor when compared with the usual slow-roll contribution.

Model-Based Recursive Partitioning for Subgroup Analyses.

Science.gov (United States)

Seibold, Heidi; Zeileis, Achim; Hothorn, Torsten

2016-05-01

The identification of patient subgroups with differential treatment effects is the first step towards individualised treatments. A current draft guideline by the EMA discusses potentials and problems in subgroup analyses and formulated challenges to the development of appropriate statistical procedures for the data-driven identification of patient subgroups. We introduce model-based recursive partitioning as a procedure for the automated detection of patient subgroups that are identifiable by predictive factors. The method starts with a model for the overall treatment effect as defined for the primary analysis in the study protocol and uses measures for detecting parameter instabilities in this treatment effect. The procedure produces a segmented model with differential treatment parameters corresponding to each patient subgroup. The subgroups are linked to predictive factors by means of a decision tree. The method is applied to the search for subgroups of patients suffering from amyotrophic lateral sclerosis that differ with respect to their Riluzole treatment effect, the only currently approved drug for this disease.

Explicit solution of the quantum three-body Calogero-Sutherland model

CERN Document Server

Perelomov, A.M.; Zaugg, P.

1998-01-01

Quantum integrable systems generalizing Calogero-Sutherland systems were introduced by Olshanetsky and Perelomov (1977). Recently, it was proved that for systems with trigonometric potential, the series in the product of two wave functions is a deformation of the Clebsch-Gordan series. This yields recursion relations for the wave functions of those systems. In this note, this approach is used to compute the explicit expressions for the three-body Calogero-Sutherland wave functions, which are the Jack polynomials. We conjecture that similar results are also valid for the more general two-parameters deformation introduced by Macdonald.

Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method.

Science.gov (United States)

Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-

2014-01-01

Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.

Direct computation of scattering matrices for general quantum graphs

International Nuclear Information System (INIS)

Caudrelier, V.; Ragoucy, E.

2010-01-01

We present a direct and simple method for the computation of the total scattering matrix of an arbitrary finite noncompact connected quantum graph given its metric structure and local scattering data at each vertex. The method is inspired by the formalism of Reflection-Transmission algebras and quantum field theory on graphs though the results hold independently of this formalism. It yields a simple and direct algebraic derivation of the formula for the total scattering and has a number of advantages compared to existing recursive methods. The case of loops (or tadpoles) is easily incorporated in our method. This provides an extension of recent similar results obtained in a completely different way in the context of abstract graph theory. It also allows us to discuss briefly the inverse scattering problem in the presence of loops using an explicit example to show that the solution is not unique in general. On top of being conceptually very easy, the computational advantage of the method is illustrated on two examples of 'three-dimensional' graphs (tetrahedron and cube) for which other methods are rather heavy or even impractical.

Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation

OpenAIRE

Mi, Yuzhen

2016-01-01

This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-v)v+ϵf(ϵ,v,vx,u,ux), uxx=-(1-u-a1v)u+ϵg(ϵ,v,vx,u,ux). By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.

Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation

Directory of Open Access Journals (Sweden)

Yuzhen Mi

2016-01-01

Full Text Available This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-vv+ϵf(ϵ,v,vx,u,ux, uxx=-(1-u-a1vu+ϵg(ϵ,v,vx,u,ux. By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.

Periodic solutions of differential equations with a general piecewise constant argument and applications

Directory of Open Access Journals (Sweden)

Kuo-Shou Chiu

2010-08-01

Full Text Available In this paper we investigate the existence of the periodic solutions of a quasilinear differential equation with piecewise constant argument of generalized type. By using some fixed point theorems and some new analysis technique, sufficient conditions are obtained for the existence and uniqueness of periodic solutions of these systems. A new Gronwall type lemma is proved. Some examples concerning biological models as Lasota-Wazewska, Nicholson's blowflies and logistic models are treated.

