Higher-Order Generalized Invexity in Control Problems
S. K. Padhan
2011-01-01
Full Text Available We introduce a higher-order duality (Mangasarian type and Mond-Weir type for the control problem. Under the higher-order generalized invexity assumptions on the functions that compose the primal problems, higher-order duality results (weak duality, strong duality, and converse duality are derived for these pair of problems. Also, we establish few examples in support of our investigation.
Higher-order harmonics of general limited diffraction Bessel beams
Ding De-Sheng; Huang Jin-Huang
2016-01-01
In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m -th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. (special topic)
Higher-order harmonics of general limited diffraction Bessel beams
Ding, De-Sheng; Huang, Jin-Huang
2016-12-01
In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).
General relativity and gauge gravity theories of higher order
Konopleva, N.P.
1998-01-01
It is a short review of today's gauge gravity theories and their relations with Einstein General Relativity. The conceptions of construction of the gauge gravity theories with higher derivatives are analyzed. GR is regarded as the gauge gravity theory corresponding to the choice of G ∞4 as the local gauge symmetry group and the symmetrical tensor of rank two g μν as the field variable. Using the mathematical technique, single for all fundamental interactions (namely variational formalism for infinite Lie groups), we can obtain Einstein's theory as the gauge theory without any changes. All other gauge approaches lead to non-Einstein theories of gravity. But above-mentioned mathematical technique permits us to construct the gauge gravity theory of higher order (for instance SO (3,1)-gravity) so that all vacuum solutions of Einstein equations are the solutions of the SO (3,1)-gravity theory. The structure of equations of SO(3,1)-gravity becomes analogous to Weeler-Misner geometrodynamics one
Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning
2016-10-01
An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.
Geometrical optics in general relativity: A study of the higher order corrections
Anile, A.M.
1976-01-01
The higher order corrections to geometrical optics are studied in general relativity for an electromagnetic test wave. An explicit expression is found for the average energy--momentum tensor which takes into account the first-order corrections. Finally the first-order corrections to the well-known area-intensity law of geometrical optics are derived
Domin, Daniel S.
1999-01-01
The science laboratory instructional environment is ideal for fostering the development of problem-solving, manipulative, and higher-order thinking skills: the skills needed by today's learner to compete in an ever increasing technology-based society. This paper reports the results of a content analysis of ten general chemistry laboratory manuals. Three experiments from each manual were examined for evidence of higher-order cognitive activities. Analysis was based upon the six major cognitive categories of Bloom's Taxonomy of Educational Objectives: knowledge, comprehension, application, analysis, synthesis, and evaluation. The results of this study show that the overwhelming majority of general chemistry laboratory manuals provide tasks that require the use of only the lower-order cognitive skills: knowledge, comprehension, and application. Two of the laboratory manuals were disparate in having activities that utilized higher-order cognition. I describe the instructional strategies used within these manuals to foster higher-order cognitive development.
Transverse vibrations of shear-deformable beams using a general higher order theory
Kosmatka, J. B.
1993-01-01
A general higher order theory is developed to study the static and vibrational behavior of beam structures having an arbitrary cross section that utilizes both out-of-plane shear-dependent warping and in-plane (anticlastic) deformations. The equations of motion are derived via Hamilton's principle, where the full 3D constitutive relations are used. A simplified version of the general higher-order theory is also presented for beams having an arbitrary cross section that includes out-of-plane shear deformation but assumes that stresses within the cross section and in-plane deformations are negligible. This simplified model, which is accurate for long to moderately short wavelengths, offers substantial improvements over existing higher order theories that are limited to beams with thin rectangular cross sections. The current approach will be very useful in the study of thin-wall closed-cell beams such as airfoil-type sections where the magnitude of shear-related cross-sectional warping is significant.
Gandini, A.
1996-01-01
The heuristically based generalized perturbation theory (HGPT), to first and higher order, applied to the neutron field of a reactor system, is discussed in relation to the criticality reset procedure. This procedure is implicit within the GPT methodology, corresponding to the so called filtering of the importance function relevant to the neutron field from the fundamental mode contamination. It is common practice to use the so called ''lambda''-mode filter. In order to account for any possible reset option, a general definition is introduced of an intensive control variable (ρ) entering into the governing equations, and correspondingly a fundamental ρ-mode filtering of the importance function is defined, relevant to the real criticality reset (control) mechanism adopted. A simple example illustrates the need to take into account the correct filtering, so as to avoid significant inaccuracies in the sensitivity calculation results. The extension of this filtering technique to other functions entering into the GPT perturbative formulations at first and higher order is also discussed. (author)
Is general intelligence little more than the speed of higher-order processing?
Schubert, Anna-Lena; Hagemann, Dirk; Frischkorn, Gidon T
2017-10-01
Individual differences in the speed of information processing have been hypothesized to give rise to individual differences in general intelligence. Consistent with this hypothesis, reaction times (RTs) and latencies of event-related potential have been shown to be moderately associated with intelligence. These associations have been explained either in terms of individual differences in some brain-wide property such as myelination, the speed of neural oscillations, or white-matter tract integrity, or in terms of individual differences in specific processes such as the signal-to-noise ratio in evidence accumulation, executive control, or the cholinergic system. Here we show in a sample of 122 participants, who completed a battery of RT tasks at 2 laboratory sessions while an EEG was recorded, that more intelligent individuals have a higher speed of higher-order information processing that explains about 80% of the variance in general intelligence. Our results do not support the notion that individuals with higher levels of general intelligence show advantages in some brain-wide property. Instead, they suggest that more intelligent individuals benefit from a more efficient transmission of information from frontal attention and working memory processes to temporal-parietal processes of memory storage. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Higher order Godunov methods for general systems of hyperbolic conservation laws
Bell, J.B.; Colella, P.; Trangenstein, J.A.
1989-01-01
We describe an extension of higher order Godunov methods to general systems of hyperbolic conservation laws. This extension allow the method to be applied to problems that are not strictly hyperbolic and exhibit local linear degeneracies in the wave fields. The method constructs an approximation of the Riemann problem from local wave information. A generalization of the Engquist--Osher flux for systems is then used to compute a numerical flux based on this approximation. This numerical flux replaces the Godunov numerical flux in the algorithm, thereby eliminating the need for a global Riemann problem solution. The additional modifications to the Godunov methodology that are needed to treat loss of strict hyperbolicity are described in detail. The method is applied to some simple model problems for which the glocal analytic structure is known. The method is also applied to the black-oil model for multiphase flow in petroleum reservoirs. copyright 1989 Academic Press, Inc
Moore, B.R.; Turinsky, P.J.
1998-01-01
Boiling water reactor (BWR) loading pattern assessment requires solving the two-group, nodal form of the neutron diffusion equation and drift-flux form of the fluid equations simultaneously because these equation sets are strongly coupled via nonlinear feedback. To reduce the computational burden associated with the calculation of the core attributes (that is, core eigenvalue and thermal margins) of a perturbed BWR loading pattern, the analytical and numerical aspects of a higher order generalized perturbation theory (GPT) method, which correctly addresses the strong nonlinear feedbacks of two-phase flow, have been established. Inclusion of Jacobian information in the definition of the generalized flux adjoints provides for a rapidly convergent iterative method for solution of the power distribution and eigenvalue of a loading pattern perturbed from a reference state. Results show that the computational speedup of GPT compared with conventional forward solution methods demanding consistent accuracy is highly dependent on the number of spatial nodes utilized by the core simulator, varying from superior to inferior performance as the number of nodes increases
Toledo, Santiago; Dubas, Justin M.
2016-01-01
An emphasis on higher-order thinking within the curriculum has been a subject of interest in the chemical and STEM literature due to its ability to promote meaningful, transferable learning in students. The systematic use of learning taxonomies could be a practical way to scaffold student learning in order to achieve this goal. This work proposes…
Akkerman, Erik M.
2010-01-01
Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional
Li, Xi-Zeng; Su, Bao-Xia
1996-01-01
It is found that the field of the combined mode of the probe wave and the phase-conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations in this process are also presented.
Wang, Xin; Chen, Yong; Cao, Jianli
2015-01-01
In this paper, we utilize generalized Darboux transformation to study higher-order rogue wave solutions of the three-wave resonant interaction equation, which describes the propagation and mixing of waves with different frequencies in weakly nonlinear dispersive media. A general Nth-order rogue wave solution with two characteristic velocities structural parameters and 3N independent parameters under a determined plane-wave background and a specific parameter condition is derived. As an application, we show that four fundamental rogue waves with fundamental, two kinds of line and quadrilateral patterns, or six fundamental rogue waves with fundamental, triangular, two kinds of quadrilateral and circular patterns can emerge in the second-order rogue waves. Moreover, several important wave characteristics including the maximum values, the corresponding coordinate positions of the humps, and the stability problem for some special higher-order rogue wave solutions such as the fundamental and quadrilateral cases are discussed. (paper)
Ernst, Erik
2003-01-01
This paper introduces the notion of higher-order inheritance hierarchies. They are useful because they provide well-known benefits of object-orientation at the level of entire hierarchies-benefits which are not available with current approaches. Three facets must be adressed: First, it must be po...
Geemert, R. van E-mail: rene.vangeemert@psi.ch; Hoogenboom, J.E. E-mail: j.e.hoogenboom@iri.tudelft.nl
2001-09-01
As nuclear fuel economy is basically a multi-cycle issue, a fair way of evaluating reload patterns is to consider their performance in the case of an equilibrium cycle. The equilibrium cycle associated with a reload pattern is defined as the limit fuel cycle that eventually emerges after multiple successive periodic refueling, each time implementing the same reload scheme. Since the equilibrium cycle is the solution of a reload operation invariance equation, it can in principle be found with sufficient accuracy only by applying an iterative procedure, simulating the emergence of the limit cycle. For a design purpose such as the optimization of reload patterns, in which many different equilibrium cycle perturbations (resulting from many different limited changes in the reload operator) must be evaluated, this requires far too much computational effort. However, for very fast calculation of these many different equilibrium cycle perturbations it is also possible to set up a generalized variational approach. This approach results in an iterative scheme that yields the exact perturbation in the equilibrium cycle solution as well, in an accelerated way. Furthermore, both the solution of the adjoint equations occurring in the perturbation theory formalism and the implementation of the optimization algorithm have been parallellized and executed on a massively parallel machine. The combination of parallellism and generalized perturbation theory offers the opportunity to perform very exhaustive, fast and accurate sampling of the solution space for the equilibrium cycle reload pattern optimization problem.
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
Yilmaz, Ferkan
2012-12-01
The higher-order statistics (HOS) of the channel capacity μn=E[logn (1+γ end)], where n ∈ N denotes the order of the statistics, has received relatively little attention in the literature, due in part to the intractability of its analysis. In this letter, we propose a novel and unified analysis, which is based on the moment generating function (MGF) technique, to exactly compute the HOS of the channel capacity. More precisely, our mathematical formalism can be readily applied to maximal-ratio-combining (MRC) receivers operating in generalized fading environments. The mathematical formalism is illustrated by some numerical examples focusing on the correlated generalized fading environments. © 2012 IEEE.
Yilmaz, Ferkan; Alouini, Mohamed-Slim
2012-01-01
The higher-order statistics (HOS) of the channel capacity μn=E[logn (1+γ end)], where n ∈ N denotes the order of the statistics, has received relatively little attention in the literature, due in part to the intractability of its analysis. In this letter, we propose a novel and unified analysis, which is based on the moment generating function (MGF) technique, to exactly compute the HOS of the channel capacity. More precisely, our mathematical formalism can be readily applied to maximal-ratio-combining (MRC) receivers operating in generalized fading environments. The mathematical formalism is illustrated by some numerical examples focusing on the correlated generalized fading environments. © 2012 IEEE.
Israelsen, Stine Møller
This PhD thesis considers higher order modes (HOMs) in optical fibers. That includes their excitation and characteristics. Within the last decades, HOMs have been applied both for space multiplexing in optical communications, group velocity dispersion management and sensing among others......-radial polarization as opposed to the linear polarization of the LP0X modes. The effect is investigated numerically in a double cladding fiber with an outer aircladding using a full vectorial modesolver. Experimentally, the bowtie modes are excited using a long period grating and their free space characteristics...... and polarization state are investigated. For this fiber, the onset of the bowtie effect is shown numerically to be LP011. The characteristics usually associated with Bessel-likes modes such as long diffraction free length and selfhealing are shown to be conserved despite the lack of azimuthal symmetry...
Abo-Dahab, S. M. [Taif University, Taif (Saudi Arabia); Abd-Alla, A. M. [SVU, Qena (Egypt); Khan, Aftab [Sohag University, Sohag (Egypt)
2015-08-15
The aim of this paper is to study the propagation of surface waves in a rotating fibre-reinforced viscoelastic media of higher order under the influence of magnetic field. The general surface wave speeds derived to study the effects of rotation and magnetic field on surface waves. Particular cases for Stoneley, Love and Rayleigh waves are also discussed and dispersion relation for the waves has been deduced. The results obtained in this investigation are more general in the sense that some earlier published results are obtained from our result as special cases. For order zero our results are well agreement to fibre-reinforced materials. Also by neglecting the reinforced elastic parameters, the results reduce to well known isotropic medium. It is observed that in a rotating medium the surface waves are dispersive. Also magnetic effects play a significant roll. It is observed that Love wave remain unaffected in a rotating medium but remain under the influence of magnetic field. Rayleigh waves are affected by rotation and magnetic field whereas Stoneley waves are independent of Maxwell stresses. It is also observed that, surface waves cannot propagate in a fast rotating medium or in the presence of magnetic field of high intensity. Numerical results for particular materials are given and illustrated graphically. The results indicate that the effect of rotation and magnetic field are very pronounced.
Abo-Dahab, S. M.; Abd-Alla, A. M.; Khan, Aftab
2015-01-01
The aim of this paper is to study the propagation of surface waves in a rotating fibre-reinforced viscoelastic media of higher order under the influence of magnetic field. The general surface wave speeds derived to study the effects of rotation and magnetic field on surface waves. Particular cases for Stoneley, Love and Rayleigh waves are also discussed and dispersion relation for the waves has been deduced. The results obtained in this investigation are more general in the sense that some earlier published results are obtained from our result as special cases. For order zero our results are well agreement to fibre-reinforced materials. Also by neglecting the reinforced elastic parameters, the results reduce to well known isotropic medium. It is observed that in a rotating medium the surface waves are dispersive. Also magnetic effects play a significant roll. It is observed that Love wave remain unaffected in a rotating medium but remain under the influence of magnetic field. Rayleigh waves are affected by rotation and magnetic field whereas Stoneley waves are independent of Maxwell stresses. It is also observed that, surface waves cannot propagate in a fast rotating medium or in the presence of magnetic field of high intensity. Numerical results for particular materials are given and illustrated graphically. The results indicate that the effect of rotation and magnetic field are very pronounced.
Higher-Order Program Generation
Rhiger, Morten
for OCaml, a dialect of ML, that provides run-time code generation for OCaml programs. We apply these byte-code combinators in semantics-directed compilation for an imperative language and in run-time specialization using type-directed partial evaluation. Finally, we present an approach to compiling goal......This dissertation addresses the challenges of embedding programming languages, specializing generic programs to specific parameters, and generating specialized instances of programs directly as executable code. Our main tools are higher-order programming techniques and automatic program generation....... It is our thesis that they synergize well in the development of customizable software. Recent research on domain-specific languages propose to embed them into existing general-purpose languages. Typed higher-order languages have proven especially useful as meta languages because they provide a rich...
Sri Priya Ponnapalli
Full Text Available The number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing in many areas of science, accompanied by a need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. The only such framework to date, the generalized singular value decomposition (GSVD, is limited to two matrices. We mathematically define a higher-order GSVD (HO GSVD for N≥2 matrices D(i∈R(m(i × n, each with full column rank. Each matrix is exactly factored as D(i=U(iΣ(iV(T, where V, identical in all factorizations, is obtained from the eigensystem SV=VΛ of the arithmetic mean S of all pairwise quotients A(iA(j(-1 of the matrices A(i=D(i(TD(i, i≠j. We prove that this decomposition extends to higher orders almost all of the mathematical properties of the GSVD. The matrix S is nondefective with V and Λ real. Its eigenvalues satisfy λ(k≥1. Equality holds if and only if the corresponding eigenvector v(k is a right basis vector of equal significance in all matrices D(i and D(j, that is σ(i,k/σ(j,k=1 for all i and j, and the corresponding left basis vector u(i,k is orthogonal to all other vectors in U(i for all i. The eigenvalues λ(k=1, therefore, define the "common HO GSVD subspace." We illustrate the HO GSVD with a comparison of genome-scale cell-cycle mRNA expression from S. pombe, S. cerevisiae and human. Unlike existing algorithms, a mapping among the genes of these disparate organisms is not required. We find that the approximately common HO GSVD subspace represents the cell-cycle mRNA expression oscillations, which are similar among the datasets. Simultaneous reconstruction in the common subspace, therefore, removes the experimental artifacts, which are dissimilar, from the datasets. In the simultaneous sequence-independent classification of the genes of the three organisms in this common subspace, genes of highly conserved sequences but significantly different cell
Certified higher-order recursive path ordering
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
Saber, Ahmed Yousuf; Chakraborty, Shantanu; Abdur Razzak, S.M.; Senjyu, Tomonobu
2009-01-01
This paper presents a modified particle swarm optimization (MPSO) for constrained economic load dispatch (ELD) problem. Real cost functions are more complex than conventional second order cost functions when multi-fuel operations, valve-point effects, accurate curve fitting, etc., are considering in deregulated changing market. The proposed modified particle swarm optimization (PSO) consists of problem dependent variable number of promising values (in velocity vector), unit vector and error-iteration dependent step length. It reliably and accurately tracks a continuously changing solution of the complex cost function and no extra concentration/effort is needed for the complex higher order cost polynomials in ELD. Constraint management is incorporated in the modified PSO. The modified PSO has balance between local and global searching abilities, and an appropriate fitness function helps to converge it quickly. To avoid the method to be frozen, stagnated/idle particles are reset. Sensitivity of the higher order cost polynomials is also analyzed visually to realize the importance of the higher order cost polynomials for the optimization of ELD. Finally, benchmark data sets and methods are used to show the effectiveness of the proposed method. (author)
Fractional Order Generalized Information
José Tenreiro Machado
2014-04-01
Full Text Available This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.
A Paraconsistent Higher Order Logic
Villadsen, Jørgen
2004-01-01
of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order...... of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens. Many non-classical logics are, at the propositional level, funny toys which work quite good, but when one wants...
Nonlocal higher order evolution equations
Rossi, Julio D.; Schö nlieb, Carola-Bibiane
2010-01-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove
Shababi, Homa; Chung, Won Sang
2018-04-01
In this paper, using the new type of D-dimensional nonperturbative Generalized Uncertainty Principle (GUP) which has predicted both a minimal length uncertainty and a maximal observable momentum,1 first, we obtain the maximally localized states and express their connections to [P. Pedram, Phys. Lett. B 714, 317 (2012)]. Then, in the context of our proposed GUP and using the generalized Schrödinger equation, we solve some important problems including particle in a box and one-dimensional hydrogen atom. Next, implying modified Bohr-Sommerfeld quantization, we obtain energy spectra of quantum harmonic oscillator and quantum bouncer. Finally, as an example, we investigate some statistical properties of a free particle, including partition function and internal energy, in the presence of the mentioned GUP.
Nonlocal higher order evolution equations
Rossi, Julio D.
2010-06-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
Classical higher-order processes
Montesi, Fabrizio
2017-01-01
Classical Processes (CP) is a calculus where the proof theory of classical linear logic types processes à la Π-calculus, building on a Curry-Howard correspondence between session types and linear propositions. We contribute to this research line by extending CP with process mobility, inspired...... by the Higher-Order Π-calculus. The key to our calculus is that sequents are asymmetric: one side types sessions as in CP and the other types process variables, which can be instantiated with process values. The controlled interaction between the two sides ensures that process variables can be used at will......, but always respecting the linear usage of sessions expected by the environment....
Saveliev Peter
2005-01-01
Full Text Available Suppose , are manifolds, are maps. The well-known coincidence problem studies the coincidence set . The number is called the codimension of the problem. More general is the preimage problem. For a map and a submanifold of , it studies the preimage set , and the codimension is . In case of codimension , the classical Nielsen number is a lower estimate of the number of points in changing under homotopies of , and for an arbitrary codimension, of the number of components of . We extend this theory to take into account other topological characteristics of . The goal is to find a "lower estimate" of the bordism group of . The answer is the Nielsen group defined as follows. In the classical definition, the Nielsen equivalence of points of based on paths is replaced with an equivalence of singular submanifolds of based on bordisms. We let , then the Nielsen group of order is the part of preserved under homotopies of . The Nielsen number of order is the rank of this group (then . These numbers are new obstructions to removability of coincidences and preimages. Some examples and computations are provided.
Resilience and Higher Order Thinking
Ioan Fazey
2010-09-01
Full Text Available To appreciate, understand, and tackle chronic global social and environmental problems, greater appreciation of the importance of higher order thinking is required. Such thinking includes personal epistemological beliefs (PEBs, i.e., the beliefs people hold about the nature of knowledge and how something is known. These beliefs have profound implications for the way individuals relate to each other and the world, such as how people understand complex social-ecological systems. Resilience thinking is an approach to environmental stewardship that includes a number of interrelated concepts and has strong foundations in systemic ways of thinking. This paper (1 summarizes a review of educational psychology literature on PEBs, (2 explains why resilience thinking has potential to facilitate development of more sophisticated PEBs, (3 describes an example of a module designed to teach resilience thinking to undergraduate students in ways conducive to influencing PEBs, and (4 discusses a pilot study that evaluates the module's impact. Theoretical and preliminary evidence from the pilot evaluation suggests that resilience thinking which is underpinned by systems thinking has considerable potential to influence the development of more sophisticated PEBs. To be effective, however, careful consideration of how resilience thinking is taught is required. Finding ways to encourage students to take greater responsibility for their own learning and ensuring close alignment between assessment and desired learning outcomes are particularly important.
Wolf, Alexander; Reiher, Markus; Hess, Bernd Artur
2004-05-08
The first molecular calculations with the generalized Douglas-Kroll method up to fifth order in the external potential (DKH5) are presented. We study the spectroscopic parameters and electron affinity of the tin oxide molecule SnO and its anion SnO(-) applying nonrelativistic as well as relativistic calculations with higher orders of the DK approximation. In order to guarantee highly accurate results close to the basis set limit, an all-electron basis for Sn of at least quintuple-zeta quality has been constructed and optimized. All-electron CCSD(T) calculations of the potential energy curves of both SnO and SnO(-) reproduce the experimental values very well. Relative energies and valence properties are already well described with the established standard second-order approximation DKH2 and the higher-order corrections DKH3-DKH5 hardly affect these quantities. However, an accurate description of total energies and inner-shell properties requires superior relativistic schemes up to DKH5. (c) 2004 American Institute of Physics.
Peter Saveliev
2005-04-01
Full Text Available Suppose X, Y are manifolds, f,g:XÃ¢Â†Â’Y are maps. The well-known coincidence problem studies the coincidence set C={x:f(x=g(x}. The number m=dimÃ¢Â€Â‰XÃ¢ÂˆÂ’dimÃ¢Â€Â‰Y is called the codimension of the problem. More general is the preimage problem. For a map f:XÃ¢Â†Â’Z and a submanifold Y of Z, it studies the preimage set C={x:f(xÃ¢ÂˆÂˆY}, and the codimension is m=dimÃ¢Â€Â‰X+dimÃ¢Â€Â‰YÃ¢ÂˆÂ’dimÃ¢Â€Â‰Z. In case of codimension 0, the classical Nielsen number N(f,Y is a lower estimate of the number of points in C changing under homotopies of f, and for an arbitrary codimension, of the number of components of C. We extend this theory to take into account other topological characteristics of C. The goal is to find a Ã¢Â€Âœlower estimateÃ¢Â€Â of the bordism group ÃŽÂ©p(C of C. The answer is the Nielsen group Sp(f,Y defined as follows. In the classical definition, the Nielsen equivalence of points of C based on paths is replaced with an equivalence of singular submanifolds of C based on bordisms. We let Sp'(f,Y=ÃŽÂ©p(C/Ã¢ÂˆÂ¼N, then the Nielsen group of order p is the part of Sp'(f,Y preserved under homotopies of f. The Nielsen number Np(F,Y of order p is the rank of this group (then N(f,Y=N0(f,Y. These numbers are new obstructions to removability of coincidences and preimages. Some examples and computations are provided.
Higher Order and Fractional Diffusive Equations
D. Assante
2015-07-01
Full Text Available We discuss the solution of various generalized forms of the Heat Equation, by means of different tools ranging from the use of Hermite-Kampé de Fériet polynomials of higher and fractional order to operational techniques. We show that these methods are useful to obtain either numerical or analytical solutions.
Abd-Alla, A. M.; Abo-Dahab, S. M. [Taif University, Taif (Egypt); Khan, Aftab [COMSATS, Chakshahzad (Pakistan)
2015-10-15
In this paper, we investigated the propagation of surface waves in a rotating fibre-reinforced viscoelastic anisotropic media of a higher order and fraction orders of nth order including time rate of strain with voids. The general surface wave speed is derived to study the effect of rotation and voids on surface waves. Particular cases for Stoneley, Love and Rayleigh waves are also discussed. The results obtained in this investigation are more general in the sense that some earlier published results are obtained from our result as special cases. In order zero our results are well agreeing with classical results. Also by neglecting the reinforced elastic parameters and voids the results reduce to well known isotropic medium. Comparison was made with the results obtained in the presence and absence of rotation and parameters for fibre-reinforced of the material medium. It is observed that Love wave remains unaffected with respect to rotation and voids. It is also observed that, surface waves cannot propagate in a fast rotating medium. Numerical results are given and illustrated graphically.
Abd-Alla, A. M.; Abo-Dahab, S. M.; Khan, Aftab
2015-01-01
In this paper, we investigated the propagation of surface waves in a rotating fibre-reinforced viscoelastic anisotropic media of a higher order and fraction orders of nth order including time rate of strain with voids. The general surface wave speed is derived to study the effect of rotation and voids on surface waves. Particular cases for Stoneley, Love and Rayleigh waves are also discussed. The results obtained in this investigation are more general in the sense that some earlier published results are obtained from our result as special cases. In order zero our results are well agreeing with classical results. Also by neglecting the reinforced elastic parameters and voids the results reduce to well known isotropic medium. Comparison was made with the results obtained in the presence and absence of rotation and parameters for fibre-reinforced of the material medium. It is observed that Love wave remains unaffected with respect to rotation and voids. It is also observed that, surface waves cannot propagate in a fast rotating medium. Numerical results are given and illustrated graphically.
XY model with higher-order exchange.
Žukovič, Milan; Kalagov, Georgii
2017-08-01
An XY model, generalized by inclusion of up to an infinite number of higher-order pairwise interactions with an exponentially decreasing strength, is studied by spin-wave theory and Monte Carlo simulations. At low temperatures the model displays a quasi-long-range-order phase characterized by an algebraically decaying correlation function with the exponent η=T/[2πJ(p,α)], nonlinearly dependent on the parameters p and α that control the number of the higher-order terms and the decay rate of their intensity, respectively. At higher temperatures the system shows a crossover from the continuous Berezinskii-Kosterlitz-Thouless to the first-order transition for the parameter values corresponding to a highly nonlinear shape of the potential well. The role of topological excitations (vortices) in changing the nature of the transition is discussed.
Li Juan; Zhang Haiqiang; Xu Tao; Zhang, Ya-Xing; Tian Bo
2007-01-01
For the long-distance communication and manufacturing problems in optical fibers, the propagation of subpicosecond or femtosecond optical pulses can be governed by the variable-coefficient nonlinear Schroedinger equation with higher order effects, such as the third-order dispersion, self-steepening and self-frequency shift. In this paper, we firstly determine the general conditions for this equation to be integrable by employing the Painleve analysis. Based on the obtained 3 x 3 Lax pair, we construct the Darboux transformation for such a model under the corresponding constraints, and then derive the nth-iterated potential transformation formula by the iterative process of Darboux transformation. Through the one- and two-soliton-like solutions, we graphically discuss the features of femtosecond solitons in inhomogeneous optical fibers
Ward identities of higher order Virasoro algebra
Zha Chaozeng; Dolate, S.
1994-11-01
The general formulations of primary fields versus quasi-primary ones in the context of high order Virasoro algebra (HOVA) and the corresponding Ward identity are explored. The primary fields of conformal spins up to 8 are given in terms of quasi-primary fields, and the general features of the higher order expressions are also discussed. It is observed that the local fields, either primary of quasi-primary, carry the same numbers of central charges, and not all the primary fields contribute to the anomalies in the Ward identities. (author). 6 refs
Frontiers of higher order fuzzy sets
Tahayori, Hooman
2015-01-01
Frontiers of Higher Order Fuzzy Sets, strives to improve the theoretical aspects of general and Interval Type-2 fuzzy sets and provides a unified representation theorem for higher order fuzzy sets. Moreover, the book elaborates on the concept of gradual elements and their integration with the higher order fuzzy sets. This book also introduces new frameworks for information granulation based on general T2FSs, IT2FSs, Gradual elements, Shadowed sets and rough sets. In particular, the properties and characteristics of the new proposed frameworks are studied. Such new frameworks are shown to be more capable to be exploited in real applications. Higher order fuzzy sets that are the result of the integration of general T2FSs, IT2FSs, gradual elements, shadowed sets and rough sets will be shown to be suitable to be applied in the fields of bioinformatics, business, management, ambient intelligence, medicine, cloud computing and smart grids. Presents new variations of fuzzy set frameworks and new areas of applicabili...
Some higher order Hardy inequalities
Kufner, Alois; Kuliev, K.; Persson, L. E.
2012-01-01
Roč. 2012, Mar 26 (2012), s. 69 ISSN 1029-242X Institutional support: RVO:67985840 Keywords : Hardy inequality Subject RIV: BA - General Mathematics Impact factor: 0.822, year: 2012 http://www.journalofinequalitiesandapplications.com/content/2012/1/69
Higher order field equations. II
Tolhoek, H.A.
1977-01-01
In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for mod(M)→infinity the Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) approach the Green's functions Δsub(R)(x) and Δsub(A)(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) is the same as of Δsub(R)(x) and Δsub(A)(x)-and also the same as for Dsub(R)(x) and Dsub(A)(x) for t→+-infinity;, where Dsub(R) and Dsub(A) are the Green's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. (Auth.)
Higher order antibunching in intermediate states
Verma, Amit; Sharma, Navneet K.; Pathak, Anirban
2008-01-01
Since the introduction of binomial state as an intermediate state, different intermediate states have been proposed. Different nonclassical effects have also been reported in these intermediate states. But till now higher order antibunching is predicted in only one type of intermediate state, which is known as shadowed negative binomial state. Recently we have shown that the higher order antibunching is not a rare phenomenon [P. Gupta, P. Pandey, A. Pathak, J. Phys. B 39 (2006) 1137]. To establish our earlier claim further, here we have shown that the higher order antibunching can be seen in different intermediate states, such as binomial state, reciprocal binomial state, hypergeometric state, generalized binomial state, negative binomial state and photon added coherent state. We have studied the possibility of observing the higher order subpoissonian photon statistics in different limits of intermediate states. The effects of different control parameters on the depth of non classicality have also been studied in this connection and it has been shown that the depth of nonclassicality can be tuned by controlling various physical parameters
Higher order mode optical fiber Raman amplifiers
Rottwitt, Karsten; Friis, Søren Michael Mørk; Usuga Castaneda, Mario A.
2016-01-01
We review higher order mode Raman amplifiers and discuss recent theoretical as well as experimental results including system demonstrations.......We review higher order mode Raman amplifiers and discuss recent theoretical as well as experimental results including system demonstrations....
Order, disorder and generalized statistics
Marino, E.C.; Swieca, J.A.
1980-06-01
We generalize the prescription of Kadanoff and Ceva for the computation of disorder variables correlation functions in the Ising model for continuous field theories with U(1) symmetry. By considering the product of order and disorder variables, we obtain a path integral representation for fields with generalized statistics. We discuss in detail the cases of massless Thirring and Schwinger models. (Author) [pt
Order, disorder and generalized statistics
Marino, E.C.; Swieca, J.A.; Pontificia Universidade Catolica do Rio de Janeiro
1980-01-01
We generalize the prescription of Kadanoff and Ceva for the computation of disorder variable correlation functions in the Ising model for continuous field theories with U(1) symmetry. By considering the product of order and disorder variables, we obtain a path integral representation for fields with generalized statistics. We discuss in detail the cases of massless Thirring and Schwinger models. (orig.)
Challenges in higher order mode Raman amplifiers
Rottwitt, Karsten; Nielsen, Kristian; Friis, Søren Michael Mørk
2015-01-01
A higher order Raman amplifier model that take random mode coupling into account ispresented. Mode dependent gain and signal power fluctuations at the output of the higher order modeRaman amplifier are discussed......A higher order Raman amplifier model that take random mode coupling into account ispresented. Mode dependent gain and signal power fluctuations at the output of the higher order modeRaman amplifier are discussed...
Higher Order Expectations in Asset Pricing
Philippe BACCHETTA; Eric VAN WINCOOP
2004-01-01
We examine formally Keynes' idea that higher order beliefs can drive a wedge between an asset price and its fundamental value based on expected future payoffs. Higher order expectations add an additional term to a standard asset pricing equation. We call this the higher order wedge, which depends on the difference between higher and first order expectations of future payoffs. We analyze the determinants of this wedge and its impact on the equilibrium price. In the context of a dynamic noisy r...
Skinner-Rusk unified formalism for higher-order systems
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2012-07-01
The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, first-order and higher-order field theories, and higher-order autonomous systems. In this work we present a generalization of this formalism for higher-order non-autonomous mechanical systems.
Higher order harmonics of reactor neutron equation
Li Fu; Hu Yongming; Luo Zhengpei
1996-01-01
The flux mapping method using the higher order harmonics of the neutron equation is proposed. Based on the bi-orthogonality of the higher order harmonics, the process and formulas for higher order harmonics calculation are derived via the source iteration method with source correction. For the first time, not only any order harmonics for up-to-3-dimensional geometry are achieved, but also the preliminary verification to the capability for flux mapping have been carried out
Higher order effects of pseudoparticles in QCD
Hietarinta, J.; Palmer, W.F.
1977-01-01
Gauge invariant Green's functions of quark-antiquark bilinear densities in massless, two-color QCD are studied. Nonzero-energy fermion modes, pseudoparticle solutions with topological charge absolute value ν > 1, and n-point functions with n > 2. Some general properties of the O(Dirac constant) approximation are developed, enabling one to isolate and define the terms which contribute to a general n-point function. The higher effects it is found preserve the symmetry breakdown found earlier in the 2-point function (U(2) x U(2) → SU(2) x SU(2) x U(1)). It is shown that a previous 2-point function analysis is exact to order Dirac constant
Appel, Claus; van Oostrom, Vincent; Simonsen, Jakob Grue
2010-01-01
We show that, contrary to the situation in first-order term rewriting, almost none of the usual properties of rewriting are modular for higher-order rewriting, irrespective of the higher-order rewriting format. We show that for the particular format of simply typed applicative term rewriting...... systems modularity of confluence, normalization, and termination can be recovered by imposing suitable linearity constraints....
Higher-order techniques in computational electromagnetics
Graglia, Roberto D
2016-01-01
Higher-Order Techniques in Computational Electromagnetics explains 'high-order' techniques that can significantly improve the accuracy, computational cost, and reliability of computational techniques for high-frequency electromagnetics, such as antennas, microwave devices and radar scattering applications.
Xiao, Xiaolin; Moreno-Moral, Aida; Rotival, Maxime; Bottolo, Leonardo; Petretto, Enrico
2014-01-01
Recent high-throughput efforts such as ENCODE have generated a large body of genome-scale transcriptional data in multiple conditions (e.g., cell-types and disease states). Leveraging these data is especially important for network-based approaches to human disease, for instance to identify coherent transcriptional modules (subnetworks) that can inform functional disease mechanisms and pathological pathways. Yet, genome-scale network analysis across conditions is significantly hampered by the paucity of robust and computationally-efficient methods. Building on the Higher-Order Generalized Singular Value Decomposition, we introduce a new algorithmic approach for efficient, parameter-free and reproducible identification of network-modules simultaneously across multiple conditions. Our method can accommodate weighted (and unweighted) networks of any size and can similarly use co-expression or raw gene expression input data, without hinging upon the definition and stability of the correlation used to assess gene co-expression. In simulation studies, we demonstrated distinctive advantages of our method over existing methods, which was able to recover accurately both common and condition-specific network-modules without entailing ad-hoc input parameters as required by other approaches. We applied our method to genome-scale and multi-tissue transcriptomic datasets from rats (microarray-based) and humans (mRNA-sequencing-based) and identified several common and tissue-specific subnetworks with functional significance, which were not detected by other methods. In humans we recapitulated the crosstalk between cell-cycle progression and cell-extracellular matrix interactions processes in ventricular zones during neocortex expansion and further, we uncovered pathways related to development of later cognitive functions in the cortical plate of the developing brain which were previously unappreciated. Analyses of seven rat tissues identified a multi-tissue subnetwork of co
Xiaolin Xiao
2014-01-01
Full Text Available Recent high-throughput efforts such as ENCODE have generated a large body of genome-scale transcriptional data in multiple conditions (e.g., cell-types and disease states. Leveraging these data is especially important for network-based approaches to human disease, for instance to identify coherent transcriptional modules (subnetworks that can inform functional disease mechanisms and pathological pathways. Yet, genome-scale network analysis across conditions is significantly hampered by the paucity of robust and computationally-efficient methods. Building on the Higher-Order Generalized Singular Value Decomposition, we introduce a new algorithmic approach for efficient, parameter-free and reproducible identification of network-modules simultaneously across multiple conditions. Our method can accommodate weighted (and unweighted networks of any size and can similarly use co-expression or raw gene expression input data, without hinging upon the definition and stability of the correlation used to assess gene co-expression. In simulation studies, we demonstrated distinctive advantages of our method over existing methods, which was able to recover accurately both common and condition-specific network-modules without entailing ad-hoc input parameters as required by other approaches. We applied our method to genome-scale and multi-tissue transcriptomic datasets from rats (microarray-based and humans (mRNA-sequencing-based and identified several common and tissue-specific subnetworks with functional significance, which were not detected by other methods. In humans we recapitulated the crosstalk between cell-cycle progression and cell-extracellular matrix interactions processes in ventricular zones during neocortex expansion and further, we uncovered pathways related to development of later cognitive functions in the cortical plate of the developing brain which were previously unappreciated. Analyses of seven rat tissues identified a multi
Order-sorted Algebraic Specifications with Higher-order Functions
Haxthausen, Anne Elisabeth
1995-01-01
This paper gives a proposal for how order-sorted algebraic specification languages can be extended with higher-order functions. The approach taken is a generalisation to the order-sorted case of an approach given by Mller, Tarlecki and Wirsing for the many-sorted case. The main idea in the proposal...
Difference equations in massive higher order calculations
Bierenbaum, I.; Bluemlein, J.; Klein, S.; Schneider, C.
2007-07-01
The calculation of massive 2-loop operator matrix elements, required for the higher order Wilson coefficients for heavy flavor production in deeply inelastic scattering, leads to new types of multiple infinite sums over harmonic sums and related functions, which depend on the Mellin parameter N. We report on the solution of these sums through higher order difference equations using the summation package Sigma. (orig.)
Higher-order force gradient symplectic algorithms
Chin, Siu A.; Kidwell, Donald W.
2000-12-01
We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10, and 12, the new algorithms are approximately a factor of 103, 104, 104, and 105 better.
HIGHER ORDER THINKING IN TEACHING GRAMMAR
Citra Dewi
2017-04-01
Full Text Available The aim of this paper discussed about how to enhance students’ higher order thinking that should be done by teacher in teaching grammar. Usually teaching grammar was boring and has the same way to learn like change the pattern of sentence into positive, negative and introgative while the students’ need more various way to develop their thinking. The outcome of students’ competence in grammar sometimes not sufficient enough when the students’ occured some test international standart like Test of English Foreign Language, International English Language Testing. Whereas in TOEFL test it needed higher order thinking answer, so teacher should develop students’ higher order thingking in daily teaching grammar in order to make the students’ enhance their thinking are higher. The method was used in this paper by using field study based on the experience of teaching grammar. It can be shown by students’ toefl score was less in stucture and written expression. The result of this paper was after teacher gave some treatments to enhance students’ higher order thinking in teaching grammar, the students’ toefl scores are sufficient enough as a part of stucture and written expression. It can concluded that it needed some strategies to enhancce students higher order thinking by teaching grammar it can make students’ higher toefl score. Teachers should be creative and inovative to teach the students’ started from giving the students’ question or test in teaching grammar.
Higher-order rewriting and partial evaluation
Danvy, Olivier; Rose, Kristoffer H.
1998-01-01
We demonstrate the usefulness of higher-order rewriting techniques for specializing programs, i.e., for partial evaluation. More precisely, we demonstrate how casting program specializers as combinatory reduction systems (CRSs) makes it possible to formalize the corresponding program...
Higher-Order Minimal Functional Graphs
Jones, Neil D; Rosendahl, Mads
1994-01-01
We present a minimal function graph semantics for a higher-order functional language with applicative evaluation order. The semantics captures the intermediate calls performed during the evaluation of a program. This information may be used in abstract interpretation as a basis for proving...
Electromagnetic cloaking in higher order spherical cloaks
Sidhwa, H. H.; Aiyar, R. P. R. C.; Kulkarni, S. V.
2017-06-01
The inception of transformation optics has led to the realisation of the invisibility devices for various applications, one of which is spherical cloaking. In this paper, a formulation for a higher-order spherical cloak has been proposed to reduce its physical thickness significantly by introducing a nonlinear relation between the original and transformed coordinate systems and it has been verified using the ray tracing approach. Analysis has been carried out to observe the anomalies in the variation of refractive index for higher order cloaks indicating the presence of poles in the relevant equations. Furthermore, a higher-order spherical cloak with predefined values of the material characteristics on its inner and outer surfaces has been designed for practical application.
Finding Higher Order Differentials of MISTY1
Tsunoo, Yukiyasu; Saito, Teruo; Kawabata, Takeshi; Nakagawa, Hirokatsu
MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it is recommended for Japanese e-Government ciphers by the CRYPTREC project. In this paper, we report on 12th order differentials in 3-round MISTY1 with FL functions and 44th order differentials in 4-round MISTY1 with FL functions both previously unknown. We also report that both data complexity and computational complexity of higher order differential attacks on 6-round MISTY1 with FL functions and 7-round MISTY1 with FL functions using the 46th order differential can be reduced to as much as 1/22 of the previous values by using multiple 44th order differentials simultaneously.
Higher-order tensors in diffusion imaging
Schultz, T.; Fuster, A.; Ghosh, A.; Deriche, R.; Florack, L.M.J.; Lim, L.H.; Westin, C.-F.; Vilanova, A.; Burgeth, B.
2014-01-01
Diffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higher-order tensors provide a powerful mathematical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion
Analogy, higher order thinking, and education.
Richland, Lindsey Engle; Simms, Nina
2015-01-01
Analogical reasoning, the ability to understand phenomena as systems of structured relationships that can be aligned, compared, and mapped together, plays a fundamental role in the technology rich, increasingly globalized educational climate of the 21st century. Flexible, conceptual thinking is prioritized in this view of education, and schools are emphasizing 'higher order thinking', rather than memorization of a cannon of key topics. The lack of a cognitively grounded definition for higher order thinking, however, has led to a field of research and practice with little coherence across domains or connection to the large body of cognitive science research on thinking. We review literature on analogy and disciplinary higher order thinking to propose that relational reasoning can be productively considered the cognitive underpinning of higher order thinking. We highlight the utility of this framework for developing insights into practice through a review of mathematics, science, and history educational contexts. In these disciplines, analogy is essential to developing expert-like disciplinary knowledge in which concepts are understood to be systems of relationships that can be connected and flexibly manipulated. At the same time, analogies in education require explicit support to ensure that learners notice the relevance of relational thinking, have adequate processing resources available to mentally hold and manipulate relations, and are able to recognize both the similarities and differences when drawing analogies between systems of relationships. © 2015 John Wiley & Sons, Ltd.
Higher-Order Components for Grid Programming
Dünnweber, Jan
2009-01-01
Higher-Order Components were developed within the CoreGRID European Network of Excellence and have become an optional extension of the popular Globus middleware. This book provides the reader with hands-on experience, describing a collection of example applications from various fields of science and engineering, including biology and physics.
Higher class groups of Eichler orders
Guo Xuejun; Kuku, Aderemi
2003-11-01
In this paper, we prove that if A is a quaternion algebra and Λ an Eichler order in A, then the only p-torsion possible in even dimensional higher class groups Cl 2n (Λ) (n ≥ 1) are for those rational primes p which lie under prime ideals of O F at which Λ are not maximal. (author)
A Higher-Order Colon Translation
Danvy, Olivier; Nielsen, Lasse Reichstein
2001-01-01
A lambda-encoding such as the CPS transformation gives rise to administrative redexes. In his seminal article ``Call-by-name, call-by-value and the lambda-calculus'', 25 years ago, Plotkin tackled administrative reductions using a so-called ``colon translation.'' 10 years ago, Danvy and Filinski...... integrated administrative reductions in the CPS transformation, making it operate in one pass. The technique applies to other lambda-encodings (e.g., variants of CPS), but we do not see it used in practice--instead, Plotkin's colon translation appears to be favored. Therefore, in an attempt to link both...... techniques, we recast Plotkin's proof of Indifference and Simulation to the higher-order specification of the one-pass CPS transformation. To this end, we extend his colon translation from first order to higher order...
Higher order cumulants in colorless partonic plasma
Cherif, S. [Sciences and Technologies Department, University of Ghardaia, Ghardaia, Algiers (Algeria); Laboratoire de Physique et de Mathématiques Appliquées (LPMA), ENS-Kouba (Bachir El-Ibrahimi), Algiers (Algeria); Ahmed, M. A. A. [Department of Physics, College of Science, Taibah University Al-Madinah Al-Mounawwarah KSA (Saudi Arabia); Department of Physics, Taiz University in Turba, Taiz (Yemen); Laboratoire de Physique et de Mathématiques Appliquées (LPMA), ENS-Kouba (Bachir El-Ibrahimi), Algiers (Algeria); Ladrem, M., E-mail: mladrem@yahoo.fr [Department of Physics, College of Science, Taibah University Al-Madinah Al-Mounawwarah KSA (Saudi Arabia); Laboratoire de Physique et de Mathématiques Appliquées (LPMA), ENS-Kouba (Bachir El-Ibrahimi), Algiers (Algeria)
2016-06-10
Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume T{sub 0}(V), a new approach based on the finite-size cumulant expansion of the order parameter and the ℒ{sub m,n}-Method is used. We have shown that both cumulants of higher order and their ratios, associated to the thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.
Pedersen, Martin Erland Vestergaard; Cheng, Ji; Xu, Chris
2013-01-01
An improved version of the generalized nonlinear Schrödinger equation is derived, which takes into account the correct dispersion of the transverse field distribution. The new improved version of the generalized nonlinear Schrödinger equation is verified to give the same results as the standard...
Higher-Order and Symbolic Computation
Danvy, Olivier; Mason, Ian
2008-01-01
a series of implementaions that properly account for multiple invocations of the derivative-taking opeatro. In "Adapting Functional Programs to Higher-Order Logic," Scott Owens and Konrad Slind present a variety of examples of terminiation proofs of functional programs written in HOL proof systems. Since......-calculus programs, historically. The anaylsis determines the possible locations of ambients and mirrors the temporla sequencing of actions in the structure of types....
Lagrangian procedures for higher order field equations
Bollini, C.G.
1987-01-01
A Lagrangian procedure for a pedagogical way is presented for the treatment of higher order field equations. The energy-momentum tensor and the conserved density current are built. In particular the case in which the derivatives appear only in the invariant D'Alembertian operator is discussed. Some examples are discussed. The fields are quantized and the corresponding Hamilonian which is shown not to be positive defructed. Rules are given to write the causal propagators. (author) [pt
Lagrangian procedures for higher order field equations
Bollini, C.G.; Giambiagi, J.J.
1986-01-01
We present in a pedagogical way a Lagrangian procedure for the treatment of higher order field equations. We build the energy-momentum tensor and the conserved density current. In particular we discuss the case in which the derivatives appear only in the invariant D'Alembertian operator. We discuss some examples. We quantize the fields and construct the corresponding Hamiltonian which is shown not to be positive definite. We give the rules for the causal propagators. (Author) [pt
Higher order correlations in computed particle distributions
Hanerfeld, H.; Herrmannsfeldt, W.; Miller, R.H.
1989-03-01
The rms emittances calculated for beam distributions using computer simulations are frequently dominated by higher order aberrations. Thus there are substantial open areas in the phase space plots. It has long been observed that the rms emittance is not an invariant to beam manipulations. The usual emittance calculation removes the correlation between transverse displacement and transverse momentum. In this paper, we explore the possibility of defining higher order correlations that can be removed from the distribution to result in a lower limit to the realizable emittance. The intent is that by inserting the correct combinations of linear lenses at the proper position, the beam may recombine in a way that cancels the effects of some higher order forces. An example might be the non-linear transverse space charge forces which cause a beam to spread. If the beam is then refocused so that the same non-linear forces reverse the inward velocities, the resulting phase space distribution may reasonably approximate the original distribution. The approach to finding the location and strength of the proper lens to optimize the transported beam is based on work by Bruce Carlsten of Los Alamos National Laboratory. 11 refs., 4 figs
Higher order corrections in quantum electrodynamics
Rafael, E.
1977-01-01
Theoretical contributions to high-order corrections in purely leptonic systems, such as electrons and muons, muonium (μ + e - ) and positronium (e + e - ), are reviewed to establish the validity of quantum electrodynamics (QED). Two types of QED contributions to the anomalous magnetic moments are considered, from diagrams with one fermion type lines and those witn two fermion type lines. The contributions up to eighth order are compared to the data available with a different accuracy. Good agreement is stated within the experimental errors. The experimental accuracy of the muonium hyperfine structure and of the radiative corrections to the decay of positronium are compared to the one attainable in theoretical calculations. The need for a higher precision in both experimental data and theoretical calculations is stated
Higher order modes of coupled optical fibres
Alexeyev, C N; Yavorsky, M A; Boklag, N A
2010-01-01
The structure of hybrid higher order modes of two coupled weakly guiding identical optical fibres is studied. On the basis of perturbation theory with degeneracy for the vector wave equation expressions for modes with azimuthal angular number l ≥ 1 are obtained that allow for the spin–orbit interaction. The spectra of polarization corrections to the scalar propagation constants are calculated in a wide range of distances between the fibres. The limiting cases of widely and closely spaced fibres are studied. The obtained results can be used for studying the tunnelling of optical vortices in directional couplers and in matters concerned with information security
Neural classifiers for learning higher-order correlations
Gueler, M.