Exact periodic solutions of the sixth-order generalized Boussinesq equation

Energy Technology Data Exchange (ETDEWEB)

Kamenov, O Y [Department of Applied Mathematics and Informatics, Technical University of Sofia, PO Box 384, 1000 Sofia (Bulgaria)], E-mail: okam@abv.bg

2009-09-18

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u{sub tt} = u{sub xx} + 3(u{sup 2}){sub xx} + u{sub xxxx} + {alpha}u{sub xxxxxx}, {alpha} in R, depending on the positive parameter {alpha}. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

The boundary length and point spectrum enumeration of partial chord diagrams using cut and join recursion

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Fuji, Hiroyuki; Penner, Robert C.

relation, which combined with an initial condition determines these numbers uniquely. This recursion relation is equivalent to a second order, non-linear, algebraic partial differential equation for the generating function of the numbers of partial chord diagrams filtered by the boundary length and point...

ACCOUNTING FUNDAMENTALS AND VARIATIONS OF STOCK PRICE: METHODOLOGICAL REFINEMENT WITH RECURSIVE SIMULTANEOUS MODEL

OpenAIRE

Sumiyana, Sumiyana; Baridwan, Zaki

2015-01-01

This study investigates association between accounting fundamentals and variations of stock prices using recursive simultaneous equation model. The accounting fundamentalsconsist of earnings yield, book value, profitability, growth opportunities and discount rate. The prior single relationships model has been investigated by Chen and Zhang (2007),Sumiyana (2011) and Sumiyana et al. (2010). They assume that all accounting fundamentals associate direct-linearly to the stock returns. This study ...

The calculation of deep levels in semiconductors by using a recursion method for super-cells

International Nuclear Information System (INIS)

Wong Yongliang.

1987-01-01

The paper presents the theory of deep levels in semiconductors, the super-cell approach to the theory of deep level impurities, the calculation of band structure by using the tight-binding method and the recursion method used to study the defects in the presence of lattice relaxation and extended defect complexes. 47 refs

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

Science.gov (United States)

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

Directory of Open Access Journals (Sweden)

Suheel Abdullah Malik

Full Text Available In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE through substitution is converted into a nonlinear ordinary differential equation (NODE. The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM, homotopy perturbation method (HPM, and optimal homotopy asymptotic method (OHAM, show that the suggested scheme is fairly accurate and viable for solving such problems.

Stochastic Recursive Algorithms for Optimization Simultaneous Perturbation Methods

CERN Document Server

Bhatnagar, S; Prashanth, L A

2013-01-01

Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from sim...

Recursive model for the fragmentation of polarized quarks

Science.gov (United States)

Kerbizi, A.; Artru, X.; Belghobsi, Z.; Bradamante, F.; Martin, A.

2018-04-01

We present a model for Monte Carlo simulation of the fragmentation of a polarized quark. The model is based on string dynamics and the 3P0 mechanism of quark pair creation at string breaking. The fragmentation is treated as a recursive process, where the splitting function of the subprocess q →h +q' depends on the spin density matrix of the quark q . The 3P0 mechanism is parametrized by a complex mass parameter μ , the imaginary part of which is responsible for single spin asymmetries. The model has been implemented in a Monte Carlo program to simulate jets made of pseudoscalar mesons. Results for single hadron and hadron pair transverse-spin asymmetries are found to be in agreement with experimental data from SIDIS and e+e- annihilation. The model predictions on the jet-handedness are also discussed.

Generalized Langevin Theory Of The Brownian Motion And The Dynamics Of Polymers In Solution

International Nuclear Information System (INIS)

Tothova, J.; Lisy, V.