1999-01-01
Studies by various authors suggest that higher-order networks can be more powerful and biologically more plausible with respect to the more traditional multilayer networks. These architecture make explicit use of nonlinear interactions between input variables in the form of higher-order units or product units. If it is known a priori that the problem to be implemented possesses a given set of invariances like in the translation, rotation, and scale invariant recognition problems, those invariances can be encoded, thus eliminating all higher-order terms which are incompatible with the invariances. In general, however, it is a serious set-back that the complexity of learning increases exponentially with the size of inputs. This paper reviews higher-order networks and introduces an implicit representation in which learning complexity is mainly decided by the number of higher-order terms to be learned and increases only linearly with the input size
Neural Classifiers for Learning Higher-Order Correlations
Güler, Marifi
1999-01-01
Studies by various authors suggest that higher-order networks can be more powerful and are biologically more plausible with respect to the more traditional multilayer networks. These architectures make explicit use of nonlinear interactions between input variables in the form of higher-order units or product units. If it is known a priori that the problem to be implemented possesses a given set of invariances like in the translation, rotation, and scale invariant pattern recognition problems, those invariances can be encoded, thus eliminating all higher-order terms which are incompatible with the invariances. In general, however, it is a serious set-back that the complexity of learning increases exponentially with the size of inputs. This paper reviews higher-order networks and introduces an implicit representation in which learning complexity is mainly decided by the number of higher-order terms to be learned and increases only linearly with the input size.
Theorem Proving In Higher Order Logics
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Higher order aberrations of the eye: Part one
Marsha Oberholzer
2016-06-01
Full Text Available This article is the first in a series of two articles that provide a comprehensive literature review of higher order aberrations (HOAs of the eye. The present article mainly explains the general principles of such HOAs as well as HOAs of importance, and the measuring apparatus used to measure HOAs of the eye. The second article in the series discusses factors contributing to variable results in measurements of HOAs of the eye. Keywords: Higher order aberrations; wavefront aberrations; aberrometer
The differential geometry of higher order jets and tangent bundles
De Leon, M.; Rodrigues, P.R.
1985-01-01
This chapter is devoted to the study of basic geometrical notions required for the development of the main object of the text. Some facts about Jet theory are reviewed. A particular case of Jet manifolds is considered: the tangent bundle of higher order. It is shown that this jet bundle possesses in a canonical way a certain kind of geometric structure, the so called almost tangent structure of higher order, and which is a generalization of the almost tangent geometry of the tangent bundle. Another important fact examined is the extension of the notion of 'spray' to higher order tangent bundles. (Auth.)
Gauge formulation for higher order gravity
Cuzinatto, R.R.; Medeiros, L.G.; Melo, C.A.M. de; Pompeia, P.J.
2008-01-01
This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained that includes derivatives of the curvature. We analyze the form of the second field strength, G=∂F+fAF, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of F and quadratic contractions of G are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his generalized electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behavior at short distances as well as a meso-large distance modification. (orig.)
Three weights higher order Hardy type inequalities
Aigerim A. Kalybay
2006-01-01
Full Text Available We investigate the following three weights higher order Hardy type inequality (0.1 ‖g‖q,u≤ C‖Dρkg‖p,v where Dρi denotes the following weighted differential operator: {dig(tdti,i=0,1,...,m−1,di−mdti−m(p(tdmg(tdtm,i=m,m+1,...,k, for a weight function ρ(⋅. A complete description of the weights u, v and ρ so that (0.1 holds was given in [4] for the case 1
Rodríguez Fonollosa, Javier; Nikias, Chrysostomos L.
1993-01-01
The Wigner higher order moment spectra (WHOS) are defined as extensions of the Wigner-Ville distribution (WD) to higher order moment spectra domains. A general class of time-frequency higher order moment spectra is also defined in terms of arbitrary higher order moments of the signal as generalizations of the Cohen’s general class of time-frequency representations. The properties of the general class of time-frequency higher order moment spectra can be related to the properties...
Unambiguous formalism for higher order Lagrangian field theories
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn; Vankerschaver, Joris
2009-01-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Multilevel Fast Multipole Method for Higher Order Discretizations
Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik
2014-01-01
The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower...... order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined....
Constrained variational calculus for higher order classical field theories
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn, E-mail: cedricmc@icmat.e, E-mail: mdeleon@icmat.e, E-mail: david.martin@icmat.e [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain)
2010-11-12
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Constrained variational calculus for higher order classical field theories
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn
2010-01-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Improved Multilevel Fast Multipole Method for Higher-Order discretizations
Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik
2014-01-01
The Multilevel Fast Multipole Method (MLFMM) allows for a reduced computational complexity when solving electromagnetic scattering problems. Combining this with the reduced number of unknowns provided by Higher-Order discretizations has proven to be a difficult task, with the general conclusion b...
Generalized Reduced Order Model Generation, Phase I
National Aeronautics and Space Administration — M4 Engineering proposes to develop a generalized reduced order model generation method. This method will allow for creation of reduced order aeroservoelastic state...
Heavy quark threshold dynamics in higher order
Piclum, J.H.
2007-05-15
In this work we discuss an important building block for the next-to-next-to-next-to leading order corrections to the pair production of top quarks at threshold. Specifically, we explain the calculation of the third order strong corrections to the matching coefficient of the vector current in non-relativistic Quantum Chromodynamics and provide the result for the fermionic part, containing at least one loop of massless quarks. As a byproduct, we obtain the matching coefficients of the axial-vector, pseudo-scalar and scalar current at the same order. Furthermore, we calculate the three-loop corrections to the quark renormalisation constants in the on-shell scheme in the framework of dimensional regularisation and dimensional reduction. Finally, we compute the third order strong corrections to the chromomagnetic interaction in Heavy Quark Effective Theory. The calculational methods are discussed in detail and results for the master integrals are given. (orig.)
Higher order multipoles and splines in plasma simulations
Okuda, H.; Cheng, C.Z.
1978-01-01
The reduction of spatial grid effects in plasma simulations has been studied numerically using higher order multipole expansions and the spline method in one dimension. It is found that, while keeping the higher order moments such as quadrupole and octopole moments substantially reduces the grid effects, quadratic and cubic splines in general have better stability properties for numerical plasma simulations when the Debye length is much smaller than the grid size. In particular the spline method may be useful in three-dimensional simulations for plasma confinement where the grid size in the axial direction is much greater than the Debye length. (Auth.)
Higher-order multipoles and splines in plasma simulations
Okuda, H.; Cheng, C.Z.
1977-12-01
Reduction of spatial grid effects in plasma simulations has been studied numerically using higher order multipole expansions and spline method in one dimension. It is found that, while keeping the higher order moments such as quadrupole and octopole moments substantially reduces the grid effects, quadratic and cubic splines in general have better stability properties for numerical plasma simulations when the Debye length is much smaller than the grid size. In particular, spline method may be useful in three dimensional simulations for plasma confinement where the grid size in the axial direction is much greater than the Debye length
Another higher order Langevin algorithm for QCD
Kronfeld, A.S.
1986-01-01
This note provides an algorithm for integrating the Langevin equation which is second order. It introduces a term into the drift force which is a product of the Gaussian noise and a second derivative of the action. The specific application presented here is for nonabelian gauge theories interacting with fermions, e.g. QCD, for which it requires less memory than the Runge-Kutta algorithm of the same order. The memory and computational requirements of Euler, Runge-Kutta, and the present algorithm are compared. (orig.)
Higher Order Continuous SI Engine Observers
Vesterholm, Thomas; Hendricks, Elbert; Houbak, Niels
1992-01-01
A nonlinear compensator for the fuel film dynamics and a second order nonlinear observer for a spark ignition engine are presented in this paper. The compensator and observer are realized as continuous differential equations and an especially designed integration algorithm is used to integrate them...
On higher order pyramidal finite elements
Liu, L.; Davies, K.B.; Křížek, Michal; Guan, L.
2011-01-01
Roč. 3, č. 2 (2011), s. 131-140 ISSN 2070-0733 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : pyramidal polynomial basis functions * finite element method * composite elements * three-dimensional mortar elements Subject RIV: BA - General Mathematics Impact factor: 0.750, year: 2011
Interactions, strings and isotopies in higher order anisotropic superspaces
Vacaru, Sergiu Ion
2001-01-01
The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions, published in J. Math. Phys., Nucl. Phys. B, Ann. Phys. (NY), JHEP, Rep. Math. Phys., Int. J. Theor. Phys. and in some former Soviet Union and Romanian scientific journals. The main subjects are in the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces with higher order anisotropy and inhomogeneity. The approach proceeds by developing the concept of higher order anisotropic (super)space which unifies the logical and manthematical aspects of modern Kaluza--Klein theories and generalized Lagrange and Finsler geometry and leads to modeling of physical processes on higher order fiber (super)bundles provided with nonlinear and distinguished connections and metric structures. This book can be also considered as a pedagogical survey on the mentioned subjects.
The instruments of higher order thinking skills
Ahmad, S.; Prahmana, R. C. I.; Kenedi, A. K.; Helsa, Y.; Arianil, Y.; Zainil, M.
2017-12-01
This research developed the standard of instrument for measuring the High Order Thinking Skill (HOTS) ability of PGSD students. The research method used is development research with eight steps namely theoretical studies, operational definition, designation construct, dimensions and indicators, the preparation of the lattice, the preparation of grain, an analysis of legibility and Social desirability, field trials, and data analysis. In accordance with the type of data to be obtained in this study, the research instrument using validation sheet, implementation observation, and questionnaire. The results show that the instruments are valid and feasible to be used by expert and have been tested on PGSD students with 60% of PGSD students with low categorization.
A Higher-Order Calculus for Categories
Cáccamo, Mario José; Winskel, Glynn
2001-01-01
A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic...... in their free variables. There are special binders for limits and more general ends. The rules for limits and ends support an algebraic manipulation of universal constructions as opposed to a more traditional diagrammatic approach. Duality within the calculus and applications in proving continuity are discussed...... with examples. The calculus gives a basis for mechanising a theory of categories in a generic theorem prover like Isabelle....
Higher order perturbation theory - An example for discussion
Lewins, J.D.; Parks, G.; Babb, A.L.
1986-01-01
Higher order perturbation theory is developed in the form of a Taylor series expansion to third order to calculate the thermal utilization of a nonuniform cell. The development takes advantage of the self-adjoint property of the diffusion operator to provide a simple development of this illustration of generalized perturbation theory employing scalar perturbation parameters. The results show how a designer might employ a second-order theory to quantify proposed design improvements, together with the limitations of second- and third-order theory. The chosen example has an exact optimization solution and thus provides a clear understanding of the role of perturbation theory at its various orders. Convergence and the computational advantages and disadvantages of the method are discussed
Concept Mapping for Higher Order Thinking
Susan Marie Zvacek
2013-02-01
Full Text Available Engineering education is facing a changing world in which how one thinks is becoming more important than what one thinks; that is, our course content is important but constantly changing and we need to help students learn how to think about that content.Today’s students have grown accustomed to immediate rewards, multi-channel stimuli, and rapid-fire communications. As a result, they are often impatient and suffer a lack of focus. When reflection is called for in the learning process - a time consuming practice - students may find it difficult to overcome the conflict between their typically speedy management of priorities and the focused, time-intensive thinking required to acquire a strong foundation of declarative knowledge.Therefore, the exploration of tools to facilitate the formation of deep knowledge structures is essential. One instructional strategy that shows promise is the use of concept mapping, a learning activity that requires students to explain their understanding of important ideas and the relationships among those ideas. This paper describes a pilot project to integrate concept mapping into a Mechanical Engineering Course and the preliminary results of that project.This project has been established within the Working Group of “Tools for Developing High Order Thinking Skills”, of the Portuguese Society for Engineering Education, in which the first author is the leader and the other two co-authors, are working group members
Developing Higher-Order Materials Knowledge Systems
Fast, Anthony Nathan
2011-12-01
Advances in computational materials science and novel characterization techniques have allowed scientists to probe deeply into a diverse range of materials phenomena. These activities are producing enormous amounts of information regarding the roles of various hierarchical material features in the overall performance characteristics displayed by the material. Connecting the hierarchical information over disparate domains is at the crux of multiscale modeling. The inherent challenge of performing multiscale simulations is developing scale bridging relationships to couple material information between well separated length scales. Much progress has been made in the development of homogenization relationships which replace heterogeneous material features with effective homogenous descriptions. These relationships facilitate the flow of information from lower length scales to higher length scales. Meanwhile, most localization relationships that link the information from a from a higher length scale to a lower length scale are plagued by computationally intensive techniques which are not readily integrated into multiscale simulations. The challenge of executing fully coupled multiscale simulations is augmented by the need to incorporate the evolution of the material structure that may occur under conditions such as material processing. To address these challenges with multiscale simulation, a novel framework called the Materials Knowledge System (MKS) has been developed. This methodology efficiently extracts, stores, and recalls microstructure-property-processing localization relationships. This approach is built on the statistical continuum theories developed by Kroner that express the localization of the response field at the microscale using a series of highly complex convolution integrals, which have historically been evaluated analytically. The MKS approach dramatically improves the accuracy of these expressions by calibrating the convolution kernels in these
On the origin of higher braces and higher-order derivations
Markl, Martin
2015-01-01
Roč. 10, č. 3 (2015), s. 637-667 ISSN 2193-8407 Institutional support: RVO:67985840 Keywords : Koszul braces * Börjeseon braces * higher-order derivation Subject RIV: BA - General Mathematics Impact factor: 0.600, year: 2015 http://link.springer.com/article/10.1007/s40062-014-0079-2
Self-similarity of higher-order moving averages
Arianos, Sergio; Carbone, Anna; Türk, Christian
2011-10-01
In this work, higher-order moving average polynomials are defined by straightforward generalization of the standard moving average. The self-similarity of the polynomials is analyzed for fractional Brownian series and quantified in terms of the Hurst exponent H by using the detrending moving average method. We prove that the exponent H of the fractional Brownian series and of the detrending moving average variance asymptotically agree for the first-order polynomial. Such asymptotic values are compared with the results obtained by the simulations. The higher-order polynomials correspond to trend estimates at shorter time scales as the degree of the polynomial increases. Importantly, the increase of polynomial degree does not require to change the moving average window. Thus trends at different time scales can be obtained on data sets with the same size. These polynomials could be interesting for those applications relying on trend estimates over different time horizons (financial markets) or on filtering at different frequencies (image analysis).
Higher-order Brunnian structures and possible physical realizations
A. Baas, Nils; V. Fedorov, D.; S. Jensen, A.
2014-01-01
We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied...... to the binding of systems in nature. It now appears that recent generalization to higher order Brunnian structures may potentially be realized as laboratory made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms...
Higher-Order Cyclostationarity Detection for Spectrum Sensing
Julien Renard
2010-01-01
Full Text Available Recent years have shown a growing interest in the concept of Cognitive Radios (CRs, able to access portions of the electromagnetic spectrum in an opportunistic operating way. Such systems require efficient detectors able to work in low Signal-to-Noise Ratio (SNR environments, with little or no information about the signals they are trying to detect. Energy detectors are widely used to perform such blind detection tasks, but quickly reach the so-called SNR wall below which detection becomes impossible Tandra (2005. Cyclostationarity detectors are an interesting alternative to energy detectors, as they exploit hidden periodicities present in man-made signals, but absent in noise. Such detectors use quadratic transformations of the signals to extract the hidden sine-waves. While most of the literature focuses on the second-order transformations of the signals, we investigate the potential of higher-order transformations of the signals. Using the theory of Higher-Order Cyclostationarity (HOCS, we derive a fourth-order detector that performs similarly to the second-order ones to detect linearly modulated signals, at SNR around 0 dB, which may be used if the signals of interest do not exhibit second-order cyclostationarity. More generally this paper reviews the relevant aspects of the cyclostationary and HOCS theory, and shows their potential for spectrum sensing.
Higher-order geodesic deviations applied to the Kerr metric
Colistete, R J; Kerner, R
2002-01-01
Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a general relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this method to the problem of closed orbital motion of test particles in the Kerr metric spacetime. With a simple circular orbit in the equatorial plane taken as the initial geodesic, we obtain finite eccentricity orbits in the form of Taylor series with the eccentricity playing the role of a small parameter. The explicit expressions of these higher-order geodesic deviations are derived using successive systems of linear equations with constant coefficients, whose solutions are of harmonic oscillator type. This scheme gives best results when applied to orbits with low eccentricities, but with arbitrary possible values of (GM/Rc sup 2).
Conceptualizing and Assessing Higher-Order Thinking in Reading
Afflerbach, Peter; Cho, Byeong-Young; Kim, Jong-Yun
2015-01-01
Students engage in higher-order thinking as they read complex texts and perform complex reading-related tasks. However, the most consequential assessments, high-stakes tests, are currently limited in providing information about students' higher-order thinking. In this article, we describe higher-order thinking in relation to reading. We provide a…
Scalar brane backgrounds in higher order curvature gravity
Charmousis, Christos; Davis, Stephen C.; Dufaux, Jean-Francois
2003-01-01
We investigate maximally symmetric brane world solutions with a scalar field. Five-dimensional bulk gravity is described by a general lagrangian which yields field equations containing no higher than second order derivatives. This includes the Gauss-Bonnet combination for the graviton. Stability and gravitational properties of such solutions are considered, and we particularly emphasise the modifications induced by the higher order terms. In particular it is shown that higher curvature corrections to Einstein theory can give rise to instabilities in brane world solutions. A method for analytically obtaining the general solution for such actions is outlined. Generically, the requirement of a finite volume element together with the absence of a naked singularity in the bulk imposes fine-tuning of the brane tension. A model with a moduli scalar field is analysed in detail and we address questions of instability and non-singular self-tuning solutions. In particular, we discuss a case with a normalisable zero mode but infinite volume element. (author)
Theory of a higher-order Sturm-Liouville equation
Kozlov, Vladimir
1997-01-01
This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.
Time-Discrete Higher-Order ALE Formulations: Stability
Bonito, Andrea
2013-01-01
Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time-dependent advection-diffusion-model problem in moving domains, and study their stability properties. The analysis hinges on the validity of the Reynold\\'s identity for dG. Exploiting the variational structure and assuming exact integration, we prove that our conservative and nonconservative dG schemes are equivalent and unconditionally stable. The same results remain true for piecewise polynomial ALE maps of any degree and suitable quadrature that guarantees the validity of the Reynold\\'s identity. This approach generalizes the so-called geometric conservation law to higher-order methods. We also prove that simpler Runge-Kutta-Radau methods of any order are conditionally stable, that is, subject to a mild ALE constraint on the time steps. Numerical experiments corroborate and complement our theoretical results. © 2013 Society for Industrial and Applied Mathematics.
Higher-order phase transitions on financial markets
Kasprzak, A.; Kutner, R.; Perelló, J.; Masoliver, J.
2010-08-01
Statistical and thermodynamic properties of the anomalous multifractal structure of random interevent (or intertransaction) times were thoroughly studied by using the extended continuous-time random walk (CTRW) formalism of Montroll, Weiss, Scher, and Lax. Although this formalism is quite general (and can be applied to any interhuman communication with nontrivial priority), we consider it in the context of a financial market where heterogeneous agent activities can occur within a wide spectrum of time scales. As the main general consequence, we found (by additionally using the Saddle-Point Approximation) the scaling or power-dependent form of the partition function, Z(q'). It diverges for any negative scaling powers q' (which justifies the name anomalous) while for positive ones it shows the scaling with the general exponent τ(q'). This exponent is the nonanalytic (singular) or noninteger power of q', which is one of the pilar of higher-order phase transitions. In definition of the partition function we used the pausing-time distribution (PTD) as the central one, which takes the form of convolution (or superstatistics used, e.g. for describing turbulence as well as the financial market). Its integral kernel is given by the stretched exponential distribution (often used in disordered systems). This kernel extends both the exponential distribution assumed in the original version of the CTRW formalism (for description of the transient photocurrent measured in amorphous glassy material) as well as the Gaussian one sometimes used in this context (e.g. for diffusion of hydrogen in amorphous metals or for aging effects in glasses). Our most important finding is the third- and higher-order phase transitions, which can be roughly interpreted as transitions between the phase where high frequency trading is most visible and the phase defined by low frequency trading. The specific order of the phase transition directly depends upon the shape exponent α defining the stretched
Higher-order automatic differentiation of mathematical functions
Charpentier, Isabelle; Dal Cappello, Claude
2015-04-01
Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.
Minimization of heat slab nodes with higher order boundary conditions
Solbrig, C.W.
1992-01-01
The accuracy of a numerical solution can be limited by the numerical approximation to the boundary conditions rather than the accuracy of the equations which describe the interior. The study presented in this paper compares the results from two different numerical formulations of the convective boundary condition on the face of a heat transfer slab. The standard representation of the boundary condition in a test problem yielded an unacceptable error even when the heat transfer slab was partitioned into over 300 nodes. A higher order boundary condition representation was obtained by using a second order approximation for the first derivative at the boundary and combining it with the general equation used for inner nodes. This latter formulation produced reasonable results when as few as ten nodes were used
Nil Bohr-sets and almost automorphy of higher order
Huang, Wen; Ye, Xiangdong
2016-01-01
Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any d\\in \\mathbb{N} does the collection of \\{n\\in \\mathbb{Z}: S\\cap (S-n)\\cap\\ldots\\cap (S-dn)\
Higher-order conditioning is impaired by hippocampal lesions.
Gilboa, Asaf; Sekeres, Melanie; Moscovitch, Morris; Winocur, Gordon
2014-09-22
Behavior in the real world is rarely motivated by primary conditioned stimuli that have been directly associated with potent unconditioned reinforcers. Instead, motivation and choice behavior are driven by complex chains of higher-order associations that are only indirectly linked to intrinsic reward and often exert their influence outside awareness. Second-order conditioning (SOC) [1] is a basic associative-learning mechanism whereby stimuli acquire motivational salience by proxy, in the absence of primary incentives [2, 3]. Memory-systems theories consider first-order conditioning (FOC) and SOC to be prime examples of hippocampal-independent nondeclarative memory [4, 5]. Accordingly, neurobiological models of SOC focus almost exclusively on nondeclarative neural systems that support motivational salience and reward value. Transfer of value from a conditioned stimulus to a neutral stimulus is thought to require the basolateral amygdala [6, 7] and the ventral striatum [2, 3], but not the hippocampus. We developed a new paradigm to measure appetitive SOC of tones in rats. Hippocampal lesions severely impaired both acquisition and expression of SOC despite normal FOC. Unlike controls, rats with hippocampal lesions could not discriminate between positive and negative secondary conditioned tones, although they exhibited general familiarity with previously presented tones compared with new tones. Importantly, normal rats' behavior, in contrast to that of hippocampal groups, also revealed different confidence levels as indexed by effort, a central characteristic of hippocampal relational memory. The results indicate, contrary to current systems models, that representations of intrinsic relationships between reward value, stimulus identity, and motivation require hippocampal mediation when these relationships are of a higher order. Copyright © 2014 Elsevier Ltd. All rights reserved.
Higher-order relativistic periastron advances and binary pulsars
Damour, T.; Schafer, G.
1988-01-01
The contributions to the periastron advance of a system of two condensed bodies coming from relativistic dynamical effects of order higher than the usual first post-Newtonian (1PN) equations of motion are investigated. The structure of the solution of the orbital second post-Newtonian (2PN) equations of motion is given in a simple parametrized form. The contributions to the secular pariastron advance, and the period, of orbital 2PN effects are then explicitly worked out by using the Hamilton-Jacobi method. The spin-orbit contribution to the secular precession of the orbit in space is rederived in a streamlined way by making full use of Hamiltonian methods. These results are then applied to the theoretical interpretation of the observational data of pulsars in close eccentric binary systems. It is shown that the higher-order relativistic contributions are already of theoretical and astophysical significance for interpreting the high-precision measurement of the secular periastron advance of PSR 1913+16 achived by Taylor and coworkers. The case of extremely fast spinning (millisecond) binary pulsars is also discussed, and shown to offer an easier ground for getting new tests of general relativity, and/or, a direct measurement of the moment of inertia of a neutron star
Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?
Troisi, Antonio [Universita degli Studi di Salerno, Dipartimento di Fisica ' ' E.R. Caianiello' ' , Salerno (Italy)
2017-03-15
Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f(R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R) = f{sub 0}R{sup n} the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions. (orig.)
Higher-Order Hybrid Gaussian Kernel in Meshsize Boosting Algorithm
In this paper, we shall use higher-order hybrid Gaussian kernel in a meshsize boosting algorithm in kernel density estimation. Bias reduction is guaranteed in this scheme like other existing schemes but uses the higher-order hybrid Gaussian kernel instead of the regular fixed kernels. A numerical verification of this scheme ...