2015-01-01

The review deals with a generalization of the Rouse and Zimm bead-spring models of the dynamics of flexible polymers in dilute solutions. As distinct from these popular theories, the memory in the polymer motion is taken into account. The memory naturally arises as a consequence of the fluid and bead inertia within the linearized Navier-Stokes hydrodynamics. We begin with a generalization of the classical theory of the Brownian motion, which forms the basis of any theory of the polymer dynamics. The random force driving the Brownian particles is not the white one as in the Langevin theory, but “colored”, i.e., statistically correlated in time, and the friction force on the particles depends on the history of their motion. An efficient method of solving the resulting generalized Langevin equations is presented and applied to the solution of the equations of motion of polymer beads. The memory effects lead to several peculiarities in the time correlation functions used to describe the dynamics of polymer chains. So, the mean square displacement of the polymer coils contains algebraic long-time tails and at short times it is ballistic. It is shown how these features reveal in the experimentally observable quantities, such as the dynamic structure factors of the scattering or the viscosity of polymer solutions. A phenomenological theory is also presented that describes the dependence of these quantities on the polymer concentration in solution. (author)

Regular Bulk Solutions in Brane-Worlds with Inhomogeneous Dust and Generalized Dark Radiation

International Nuclear Information System (INIS)

Rocha, Roldão da; Kuerten, A. M.; Herrera-Aguilar, A.

2015-01-01

From the dynamics of a brane-world with matter fields present in the bulk, the bulk metric and the black string solution near the brane are generalized, when both the dynamics of inhomogeneous dust/generalized dark radiation on the brane-world and inhomogeneous dark radiation in the bulk as well are considered as exact dynamical collapse solutions. Based on the analysis on the inhomogeneous static exterior of a collapsing sphere of homogeneous dark radiation on the brane, the associated black string warped horizon is studied, as well as the 5D bulk metric near the brane. Moreover, the black string and the bulk are shown to be more regular upon time evolution, for suitable values for the dark radiation parameter in the model, by analyzing the soft physical singularities

Existence and Solution-representation of IVP for LFDE with Generalized Riemann-Liouville fractional derivatives and $n$ terms

OpenAIRE

Kim, Myong-Ha; Ri, Guk-Chol; O, Hyong-Chol

2013-01-01

This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.

On the theory of generalized entropy solutions of the Cauchy problem for a class of non-strictly hyperbolic systems of conservation laws

International Nuclear Information System (INIS)

Panov, E Yu

2000-01-01

Many-dimensional non-strictly hyperbolic systems of conservation laws with a radially degenerate flux function are considered. For such systems the set of entropies is defined and described, the concept of generalized entropy solution of the Cauchy problem is introduced, and the properties of generalized entropy solutions are studied. The class of strong generalized entropy solutions is distinguished, in which the Cauchy problem in question is uniquely soluble. A condition on the initial data is described that ensures that the generalized entropy solution is strong and therefore unique. Under this condition the convergence of the 'vanishing viscosity' method is established. An example presented in the paper shows that a generalized entropy solution is not necessarily unique in the general case

General N-Dark Soliton Solutions of the Multi-Component Mel'nikov System

Science.gov (United States)

Han, Zhong; Chen, Yong; Chen, Junchao

2017-07-01

A general form of N-dark soliton solutions of the multi-component Mel'nikov system are presented. Taking the coupled Mel'nikov system comprised of two-component short waves and one-component long wave as an example, its general N-dark-dark soliton solutions in Gram determinant form are constructed through the KP hierarchy reduction method. The dynamics of single dark-dark soliton and two dark-dark solitons are discussed in detail. It can be shown that the collisions of dark-dark solitons are elastic and energies of the solitons in different components completely transmit through. In addition, the dark-dark soliton bound states including both stationary and moving cases are also investigated. An interesting feature for the coupled Mel'nikov system is that the stationary dark-dark soliton bound states can exist for all possible combinations of nonlinearity coefficients including positive, negative and mixed types, while the moving case are possible when nonlinearity coefficients take opposite signs or they are both negative.