Higher-order Jordan Osserman pseudo-Riemannian manifolds
Gilkey, Peter B; Ivanova, Raina; Zhang Tan
2002-01-01
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds
Higher-order Jordan Osserman pseudo-Riemannian manifolds
Gilkey, Peter B [Mathematics Department, University of Oregon, Eugene, OR 97403 (United States); Ivanova, Raina [Mathematics Department, University of Hawaii - Hilo, 200 W Kawili St, Hilo, HI 96720 (United States); Zhang Tan [Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 (United States)
2002-09-07
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds.
Exact solutions to two higher order nonlinear Schroedinger equations
Xu Liping; Zhang Jinliang
2007-01-01
Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)
Higher order Lie-Baecklund symmetries of evolution equations
Roy Chowdhury, A.; Roy Chowdhury, K.; Paul, S.
1983-10-01
We have considered in detail the analysis of higher order Lie-Baecklund symmetries for some representative nonlinear evolution equations. Until now all such symmetry analyses have been restricted only to the first order of the infinitesimal parameter. But the existence of Baecklund transformation (which can be shown to be an overall sum of higher order Lie-Baecklund symmetries) makes it necessary to search for such higher order Lie-Baecklund symmetries directly without taking recourse to the Baecklund transformation or inverse scattering technique. (author)
Application of Mass Lumped Higher Order Finite Elements
J. Chen, H.R. Strauss, S.C. Jardin, W. Park, L.E. Sugiyama, G. Fu, J. Breslau
2005-01-01
There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied
Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems
Prieto-Martinez, Pedro Daniel; Roman-Roy, Narciso
2011-01-01
The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view. (paper)
Threshold resummation and higher order effects in QCD
Ringer, Felix Maximilian
2015-01-01
Quantum chromodynamics (QCD) is a quantum field theory that describes the strong interactions between quarks and gluons, the building blocks of all hadrons. Thanks to the experimental progress over the past decades, there has been an ever-growing need for QCD precision calculations for scattering processes involving hadrons. For processes at large momentum transfer, perturbative QCD offers a systematic approach for obtaining precise predictions. This approach relies on two key concepts: the asymptotic freedom of QCD and factorization. In a perturbative calculation at higher orders, the infrared cancellation between virtual and real emission diagrams generally leaves behind logarithmic contributions. In many observables relevant for hadronic scattering these logarithms are associated with a kinematic threshold and are hence known as ''threshold logarithms''. They become large when the available phase space for real gluon emission shrinks. In order to obtain a reliable prediction from QCD, the threshold logarithms need to be taken into account to all orders in the strong coupling constant, a procedure known as ''threshold resummation''. The main focus of my PhD thesis is on studies of QCD threshold resummation effects beyond the next-to-leading logarithmic order. Here we primarily consider the production of hadron pairs in hadronic collisions as an example. In addition, we also consider hadronic jet production, which is particularly interesting for the phenomenology at the LHC. For both processes, we fully take into account the non-trivial QCD color structure of the underlying partonic hard- scattering cross sections. We find that threshold resummation leads to sizable numerical effects in the kinematic regimes relevant for comparisons to experimental data.
Higher order effects in electroweak theory 1981-12 (KEK)
Aoki, Ken-ichi
1982-01-01
This is a brief report on the higher order or loop effects in electroweak theory. The discussion is based on the Weinberg Salam model and QCD. The loop correction to weak interaction is described. The renormalization conditions were applied to physical parameters, α(QED), M(W) and M(Z). It is expected to obtain experimentally the values of M(W) and M(Z) with the accuracy of 0.1 percent. In this scheme, the parameters were fixed loop by loop. The correction was evaluated along the present on-shell scheme. The general estimation of the order of correction was performed. The evaluation of the size of terms in one-loop correction was made. The examples of one loop analysis are presented. The leading logarithmic correction such as α ln(m 2 q 2 /M 2 ) is discussed. The system was described by H(eff) with the local operator O(i), in which the propagator of heavy particles was contracted. The effective interaction was obtained as C(i) (q 2 ) O(i), where C(i)(q 2 ) satisfies a proper equation of a renormalization group. As the practical examples, μ-decay, charged current and neutral current were studied. The correction to electron neutral current and the shift of M(W) and M(Z) were numerically obtained. Comments on quark mass and the uncertainty of sin 2 (theta) from the νN reaction are presented. (Kato, T.)
Higher-order gravity and the classical equivalence principle
Accioly, Antonio; Herdy, Wallace
2017-11-01
As is well known, the deflection of any particle by a gravitational field within the context of Einstein’s general relativity — which is a geometrical theory — is, of course, nondispersive. Nevertheless, as we shall show in this paper, the mentioned result will change totally if the bending is analyzed — at the tree level — in the framework of higher-order gravity. Indeed, to first order, the deflection angle corresponding to the scattering of different quantum particles by the gravitational field mentioned above is not only spin dependent, it is also dispersive (energy-dependent). Consequently, it violates the classical equivalence principle (universality of free fall, or equality of inertial and gravitational masses) which is a nonlocal principle. However, contrary to popular belief, it is in agreement with the weak equivalence principle which is nothing but a statement about purely local effects. It is worthy of note that the weak equivalence principle encompasses the classical equivalence principle locally. We also show that the claim that there exists an incompatibility between quantum mechanics and the weak equivalence principle, is incorrect.
Higher order total variation regularization for EIT reconstruction.
Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Zhang, Fan; Mueller-Lisse, Ullrich; Moeller, Knut
2018-01-08
Electrical impedance tomography (EIT) attempts to reveal the conductivity distribution of a domain based on the electrical boundary condition. This is an ill-posed inverse problem; its solution is very unstable. Total variation (TV) regularization is one of the techniques commonly employed to stabilize reconstructions. However, it is well known that TV regularization induces staircase effects, which are not realistic in clinical applications. To reduce such artifacts, modified TV regularization terms considering a higher order differential operator were developed in several previous studies. One of them is called total generalized variation (TGV) regularization. TGV regularization has been successively applied in image processing in a regular grid context. In this study, we adapted TGV regularization to the finite element model (FEM) framework for EIT reconstruction. Reconstructions using simulation and clinical data were performed. First results indicate that, in comparison to TV regularization, TGV regularization promotes more realistic images. Graphical abstract Reconstructed conductivity changes located on selected vertical lines. For each of the reconstructed images as well as the ground truth image, conductivity changes located along the selected left and right vertical lines are plotted. In these plots, the notation GT in the legend stands for ground truth, TV stands for total variation method, and TGV stands for total generalized variation method. Reconstructed conductivity distributions from the GREIT algorithm are also demonstrated.
Higher order derivatives via Hamilton-Jacobi approach
Bertin, M.C.; Pimentel, B.M.; Pompeia, P.J.
2006-01-01
In this work we will show how can be derived a general method for dealing with Lagrangians containing high order derivatives using the Hamilton-Jacobi Formalism for singular systems. By the expansion the configuration space of a n dimensional system we will be able to introduce first order actions and build the equations of motion of the system. We will work with the Generalized Electrodynamics of Podolsky as an example. (author)
Protein scaffolds and higher-order complexes in synthetic biology
den Hamer, A.; Rosier, B.J.H.M.; Brunsveld, L.; de Greef, T.F.A.; Ryadnov, M.; Brunsveld, L.; Suga, H.
2017-01-01
Interactions between proteins control molecular functions such as signalling or metabolic activity. Assembly of proteins via scaffold proteins or in higher-order complexes is a key regulatory mechanism. Understanding and functionally applying this concept requires the construction, study, and
Generating superpositions of higher order bessel beams [Conference paper
Vasilyeu, R
2009-10-01
Full Text Available An experimental setup to generate a superposition of higher-order Bessel beams by means of a spatial light modulator and ring aperture is presented. The experimentally produced fields are in good agreement with those calculated theoretically....
Higher-order curvature terms and extended inflation
Wang Yun
1990-01-01
We consider higher-order curvature terms in context of the Brans-Dicke theory of gravity, and investigate the effects of these terms on extended inflationary theories. We find that the higher-order curvature terms tend to speed up inflation, although the original extended-inflation solutions are stable when these terms are small. Analytical solutions are found for two extreme cases: when the higher-order curvature terms are small, and when they dominate. A conformal transformation is employed in solving the latter case, and some of the subtleties in this technique are discussed. We note that percolation is less likely to occur when the higher-order curvature terms are present. An upper bound on α is expected if we are to avoid excessive and inadequate percolation of true-vacuum bubbles
Higher-order RANS turbulence models for separated flows
National Aeronautics and Space Administration — Higher-order Reynolds-averaged Navier-Stokes (RANS) models are developed to overcome the shortcomings of second-moment RANS models in predicting separated flows....
A simplified parsimonious higher order multivariate Markov chain model
Wang, Chao; Yang, Chuan-sheng
2017-09-01
In this paper, a simplified parsimonious higher-order multivariate Markov chain model (SPHOMMCM) is presented. Moreover, parameter estimation method of TPHOMMCM is give. Numerical experiments shows the effectiveness of TPHOMMCM.
A tridiagonal parsimonious higher order multivariate Markov chain model
Wang, Chao; Yang, Chuan-sheng
2017-09-01
In this paper, we present a tridiagonal parsimonious higher-order multivariate Markov chain model (TPHOMMCM). Moreover, estimation method of the parameters in TPHOMMCM is give. Numerical experiments illustrate the effectiveness of TPHOMMCM.
The role of formative feedback in promoting higher order thinking ...
The role of formative feedback in promoting higher order thinking skills in ... activities, task characteristics, validating students' thinking, and providing feedback. ... Keywords: classroom environment, formative assessment, formative feedback, ...
Higher Order Lagrange Finite Elements In M3D
Chen, J.; Strauss, H.R.; Jardin, S.C.; Park, W.; Sugiyama, L.E.; Fu, G.; Breslau, J.
2004-01-01
The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles
Generating higher-order Lie algebras by expanding Maurer-Cartan forms
Caroca, R.; Merino, N.; Salgado, P.; Perez, A.
2009-01-01
By means of a generalization of the Maurer-Cartan expansion method, we construct a procedure to obtain expanded higher-order Lie algebras. The expanded higher-order Maurer-Cartan equations for the case G=V 0 +V 1 are found. A dual formulation for the S-expansion multialgebra procedure is also considered. The expanded higher-order Maurer-Cartan equations are recovered from S-expansion formalism by choosing a special semigroup. This dual method could be useful in finding a generalization to the case of a generalized free differential algebra, which may be relevant for physical applications in, e.g., higher-spin gauge theories.
Asymptotic Expansions for Higher-Order Scalar Difference Equations
Ravi P. Agarwal
2007-04-01
Full Text Available We give an asymptotic expansion of the solutions of higher-order PoincarÃƒÂ© difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.
Asymptotic Expansions for Higher-Order Scalar Difference Equations
Pituk Mihály
2007-01-01
Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.
All-fiber Raman Probe using Higher Order Modes
Larsen, Stine Højer Møller; Rishøj, Lars Søgaard; Rottwitt, Karsten
2013-01-01
We demonstrate the first all-fiber Raman probe utilizing higher order modes for the excitation. The spectrum of cyclohexane is measured using both the fundamental mode as well as in-fiber-generated Bessel-like modes.......We demonstrate the first all-fiber Raman probe utilizing higher order modes for the excitation. The spectrum of cyclohexane is measured using both the fundamental mode as well as in-fiber-generated Bessel-like modes....
Linear matrix differential equations of higher-order and applications
Mustapha Rachidi
2008-07-01
Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.
Time-Discrete Higher-Order ALE Formulations: Stability
Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.
2013-01-01
on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time
Meta-Logical Reasoning in Higher-Order Logic
Villadsen, Jørgen; Schlichtkrull, Anders; Hess, Andreas Viktor
The semantics of first-order logic (FOL) can be described in the meta-language of higher-order logic (HOL). Using HOL one can prove key properties of FOL such as soundness and completeness. Furthermore, one can prove sentences in FOL valid using the formalized FOL semantics. To aid...
Higher-order chaotic oscillator using active bessel filter
Lindberg, Erik; Mykolaitis, Gytis; Bumelien, Skaidra
2010-01-01
A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel filter is described. The Bessel unit plays the role of "three-in-one": a delay line, an amplifier and a filter. Results of hardware experiments and numerical simulation are presented. Depending...
Higher-Order Integral Equation Methods in Computational Electromagnetics
Jørgensen, Erik; Meincke, Peter
Higher-order integral equation methods have been investigated. The study has focused on improving the accuracy and efficiency of the Method of Moments (MoM) applied to electromagnetic problems. A new set of hierarchical Legendre basis functions of arbitrary order is developed. The new basis...
Higher-Order Separation Logic in Isabelle/HOLCF
Varming, Carsten; Birkedal, Lars
2008-01-01
We formalize higher-order separation logic for a first-order imperative language with procedures and local variables in Isabelle/HOLCF. The assertion language is modeled in such a way that one may use any theory defined in Isabelle/HOLCF to construct assertions, e.g., primitive recursion, least o...
Higher-derivative generalization of conformal mechanics
Baranovsky, Oleg
2017-08-01
Higher-derivative analogs of multidimensional conformal particle and many-body conformal mechanics are constructed. Their Newton-Hooke counterparts are derived by applying appropriate coordinate transformations.
The Cauchy problem for higher order abstract differential equations
Xiao, Ti-Jun
1998-01-01
This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis.
Does Education Lead to Higher Generalized Trust?
Charron, Nicholas; Rothstein, Bo
2016-01-01
to ‘trust others'. We hypothesize that higher levels of education will lead to higher social trust in individuals, given that the context (country or regions within countries) in which they reside has a sufficiently impartial and non-corrupt institutional setting. However, the positive effect of education...
Practical implementation of a higher order transverse leakage approximation
Prinsloo, Rian H.; Tomašević
2011-01-01
Transverse integrated nodal diffusion methods currently represent the standard in full core neutronic simulation. The primary shortcoming in this approach, be it via the Analytic Nodal Method or Nodal Expansion Method, is the utilization of the quadratic transverse leakage approximation. This approach, although proven to work well for typical LWR problems, is not consistent with the formulation of nodal methods and can cause accuracy and convergence problems. In this work an improved, consistent quadratic leakage approximation is formulated, which derives from the class of higher order nodal methods developed some years ago. In this new approach, only information relevant to describing the transverse leak- age terms in the zero-order nodal equations are obtained from the higher order formalism. The method yields accuracy comparable to full higher order methods, but does not suffer from the same computational burden which these methods typically incur. (author)
Effective description of higher-order scalar-tensor theories
Langlois, David [APC—Astroparticule et Cosmologie, Université Paris Diderot Paris 7, 75013 Paris (France); Mancarella, Michele; Vernizzi, Filippo [Institut de physique théorique, Université Paris Saclay, CEA, CNRS, 91191 Gif-sur-Yvette (France); Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: michele.mancarella@cea.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: filippo.vernizzi@cea.fr [Laboratoire de Mathématiques et Physique Théorique, Université François Rabelais, Parc de Grandmont, 37200 Tours (France)
2017-05-01
Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called 'beyond Horndeski' theories. We also discuss Lorentz-breaking models inspired by Horava gravity.
Higher order energy transfer. Quantum electrodynamical calculations and graphical representation
Jenkins, R.D.
2000-01-01
In Chapter 1, a novel method of calculating quantum electrodynamic amplitudes is formulated using combinatorial theory. This technique is used throughout instead of conventional time-ordered methods. A variety of hyperspaces are discussed to highlight isomorphism between a number of A generalisation of Pascal's triangle is shown to be beneficial in determining the form of hyperspace graphs. Chapter 2 describes laser assisted resonance energy transfer (LARET), a higher order perturbative contribution to the well-known process resonance energy transfer, accommodating an off resonance auxiliary laser field to stimulate the migration. Interest focuses on energy exchanges between two uncorrelated molecular species, as in a system where molecules are randomly oriented. Both phase-weighted and standard isotropic averaging are required for the calculations. Results are discussed in terms of a laser intensity-dependent mechanism. Identifying the applied field regime where LARET should prove experimentally significant, transfer rate increases of up to 30% are predicted. General results for three-center energy transfer are elucidated in chapter 3. Cooperative and accretive mechanistic pathways are identified with theory formulated to elicit their role in a variety of energy transfer phenomena and their relative dominance. In multichromophoric the interplay of such factors is analysed with regard to molecular architectures. The alignments and magnitudes of donor and acceptor transition moments and polarisabilities prove to have profound effects on achievable pooling efficiency for linear configurations. Also optimum configurations are offered. In ionic lattices, although both mechanisms play significant roles in pooling and cutting processes, only the accretive is responsible for sensitisation. The local, microscopic level results are used to gauge the lattice response, encompassing concentration and structural effects. (author)
Higher order QCD corrections in small x physics
Chachamis, G.
2006-11-01
We study higher order QCD corrections in small x Physics. The numerical implementation of the full NLO photon impact factor is the remaining necessary piece for the testing of the NLO BFKL resummation against data from physical processes, such as γ * γ * collisions. We perform the numerical integration over phase space for the virtual corrections to the NLO photon impact factor. This, along with the previously calculated real corrections, makes feasible in the near future first estimates for the γ*γ* total cross section, since the convolution of the full impact factor with the NLO BFKL gluon Green's function is now straightforward. The NLO corrections for the photon impact factor are sizeable and negative. In the second part of this thesis, we estimate higher order correction to the BK equation. We are mainly interested in whether partonic saturation delays or not in rapidity when going beyond the leading order. In our investigation, we use the so called 'rapidity veto' which forbid two emissions to be very close in rapidity, to 'switch on' higher order corrections to the BK equation. From analytic and numerical analysis, we conclude that indeed saturation does delay in rapidity when higher order corrections are taken into account. In the last part, we investigate higher order QCD corrections as additional corrections to the Electroweak (EW) sector. The question of whether BFKL corrections are of any importance in the Regge limit for the EW sector seems natural; although they arise in higher loop level, the accumulation of logarithms in energy s at high energies, cannot be dismissed without an investigation. We focus on the process γγ→ZZ. We calculate the pQCD corrections in the forward region at leading logarithmic (LL) BFKL accuracy, which are of the order of few percent at the TeV energy scale. (orig.)
Higher order QCD corrections in small x physics
Chachamis, G.
2006-11-15
We study higher order QCD corrections in small x Physics. The numerical implementation of the full NLO photon impact factor is the remaining necessary piece for the testing of the NLO BFKL resummation against data from physical processes, such as {gamma}{sup *}{gamma}{sup *} collisions. We perform the numerical integration over phase space for the virtual corrections to the NLO photon impact factor. This, along with the previously calculated real corrections, makes feasible in the near future first estimates for the {gamma}*{gamma}* total cross section, since the convolution of the full impact factor with the NLO BFKL gluon Green's function is now straightforward. The NLO corrections for the photon impact factor are sizeable and negative. In the second part of this thesis, we estimate higher order correction to the BK equation. We are mainly interested in whether partonic saturation delays or not in rapidity when going beyond the leading order. In our investigation, we use the so called 'rapidity veto' which forbid two emissions to be very close in rapidity, to 'switch on' higher order corrections to the BK equation. From analytic and numerical analysis, we conclude that indeed saturation does delay in rapidity when higher order corrections are taken into account. In the last part, we investigate higher order QCD corrections as additional corrections to the Electroweak (EW) sector. The question of whether BFKL corrections are of any importance in the Regge limit for the EW sector seems natural; although they arise in higher loop level, the accumulation of logarithms in energy s at high energies, cannot be dismissed without an investigation. We focus on the process {gamma}{gamma}{yields}ZZ. We calculate the pQCD corrections in the forward region at leading logarithmic (LL) BFKL accuracy, which are of the order of few percent at the TeV energy scale. (orig.)
Higher-order modulation instability in nonlinear fiber optics.
Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry
2011-12-16
We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves. © 2011 American Physical Society
Analysis of wheezes using wavelet higher order spectral features.
Taplidou, Styliani A; Hadjileontiadis, Leontios J
2010-07-01
Wheezes are musical breath sounds, which usually imply an existing pulmonary obstruction, such as asthma and chronic obstructive pulmonary disease (COPD). Although many studies have addressed the problem of wheeze detection, a limited number of scientific works has focused in the analysis of wheeze characteristics, and in particular, their time-varying nonlinear characteristics. In this study, an effort is made to reveal and statistically analyze the nonlinear characteristics of wheezes and their evolution over time, as they are reflected in the quadratic phase coupling of their harmonics. To this end, the continuous wavelet transform (CWT) is used in combination with third-order spectra to define the analysis domain, where the nonlinear interactions of the harmonics of wheezes and their time variations are revealed by incorporating instantaneous wavelet bispectrum and bicoherence, which provide with the instantaneous biamplitude and biphase curves. Based on this nonlinear information pool, a set of 23 features is proposed for the nonlinear analysis of wheezes. Two complementary perspectives, i.e., general and detailed, related to average performance and to localities, respectively, were used in the construction of the feature set, in order to embed trends and local behaviors, respectively, seen in the nonlinear interaction of the harmonic elements of wheezes over time. The proposed feature set was evaluated on a dataset of wheezes, acquired from adult patients with diagnosed asthma and COPD from a lung sound database. The statistical evaluation of the feature set revealed discrimination ability between the two pathologies for all data subgroupings. In particular, when the total breathing cycle was examined, all 23 features, but one, showed statistically significant difference between the COPD and asthma pathologies, whereas for the subgroupings of inspiratory and expiratory phases, 18 out of 23 and 22 out of 23 features exhibited discrimination power, respectively
Dynamics and phenomenology of higher order gravity cosmological models
Moldenhauer, Jacob Andrew
2010-10-01
I present here some new results about a systematic approach to higher-order gravity (HOG) cosmological models. The HOG models are derived from curvature invariants that are more general than the Einstein-Hilbert action. Some of the models exhibit late-time cosmic acceleration without the need for dark energy and fit some current observations. The open question is that there are an infinite number of invariants that one could select, and many of the published papers have stressed the need to find a systematic approach that will allow one to study methodically the various possibilities. We explore a new connection that we made between theorems from the theory of invariants in general relativity and these cosmological models. In summary, the theorems demonstrate that curvature invariants are not all independent from each other and that for a given Ricci Segre type and Petrov type (symmetry classification) of the space-time, there exists a complete minimal set of independent invariants (a basis) in terms of which all the other invariants can be expressed. As an immediate consequence of the proposed approach, the number of invariants to consider is dramatically reduced from infinity to four invariants in the worst case and to only two invariants in the cases of interest, including all Friedmann-Lemaitre-Robertson-Walker metrics. We derive models that pass stability and physical acceptability conditions. We derive dynamical equations and phase portrait analyses that show the promise of the systematic approach. We consider observational constraints from magnitude-redshift Supernovae Type Ia data, distance to the last scattering surface of the Cosmic Microwave Background radiation, and Baryon Acoustic Oscillations. We put observational constraints on general HOG models. We constrain different forms of the Gauss-Bonnet, f(G), modified gravity models with these observations. We show some of these models pass solar system tests. We seek to find models that pass physical and
Higher dimensional generalizations of the SYK model
Berkooz, Micha [Department of Particle Physics and Astrophysics, Weizmann Institute of Science,Rehovot 7610001 (Israel); Narayan, Prithvi [International Centre for Theoretical Sciences, Hesaraghatta,Bengaluru North, 560 089 (India); Rozali, Moshe [Department of Physics and Astronomy, University of British Columbia,Vancouver, BC V6T 1Z1 (Canada); Simón, Joan [School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh,King’s Buildings, Edinburgh EH9 3FD (United Kingdom)
2017-01-31
We discuss a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model. The model contains N Majorana fermions at each lattice site with a nearest-neighbour hopping term. The SYK random interaction is restricted to low momentum fermions of definite chirality within each lattice site. This gives rise to an ordinary 1+1 field theory above some energy scale and a low energy SYK-like behavior. We exhibit a class of low-pass filters which give rise to a rich variety of hyperscaling behaviour in the IR. We also discuss another set of generalizations which describes probing an SYK system with an external fermion, together with the new scaling behavior they exhibit in the IR.
Generalized semilocal theories and higher Hopf maps
Hindmarsh, M.; Holman, R.; Kephart, T.W.; Vachaspati, T.
1993-01-01
In semilocal theories, the vacuum manifold is fibered in a non-trivial way by the action of the gauge group. Here we generalize the original semilocal theory (which was based on the Hopf bundle S 3 → S1 S 2 ) to realize the next Hopf bundle S 7 →S 3 S 4 , and its extensions S 2n+1 → S3 HP n . The semilocal defects in this class of theories are classified by π 3 (S 3 ), and are interpreted as constrained instantons or generalized sphaleron configurations. We fail to find a field theoretic realization of the final Hopf bundle S 15 →S 7 S 8 , but are able to construct other semilocal spaces realizing Stiefel bundles over grassmannian spaces. (orig.)
On discrete 2D integrable equations of higher order
Adler, V E; Postnikov, V V
2014-01-01
We study two-dimensional discrete integrable equations of order 1 with respect to one independent variable and m with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The examples are related to the Bäcklund–Darboux transformations for the lattice equations of Bogoyavlensky type. (paper)
Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation
Ren Ji; Ruan Hangyu
2008-01-01
We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained
Higher-Order Finite Element Solutions of Option Prices
Raahauge, Peter
2004-01-01
Kinks and jumps in the payoff function of option contracts prevent an effectiveimplementation of higher-order numerical approximation methods. Moreover, thederivatives (the greeks) are not easily determined around such singularities, even withstandard lower-order methods. This paper suggests...... for prices as well as for first and second order derivatives(delta and gamma). Unlike similar studies, numerical approximation errors aremeasured both as weighted averages and in the supnorm over a state space includingtime-to-maturities down to a split second.KEYWORDS: Numerical option pricing, Transformed...
Oscillation of solutions of some higher order linear differential equations
Hong-Yan Xu
2009-11-01
Full Text Available In this paper, we deal with the order of growth and the hyper order of solutions of higher order linear differential equations $$f^{(k}+B_{k-1}f^{(k-1}+\\cdots+B_1f'+B_0f=F$$ where $B_j(z (j=0,1,\\ldots,k-1$ and $F$ are entire functions or polynomials. Some results are obtained which improve and extend previous results given by Z.-X. Chen, J. Wang, T.-B. Cao and C.-H. Li.
Generalized Reduced Order Modeling of Aeroservoelastic Systems
Gariffo, James Michael
Transonic aeroelastic and aeroservoelastic (ASE) modeling presents a significant technical and computational challenge. Flow fields with a mixture of subsonic and supersonic flow, as well as moving shock waves, can only be captured through high-fidelity CFD analysis. With modern computing power, it is realtively straightforward to determine the flutter boundary for a single structural configuration at a single flight condition, but problems of larger scope remain quite costly. Some such problems include characterizing a vehicle's flutter boundary over its full flight envelope, optimizing its structural weight subject to aeroelastic constraints, and designing control laws for flutter suppression. For all of these applications, reduced-order models (ROMs) offer substantial computational savings. ROM techniques in general have existed for decades, and the methodology presented in this dissertation builds on successful previous techniques to create a powerful new scheme for modeling aeroelastic systems, and predicting and interpolating their transonic flutter boundaries. In this method, linear ASE state-space models are constructed from modal structural and actuator models coupled to state-space models of the linearized aerodynamic forces through feedback loops. Flutter predictions can be made from these models through simple eigenvalue analysis of their state-transition matrices for an appropriate set of dynamic pressures. Moreover, this analysis returns the frequency and damping trend of every aeroelastic branch. In contrast, determining the critical dynamic pressure by direct time-marching CFD requires a separate run for every dynamic pressure being analyzed simply to obtain the trend for the critical branch. The present ROM methodology also includes a new model interpolation technique that greatly enhances the benefits of these ROMs. This enables predictions of the dynamic behavior of the system for flight conditions where CFD analysis has not been explicitly
Higher order Cambell techniques for neutron flux measurement. Pt. 1
Lux, I.; Baranyai, A.
1982-01-01
An exact mathematical description of arbitrary high order Campbell techniques for measuring particle fluxes is given. The nth order Campbell technique assumes the measurement of the moments of the outcoming voltage up to the nth one. A simple relation is derived among the various moments of the total measured voltage and of the detector signal caused by one incident particle. It is proven that in the monoparticle case combination of the measured moments up to the order n provides an expression proportional to the particle flux and to the nth moment of the detector signal. Generalization to several different particles is given and it is shown that if the flux of the particle causing the largest detector signal is measured with a relative error epsilon in the dc method and the error is due to the signals of other particles, then in the nth order campbelling the error will be of order epsilonsup(n). The effect of a random background on the measured voltage is also investigated and it is established that the nth order campbelling supresses the noise according to the nth power of the relative amplitude of the noise to the signal. The results concerning constant fluxes are generalized to time dependent particle fluxes and a method assuming a Fourier transform of the measured quantities is proposed for their determination. (orig.)
The Role of Formative Feedback in Promoting Higher Order ...
DrNneka
An International Multi-disciplinary Journal, Ethiopia. AFRREV ... make contribution to this research gap by proposing a theoretical feedback model that can promote higher order thinking skills in the classroom. The proposed ..... process; students provided with tasks that are novel, complex, creative, and non- algorithmic ...
Developing Higher-Order Thinking Skills through WebQuests
Polly, Drew; Ausband, Leigh
2009-01-01
In this study, 32 teachers participated in a year-long professional development project related to technology integration in which they designed and implemented a WebQuest. This paper describes the extent to which higher-order thinking skills (HOTS) and levels of technology implementation (LoTI) occur in the WebQuests that participants designed.…
Hamiltonian formulation of theory with higher order derivatives
Gitman, D.M.; Lyakhovich, S.L.; Tyutin, I.V.
1983-01-01
A method of ''hamiltonization'' of a special theory with higher order derivatives is described. In a nonspecial case the result coincides with the known Ostrogradsky formulation. It is shown that in the nonspecial theory the lagrange equations of motion are reduced to the normal form
Numerical methods of higher order of accuracy for incompressible flows
Kozel, K.; Louda, Petr; Příhoda, Jaromír
2010-01-01
Roč. 80, č. 8 (2010), s. 1734-1745 ISSN 0378-4754 Institutional research plan: CEZ:AV0Z20760514 Keywords : higher order methods * upwind methods * backward-facing step Subject RIV: BK - Fluid Dynamics Impact factor: 0.812, year: 2010
First Measurements of Higher Order Optics Parameters in the LHC
Vanbavinckhove, G; Bartolini, R; Calaga, R; Giovannozzi, M; Maclean, E H; Miyamoto, R; Schmidt, F; Tomas, R
2011-01-01
Higher order effects can play an important role in the performance of the LHC. Lack of knowledge of these pa- rameters can increase the tune footprint and compromise the beam lifetime. First measurements of these parameters at injection and flattop have been conducted. Detailed sim- ulations are compared to the measurements together with discussions on the measurement limitations.
Decidable Fragments of a Higher Order Calculus with Locations
Bundgaard, Mikkel; Godskesen, Jens Christian; Huttel, Hans
2009-01-01
Homer is a higher order process calculus with locations. In this paper we study Homer in the setting of the semantic finite control property, which is a finite reachability criterion that implies decidability of barbed bisimilarity. We show that strong and weak barbed bisimilarity are undecidable...
Computer-Mediated Assessment of Higher-Order Thinking Development
Tilchin, Oleg; Raiyn, Jamal
2015-01-01
Solving complicated problems in a contemporary knowledge-based society requires higher-order thinking (HOT). The most productive way to encourage development of HOT in students is through use of the Problem-based Learning (PBL) model. This model organizes learning by solving corresponding problems relative to study courses. Students are directed…
Enhancing Higher Order Thinking Skills through Clinical Simulation
Varutharaju, Elengovan; Ratnavadivel, Nagendralingan
2014-01-01
Purpose: The study aimed to explore, describe and analyse the design and implementation of clinical simulation as a pedagogical tool in bridging the deficiency of higher order thinking skills among para-medical students, and to make recommendations on incorporating clinical simulation as a pedagogical tool to enhance thinking skills and align the…
Higher-Order Hierarchical Legendre Basis Functions in Applications
Kim, Oleksiy S.; Jørgensen, Erik; Meincke, Peter
2007-01-01
The higher-order hierarchical Legendre basis functions have been developed for eﬀective solution of integral equations with the method of moments. They are derived from orthogonal Legendre polynomials modiﬁed to enforce normal continuity between neighboring mesh elements, while preserving a high...
Higher order mode damping in Kaon factory RF cavities
Enegren, T.; Poirier, R.; Griffin, J.; Walling, L.; Thiessen, H.A.; Smythe, W.R.
1989-05-01
Proposed designs for Kaon factory accelerators require that the rf cavities support beam currents on the order of several amperes. The beam current has Fourier components at all multiples of the rf frequency. Empty rf buckets produce additional components at all multiples of the revolution frequency. If a Fourier component of the beam coincides with the resonant frequency of a higher order mode of the cavity, which is inevitable if the cavity has a large frequency swing, significant excitation of this mode can occur. The induced voltage may then excite coupled bunch mode instabilities. Effective means are required to damp higher order modes without significantly affecting the fundamental mode. A mode damping scheme based on coupled transmission lines has been investigated and is report
An Algorithm for Higher Order Hopf Normal Forms
A.Y.T. Leung
1995-01-01
Full Text Available Normal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit. However, the computation of high-order normal forms is usually quite complicated. This article provides an explicit formula for the normalization of nonlinear differential equations. The higher order normal form is given explicitly. Illustrative examples include a cubic system, a quadratic system and a Duffing–Van der Pol system. We use exact arithmetic and find that the undamped Duffing equation can be represented by an exact polynomial differential amplitude equation in a finite number of terms.
Higher Order Thinking in the Australian Army Suite of Logistic Officer Courses
Bradford, Scott R
2006-01-01
.... The current Suite of Logistic Officer Courses (SOLOC) has been recently criticized for failing to meet this requirement, with the general perception that there is a distinct lack of higher-order thinking competencies within this continuum...
Exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres
Liu Chunping
2005-01-01
First, by using the generally projective Riccati equation method, many kinds of exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres are obtained in a unified way. Then, some relations among these solutions are revealed
Higher-order techniques for some problems of nonlinear control
Sarychev Andrey V.
2002-01-01
Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.
Higher-Order Spectrum in Understanding Nonlinearity in EEG Rhythms
Cauchy Pradhan
2012-01-01
Full Text Available The fundamental nature of the brain's electrical activities recorded as electroencephalogram (EEG remains unknown. Linear stochastic models and spectral estimates are the most common methods for the analysis of EEG because of their robustness, simplicity of interpretation, and apparent association with rhythmic behavioral patterns in nature. In this paper, we extend the use of higher-order spectrum in order to indicate the hidden characteristics of EEG signals that simply do not arise from random processes. The higher-order spectrum is an extension Fourier spectrum that uses higher moments for spectral estimates. This essentially nullifies all Gaussian random effects, therefore, can reveal non-Gaussian and nonlinear characteristics in the complex patterns of EEG time series. The paper demonstrates the distinguishing features of bispectral analysis for chaotic systems, filtered noises, and normal background EEG activity. The bispectrum analysis detects nonlinear interactions; however, it does not quantify the coupling strength. The squared bicoherence in the nonredundant region has been estimated to demonstrate nonlinear coupling. The bicoherence values are minimal for white Gaussian noises (WGNs and filtered noises. Higher bicoherence values in chaotic time series and normal background EEG activities are indicative of nonlinear coupling in these systems. The paper shows utility of bispectral methods as an analytical tool in understanding neural process underlying human EEG patterns.
Higher-order structure of Saccharomyces cerevisiae chromatin
Lowary, P.T.; Widom, J.
1989-01-01
We have developed a method for partially purifying chromatin from Saccharomyces cerevisiae (baker's yeast) to a level suitable for studies of its higher-order folding. This has required the use of yeast strains that are free of the ubiquitous yeast killer virus. Results from dynamic light scattering, electron microscopy, and x-ray diffraction show that the yeast chromatin undergoes a cation-dependent folding into 30-nm filaments that resemble those characteristic of higher-cell chromatin; moreover, the packing of nucleosomes within the yeast 30-nm filaments is similar to that of higher cells. These results imply that yeast has a protein or protein domain that serves the role of the histone H 1 found in higher cells; physical and genetic studies of the yeast activity could help elucidate the structure and function of H 1. Images of the yeast 30-nm filaments can be used to test crossed-linker models for 30-nm filament structure
Analysis of higher order harmonics with holographic reflection gratings
Mas-Abellan, P.; Madrigal, R.; Fimia, A.
2017-05-01
Silver halide emulsions have been considered one of the most energetic sensitive materials for holographic applications. Nonlinear recording effects on holographic reflection gratings recorded on silver halide emulsions have been studied by different authors obtaining excellent experimental results. In this communication specifically we focused our investigation on the effects of refractive index modulation, trying to get high levels of overmodulation that will produce high order harmonics. We studied the influence of the overmodulation and its effects on the transmission spectra for a wide exposure range by use of 9 μm thickness films of ultrafine grain emulsion BB640, exposed to single collimated beams using a red He-Ne laser (wavelength 632.8 nm) with Denisyuk configuration obtaining a spatial frequency of 4990 l/mm recorded on the emulsion. The experimental results show that high overmodulation levels of refractive index produce second order harmonics with high diffraction efficiency (higher than 75%) and a narrow grating bandwidth (12.5 nm). Results also show that overmodulation produce diffraction spectra deformation of the second order harmonic, transforming the spectrum from sinusoidal to approximation of square shape due to very high overmodulation. Increasing the levels of overmodulation of refractive index, we have obtained higher order harmonics, obtaining third order harmonic with diffraction efficiency (up to 23%) and narrowing grating bandwidth (5 nm). This study is the first step to develop a new easy technique to obtain narrow spectral filters based on the use of high index modulation reflection gratings.
Higher-order dynamical effects in Coulomb dissociation
Esbensen, H.
1994-06-01
We study the effect of higher-order processes in Coulomb dissociation of 11 Li by numerically solving the three-dimensional time-dependent Schroedinger equation for the relative motion of a di-neutron and the 9 Li core. Comparisons are made to first-order perturbation theory and to measurements. The calculated Coulomb reacceleration effects improve the agreement with experiment, but some discrepancy remains. The effects are much smaller in the dissociation of 11 Be, and they decrease with increasing beam energy. (orig.)
Inseparability inequalities for higher order moments for bipartite systems
Agarwal, G S; Biswas, Asoka
2005-01-01
There are several examples of bipartite entangled states of continuous variables for which the existing criteria for entanglement using the inequalities involving the second-order moments are insufficient. We derive new inequalities involving higher order correlation, for testing entanglement in non-Gaussian states. In this context, we study an example of a non-Gaussian state, which is a bipartite entangled state of the form Ψ(x a , x b ) ∝ (αx a + βx b ) e -(x a 2 +x b 2 )/2 . Our results open up an avenue to search for new inequalities to test entanglement in non-Gaussian states
Reduced Order Modeling in General Relativity
Tiglio, Manuel
2014-03-01
Reduced Order Modeling is an emerging yet fast developing filed in gravitational wave physics. The main goals are to enable fast modeling and parameter estimation of any detected signal, along with rapid matched filtering detecting. I will focus on the first two. Some accomplishments include being able to replace, with essentially no lost of physical accuracy, the original models with surrogate ones (which are not effective ones, that is, they do not simplify the physics but go on a very different track, exploiting the particulars of the waveform family under consideration and state of the art dimensional reduction techniques) which are very fast to evaluate. For example, for EOB models they are at least around 3 orders of magnitude faster than solving the original equations, with physically equivalent results. For numerical simulations the speedup is at least 11 orders of magnitude. For parameter estimation our current numbers are about bringing ~100 days for a single SPA inspiral binary neutron star Bayesian parameter estimation analysis to under a day. More recently, it has been shown that the full precessing problem for, say, 200 cycles, can be represented, through some new ideas, by a remarkably compact set of carefully chosen reduced basis waveforms (~10-100, depending on the accuracy requirements). I will highlight what I personally believe are the challenges to face next in this subarea of GW physics and where efforts should be directed. This talk will summarize work in collaboration with: Harbir Antil (GMU), Jonathan Blackman (Caltech), Priscila Canizares (IoA, Cambridge, UK), Sarah Caudill (UWM), Jonathan Gair (IoA. Cambridge. UK), Scott Field (UMD), Chad R. Galley (Caltech), Frank Herrmann (Germany), Han Hestahven (EPFL, Switzerland), Jason Kaye (Brown, Stanford & Courant). Evan Ochsner (UWM), Ricardo Nochetto (UMD), Vivien Raymond (LIGO, Caltech), Rory Smith (LIGO, Caltech) Bela Ssilagyi (Caltech) and MT (UMD & Caltech).
Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order
Taher S. Hassan
2016-01-01
Full Text Available We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t≔ri(tϕαixi-1Δ(t, i=1,…,n-1, with x0=x, ϕβ(u≔uβsgnu, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous function such that limt→∞φi(t=∞ for j=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.
Higher Order Differential Attack on 6-Round MISTY1
Tsunoo, Yukiyasu; Saito, Teruo; Nakashima, Hiroki; Shigeri, Maki
MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it has been recommended for Japanese e-Government ciphers by the CRYPTREC project. This paper reports a previously unknown higher order differential characteristic of 4-round MISTY1 with the FL functions. It also shows that a higher order differential attack that utilizes this newly discovered characteristic is successful against 6-round MISTY1 with the FL functions. This attack can recover a partial subkey with a data complexity of 253.7 and a computational complexity of 264.4, which is better than any previous cryptanalysis of MISTY1.
Higher-order risk preferences in social settings.
Heinrich, Timo; Mayrhofer, Thomas
2018-01-01
We study prudence and temperance (next to risk aversion) in social settings. Previous experimental studies have shown that these higher-order risk preferences affect the choices of individuals deciding privately on lotteries that only affect their own payoff. Yet, many risky and financially relevant decisions are made in the social settings of households or organizations. We elicit higher-order risk preferences of individuals and systematically vary how an individual's decision is made (alone or while communicating with a partner) and who is affected by the decision (only the individual or the partner as well). In doing so, we can isolate the effects of other-regarding concerns and communication on choices. Our results reveal that the majority of choices are risk averse, prudent, and temperate across social settings. We also observe that individuals are influenced significantly by the preferences of a partner when they are able to communicate and choices are payoff-relevant for both of them.
The higher order flux mapping method in large size PHWRs
Kulkarni, A.K.; Balaraman, V.; Purandare, H.D.
1997-01-01
A new higher order method is proposed for obtaining flux map using single set of expansion mode. In this procedure, one can make use of the difference between predicted value of detector reading and their actual values for determining the strength of local fluxes around detector site. The local fluxes are arising due to constant perturbation changes (both extrinsic and intrinsic) taking place in the reactor. (author)
Practical Programming with Higher-Order Encodings and Dependent Types
Poswolsky, Adam; Schürmann, Carsten
2008-01-01
, tedious, and error-prone. In this paper, we describe the underlying calculus of Delphin. Delphin is a fully implemented functional-programming language supporting reasoning over higher-order encodings and dependent types, while maintaining the benefits of HOAS. More specifically, just as representations...... for instantiation from those that will remain uninstantiated, utilizing a variation of Miller and Tiu’s ∇-quantifier [1]....
Modeling Human Behaviour with Higher Order Logic: Insider Threats
Boender, Jaap; Ivanova, Marieta Georgieva; Kammuller, Florian
2014-01-01
it to the sociological process of logical explanation. As a case study on modeling human behaviour, we present the modeling and analysis of insider threats as a Higher Order Logic theory in Isabelle/HOL. We show how each of the three step process of sociological explanation can be seen in our modeling of insider’s state......, its context within an organisation and the effects on security as outcomes of a theorem proving analysis....
Higher order Bose-Einstein correlations in identical particle production
Biyajima, M.
1990-01-01
A diagram technique to calculate the higher order Bose-Einstein correlations is formulated. This technique is applied to derive explicit expressions for the n-pion correlation functions for n = 2, 3, 4, and 5, and numerical predictions are given. In a comparison with the AFS and NA23 data on two-pion and three-pion Bose-Einstein correlations good agreement is obtained. 21 refs., 5 figs. (Authors)
Higher-order force moments of active particles
Nasouri, Babak; Elfring, Gwynn J.
2018-04-01
Active particles moving through fluids generate disturbance flows due to their activity. For simplicity, the induced flow field is often modeled by the leading terms in a far-field approximation of the Stokes equations, whose coefficients are the force, torque, and stresslet (zeroth- and first-order force moments) of the active particle. This level of approximation is quite useful, but may also fail to predict more complex behaviors that are observed experimentally. In this study, to provide a better approximation, we evaluate the contribution of the second-order force moments to the flow field and, by reciprocal theorem, present explicit formulas for the stresslet dipole, rotlet dipole, and potential dipole for an arbitrarily shaped active particle. As examples of this method, we derive modified Faxén laws for active spherical particles and resolve higher-order moments for active rod-like particles.
Influence of higher order modes on angled-facet amplifiers
Wang, Z.; Mikkelsen, B.; Stubkjær, Kristian
1991-01-01
The influence of the first-order mode on the residual reflectivity of angled-facet amplifiers is analyzed. For a 7 degrees angled-facet ridge waveguide amplifier with a single-layer antireflective (AR) coating, a gain ripple lower than 1-dB at 25-dB gain can be obtained independent...... of the polarization, even in the presence of a first-order mode with a 15-dB gain. The tolerances for the thickness and refractive index of the AR coating are reduced by a factor of three compared to operation in the fundamental mode only. The influence of the higher order mode can virtually be suppressed...
Higher-order momentum distributions and locally affine LDDMM registration
Sommer, Stefan Horst; Nielsen, Mads; Darkner, Sune
2013-01-01
description of affine transformations and subsequent compact description of non-translational movement in a globally nonrigid deformation. The resulting representation contains directly interpretable information from both mathematical and modeling perspectives. We develop the mathematical construction......To achieve sparse parametrizations that allow intuitive analysis, we aim to represent deformation with a basis containing interpretable elements, and we wish to use elements that have the description capacity to represent the deformation compactly. To accomplish this, we introduce in this paper...... higher-order momentum distributions in the large deformation diffeomorphic metric mapping (LDDMM) registration framework. While the zeroth-order moments previously used in LDDMM only describe local displacement, the first-order momenta that are proposed here represent a basis that allows local...
Near integrability of kink lattice with higher order interactions
Jiang, Yun-Guo; Liu, Jia-Zhen; He, Song
2017-11-01
We make use of Manton’s analytical method to investigate the force between kinks and anti-kinks at large distances in 1+1 dimensional field theory. The related potential has infinite order corrections of exponential pattern, and the coefficients for each order are determined. These coefficients can also be obtained by solving the equation of the fluctuations around the vacuum. At the lowest order, the kink lattice represents the Toda lattice. With higher order correction terms, the kink lattice can represent one kind of generic Toda lattice. With only two sites, the kink lattice is classically integrable. If the number of sites of the lattice is larger than two, the kink lattice is not integrable but is a near integrable system. We make use of Flaschka’s variables to study the Lax pair of the kink lattice. These Flaschka’s variables have interesting algebraic relations and non-integrability can be manifested. We also discuss the higher Hamiltonians for the deformed open Toda lattice, which has a similar result to the ordinary deformed Toda. Supported by Shandong Provincial Natural Science Foundation (ZR2014AQ007), National Natural Science Foundation of China (11403015, U1531105), S. He is supported by Max-Planck fellowship in Germany and National Natural Science Foundation of China (11305235)
Compiler-Directed Transformation for Higher-Order Stencils
Basu, Protonu [Univ. of Utah, Salt Lake City, UT (United States); Hall, Mary [Univ. of Utah, Salt Lake City, UT (United States); Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Straalen, Brian Van [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Oliker, Leonid [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Colella, Phillip [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2015-07-20
As the cost of data movement increasingly dominates performance, developers of finite-volume and finite-difference solutions for partial differential equations (PDEs) are exploring novel higher-order stencils that increase numerical accuracy and computational intensity. This paper describes a new compiler reordering transformation applied to stencil operators that performs partial sums in buffers, and reuses the partial sums in computing multiple results. This optimization has multiple effect son improving stencil performance that are particularly important to higher-order stencils: exploits data reuse, reduces floating-point operations, and exposes efficient SIMD parallelism to backend compilers. We study the benefit of this optimization in the context of Geometric Multigrid (GMG), a widely used method to solvePDEs, using four different Jacobi smoothers built from 7-, 13-, 27-and 125-point stencils. We quantify performance, speedup, andnumerical accuracy, and use the Roofline model to qualify our results. Ultimately, we obtain over 4× speedup on the smoothers themselves and up to a 3× speedup on the multigrid solver. Finally, we demonstrate that high-order multigrid solvers have the potential of reducing total data movement and energy by several orders of magnitude.
Holographic entanglement entropy for the most general higher derivative gravity
Miao, Rong-Xin; Guo, Wu-zhong
2015-01-01
The holographic entanglement entropy for the most general higher derivative gravity is investigated. We find a new type of Wald entropy, which appears on entangling surface without the rotational symmetry and reduces to usual Wald entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for the most general higher derivative gravity and work it out exactly for some squashed cones. As an important application, we derive HEE for gravitational action with one derivative of the curvature when the extrinsic curvature vanishes. We also study some toy models with non-zero extrinsic curvature. We prove that our formula yields the correct universal term of entanglement entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and Smolkin that the logarithmic term of entanglement entropy derived from Weyl anomaly of CFTs does not match the holographic result even if the extrinsic curvature vanishes. We find that such mismatch comes from the ‘anomaly of entropy’ of the derivative of curvature. After considering such contributions carefully, we resolve the puzzle successfully. In general, we need to fix the splitting problem for the conical metrics in order to derive the holographic entanglement entropy. We find that, at least for Einstein gravity, the splitting problem can be fixed by using equations of motion. How to derive the splittings for higher derivative gravity is a non-trivial and open question. For simplicity, we ignore the splitting problem in this paper and find that it does not affect our main results.
Higher order corrections to energy levels of muonic atoms
Rinker, G.A. Jr.; Steffen, R.M.