Normalized Minimum Error Entropy Algorithm with Recursive Power Estimation

Directory of Open Access Journals (Sweden)

Namyong Kim

2016-06-01

Full Text Available The minimum error entropy (MEE algorithm is known to be superior in signal processing applications under impulsive noise. In this paper, based on the analysis of behavior of the optimum weight and the properties of robustness against impulsive noise, a normalized version of the MEE algorithm is proposed. The step size of the MEE algorithm is normalized with the power of input entropy that is estimated recursively for reducing its computational complexity. The proposed algorithm yields lower minimum MSE (mean squared error and faster convergence speed simultaneously than the original MEE algorithm does in the equalization simulation. On the condition of the same convergence speed, its performance enhancement in steady state MSE is above 3 dB.

Generalized nonlinear Proca equation and its free-particle solutions

Energy Technology Data Exchange (ETDEWEB)

Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)

2016-06-15

We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)

Recursive Pyramid Algorithm-Based Discrete Wavelet Transform for Reactive Power Measurement in Smart Meters

Directory of Open Access Journals (Sweden)

Mahin K. Atiq

2013-09-01

Full Text Available Measurement of the active, reactive, and apparent power is one of the most fundamental tasks of smart meters in energy systems. Recently, a number of studies have employed the discrete wavelet transform (DWT for power measurement in smart meters. The most common way to implement DWT is the pyramid algorithm; however, this is not feasible for practical DWT computation because it requires either a log N cascaded filter or O (N word size memory storage for an input signal of the N-point. Both solutions are too expensive for practical applications of smart meters. It is proposed that the recursive pyramid algorithm is more suitable for smart meter implementation because it requires only word size storage of L × Log (N-L, where L is the length of filter. We also investigated the effect of varying different system parameters, such as the sampling rate, dc offset, phase offset, linearity error in current and voltage sensors, analog to digital converter resolution, and number of harmonics in a non-sinusoidal system, on the reactive energy measurement using DWT. The error analysis is depicted in the form of the absolute difference between the measured and the true value of the reactive energy.

Working Memory: A Cognitive Limit to Non-Human Primate Recursive Thinking Prior to Hominid Evolution

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Dwight W. Read

2008-10-01

Full Text Available In this paper I explore the possibility that recursion is not part of the cognitive repertoire of non-human primates such as chimpanzees due to limited working memory capacity. Multiple lines of data, from nut cracking to the velocity and duration of cognitive development, imply that chimpanzees have a short-term memory size that limits working memory to dealing with two, or at most three, concepts at a time. If so, as a species they lack the cognitive capacity for recursive thinking to be integrated into systems of social organization and communication. If this limited working memory capacity is projected back to a common ancestor for Pan and Homo, it follows that early hominid ancestors would have had limited working memory capacity. Hence we should find evidence for expansion of working memory capacity during hominid evolution reflected in changes in the products of conceptually framed activities such as stone tool production. Data on the artifacts made by our hominid ancestors support this expansion hypothesis for hominid working memory, thereby leading to qualitative differences between Pan and Homo.

Elliptic solutions of generalized Brans-Dicke gravity with a non-universal coupling

Energy Technology Data Exchange (ETDEWEB)

Alimi, J.M.; Reverdy, V. [Observatoire de Paris, Laboratoire Univers et Theories (LUTh), Meudon (France); Golubtsova, A.A. [Observatoire de Paris, Laboratoire Univers et Theories (LUTh), Meudon (France); Peoples' Friendship University of Russia, Institute of Gravitation and Cosmology, Moscow (Russian Federation)

2014-10-15

We study a model of the generalized Brans-Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics equations on the target space of the nonlinear sigma model. The analytical solutions in elliptical functions are obtained when the conformal couplings are given by reciprocal exponential functions. The behavior of the scale factor in the Jordan frame is studied using numerical computations. For certain parameters the solutions can describe an accelerated expansion. We also derive an analytical approximation in exponential functions. (orig.)