1975-08-01
In order to facilitate the analysis of muonic x-ray spectra, the results of numerical computations of all higher order quantum electrodynamical corrections to the energy levels of muonic atoms are presented in tabular and graphical form. These corrections include the vacuum polarization corrections caused by emission and reabsorption of virtual electron pairs to all orders, including ''double-bubble'' and ''cracked-egg'' diagrams. An estimate of the Delbruecke scattering-type correction is presented. The Lamb-shift (second- and fourth-order vertex) corrections have been calculated including the correction for the anomalous magnetic moment of the muon. The relativistic nuclear motion (or recoil) correction as well as the correction caused by the screening of the atomic electrons is presented in graphs. For the sake of completeness a graph of the nuclear polarization as computed on the basis of Chen's approach has been included. All calculations were made with a two-parameter Fermi distribution of the nuclear charge density. 7 figures, 23 references
Higher-order Skyrme hair of black holes
Gudnason, Sven Bjarke; Nitta, Muneto
2018-05-01
Higher-order derivative terms are considered as replacement for the Skyrme term in an Einstein-Skyrme-like model in order to pinpoint which properties are necessary for a black hole to possess stable static scalar hair. We find two new models able to support stable black hole hair in the limit of the Skyrme term being turned off. They contain 8 and 12 derivatives, respectively, and are roughly the Skyrme-term squared and the so-called BPS-Skyrme-term squared. In the twelfth-order model we find that the lower branches, which are normally unstable, become stable in the limit where the Skyrme term is turned off. We check this claim with a linear stability analysis. Finally, we find for a certain range of the gravitational coupling and horizon radius, that the twelfth-order model contains 4 solutions as opposed to 2. More surprisingly, the lowest part of the would-be unstable branch turns out to be the stable one of the 4 solutions.
Higher order branching of periodic orbits from polynomial isochrones
B. Toni
1999-09-01
Full Text Available We discuss the higher order local bifurcations of limit cycles from polynomial isochrones (linearizable centers when the linearizing transformation is explicitly known and yields a polynomial perturbation one-form. Using a method based on the relative cohomology decomposition of polynomial one-forms complemented with a step reduction process, we give an explicit formula for the overall upper bound of branch points of limit cycles in an arbitrary $n$ degree polynomial perturbation of the linear isochrone, and provide an algorithmic procedure to compute the upper bound at successive orders. We derive a complete analysis of the nonlinear cubic Hamiltonian isochrone and show that at most nine branch points of limit cycles can bifurcate in a cubic polynomial perturbation. Moreover, perturbations with exactly two, three, four, six, and nine local families of limit cycles may be constructed.
Development of higher order mode couplers at Cornell
Amato, J.C.
1988-01-01
Higher order mode (HOM) couplers are integral parts of a superconducting accelerator cavity. The damping which the couplers must provide is dictated by the frequency and shunt impedance of the cavity modes as well as by the stability requirements of the accelerator incorporating the cavities. Cornell's 5-cell 1500 MHz elliptical cavity was designed for use in a 50 x 50 GeV electron-positron storage ring with a total beam current of 3.5 mA (CESR-II). HOM couplers for the Cornell cavity were designed and evaluated with this machine in mind. The development of these couplers is described in this paper. 8 references, 8 figures
Integrable higher order deformations of Heisenberg supermagnetic model
Guo Jiafeng; Yan Zhaowen; Wang Shikun; Wu Ke; Zhao Weizhong
2009-01-01
The Heisenberg supermagnet model is an integrable supersymmetric system and has a close relationship with the strong electron correlated Hubbard model. In this paper, we investigate the integrable higher order deformations of Heisenberg supermagnet models with two different constraints: (i) S 2 =3S-2I for S is an element of USPL(2/1)/S(U(2)xU(1)) and (ii) S 2 =S for S is an element of USPL(2/1)/S(L(1/1)xU(1)). In terms of the gauge transformation, their corresponding gauge equivalent counterparts are derived.
Higher order temporal finite element methods through mixed formalisms.
Kim, Jinkyu
2014-01-01
The extended framework of Hamilton's principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primarily considered to validate and to investigate the performance of the numerical algorithms developed from both formulations. For the undamped system, all the algorithms are symplectic and unconditionally stable with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.
Programming real-time executives in higher order language
Foudriat, E. C.
1982-01-01
Methods by which real-time executive programs can be implemented in a higher order language are discussed, using HAL/S and Path Pascal languages as program examples. Techniques are presented by which noncyclic tasks can readily be incorporated into the executive system. Situations are shown where the executive system can fail to meet its task scheduling and yet be able to recover either by rephasing the clock or stacking the information for later processing. The concept of deadline processing is shown to enable more effective mixing of time and information synchronized systems.
Squeezing of higher order Hermite-Gauss modes
Lassen, Mikael Østergaard
2008-01-01
The present paper gives an overview of the experimental generation of squeezing in higher order Hermite-Gaussian modes with an optical parametric ampli¯er (OPA). This work was awarded with The European Optical Society (EOS) price 2007. The purpose of the prize is to encourage a European dimension...... in research in pure and applied optics. The EOS prize is awarded based on the selection criteria of high professionalism, academic and technical quality. Following the EOS Prize rules, the conditions for eligibility are that the work was performed in Europe and that it is published under the auspices...
Higher-order thinking in foreign language learning
Bastos, Ascensão; Ramos, Altina
2017-01-01
A project is being conducted in English as a foreign language (EFL), involving eleventh graders in formal and non-formal learning contexts, in a Portuguese high school. The goal of this study is to examine the impact of cognitive tools and higher-order thinking processes on the learning of EFL and achievement of larger processes oriented to action, involving problem solving, decision-making and creation of new products. YouTube videos emerge as cognitive tools in the process. Final results sh...
The advantage of higher-order theory of mind in the game of limited bidding
De Weerd, H.; Verheij, B.; van Eijck, J.; Verbrugge, L. C.
2011-01-01
Higher-order theory of mind is the ability to recursively model mental states of other agents. It is known that adults in general can reason adequately at the second order (covering attributions like "Alice knows that Bob knows that she wrote a novel under pseudonym"), but there are cognitive limits
Holographic conductivity of holographic superconductors with higher-order corrections
Sheykhi, Ahmad [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Ghazanfari, Afsoon; Dehyadegari, Amin [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)
2018-02-15
We analytically and numerically disclose the effects of the higher-order correction terms in the gravity and in the gauge field on the properties of s-wave holographic superconductors. On the gravity side, we consider the higher curvature Gauss-Bonnet corrections and on the gauge field side, we add a quadratic correction term to the Maxwell Lagrangian. We show that, for this system, one can still obtain an analytical relation between the critical temperature and the charge density. We also calculate the critical exponent and the condensation value both analytically and numerically. We use a variational method, based on the Sturm-Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. For a fixed value of the Gauss-Bonnet parameter, we observe that the critical temperature decreases with increasing the nonlinearity of the gauge field. This implies that the nonlinear correction term to the Maxwell electrodynamics makes the condensation harder. We also study the holographic conductivity of the system and disclose the effects of the Gauss-Bonnet and nonlinear parameters α and b on the superconducting gap. We observe that, for various values of α and b, the real part of the conductivity is proportional to the frequency per temperature, ω/T, as the frequency is large enough. Besides, the conductivity has a minimum in the imaginary part which is shifted toward greater frequency with decreasing temperature. (orig.)
Predictors of third and Higher order births in India
Payal Singh
2015-12-01
Full Text Available Background: Total fertility rate (TFR reflecting population growth is closely related to higher order parity progression. Many Indian states reached replacement level of TFR, but still states constituting nearly 40% population are with TFR ≥ 3. The predictors are the desire of son’s, poor contraceptives practices, younger age at marriage, child loss and shorter birth spacing. Objective: This analysis assessed the degree of relation of 3rd and higher order parity progression with the above mentioned predictors. Material and Methods: State/Union Territories wise proportions of women: progressing to ≥3 births, more sons desire, birth spacing <24 months, adopting modern contraception and median marriage age <18 years along with infant mortality rate (IMR were taken from NFHS-III report. Correlation matrix and stepwise forward multiple regression carried. Significance was seen at 5%. Results: Hindi speaking states constituting 38.92% nation population recorded TFR ≥3. Positive correlation of mothers progressing ≥ 3 births was highest (0.746 with those desiring more sons followed by IMR (0.445; while maximum negative correlation with those practicing modern contraceptives (-0.565 followed by median age at marriage (-0.391. Multiple regression analysis in order identified desire of more sons, practicing modern contraception and shorter birth spacing as the significant predictors and jointly explained 77.9% of the total variation with gain of 15.5% by adding modern contraceptive practice and 8.3% by adding shorter birth spacing. Conclusions: Desire of more sons appeared the most important predictor to progress ≥3 births that is governed by society culture and educational attainment, require attitudinal change. Further, mothers need motivation to practice both spacing and terminal methods once family is complete.
Higher order BLG supersymmetry transformations from 10-dimensional super Yang Mills
Hall, John [Alumnus of Physics Department, Imperial College,South Kensington, London, SW7 2AZ (United Kingdom); Low, Andrew [Physics Department, Wimbledon High School,Mansel Road, London, SW19 4AB (United Kingdom)
2014-06-26
We study a Simple Route for constructing the higher order Bagger-Lambert-Gustavsson theory - both supersymmetry transformations and Lagrangian - starting from knowledge of only the 10-dimensional Super Yang Mills Fermion Supersymmetry transformation. We are able to uniquely determine the four-derivative order corrected supersymmetry transformations, to lowest non-trivial order in Fermions, for the most general three-algebra theory. For the special case of Euclidean three-algbera, we reproduce the result presented in arXiv:1207.1208, with significantly less labour. In addition, we apply our method to calculate the quadratic fermion terms in the higher order BLG fermion supersymmetry transformation.
Neutron scattering studies on chromatin higher-order structure
Graziano, V.; Gerchman, S.E.; Schneider, D.K.; Ramakrishnan, V. [Brookhaven National Laboratory, Upton, NY (United States)
1994-12-31
We have been engaged in studies of the structure and condensation of chromatin into the 30nm filament using small-angle neutron scattering. We have also used deuterated histone H1 to determine its location in the chromatin 30nm filament. Our studies indicate that chromatin condenses with increasing ionic strength to a limiting structure that has a mass per unit length of 6-7 nucleosomes/11 nm. They also show that the linker histone H1/H5 is located in the interior of the chromatin filament, in a position compatible with its binding to the inner face of the nucleosome. Analysis of the mass per unit length as a function of H5 stoichiometry suggests that 5-7 contiguous nucleosomes need to have H5 bound before a stable higher order structure can exist.
Mixed Higher Order Variational Model for Image Recovery
Pengfei Liu
2014-01-01
Full Text Available A novel mixed higher order regularizer involving the first and second degree image derivatives is proposed in this paper. Using spectral decomposition, we reformulate the new regularizer as a weighted L1-L2 mixed norm of image derivatives. Due to the equivalent formulation of the proposed regularizer, an efficient fast projected gradient algorithm combined with monotone fast iterative shrinkage thresholding, called, FPG-MFISTA, is designed to solve the resulting variational image recovery problems under majorization-minimization framework. Finally, we demonstrate the effectiveness of the proposed regularization scheme by the experimental comparisons with total variation (TV scheme, nonlocal TV scheme, and current second degree methods. Specifically, the proposed approach achieves better results than related state-of-the-art methods in terms of peak signal to ratio (PSNR and restoration quality.
MHD stability analysis using higher order spline functions
Ida, Akihiro [Department of Energy Engineering and Science, Graduate School of Engineering, Nagoya University, Nagoya, Aichi (Japan); Todoroki, Jiro; Sanuki, Heiji
1999-04-01
The eigenvalue problem of the linearized magnetohydrodynamic (MHD) equation is formulated by using higher order spline functions as the base functions of Ritz-Galerkin approximation. When the displacement vector normal to the magnetic surface (in the magnetic surface) is interpolated by B-spline functions of degree p{sub 1} (degree p{sub 2}), which is continuously c{sub 1}-th (c{sub 2}-th) differentiable on neighboring finite elements, the sufficient conditions for the good approximation is given by p{sub 1}{>=}p{sub 2}+1, c{sub 1}{<=}c{sub 2}+1, (c{sub 1}{>=}1, p{sub 2}{>=}c{sub 2}{>=}0). The influence of the numerical integration upon the convergence of calculated eigenvalues is discussed. (author)
Higher order corrections to asymptotic-de Sitter inflation
Mohsenzadeh, M.; Yusofi, E.
2017-08-01
Since trans-Planckian considerations can be associated with the re-definition of the initial vacuum, we investigate further the influence of trans-Planckian physics on the spectra produced by the initial quasi-de Sitter (dS) state during inflation. We use the asymptotic-dS mode to study the trans-Planckian correction of the power spectrum to the quasi-dS inflation. The obtained spectra consist of higher order corrections associated with the type of geometry and harmonic terms sensitive to the fluctuations of space-time (or gravitational waves) during inflation. As an important result, the amplitude of the power spectrum is dependent on the choice of c, i.e. the type of space-time in the period of inflation. Also, the results are always valid for any asymptotic dS space-time and particularly coincide with the conventional results for dS and flat space-time.
Neutron scattering studies on chromatin higher-order structure
Graziano, V.; Gerchman, S.E.; Schneider, D.K.; Ramakrishnan, V.
1994-01-01
We have been engaged in studies of the structure and condensation of chromatin into the 30nm filament using small-angle neutron scattering. We have also used deuterated histone H1 to determine its location in the chromatin 30nm filament. Our studies indicate that chromatin condenses with increasing ionic strength to a limiting structure that has a mass per unit length of 6-7 nucleosomes/11 nm. They also show that the linker histone H1/H5 is located in the interior of the chromatin filament, in a position compatible with its binding to the inner face of the nucleosome. Analysis of the mass per unit length as a function of H5 stoichiometry suggests that 5-7 contiguous nucleosomes need to have H5 bound before a stable higher order structure can exist
Higher order statistical moment application for solar PV potential analysis
Basri, Mohd Juhari Mat; Abdullah, Samizee; Azrulhisham, Engku Ahmad; Harun, Khairulezuan
2016-10-01
Solar photovoltaic energy could be as alternative energy to fossil fuel, which is depleting and posing a global warming problem. However, this renewable energy is so variable and intermittent to be relied on. Therefore the knowledge of energy potential is very important for any site to build this solar photovoltaic power generation system. Here, the application of higher order statistical moment model is being analyzed using data collected from 5MW grid-connected photovoltaic system. Due to the dynamic changes of skewness and kurtosis of AC power and solar irradiance distributions of the solar farm, Pearson system where the probability distribution is calculated by matching their theoretical moments with that of the empirical moments of a distribution could be suitable for this purpose. On the advantage of the Pearson system in MATLAB, a software programming has been developed to help in data processing for distribution fitting and potential analysis for future projection of amount of AC power and solar irradiance availability.
Recognition of higher order patterns in proteins: immunologic kernels.
Robert D Bremel
Full Text Available By applying analysis of the principal components of amino acid physical properties we predicted cathepsin cleavage sites, MHC binding affinity, and probability of B-cell epitope binding of peptides in tetanus toxin and in ten diverse additional proteins. Cross-correlation of these metrics, for peptides of all possible amino acid index positions, each evaluated in the context of a ±25 amino acid flanking region, indicated that there is a strongly repetitive pattern of short peptides of approximately thirty amino acids each bounded by cathepsin cleavage sites and each comprising B-cell linear epitopes, MHC-I and MHC-II binding peptides. Such "immunologic kernel" peptides comprise all signals necessary for adaptive immunologic cognition, response and recall. The patterns described indicate a higher order spatial integration that forms a symbolic logic coordinating the adaptive immune system.
Estimation of uncertainties from missing higher orders in perturbative calculations
Bagnaschi, E.
2015-05-01
In this proceeding we present the results of our recent study (hep-ph/1409.5036) of the statistical performances of two different approaches, Scale Variation (SV) and the Bayesian model of Cacciari and Houdeau (CH)(hep-ph/1105.5152) (which we also extend to observables with initial state hadrons), to the estimation of Missing Higher-Order Uncertainties (MHOUs)(hep-ph/1307.1843) in perturbation theory. The behavior of the models is determined by analyzing, on a wide set of observables, how the MHOU intervals they produce are successful in predicting the next orders. We observe that the Bayesian model behaves consistently, producing intervals at 68% Degree of Belief (DoB) comparable with the scale variation intervals with a rescaling factor r larger than 2 and closer to 4. Concerning SV, our analysis allows the derivation of a heuristic Confidence Level (CL) for the intervals. We find that assigning a CL of 68% to the intervals obtained with the conventional choice of varying the scales within a factor of two with respect to the central scale could potentially lead to an underestimation of the uncertainties in the case of observables with initial state hadrons.
Higher order mode analysis of the SNS superconducting linac
Sang Ho Kim; Dong Jeon; Sundelin, R
2001-01-01
Higher order modes (HOM's) of monopoles, dipoles, quadrupoles and sextupoles in beta =0.61 and beta =0.81 6-cell superconducting (SC) cavities for the Spallation Neutron Source (SNS) project, have been found up to about 3 GHz and their properties such as R/Q, trapping possibility, etc have been figured out concerning manufacturing imperfection. The main issues of HOM's are beam instabilities (published separately) and HOM induced power especially from TM monopoles. The time structure of SNS beam has three different time scales of pulses, which are micro-pulse, midi-pulse and macropulse. Each time structure will generate resonances. When a mode is near these resonance frequencies, the induced voltage could be large and accordingly the resulting HOM power. In order to understand the effects from such a complex beam time structure on the mode excitation and resulting HOM power, analytic expressions are developed. With these analytic expressions, the induced HOM voltage and HOM power were calculated by assuming e...
Correlated stopping, proton clusters and higher order proton cumulants
Bzdak, Adam [AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow (Poland); Koch, Volker [Lawrence Berkeley National Laboratory, Nuclear Science Division, Berkeley, CA (United States); Skokov, Vladimir [RIKEN/BNL, Brookhaven National Laboratory, Upton, NY (United States)
2017-05-15
We investigate possible effects of correlations between stopped nucleons on higher order proton cumulants at low energy heavy-ion collisions. We find that fluctuations of the number of wounded nucleons N{sub part} lead to rather nontrivial dependence of the correlations on the centrality; however, this effect is too small to explain the large and positive four-proton correlations found in the preliminary data collected by the STAR collaboration at √(s) = 7.7 GeV. We further demonstrate that, by taking into account additional proton clustering, we are able to qualitatively reproduce the preliminary experimental data. We speculate that this clustering may originate either from collective/multi-collision stopping which is expected to be effective at lower energies or from a possible first-order phase transition, or from (attractive) final state interactions. To test these ideas we propose to measure a mixed multi-particle correlation between stopped protons and a produced particle (e.g. pion, antiproton). (orig.)
Higher Order Modes Excitation of Micro Cantilever Beams
Jaber, Nizar
2014-05-01
In this study, we present analytical and experimental investigation of electrically actuated micro cantilever based resonators. These devices are fabricated using polyimide and coated with chrome and gold layers from both sides. The cantilevers are highly curled up due to stress gradient, which is a common imperfection in surface micro machining. Using a laser Doppler vibrometer, we applied a noise signal to experimentally find the first four resonance frequencies. Then, using a data acquisition card, we swept the excitation frequency around the first four natural modes of vibrations. Theoretically, we derived a reduced order model using the Galerkin method to simulate the dynamics of the system. Extensive numerical analysis and computations were performed. The numerical analysis was able to provide good matching with experimental values of the resonance frequencies. Also, we proved the ability to excite higher order modes using partial electrodes with shapes that resemble the shape of the mode of interest. Such micro-resonators are shown to be promising for applications in mass and gas sensing.
On higher-order corrections in M theory
Howe, P.S.; Tsimpis, D.
2003-01-01
A theoretical analysis of higher-order corrections to D=11 supergravity is given in a superspace framework. It is shown that any deformation of D=11 supergravity for which the lowest-dimensional component of the four-form G 4 vanishes is trivial. This implies that the equations of motion of D=11 supergravity are specified by an element of a certain spinorial cohomology group and generalises previous results obtained using spinorial or pure spinor cohomology to the fully non-linear theory. The first deformation of the theory is given by an element of a different spinorial cohomology group with coefficients which are local tensorial functions of the massless supergravity fields. The four-form Bianchi Identities are solved, to first order and at dimension -{1/2}, in the case that the lowest-dimensional component of G 4 is non-zero. Moreover, it is shown how one can calculate the first-order correction to the dimension-zero torsion and thus to the supergravity equations of motion given an explicit expression for this object in terms of the supergravity fields. The version of the theory with both a four-form and a seven-form is discussed in the presence of the five-brane anomaly-cancelling term. It is shown that the supersymmetric completion of this term exists and it is argued that it is the unique anomaly-cancelling invariant at this dimension which is at least quartic in the fields. This implies that the first deformation of the theory is completely determined by the anomaly term from which one can, in principle, read off the corrections to all of the superspace field strength tensors. (author)
Predicting perceptual learning from higher-order cortical processing.
Wang, Fang; Huang, Jing; Lv, Yaping; Ma, Xiaoli; Yang, Bin; Wang, Encong; Du, Boqi; Li, Wu; Song, Yan
2016-01-01
Visual perceptual learning has been shown to be highly specific to the retinotopic location and attributes of the trained stimulus. Recent psychophysical studies suggest that these specificities, which have been associated with early retinotopic visual cortex, may in fact not be inherent in perceptual learning and could be related to higher-order brain functions. Here we provide direct electrophysiological evidence in support of this proposition. In a series of event-related potential (ERP) experiments, we recorded high-density electroencephalography (EEG) from human adults over the course of learning in a texture discrimination task (TDT). The results consistently showed that the earliest C1 component (68-84ms), known to reflect V1 activity driven by feedforward inputs, was not modulated by learning regardless of whether the behavioral improvement is location specific or not. In contrast, two later posterior ERP components (posterior P1 and P160-350) over the occipital cortex and one anterior ERP component (anterior P160-350) over the prefrontal cortex were progressively modified day by day. Moreover, the change of the anterior component was closely correlated with improved behavioral performance on a daily basis. Consistent with recent psychophysical and imaging observations, our results indicate that perceptual learning can mainly involve changes in higher-level visual cortex as well as in the neural networks responsible for cognitive functions such as attention and decision making. Copyright © 2015 Elsevier Inc. All rights reserved.
Controlling general projective synchronization of fractional order Rossler systems
Shao Shiquan
2009-01-01
This paper proposed a method to achieve general projective synchronization of two fractional order Rossler systems. First, we construct the fractional order Rossler system's corresponding approximation integer order system. Then, a control method based on a partially linear decomposition and negative feedback of state errors was utilized on the integer order system. Numerical simulations show the effectiveness of the proposed method.
49 CFR 510.7 - General or special orders.
2010-10-01
... NHTSA may require by the issuance of general or special orders any person, sole proprietorship..., information relating to the organization of that person, sole proprietorship, partnership, corporation, or...
Preparation and characterization of stable aqueous higher-order fullerenes
Aich, Nirupam; Flora, Joseph R V; Saleh, Navid B
2012-01-01
Stable aqueous suspensions of nC 60 and individual higher fullerenes, i.e. C 70 , C 76 and C 84 , are prepared by a calorimetric modification of a commonly used liquid–liquid extraction technique. The energy requirement for synthesis of higher fullerenes has been guided by molecular-scale interaction energy calculations. Solubilized fullerenes show crystalline behavior by exhibiting lattice fringes in high resolution transmission electron microscopy images. The fullerene colloidal suspensions thus prepared are stable with a narrow distribution of cluster radii (42.7 ± 0.8 nm, 46.0 ± 14.0 nm, 60 ± 3.2 nm and 56.3 ± 1.1 nm for nC 60 , nC 70 , nC 76 and nC 84 , respectively) as measured by time-resolved dynamic light scattering. The ζ-potential values for all fullerene samples showed negative surface potentials with similar magnitude ( − 38.6 ± 5.8 mV, − 39.1 ± 4.2 mV, − 38.9 ± 5.8 mV and − 41.7 ± 5.1 mV for nC 60 , nC 70 , nC 76 and nC 84 , respectively), which provide electrostatic stability to the colloidal clusters. This energy-based modified solubilization technique to produce stable aqueous fullerenes will likely aid in future studies focusing on better applicability, determination of colloidal properties, and understanding of environmental fate, transport and toxicity of higher-order fullerenes. (paper)
Higher education and general studies in Nigeria: A philosophical ...
Higher education and general studies in Nigeria: A philosophical investigation. ... Mgbakoigba: Journal of African Studies ... national policy on education on tertiary or higher education reveals a startling chasm of gap between the goals of the policy through General Studies Programme and their expected actualizations.
Higher order mode damping of a higher harmonic superconducting cavity for SSRF
Yu Haibo; Liu Jianfei; Hou Hongtao; Ma Zhenyu; Feng Xiqiang; Mao Dongqing
2012-01-01
Adopting a higher harmonic cavity on a synchrotron radiation facility can increase the beam lifetime and suppress the beam instability. In this paper, we report the simulation and preliminary design on higher order modes (HOMs) damping of the designed and fabricated higher harmonic superconducting cavity for Shanghai Synchrotron Radiation Facility (SSRF). The requirements for the HOM damping are analyzed, and the length and location of the HOM damper are optimized by using the SEAFISH code. The results show that the design can provide heavy damping for harmful HOMs with decreased impedance, and the beam instability requirement of SSRF can be satisfied. By using the ABCI code, the loss factor is obtained and the HOM power is estimated. (authors)
Higher-order aberrations and visual acuity after LASEK.
Urgancioglu, Berrak; Bilgihan, Kamil; Ozturk, Sertac
2008-08-01
To determine ocular higher-order aberrations (HOAs) in eyes with supernormal vision after myopic astigmatic laser subepithelial keratomileusis (LASEK) and to compare the findings with those in eyes with natural supernormal vision. Ocular HOAs were measured after LASEK in 20 eyes of 12 myopic astigmatic patients with postoperative uncorrected visual acuity (UCVA) of >20/16 (group 1). Patients who were included in the study had no visual symptoms like glare, halo or double vision. The measurements were taken 8.3 +/- 3 months after LASEK surgery. In group 2 ocular HOAs were examined in 20 eyes of 10 subjects with natural UCVA of >20/16 as a control. Measurements were taken across a pupil with a diameter of 4.0 mm and 6.0 mm. Root-mean-square (RMS) values of HOAs, Z(3)-1, Z(3)1, Z(4)0, Z(5)-1, Z(5)1 and Z(6)0 were analyzed. The mean RMS values for each order were higher in group 1 when compared with group 2 at 4.0 mm and 6.0 mm pupil diameters. There was no statistically significant difference between groups in spherical and coma aberrations (P > 0.05). Mean RMS values for total HOAs were 0.187 +/- 0.09 microm at 4.0 mm and 0.438 +/- 0.178 microm at 6.0 mm pupil in group 1 and 0.120 +/- 0.049 microm at 4.0 mm and 0.344 +/- 0.083 microm at 6.0 mm pupil in group 2. The difference between groups in total HOAs was statistically significant at 4.0 mm and 6.0 mm pupil diameters (P < 0.05). Ocular HOAs exist in eyes with supernormal vision. After LASEK, the amount of HOAs of the eye increases under both mesopic and photopic conditions. However the amount of HOA increase does not seem to be consistent with visual symptoms.
Average gluon and quark jet multiplicities at higher orders
Bolzoni, Paolo; Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kotikov, Anatoly V. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics
2013-05-15
We develop a new formalism for computing and including both the perturbative and nonperturbative QCD contributions to the scale evolution of average gluon and quark jet multiplicities. The new method is motivated by recent progress in timelike small-x resummation obtained in the MS factorization scheme. We obtain next-to-next-to-leading-logarithmic (NNLL) resummed expressions, which represent generalizations of previous analytic results. Our expressions depend on two nonperturbative parameters with clear and simple physical interpretations. A global fit of these two quantities to all available experimental data sets that are compatible with regard to the jet algorithms demonstrates by its goodness how our results solve a longstanding problem of QCD. We show that the statistical and theoretical uncertainties both do not exceed 5% for scales above 10 GeV. We finally propose to use the jet multiplicity data as a new way to extract the strong-coupling constant. Including all the available theoretical input within our approach, we obtain {alpha}{sub s}{sup (5)}(M{sub Z})=0.1199{+-}0.0026 in the MS scheme in an approximation equivalent to next-to-next-to-leading order enhanced by the resummations of ln(x) terms through the NNLL level and of ln Q{sup 2} terms by the renormalization group, in excellent agreement with the present world average.
Higher-order-mode damper as beam-position monitors; Higher-Order-Mode Daempfer als Stahllagemonitore
Peschke, C.
2006-03-15
In the framework of this thesis a beam-position monitor was developed, which can only because of the signals from the HOM dampers of a linear-accelerator structure determine the beam position with high accuracy. For the unique determination of the beam position in the plane a procedure was developed, which uses the amplitudes and the start-phase difference between a dipole mode and a higher monopole mode. In order tocheck the suitability of the present SBLC-HOM damper as beam position monitor three-dimensional numerical field calculations in the frequency and time range and measurements on the damper cell were performed. For the measurements without beam a beam simulator was constructed, which allows computer-driven measurements with variable depositions of the simulated beam with a resolution of 1.23 {mu}m. Because the complete 6 m long, 180-cell accelerator structure was not available for measurements and could also with the available computers not be three-dimensionally simulated simulated, a one-dimensional equivalent-circuit based model of the multi-cell was studied. The equivalent circuits with 879 concentrated components regards the detuning from cell to cell, the cell losses, the damper losses, and the beam excitation in dependence on the deposition. the measurements and simulations let a resolution of the ready beam-position monitor on the 180-cell in the order of magnitude of 1-10 {mu}m and a relative accuracy smaller 6.2% be expected.
Higher-order scalar interactions and SM vacuum stability
Lalak, Zygmunt; Lewicki, Marek; Olszewski, Paweł [Institute of Theoretical Physics, Faculty of Physics, University of Warsawul. Hoża 69, Warsaw (Poland)
2014-05-26
Investigation of the structure of the Standard Model effective potential at very large field strengths opens a window towards new phenomena and can reveal properties of the UV completion of the SM. The map of the lifetimes of the vacua of the SM enhanced by nonrenormalizable scalar couplings has been compiled to show how new interactions modify stability of the electroweak vacuum. Whereas it is possible to stabilize the SM by adding Planck scale suppressed interactions and taking into account running of the new couplings, the generic effect is shortening the lifetime and hence further destabilisation of the SM electroweak vacuum. These findings have been illustrated with phase diagrams of modified SM-like models. It has been demonstrated that stabilisation can be achieved by lowering the suppression scale of higher order operators while picking up such combinations of new couplings, which do not deepen the new minima of the potential. Our results show the dependence of the lifetime of the electroweak minimum on the magnitude of the new couplings, including cases with very small couplings (which means very large effective suppression scale) and couplings vastly different in magnitude (which corresponds to two different suppression scales)
Higher-Order Synaptic Interactions Coordinate Dynamics in Recurrent Networks.
Brendan Chambers
2016-08-01
Full Text Available Linking synaptic connectivity to dynamics is key to understanding information processing in neocortex. Circuit dynamics emerge from complex interactions of interconnected neurons, necessitating that links between connectivity and dynamics be evaluated at the network level. Here we map propagating activity in large neuronal ensembles from mouse neocortex and compare it to a recurrent network model, where connectivity can be precisely measured and manipulated. We find that a dynamical feature dominates statistical descriptions of propagating activity for both neocortex and the model: convergent clusters comprised of fan-in triangle motifs, where two input neurons are themselves connected. Fan-in triangles coordinate the timing of presynaptic inputs during ongoing activity to effectively generate postsynaptic spiking. As a result, paradoxically, fan-in triangles dominate the statistics of spike propagation even in randomly connected recurrent networks. Interplay between higher-order synaptic connectivity and the integrative properties of neurons constrains the structure of network dynamics and shapes the routing of information in neocortex.
Higher-order scene statistics of breast images
Abbey, Craig K.; Sohl-Dickstein, Jascha N.; Olshausen, Bruno A.; Eckstein, Miguel P.; Boone, John M.
2009-02-01
Researchers studying human and computer vision have found description and construction of these systems greatly aided by analysis of the statistical properties of naturally occurring scenes. More specifically, it has been found that receptive fields with directional selectivity and bandwidth properties similar to mammalian visual systems are more closely matched to the statistics of natural scenes. It is argued that this allows for sparse representation of the independent components of natural images [Olshausen and Field, Nature, 1996]. These theories have important implications for medical image perception. For example, will a system that is designed to represent the independent components of natural scenes, where objects occlude one another and illumination is typically reflected, be appropriate for X-ray imaging, where features superimpose on one another and illumination is transmissive? In this research we begin to examine these issues by evaluating higher-order statistical properties of breast images from X-ray projection mammography (PM) and dedicated breast computed tomography (bCT). We evaluate kurtosis in responses of octave bandwidth Gabor filters applied to PM and to coronal slices of bCT scans. We find that kurtosis in PM rises and quickly saturates for filter center frequencies with an average value above 0.95. By contrast, kurtosis in bCT peaks near 0.20 cyc/mm with kurtosis of approximately 2. Our findings suggest that the human visual system may be tuned to represent breast tissue more effectively in bCT over a specific range of spatial frequencies.
Covariant quantization of infinite spin particle models, and higher order gauge theories
Edgren, Ludde; Marnelius, Robert
2006-01-01
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in the quantization process. A consistent covariant quantization is shown to exist. Also a recently proposed supersymmetric version for half-odd integer spins is quantized. A general algorithm to derive gauge invariances of higher order Lagrangians is given and applied to the infinite spin particle model, and to a new higher order model for a spinning particle which is proposed here, as well as to a previously given higher order rigid particle model. The latter two models are also covariantly quantized
Generalized Unitary Cuts and Integrand Reduction at Higher Loop Orders
Frellesvig, Hjalte Axel
-generation software on equal footing with the tree contributions. More specifically, the OPP method calculates individually each topology in the expansion given by the integrand reduction. First it calculates the topologies with the most propagators, and when they are known one may calculate the lower topologies....... It is based on a categorization of the integrand using algebraic geometry, in which the set of propagators corresponding to each topology is identified with an algebraic ideal I. This allows for the identification of the set of terms which are allowed in the numerator corresponding to each topology...
Higher-Order Inhomogeneous Generalized Heisenberg Supermagnetic Model
Yan, Zhao-Wen; Zhang, Mei-Na; Cui, Ji-Feng
2018-05-01
Not Available Supported by the National Natural Science Foundation of China under Grant Nos 11605096 and 11601247, the Science Research Project of Inner Mongolia University of Technology under Grant No ZD201613, and the Innovation Foundation of Inner Mongolia University for the College Students under Grant No 201711208.
asking questions for higher order thinking in visual literacy
Numerous factors such as socio-economic back- ground of .... questions should comprise 40% low-order questions (Knowledge), 40% middle-order questions ... The data obtained from the class participants comprise details of a two-step tea-.
On the limit distribution of lower extreme generalized order statistics
Abstract. In a wide subclass of generalized order statistics (gOs), which contains most of the known and important models of ordered random variables, weak conver- gence of lower extremes are developed. A recent result of extreme value theory of m−gOs (as well as the classical extreme value theory of ordinary order ...
On the Limit Distribution of Lower Extreme Generalized Order Statistics
In a wide subclass of generalized order statistics ( g O s ) , which contains most of the known and important models of ordered random variables, weak convergence of lower extremes are developed. A recent result of extreme value theory of m − g O s (as well as the classical extreme value theory of ordinary order statistics) ...
Shukla, Divya; Dungsungnoen, Aj Pattaradanai
2016-01-01
Higher order thinking skills (HOTS) has portrayed immense industry demand and the major goal of educational institution in imparting education is to inculcate higher order thinking skills. This compiles and mandate the institutions and instructor to develop the higher order thinking skills among students in order to prepare them for effective…
1957-2007: 50 Years of Higher Order Programming Languages
Alen Lovrenčić
2009-06-01
Full Text Available Fifty years ago one of the greatest breakthroughs in computer programming and in the history of computers happened -- the appearance of FORTRAN, the first higher-order programming language. From that time until now hundreds of programming languages were invented, different programming paradigms were defined, all with the main goal to make computer programming easier and closer to as many people as possible. Many battles were fought among scientists as well as among developers around concepts of programming, programming languages and paradigms. It can be said that programming paradigms and programming languages were very often a trigger for many changes and improvements in computer science as well as in computer industry. Definitely, computer programming is one of the cornerstones of computer science.Today there are many tools that give a help in the process of programming, but there is still a programming tasks that can be solved only manually. Therefore, programming is still one of the most creative parts of interaction with computers.Programmers should chose programming language in accordance to task they have to solve, but very often, they chose it in accordance to their personal preferences, their beliefs and many other subjective reasons.Nevertheless, the market of programming languages can be merciless to languages as history was merciless to some people, even whole nations. Programming languages and developers get born, live and die leaving more or less tracks and successors, and not always the best survives. The history of programming languages is closely connected to the history of computers and computer science itself. Every single thing from one of them has its reflexions onto the other. This paper gives a short overview of last fifty years of computer programming and computer programming languages, but also gives many ideas that influenced other aspects of computer science. Particularly, programming paradigms are described, their
Mukhigulashvili, Sulkhan
-, č. 35 (2015), s. 23-50 ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili.pdf
Massive, massless and ghost modes of gravitational waves from higher-order gravity
Bogdanos, Charalampos; Capozziello, Salvatore; De Laurentis, Mariafelicia
We linearize the field equations for higher order theories that contain scalar invariants other than the Ricci scalar. We find that besides a massless spin-2 field (the standard graviton), the theory contains also spin-0 and spin-2 massive modes with the latter being, in general, ghost modes. Then...
Compound waves in a higher order nonlinear model of thermoviscous fluids
Rønne Rasmussen, Anders; Sørensen, Mads Peter; Gaididei, Yuri B.
2016-01-01
A generalized traveling wave ansatz is used to investigate compound shock waves in a higher order nonlinear model of a thermoviscous fluid. The fluid velocity potential is written as a traveling wave plus a linear function of space and time. The latter offers the possibility of predicting...
Mukhigulashvili, Sulkhan; Půža, B.
2015-01-01
Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1
Asymptotic estimates and exponential stability for higher-order monotone difference equations
Pituk Mihály
2005-01-01
Full Text Available Asymptotic estimates are established for higher-order scalar difference equations and inequalities the right-hand sides of which generate a monotone system with respect to the discrete exponential ordering. It is shown that in some cases the exponential estimates can be replaced with a more precise limit relation. As corollaries, a generalization of discrete Halanay-type inequalities and explicit sufficient conditions for the global exponential stability of the zero solution are given.
Asymptotic estimates and exponential stability for higher-order monotone difference equations
Mihály Pituk
2005-03-01
Full Text Available Asymptotic estimates are established for higher-order scalar difference equations and inequalities the right-hand sides of which generate a monotone system with respect to the discrete exponential ordering. It is shown that in some cases the exponential estimates can be replaced with a more precise limit relation. As corollaries, a generalization of discrete Halanay-type inequalities and explicit sufficient conditions for the global exponential stability of the zero solution are given.
Higher order QCD corrections in exclusive charmless B decays
Bell, G.
2006-10-01
We discuss exclusive charmless B decays within the Standard Model of particle physics. These decays play a central role in the on-going process to constrain the parameters of the CKM matrix and to clarify the nature of CP violation. In order to exploit the rich source of data that is currently being collected at the experiments, a systematic theoretical treatment of the complicated hadronic dynamics is strongly desired. QCD Factorization represents a model-independent framework to compute hadronic matrix elements from first principles. It is based on a power expansion in Λ QCD /m b and allows for the systematic implementation of perturbative corrections. In particular, we consider hadronic two-body decays as B → ππ and perform a conceptual analysis of heavy-to-light form factors which encode the strong interaction effects in semi-leptonic decays as B → πlν. Concerning the hadronic decays we compute NNLO QCD corrections which are particularly important with respect to strong interaction phases and hence direct CP asymmetries. On the technical level, we perform a 2-loop calculation which is based on an automatized reduction algorithm and apply sophisticated techniques for the calculation of loop-integrals. We indeed find that the considered quantities are well-defined as predicted by QCD Factorization, which is the result of a highly complicated subtraction procedure. We present results for the imaginary part of the topological tree amplitudes and observe that the considered corrections are substantial. The calculation of the real part of the amplitudes is far more complicated and we present a preliminary result which is based on certain simplifications. Our calculation is one part of the full NNLO analysis of nonleptonic B decays within QCD Factorization which is currently pursued by various groups. In our conceptual analysis of the QCD dynamics in heavy-to-light transitions we consider form factors between non-relativistic bound states which can be
Higher order QCD corrections in exclusive charmless B decays
Bell, G.
2006-10-15
We discuss exclusive charmless B decays within the Standard Model of particle physics. These decays play a central role in the on-going process to constrain the parameters of the CKM matrix and to clarify the nature of CP violation. In order to exploit the rich source of data that is currently being collected at the experiments, a systematic theoretical treatment of the complicated hadronic dynamics is strongly desired. QCD Factorization represents a model-independent framework to compute hadronic matrix elements from first principles. It is based on a power expansion in {lambda}{sub QCD}/m{sub b} and allows for the systematic implementation of perturbative corrections. In particular, we consider hadronic two-body decays as B {yields} {pi}{pi} and perform a conceptual analysis of heavy-to-light form factors which encode the strong interaction effects in semi-leptonic decays as B {yields} {pi}l{nu}. Concerning the hadronic decays we compute NNLO QCD corrections which are particularly important with respect to strong interaction phases and hence direct CP asymmetries. On the technical level, we perform a 2-loop calculation which is based on an automatized reduction algorithm and apply sophisticated techniques for the calculation of loop-integrals. We indeed find that the considered quantities are well-defined as predicted by QCD Factorization, which is the result of a highly complicated subtraction procedure. We present results for the imaginary part of the topological tree amplitudes and observe that the considered corrections are substantial. The calculation of the real part of the amplitudes is far more complicated and we present a preliminary result which is based on certain simplifications. Our calculation is one part of the full NNLO analysis of nonleptonic B decays within QCD Factorization which is currently pursued by various groups. In our conceptual analysis of the QCD dynamics in heavy-to-light transitions we consider form factors between non
Higher-order harmonics of limited diffraction Bessel beams
Ding; Lu
2000-03-01
We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.
An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs
Eman S. Alaidarous
2013-01-01
Full Text Available In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013. The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.
Extensions of guiding center motion to higher order
Northrop, T.G.; Rome, J.A.
1978-01-01
In a static magnetic field, some well-known guiding center equations maintain their form when extended to next order in gyroradius. In these cases, it is only necessary to include the next order term in the magnetic moment series. The differential equation for guiding center motion which describes both the parallel and perpendicular velocities correctly through first order in gyroradius is given. The question of how to define the guiding center position through second order arises and is discussed, and second order drifts are derived for one usual definition. The toroidal canonical angular momentum, P/sub phi/, of the guiding center in an axisymmetric field is shown to be conserved using the guiding center velocity correct through first order. When second-order motion is included, P/sub phi/ is no longer a constant. The above extensions of guiding center theory help to resolve the different tokamak orbits obtained either by using the guiding center equations of motion or by using conservation of P/sub phi/
Extensions of guiding center motion to higher order
Northrop, T.G.; Rome, J.A.
1977-07-01
In a static magnetic field, some well-known guiding center equations maintain their form when extended to next order in gyroradius. In these cases, it is only necessary to include the next order term in the magnetic moment series. The differential equation for guiding center motion which describes both the parallel and perpendicular velocities correctly through first order in gyroradius is given. The question of how to define the guiding center position through second order arises and is discussed, and second order drifts are derived for one usual definition. The toroidal canonical angular momentum, P/sub phi/, of the guiding center in an axisymmetric field is shown to be conserved using the guiding center velocity correct through first order. When second order motion is included, P/sub phi/ is no longer a constant. The above extensions of guiding center theory help to resolve the different tokamak orbits obtained either by using the guiding center equations of motion or by using conservation of P/sub phi/
Spherically symmetric solutions of general second-order gravity
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
General solution for first order elliptic systems in the plane
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
Generalized Sudan's List Decoding for Order Domain Codes
Geil, Hans Olav; Matsumoto, Ryutaroh
2007-01-01
We generalize Sudan's list decoding algorithm without multiplicity to evaluation codes coming from arbitrary order domains. The number of correctable errors by the proposed method is larger than the original list decoding without multiplicity....
Higher-order Cn dispersion coefficients for hydrogen
Mitroy, J.; Bromley, M.W.J.
2005-01-01
The complete set of second-, third-, and fourth-order van der Waals coefficients C n up to n=32 for the H(1s)-H(1s) dimer have been determined. They are computed by diagonalizing the nonrelativistic Hamiltonian for hydrogen to obtain a set of pseudostates that are used to evaluate the appropriate sum rules. A study of the convergence pattern for n≤16 indicates that all the C n/16 coefficients are accurate to 13 significant digits. The relative size of the fourth-order C n (4) to the second-order C n (2) coefficients is seen to increase as n increases and at n=32 the fourth-order term is actually larger
The s-Ordered Fock Space Projectors Gained by the General Ordering Theorem
Shähandeh Farid; Bazrafkan Mohammad Reza; Ashrafi Mahmoud
2012-01-01
Employing the general ordering theorem (GOT), operational methods and incomplete 2-D Hermite polynomials, we derive the t-ordered expansion of Fock space projectors. Using the result, the general ordered form of the coherent state projectors is obtained. This indeed gives a new integration formula regarding incomplete 2-D Hermite polynomials. In addition, the orthogonality relation of the incomplete 2-D Hermite polynomials is derived to resolve Dattoli's failure
Higher-order geodesic deviation for charged particles and resonance induced by gravitational waves
Heydari-Fard, M.; Hasani, S. N.
We generalize the higher-order geodesic deviation for the structure-less test particles to the higher-order geodesic deviation equations of the charged particles [R. Kerner, J. W. van Holten and R. Colistete Jr., Class. Quantum Grav. 18 (2001) 4725]. By solving these equations for charged particles moving in a constant magnetic field in the spacetime of a gravitational wave, we show for both cases when the gravitational wave is parallel and perpendicular to the constant magnetic field, a magnetic resonance appears at wg = Ω. This feature might be useful to detect the gravitational wave with high frequencies.
A controllability test for general first-order representations
U. Helmke; J. Rosenthal; J.M. Schumacher (Hans)
1995-01-01
textabstractIn this paper we derive a new controllability rank test for general first-order representations. The criterion generalizes the well-known controllability rank test for linear input-state systems as well as a controllability rank test by Mertzios et al. for descriptor systems.
28 CFR 30.4 - What are the Attorney General's general responsibilities under the Order?
2010-07-01
... 28 Judicial Administration 1 2010-07-01 2010-07-01 false What are the Attorney General's general... REVIEW OF DEPARTMENT OF JUSTICE PROGRAMS AND ACTIVITIES § 30.4 What are the Attorney General's general responsibilities under the Order? (a) The Attorney General provides opportunities for consultation by elected...
Higher order harmonic generation in the intense laser pulse
Parvizi, R.; Bahrampour, A.; Karimi, M.
2006-01-01
The high intensity pulse of laser field ionizes the atoms and electrons are going to the continuum states of atoms. electrons absorb energy from the strong laser field. The back ground electromagnetic field causes to come back the electrons to ground states of atoms and the absorbed energy is emitted as a high order odd harmonics of incident light. The intensity of emitted harmonics depends on the material atoms and the laser pulse shape. I this paper the effects of step pulse duration on the high order harmonic radiated by the Argon, Helium, and Hydrogen atoms are reported.
Higher Order Heavy Quark Corrections to Deep-Inelastic Scattering
Blümlein, Johannes; DeFreitas, Abilio; Schneider, Carsten
2015-04-01
The 3-loop heavy flavor corrections to deep-inelastic scattering are essential for consistent next-to-next-to-leading order QCD analyses. We report on the present status of the calculation of these corrections at large virtualities Q2. We also describe a series of mathematical, computer-algebraic and combinatorial methods and special function spaces, needed to perform these calculations. Finally, we briefly discuss the status of measuring αs (MZ), the charm quark mass mc, and the parton distribution functions at next-to-next-to-leading order from the world precision data on deep-inelastic scattering.
Higher order heavy quark corrections to deep-inelastic scattering
Bluemlein, J.; Freitas, A. de; Johannes Kepler Univ., Linz; Schneider, C.
2014-11-01
The 3-loop heavy flavor corrections to deep-inelastic scattering are essential for consistent next-to-next-to-leading order QCD analyses. We report on the present status of the calculation of these corrections at large virtualities Q 2 . We also describe a series of mathematical, computer-algebraic and combinatorial methods and special function spaces, needed to perform these calculations. Finally, we briefly discuss the status of measuring α s (M Z ), the charm quark mass m c , and the parton distribution functions at next-to-next-to-leading order from the world precision data on deep-inelastic scattering.
Equivalence of two formalisms for calculating higher order synchrotron sideband spin resonances
Mane, S.R.
1988-01-01
Synchrotron sideband resonances of a first order spin resonance are generally regarded as the most important higher order spin resonances in a high-energy storage ring. Yokoya's formula for these resonances is rederived, including some extra terms, which he neglected, but which turn out to be of comparable magnitude to the terms retained. Including these terms, Yokoya's formalism and the SMILE algorithm are shown to be equivalent to leading order in the resonance strengths. The theoretical calculations are shown to agree with certain measurements from SPEAR
First-order and higher order sequence learning in specific language impairment.
Clark, Gillian M; Lum, Jarrad A G
2017-02-01
A core claim of the procedural deficit hypothesis of specific language impairment (SLI) is that the disorder is associated with poor implicit sequence learning. This study investigated whether implicit sequence learning problems in SLI are present for first-order conditional (FOC) and higher order conditional (HOC) sequences. Twenty-five children with SLI and 27 age-matched, nonlanguage-impaired children completed 2 serial reaction time tasks. On 1 version, the sequence to be implicitly learnt comprised a FOC sequence and on the other a HOC sequence. Results showed that the SLI group learned the HOC sequence (η p ² = .285, p = .005) but not the FOC sequence (η p ² = .099, p = .118). The control group learned both sequences (FOC η p ² = .497, HOC η p 2= .465, ps < .001). The SLI group's difficulty learning the FOC sequence is consistent with the procedural deficit hypothesis. However, the study provides new evidence that multiple mechanisms may underpin the learning of FOC and HOC sequences. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Fractional Hamiltonian analysis of higher order derivatives systems
Baleanu, Dumitru; Muslih, Sami I.; Tas, Kenan
2006-01-01
The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives
Higher order methods for burnup calculations with Bateman solutions
Isotalo, A.E.; Aarnio, P.A.