The general Klein-Gordon-Schroedinger system: modulational instability and exact solutions

International Nuclear Information System (INIS)

Tang Xiaoyan; Ding Wei

2008-01-01

The general Klein-Gordon-Schroedinger (gKGS) system is studied where the cubic auto-interactions are introduced in both the nonlinear Schroedinger and the nonlinear Klein-Gordon fields. We first investigate the modulational instability (MI) of the system, and thus derive the general dispersion relation between the frequency and wavenumber of the modulating perturbations, which demonstrates many possibilities for the MI regions. Using the travelling wave reduction, the gKGS system is greatly simplified. Via a simple function expansion method, we obtain some exact travelling wave solutions. Under some special parameter values, some representative wave structures are graphically displayed including the kink, anti-kink, bright, dark, grey and periodic solitons

Exact Calculation of the Thermodynamics of Biomacromolecules on Cubic Recursive Lattice.

Science.gov (United States)

Huang, Ran

The thermodynamics of biomacromolecules featured as foldable polymer with inner-linkage of hydrogen bonds, e. g. protein, RNA and DNA, play an impressive role in either physical, biological, and polymer sciences. By treating the foldable chains to be the two-tolerate self-avoiding trails (2T polymer), abstract lattice modeling of these complex polymer systems to approach their thermodynamics and subsequent bio-functional properties have been developed for decades. Among these works, the calculations modeled on Bethe and Husimi lattice have shown the excellence of being exactly solvable. Our project extended this effort into the 3D situation, i.e. the cubic recursive lattice. The preliminary exploration basically confirmed others' previous findings on the planar structure, that we have three phases in the grand-canonical phase diagram, with a 1st order transition between non-polymerized and polymer phases, and a 2nd order transition between two distinguishable polymer phases. However the hydrogen bond energy J, stacking energy ɛ, and chain rigidity energy H play more vigorous effects on the thermal behaviors, and this is hypothesized to be due to the larger number of possible configurations provided by the complicated 3D model. By the so far progress, the calculation of biomacromolecules may be applied onto more complex recursive lattices, such as the inhomogeneous lattice to describe the cross-dimensional situations, and beside the thermal properties of the 2T polymers, we may infer some interesting insights of the mysterious folding problem itself. National Natural Science Foundation of China.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

Science.gov (United States)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Real time damage detection using recursive principal components and time varying auto-regressive modeling

Science.gov (United States)

Krishnan, M.; Bhowmik, B.; Hazra, B.; Pakrashi, V.

2018-02-01

In this paper, a novel baseline free approach for continuous online damage detection of multi degree of freedom vibrating structures using Recursive Principal Component Analysis (RPCA) in conjunction with Time Varying Auto-Regressive Modeling (TVAR) is proposed. In this method, the acceleration data is used to obtain recursive proper orthogonal components online using rank-one perturbation method, followed by TVAR modeling of the first transformed response, to detect the change in the dynamic behavior of the vibrating system from its pristine state to contiguous linear/non-linear-states that indicate damage. Most of the works available in the literature deal with algorithms that require windowing of the gathered data owing to their data-driven nature which renders them ineffective for online implementation. Algorithms focussed on mathematically consistent recursive techniques in a rigorous theoretical framework of structural damage detection is missing, which motivates the development of the present framework that is amenable for online implementation which could be utilized along with suite experimental and numerical investigations. The RPCA algorithm iterates the eigenvector and eigenvalue estimates for sample covariance matrices and new data point at each successive time instants, using the rank-one perturbation method. TVAR modeling on the principal component explaining maximum variance is utilized and the damage is identified by tracking the TVAR coefficients. This eliminates the need for offline post processing and facilitates online damage detection especially when applied to streaming data without requiring any baseline data. Numerical simulations performed on a 5-dof nonlinear system under white noise excitation and El Centro (also known as 1940 Imperial Valley earthquake) excitation, for different damage scenarios, demonstrate the robustness of the proposed algorithm. The method is further validated on results obtained from case studies involving

Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Chekhov, Leonid O.; Penner, Robert

2013-01-01

and free energies are convergent for small t and all s as a perturbation of the Gaussian potential, which arises for st=0. This perturbation is computed using the formalism of the topological recursion. The corresponding enumeration of chord diagrams gives at once the number of RNA complexes of a given...... topology as well as the number of cells in Riemann's moduli spaces for bordered surfaces. The free energies are computed here in principle for all genera and explicitly for genera less than four....

Loop equations and topological recursion for the arbitrary-$\\beta$ two-matrix model

CERN Document Server

Bergère, Michel; Marchal, Olivier; Prats-Ferrer, Aleix

2012-01-01

We write the loop equations for the $\\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral curve, i.e. it is given by a differential operator (instead of an algebraic equation for the hermitian case). Here, we study the case where that quantum spectral curve is completely degenerate, it satisfies a Bethe ansatz, and the spectral curve is the Baxter TQ relation.

Understanding who benefits at each step in an internet-based diabetes self-management program: application of a recursive partitioning approach.

Science.gov (United States)

Glasgow, Russell E; Strycker, Lisa A; King, Diane K; Toobert, Deborah J

2014-02-01

Efforts to predict success in chronic disease management programs have been generally unsuccessful. To identify patient subgroups associated with success at each of 6 steps in a diabetes self-management (DSM) program. Using data from a randomized trial, recursive partitioning with signal detection analysis was used to identify subgroups associated with 6 sequential steps of program success: agreement to participate, completion of baseline, initial website engagement, 4-month behavior change, later engagement, and longer-term maintenance. The study was conducted in 5 primary care clinics within Kaiser Permanente Colorado. Different numbers of patients participated in each step, including 2076, 544, 270, 219, 127, and 89. All measures available were used to address success at each step. Intervention. Participants were randomized to receive either enhanced usual care or 1 of 2 Internet-based DSM programs: 1) self-administered, computer-assisted self-management and 2) the self-administered program with the addition of enhanced social support. Two sets of potential predictor variables and 6 dichotomous outcomes were created. Signal detection analysis differentiated successful and unsuccessful subgroups at all but the final step. Different patient subgroups were associated with success at these different steps. Demographic factors (education, ethnicity, income) were associated with initial participation but not with later steps, and the converse was true of health behavior variables. Analyses were limited to one setting, and the sample sizes for some of the steps were modest. Signal detection and recursive partitioning methods may be useful for identifying subgroups that are more or less successful at different steps of intervention and may aid in understanding variability in outcomes.

Recursive formulae and performance comparisons for first mode dynamics of periodic structures

Science.gov (United States)

Hobeck, Jared D.; Inman, Daniel J.

2017-05-01

Periodic structures are growing in popularity especially in the energy harvesting and metastructures communities. Common types of these unique structures are referred to in the literature as zigzag, orthogonal spiral, fan-folded, and longitudinal zigzag structures. Many of these studies on periodic structures have two competing goals in common: (a) minimizing natural frequency, and (b) minimizing mass or volume. These goals suggest that no single design is best for all applications; therefore, there is a need for design optimization and comparison tools which first require efficient easy-to-implement models. All available structural dynamics models for these types of structures do provide exact analytical solutions; however, they are complex requiring tedious implementation and providing more information than necessary for practical applications making them computationally inefficient. This paper presents experimentally validated recursive models that are able to very accurately and efficiently predict the dynamics of the four most common types of periodic structures. The proposed modeling technique employs a combination of static deflection formulae and Rayleigh’s Quotient to estimate the first mode shape and natural frequency of periodic structures having any number of beams. Also included in this paper are the results of an extensive experimental validation study which show excellent agreement between model prediction and measurement. Lastly, the proposed models are used to evaluate the performance of each type of structure. Results of this performance evaluation reveal key advantages and disadvantages associated with each type of structure.

Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation

Directory of Open Access Journals (Sweden)

Huanhe Dong

2014-01-01

Full Text Available We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.

Recursive polarization of nuclear spins in diamond at arbitrary magnetic fields

International Nuclear Information System (INIS)

Pagliero, Daniela; Laraoui, Abdelghani; Henshaw, Jacob D.; Meriles, Carlos A.

2014-01-01

We introduce an alternate route to dynamically polarize the nuclear spin host of nitrogen-vacancy (NV) centers in diamond. Our approach articulates optical, microwave, and radio-frequency pulses to recursively transfer spin polarization from the NV electronic spin. Using two complementary variants of the same underlying principle, we demonstrate nitrogen nuclear spin initialization approaching 80% at room temperature both in ensemble and single NV centers. Unlike existing schemes, our approach does not rely on level anti-crossings and is thus applicable at arbitrary magnetic fields. This versatility should prove useful in applications ranging from nanoscale metrology to sensitivity-enhanced NMR

A general solution of the BV-master equation and BRST field theories

International Nuclear Information System (INIS)

Dayi, O.F.

1993-05-01

For a class of first order gauge theories it was shown that the proper solution of the BV-master equation can be obtained straightforwardly. Here we present the general condition which the gauge generators should satisfy to conclude that this construction is relevant. The general procedure is illustrated by its application to the Chern-Simons theory in any odd-dimension. Moreover, it is shown that this formalism is also applicable to BRST field theories, when one replaces the role of the exterior derivative with the BRST charge of first quantization. (author). 17 refs

Generalized hyperbolic functions to find soliton-like solutions for a system of coupled nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schroedinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons

General classical solutions of the complex Grassmannian and CP sub(N-1) sigma models

International Nuclear Information System (INIS)

Sasaki, Ryu.

1983-05-01

General classical solutions are constructed for the complex Grassmannian non-linear sigma models in two euclidean dimensions in terms of holomorphic functions. The Grassmannian sigma models are a simple generalization of the well known CP sup(N-1) model in two dimensions and they share various interesting properties; existence of (anti-) instantons, an infinite number of conserved quantities and complete integrability. (author)

Implicit Learning of Recursive Context-Free Grammars

Science.gov (United States)

Rohrmeier, Martin; Fu, Qiufang; Dienes, Zoltan

2012-01-01

Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams) between individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex context-free structures, which model some features of natural languages. They support the relevance of artificial grammar learning for probing mechanisms of language learning and challenge existing theories and computational models of implicit learning. PMID:23094021

Implicit learning of recursive context-free grammars.

Science.gov (United States)

Rohrmeier, Martin; Fu, Qiufang; Dienes, Zoltan

2012-01-01

Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams) between individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex context-free structures, which model some features of natural languages. They support the relevance of artificial grammar learning for probing mechanisms of language learning and challenge existing theories and computational models of implicit learning.

Implicit learning of recursive context-free grammars.

Directory of Open Access Journals (Sweden)

Martin Rohrmeier

Full Text Available Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams between individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex context-free structures, which model some features of natural languages. They support the relevance of artificial grammar learning for probing mechanisms of language learning and challenge existing theories and computational models of implicit learning.

A general solution for the dynamics of a generalized non-degenerate optical parametric down-conversion interaction by virtue of the Lewis-Riesenfeld invariant theory

International Nuclear Information System (INIS)

Li Jiangfan; Jiang Zongfu; Xiao Fuliang; Huang Chunjia

2005-01-01

The dynamics of a generalized non-degenerate optical parametric down-conversion interaction whose Hamiltonian includes an arbitrary time-dependent driving part and a two-mode coupled part is studied by adopting the Lewis-Riesenfeld invariant theory. The closed formulae for the evolution of the quantum states and the evolution operators of the system are obtained. It is shown that various generalized squeezed states arise naturally in the process, and the two-mode squeezed effect is independent of the driving part. An explicitly analytical solution of the Schroedinger equation is further derived as the classical generalized force acting on each mode and the coupling of the two modes both have harmonic time dependences. This solution is found to be in agreement with previous research in special cases

Variance-optimal hedging for processes with stationary independent increments

DEFF Research Database (Denmark)

Hubalek, Friedrich; Kallsen, J.; Krawczyk, L.

We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation, we...

A new term in the recursive expansion of the inverse Baker-Campbell-Hausdorff formula

International Nuclear Information System (INIS)

Riccardi, A.

1984-01-01

A recursive algorithm is derived, allowing the expansion in lambda of z=exp(x+lambda y) for noncommuting x and y, written as ordered product of exponentials. Such an expansion is the inverse of the usual Baker-Campbell-Hausdorff formula. The explicit form of the terms, up to third order in lambda is also given. The same method provides the explicit expansion to any order for the matrix elements of z

Event-triggered sensor data transmission policy for receding horizon recursive state estimation

Directory of Open Access Journals (Sweden)

Yunji Li

2017-06-01

Full Text Available We consider a sensor data transmission policy for receding horizon recursive state estimation in a networked linear system. A good tradeoff between estimation error and communication rate could be achieved according to a transmission strategy, which decides the transfer time of the data packet. Here we give this transmission policy through proving the upper bound of system performance. Moreover, the lower bound of system performance is further analyzed in detail. A numerical example is given to verify the potential and effectiveness of the theoretical results.

Gluon and quark jets in a recursive model motivated by quantum chromodynamics

International Nuclear Information System (INIS)

Sukhatme, U.P.

1979-01-01

We compute observable quantities like the multiplicity and momentum distributions of hadrons in gluon and quark jets in the framework of a recursive cascade model, which is strongly motivated by the fundamental interactions of QCD. Fragmentation occurs via 3 types of breakups: quark → meson + quark, gluon → meson + gluon, gluon → quark + antiquark. In our model gluon jets are softer than quark jets. The ratio of gluon jet to quark jet multiplicity is found to be 2 asymptotically, but much less at lower energies. Some phenomenological consequences for γ decay are discussed. (orig.)

On the multi-level solution algorithm for Markov chains

Energy Technology Data Exchange (ETDEWEB)

Horton, G. [Univ. of Erlangen, Nuernberg (Germany)

1996-12-31

We discuss the recently introduced multi-level algorithm for the steady-state solution of Markov chains. The method is based on the aggregation principle, which is well established in the literature. Recursive application of the aggregation yields a multi-level method which has been shown experimentally to give results significantly faster than the methods currently in use. The algorithm can be reformulated as an algebraic multigrid scheme of Galerkin-full approximation type. The uniqueness of the scheme stems from its solution-dependent prolongation operator which permits significant computational savings in the evaluation of certain terms. This paper describes the modeling of computer systems to derive information on performance, measured typically as job throughput or component utilization, and availability, defined as the proportion of time a system is able to perform a certain function in the presence of component failures and possibly also repairs.

Holographic thermalization and generalized Vaidya-AdS solutions in massive gravity

International Nuclear Information System (INIS)

Hu, Ya-Peng; Zeng, Xiao-Xiong; Zhang, Hai-Qing

2017-01-01

We investigate the effect of massive graviton on the holographic thermalization process. Before doing this, we first find out the generalized Vaidya-AdS solutions in the de Rham–Gabadadze–Tolley (dRGT) massive gravity by directly solving the gravitational equations. Then, we study the thermodynamics of these Vaidya-AdS solutions by using the Misner–Sharp energy and unified first law, which also shows that the massive gravity is in a thermodynamic equilibrium state. Moreover, we adopt the two-point correlation function at equal time to explore the thermalization process in the dual field theory, and to see how the graviton mass parameter affects this process from the viewpoint of AdS/CFT correspondence. Our results show that the graviton mass parameter will increase the holographic thermalization process.