2011-01-01
Highlights: → Average microscopic reaction rates need to be estimated at each step. → Traditional predictor-corrector methods use zeroth and first order predictions. → Increasing predictor order greatly improves results. → Increasing corrector order does not improve results. - Abstract: A group of methods for burnup calculations solves the changes in material compositions by evaluating an explicit solution to the Bateman equations with constant microscopic reaction rates. This requires predicting representative averages for the one-group cross-sections and flux during each step, which is usually done using zeroth and first order predictions for their time development in a predictor-corrector calculation. In this paper we present the results of using linear, rather than constant, extrapolation on the predictor and quadratic, rather than linear, interpolation on the corrector. Both of these are done by using data from the previous step, and thus do not affect the stepwise running time. The methods were tested by implementing them into the reactor physics code Serpent and comparing the results from four test cases to accurate reference results obtained with very short steps. Linear extrapolation greatly improved results for thermal spectra and should be preferred over the constant one currently used in all Bateman solution based burnup calculations. The effects of using quadratic interpolation on the corrector were, on the other hand, predominantly negative, although not enough so to conclusively decide between the linear and quadratic variants.
Multilevel Higher-Order Item Response Theory Models
Huang, Hung-Yu; Wang, Wen-Chung
2014-01-01
In the social sciences, latent traits often have a hierarchical structure, and data can be sampled from multiple levels. Both hierarchical latent traits and multilevel data can occur simultaneously. In this study, we developed a general class of item response theory models to accommodate both hierarchical latent traits and multilevel data. The…
Equivalence of two Fixed-Point Semantics for Definitional Higher-Order Logic Programs
Angelos Charalambidis
2015-09-01
Full Text Available Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point construction defined on a syntactic instantiation of the source program. The relationships between these two approaches had not been investigated until now. In this paper we demonstrate that for a very broad class of programs, namely the class of definitional programs introduced by W. W. Wadge, the two approaches coincide (with respect to ground atoms that involve symbols of the program. On the other hand, we argue that if existential higher-order variables are allowed to appear in the bodies of program rules, the two approaches are in general different. The results of the paper contribute to a better understanding of the semantics of higher-order logic programming.
Encouraging Student Autonomy through Higher Order Thinking Skills
Smith, Victoria D.; Darvas, Janet W.
2017-01-01
This article discusses how to empower students to work, think, and act independently in the higher education setting. Inspiring students to progress through the stages of Bloom's Taxonomy emboldens them to discover intrinsic motivation and self-regulated learning. This article defines and focuses on the importance of teaching intrinsic motivation…
Higher-Order Hamiltonian Model for Unidirectional Water Waves
Bona, J. L.; Carvajal, X.; Panthee, M.; Scialom, M.
2018-04-01
Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of these more complex equations is that their solutions corresponding to physically relevant initial perturbations of the rest state may be accurate on a much longer timescale. The initial value problem for the class of equations that emerges from our derivation is then considered. A local well-posedness theory is straightforwardly established by a contraction mapping argument. A subclass of these equations possess a special Hamiltonian structure that implies the local theory can be continued indefinitely.
Passivity analysis of higher order evolutionary dynamics and population games
Mabrok, Mohamed
2017-01-05
Evolutionary dynamics describe how the population composition changes in response to the fitness levels, resulting in a closed-loop feedback system. Recent work established a connection between passivity theory and certain classes of population games, namely so-called “stable games”. In particular, it was shown that a combination of stable games and (an analogue of) passive evolutionary dynamics results in stable convergence to Nash equilibrium. This paper considers the converse question of necessary conditions for evolutionary dynamics to exhibit stable behaviors for all generalized stable games. Using methods from robust control analysis, we show that if an evolutionary dynamic does not satisfy a passivity property, then it is possible to construct a generalized stable game that results in instability. The results are illustrated on selected evolutionary dynamics with particular attention to replicator dynamics, which are also shown to be lossless, a special class of passive systems.
Higher-order probabilistic perceptrons as Bayesian inference engines
Clark, J.W.; Ristig, M.L.
1994-08-01
This letter makes explicit a structural connection between the Bayes optimal classifier operating on K binary input variables and corresponding two-layer perceptron having normalized output activities and couplings from input to output units of all orders up to K. Given a large and unbiased training set and an effective learning algorithm, such a neural network should be able to learn the statistics of the classification problem and match the a posteriori probabilities given by the Bayes optimal classifier. (author). 18 refs
Machine learning using a higher order correlation network
Lee, Y.C.; Doolen, G.; Chen, H.H.; Sun, G.Z.; Maxwell, T.; Lee, H.Y.
1986-01-01
A high-order correlation tensor formalism for neural networks is described. The model can simulate auto associative, heteroassociative, as well as multiassociative memory. For the autoassociative model, simulation results show a drastic increase in the memory capacity and speed over that of the standard Hopfield-like correlation matrix methods. The possibility of using multiassociative memory for a learning universal inference network is also discussed. 9 refs., 5 figs.
Efficient analytic computation of higher-order QCD amplitudes
Bern, Z.; Chalmers, G.; Dunbar, D.C.; Kosower, D.A.
1995-01-01
The authors review techniques simplifying the analytic calculation of one-loop QCD amplitudes with many external legs, for use in next-to-leading-order corrections to multi-jet processes. Particularly useful are the constraints imposed by perturbative unitarity, collinear singularities and a supersymmetry-inspired organization of helicity amplitudes. Certain sequences of one-loop helicity amplitudes with an arbitrary number of external gluons have been obtained using these constraints
Loop vertex expansion for higher-order interactions
Rivasseau, Vincent
2018-05-01
This note provides an extension of the constructive loop vertex expansion to stable interactions of arbitrarily high order, opening the way to many applications. We treat in detail the example of the (\\bar{φ } φ )^p field theory in zero dimension. We find that the important feature to extend the loop vertex expansion is not to use an intermediate field representation, but rather to force integration of exactly one particular field per vertex of the initial action.
INARCH(1) processes: Higher-order moments and jumps
Weiß , Christian H.
2010-01-01
Abstract The INARCH(1) model is a simple but practically relevant, two-parameter model for processes of overdispersed counts with an autoregressive serial dependence structure. We derive closed-form expressions for the joint (central) moments and cumulants of the INARCH(1) model up to order 4. These expressions are applied to derive moments of jumps in INARCH(1) processes. We illustrate this kind of application with a real-data example, and outline further potential applications. ...
Imposing orthogonality to hierarchic higher-order finite elements
Šolín, P.; Vejchodský, Tomáš; Zítka, M.; Ávila, F.
2007-01-01
Roč. 76, 1-3 (2007), s. 211-217 ISSN 0378-4754 R&D Projects: GA ČR GP201/04/P021 Institutional research plan: CEZ:AV0Z10190503 Keywords : optimal shape functions * energetic inner product * Laplace equation * symmetric linear elliptic problems * numerical experiments * hp-finite element method Subject RIV: BA - General Mathematics Impact factor: 0.738, year: 2007
Higher order differential calculus on SLq(N)
Heckenberger, I.; Schueler, A.
1997-01-01
Let Γ be a bicovariant first order differential calculus on a Hopf algebra A. There are three possibilities to construct a differential N 0 -graded Hopf algebra Γcirconflex which contains Γ as its first order part. In all cases Γcirconflex is a quotient Γcirconflex = Γ x /J of the tensor algebra by some suitable ideal. We distinguish three possible choices u J, s J, and w J, where the first one generates the universal differential calculus (over Γ) and the last one is Woronowicz' external algebra. Let q be a transcendental complex number and let Γ be one of the N 2 -dimensional bicovariant first order differential calculi on the quantum group SL q (N). Then for N ≥ 3 the three ideals coincide. For Woronowicz' external algebra we calculate the dimensions of the spaces of left-invariant and bi-invariant k-forms. In this case each bi-invariant form is closed. In case of 4D ± calculi on SL q (2) the universal calculus is strictly larger than the other two calculi. In particular, the bi-invariant 1-form is not closed. (author)
Higher-order conductivity corrections to the Casimir force
Bezerra, Valdir Barbosa; Klimchitskaya, Galina; Mostepanenko, Vladimir
2000-01-01
Full text follows: Considerable recent attention has been focused on the new experiments on measuring the Casimir force. To be confident that experimental data fit theory at a level of several percent, a variety of corrections to the ideal expression for the Casimir force should be taken into account. One of the main corrections at small separations between interacting bodies is the one due to finite conductivity of the boundary metal. This correction has its origin in non-zero penetration depth δ 0 of electromagnetic vacuum oscillations into the metal (for a perfect metal of infinitely large conductivity δ 0 = 0). The other quantity of the dimension of length is the space separation a between two plates or a plate and a sphere. Their relation δ 0 /a is the natural perturbation parameter in which powers the corrections to the Casimir force due to finite conductivity can be expanded. Such an expansion works good for all separations a >> δ 0 (i.e. for separations larger than 100-150 nm). The first-order term of this expansion was calculated almost forty years ago, and the second-order one in 1985 [1]. These two terms are not sufficient for the comparison of the theory with precision modern experiments. In this talk we report the results of paper [2] where the third- and fourth-order terms in δ 0 /a expansion of the Casimir force were calculated first. They gave the possibility to achieve an excellent agreement of a theory and experiment. (author)
Higher-order photon bunching in a semiconductor microcavity
Assmann, M.; Veit, F.; Bayer, M.
2009-01-01
Quantum mechanically indistinguishable particles such as photons may show collective behavior. Therefore, an appropriate description of a light field must consider the properties of an assembly of photons instead of independent particles. We have studied multiphoton correlations up to fourth order...... in the single-mode emission of a semiconductor microcavity in the weak and strong coupling regimes. The counting statistics of single photons were recorded with picosecond time resolution, allowing quantitative measurement of the few-photon bunching inside light pulses. Our results show bunching behavior...
COMPUTER EXPERIMENTS WITH FINITE ELEMENTS OF HIGHER ORDER
Khomchenko A.
2017-12-01
Full Text Available The paper deals with the problem of constructing the basic functions of a quadrilateral finite element of the fifth order by the means of the computer algebra system Maple. The Lagrangian approximation of such a finite element contains 36 nodes: 20 nodes perimeter and 16 internal nodes. Alternative models with reduced number of internal nodes are considered. Graphs of basic functions and cognitive portraits of lines of zero level are presented. The work is aimed at studying the possibilities of using modern information technologies in the teaching of individual mathematical disciplines.
Special issue of Higher-Order and Symbolic Computation
Danvy, Olivier
, they should have a large range of applicability for a large class of specifications or programs. Only general ideas could become the basis for an automatic system for program development. Bob’s APTS system is indeed the incarnation of most of the techniques he proposed (cf. Leonard and Heitmeyer...... specification, expressed in SCR notation, into C. Two translation strategies are discussed in the paper. Both were implemented using Bob Paige’s APTS programtransformation system. “Computational Divided Differencing and Divided-Difference Arithmetics” uses an approach conceptually similar to the Computational...
Special issue of Higher-Order and Symbolic Computation
Danvy, Olivier; Sabry, Amr
This issue of HOSC is dedicated to the general topic of continuations. It grew out of the third ACM SIGPLAN Workshop on Continuations (CW'01), which took place in London, UK on January 16, 2001 [3]. The notion of continuation is ubiquitous in many different areas of computer science, including...... and streamline Filinski's earlier work in the previous special issue of HOSC (then LISP and Symbolic Computation) that grew out of the first ACM SIGPLAN Workshop on Continuations [1, 2]. Hasegawa and Kakutani's article is the journal version of an article presented at FOSSACS 2001 and that received the EATCS...
Higher order Riesz transforms associated with Bessel operators
Betancor, Jorge J.; Fariña, Juan C.; Martinez, Teresa; Rodríguez-Mesa, Lourdes
2008-10-01
In this paper we investigate Riesz transforms R μ ( k) of order k≥1 related to the Bessel operator Δμ f( x)=- f”( x)-((2μ+1)/ x) f’( x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We obtain that for every k≥1, R μ ( k) is a principal value operator of strong type ( p, p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ( x)= x 2μ+1 dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R μ ( k) maps L p (ω) into itself and L 1(ω) into L 1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class mathcal{A}p^μ of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman.
Higher-order predictions for supersymmetric particle decays
Landwehr, Ananda Demian Patrick
2012-06-12
We analyze particle decays including radiative corrections at the next-to-leading order (NLO) within the Minimal Supersymmetric Standard Model (MSSM). If the MSSM is realized at the TeV scale, squark and gluino production and decays yield relevant rates at the LHC. Hence, in the first part of this thesis, we compute decay widths including QCD and electroweak NLO corrections to squark and gluino decays. Furthermore, the Higgs sector of the MSSM is enhanced compared to the one of the Standard Model. Thus, the additional Higgs bosons decay also into supersymmetric particles. These decays and the according NLO corrections are analyzed in the second part of this thesis. The calculations are performed within a common renormalization framework and numerically evaluated in specific benchmark scenarios.
On higher order corrections to three-jet cross sections
Schierholz, G.
1981-07-01
In this talk I report a calculation of the Sterman-Weinberg type 3-jet cross section to order a 2 sub(s). We have chosen a Sterman-Weinberg type angle and energy cut off for a variety of reasons. In particular, an acceptable 3-jet measure must be insensitive to the emission of soft and/or collinear radiation and to the process of hadronization which, in contrast to many popular 3-jet measures, is uniquely met by the Sterman-Weinberg definition of 3-jet events. The talk is divided into three parts. In the first part I present the results. The second part discusses an independent (algebraic) test of the cross section formula. Finally, in the third part I comment on the contrasting results pioneered by the CALTECH group. (orig.)
A single dose of oxytocin nasal spray improves higher-order social cognition in schizophrenia.
Guastella, Adam J; Ward, Philip B; Hickie, Ian B; Shahrestani, Sara; Hodge, Marie Antoinette Redoblado; Scott, Elizabeth M; Langdon, Robyn
2015-11-01
Schizophrenia is associated with significant impairments in both higher and lower order social cognitive performance and these impairments contribute to poor social functioning. People with schizophrenia report poor social functioning to be one of their greatest unmet treatment needs. Recent studies have suggested the potential of oxytocin as such a treatment, but mixed results render it uncertain what aspects of social cognition are improved by oxytocin and, subsequently, how oxytocin might best be applied as a therapeutic. The aim of this study was to determine whether a single dose of oxytocin improved higher-order and lower-order social cognition performance for patients with schizophrenia across a well-established battery of social cognition tests. Twenty-one male patients received both a single dose of oxytocin nasal spray (24IU) and a placebo, two weeks apart in a randomized within-subjects placebo controlled design. Following each administration, participants completed the social cognition tasks, as well as a test of general neurocognition. Results revealed that oxytocin particularly enhanced performance on higher order social cognition tasks, with no effects on general neurocognition. Results for individual tasks showed most improvement on tests measuring appreciation of indirect hints and recognition of social faux pas. These results suggest that oxytocin, if combined to enhance social cognition learning, may be beneficial when targeted at higher order social cognition domains. This study also suggests that these higher order tasks, which assess social cognitive processing in a social communication context, may provide useful markers of response to oxytocin in schizophrenia. Copyright © 2015 Elsevier B.V. All rights reserved.
Testing for one Generalized Linear Single Order Parameter
Ellegaard, Niels Langager; Christensen, Tage Emil; Dyre, Jeppe
We examine a linear single order parameter model for thermoviscoelastic relaxation in viscous liquids, allowing for a distribution of relaxation times. In this model the relaxation of volume and entalpy is completely described by the relaxation of one internal order parameter. In contrast to prior...... work the order parameter may be chosen to have a non-exponential relaxation. The model predictions contradict the general consensus of the properties of viscous liquids in two ways: (i) The model predicts that following a linear isobaric temperature step, the normalized volume and entalpy relaxation...... responses or extrapolate from measurements of a glassy state away from equilibrium. Starting from a master equation description of inherent dynamics, we calculate the complex thermodynamic response functions. We device a way of testing for the generalized single order parameter model by measuring 3 complex...
Constrained generalized mechanics. The second-order case
Tapia, V.
1985-01-01
The Dirac formalism for constrained systems is developed for systems described by a Lagrangian depending on up to a second-order time derivatives of the generalized co-ordinates (accelerations). It turns out that for a Lagrangian of this kind differing by a total time derivative from a Lagrangian depending on only up to first-order time-derivatives of the generalized co-ordinates (velocities), both classical mechanics at the Lagrangian level are the same; at the Hamiltonian level the two classical mechanics differ conceptually even when the solutions to both sets of Hamiltonian equations of motion are the same
Discrete Maximum Principle for Higher-Order Finite Elements in 1D
Vejchodský, Tomáš; Šolín, Pavel
2007-01-01
Roč. 76, č. 260 (2007), s. 1833-1846 ISSN 0025-5718 R&D Projects: GA ČR GP201/04/P021 Institutional research plan: CEZ:AV0Z10190503; CEZ:AV0Z20760514 Keywords : discrete maximum principle * discrete Grren´s function * higher-order elements Subject RIV: BA - General Mathematics Impact factor: 1.230, year: 2007
On the formulations of higher-order strain gradient crystal plasticity models
Kuroda, M.; Tvergaard, Viggo
2008-01-01
Recently, several higher-order extensions to the crystal plasticity theory have been proposed to incorporate effects of material length scales that were missing links in the conventional continuum mechanics. The extended theories are classified into work-conjugate and non-work-conjugate types. A ...... deformation. In this paper, the discussion is extended to a more general situation, i.e. the context of multiple and three-dimensional slip deformations....
General Nth order integrals of motion in the Euclidean plane
Post, S; Winternitz, P
2015-01-01
The general form of an integral of motion that is a polynomial of order N in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and the quantum cases are treated separately, emphasizing both the similarities and the differences between the two. The main application will be to study Nth order superintegrable systems that allow separation of variables in the Hamilton–Jacobi and Schrödinger equations, respectively. (paper)
An efficient higher order family of root finders
Petkovic, Ljiljana D.; Rancic, Lidija; Petkovic, Miodrag S.
2008-06-01
A one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial, based on a cubically convergent Hansen-Patrick's family, is studied. We show that the convergence of the basic family of the fourth order can be increased to five and six using Newton's and Halley's corrections, respectively. Since these corrections use the already calculated values, the computational efficiency of the accelerated methods is significantly increased. Further acceleration is achieved by applying the Gauss-Seidel approach (single-step mode). One of the most important problems in solving nonlinear equations, the construction of initial conditions which provide both the guaranteed and fast convergence, is considered for the proposed accelerated family. These conditions are computationally verifiable; they depend only on the polynomial coefficients, its degree and initial approximations, which is of practical importance. Some modifications of the considered family, providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions, are also studied. Numerical examples demonstrate the convergence properties of the presented family of root-finding methods.
Higher-order stochastic differential equations and the positive Wigner function
Drummond, P. D.
2017-12-01
General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.
Critical Combinations of Higher-Order Terms in Einstein-Maxwell Theory and Compactification
Nahomi Kan
2015-01-01
Full Text Available We discuss the role of a particular combination of higher derivative terms in higher dimensional theories, particularly in the background of spontaneous compactification. Two classes of theories are proposed in this paper. The first model as a generalization of the critical gravity with the Maxwell field could have a de Sitter solution. We consider the Lanczos-Lovelock term and Horndeski term as well as the higher-order Maxwell term for the second model, which contains a possible longer expansion time for the inflationary phase. It is interesting that both models can be regarded as the generalization of the Randjbar-Daemi, Salam and Strathdee (RSS model and give the well behavior for inflation stage under the specific assumptions.
A New Factorisation of a General Second Order Differential Equation
Clegg, Janet
2006-01-01
A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…
Generalized second-order Coulomb phase shift functions
Rosendorff, S.
1982-01-01
Some specific properties and the evaluation of the generalized second-order Coulomb phase shift functions (two-dimensional integrals of four spherical cylinder functions) are discussed. The dependence on the three momenta k 1 ,k-bar,k 2 , corresponding to the final, intermediate, and initial states is illustrated
Higher-order terms in the nuclear-energy-density functional
Carlsson, B. G.; Borucki, M.; Dobaczewski, J.
2009-01-01
One of the current projects at the Department of Physics in the University of Jyvaeskylae is to explore more general forms of the Skyrme energy-density functional (EDF). The aim is to find new phenomenological terms which are sensitive to experimental data. In this context we have extended the Skyrme functional by including terms which contain higher orders of derivatives allowing for a better description of finite range effects. This was done by employing an expansion in derivatives in a spherical-tensor formalism [1] motivated by ideas of the density-matrix expansion. The resulting functionals have different number of free parameters depending on the order in derivatives and assumed symmetries, see Fig. 1. The usual Skyrme EDF is obtained as a second order expansion while we keep terms up to sixth order.(author)
Avellar, J.; Claudino, A. L. G. C.; Duarte, L. G. S.; da Mota, L. A. C. P.
2015-10-01
For the Darbouxian methods we are studying here, in order to solve first order rational ordinary differential equations (1ODEs), the most costly (computationally) step is the finding of the needed Darboux polynomials. This can be so grave that it can render the whole approach unpractical. Hereby we introduce a simple heuristics to speed up this process for a class of 1ODEs.
Higher-Order Statistical Correlations and Mutual Information Among Particles in a Quantum Well
Yépez, V. S.; Sagar, R. P.; Laguna, H. G.
2017-01-01
The influence of wave function symmetry on statistical correlation is studied for the case of three non-interacting spin-free quantum particles in a unidimensional box, in position and in momentum space. Higher-order statistical correlations occurring among the three particles in this quantum system is quantified via higher-order mutual information and compared to the correlation between pairs of variables in this model, and to the correlation in the two-particle system. The results for the higher-order mutual information show that there are states where the symmetric wave functions are more correlated than the antisymmetric ones with same quantum numbers. This holds in position as well as in momentum space. This behavior is opposite to that observed for the correlation between pairs of variables in this model, and the two-particle system, where the antisymmetric wave functions are in general more correlated. These results are also consistent with those observed in a system of three uncoupled oscillators. The use of higher-order mutual information as a correlation measure, is monitored and examined by considering a superposition of states or systems with two Slater determinants. (author)
Higher-Order Statistical Correlations and Mutual Information Among Particles in a Quantum Well
Yépez, V. S.; Sagar, R. P.; Laguna, H. G.
2017-12-01
The influence of wave function symmetry on statistical correlation is studied for the case of three non-interacting spin-free quantum particles in a unidimensional box, in position and in momentum space. Higher-order statistical correlations occurring among the three particles in this quantum system is quantified via higher-order mutual information and compared to the correlation between pairs of variables in this model, and to the correlation in the two-particle system. The results for the higher-order mutual information show that there are states where the symmetric wave functions are more correlated than the antisymmetric ones with same quantum numbers. This holds in position as well as in momentum space. This behavior is opposite to that observed for the correlation between pairs of variables in this model, and the two-particle system, where the antisymmetric wave functions are in general more correlated. These results are also consistent with those observed in a system of three uncoupled oscillators. The use of higher-order mutual information as a correlation measure, is monitored and examined by considering a superposition of states or systems with two Slater determinants.
The Meaning of Higher-Order Factors in Reflective-Measurement Models
Eid, Michael; Koch, Tobias
2014-01-01
Higher-order factor analysis is a widely used approach for analyzing the structure of a multidimensional test. Whenever first-order factors are correlated researchers are tempted to apply a higher-order factor model. But is this reasonable? What do the higher-order factors measure? What is their meaning? Willoughby, Holochwost, Blanton, and Blair…
Analysis of Buried Dielectric Objects Using Higher-Order MoM for Volume Integral Equations
Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav
2004-01-01
A higher-order method of moments (MoM) is applied to solve a volume integral equation for dielectric objects in layered media. In comparison to low-order methods, the higher-order MoM, which is based on higher-order hierarchical Legendre vector basis functions and curvilinear hexahedral elements,...
A Generalized Runge-Kutta Method of order three
Thomsen, Per Grove
2002-01-01
The report presents a numerical method for the solution of stiff systems of ODE's and index one DAE's. The type of method is a 4- stage Generalized Linear Method that is reformulated in a special Semi Implicit Runge Kutta Method of SDIRK type. Error estimation is by imbedding a method of order 4...... based on the same stages as the method and the coefficients are selected for ease of implementation. The method has 4 stages and the stage-order is 2. For purposes of generating dense output and for initializing the iteration in the internal stages a continuous extension is derived. The method is A......-stable and we present the region of absolute stability and the order star of the order 3 method that is used for computing the solution....
Attempt to generalize fractional-order electric elements to complex-order ones
Si, Gangquan; Diao, Lijie; Zhu, Jianwei; Lei, Yuhang; Zhang, Yanbin
2017-06-01
The complex derivative {D}α +/- {{j}β }, with α, β \\in R+ is a generalization of the concept of integer derivative, where α=1, β=0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complex-order electric elements concept is proposed for the first time, and the complex-order elements are modeled and analyzed. Some interesting phenomena are found that the real part of the order affects the phase of output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor. More interesting is that the complex-order capacitor can do well at the time of fitting electrochemistry impedance spectra. The complex-order memristor is also analyzed. The area inside the hysteresis loops increases with the increasing of the imaginary part of the order and decreases with the increasing of the real part. Some complex case of complex-order memristors hysteresis loops are analyzed at last, whose loop has touching points beyond the origin of the coordinate system.
A higher-order numerical framework for stochastic simulation of chemical reaction systems.
Székely, Tamás
2012-07-15
BACKGROUND: In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulation, biochemical cascades and cell-cell interaction. However most discrete stochastic simulation techniques are slow. We apply Richardson extrapolation to the moments of three fixed-step methods, the Euler, midpoint and θ-trapezoidal τ-leap methods, to demonstrate the power of stochastic extrapolation. The extrapolation framework can increase the order of convergence of any fixed-step discrete stochastic solver and is very easy to implement; the only condition for its use is knowledge of the appropriate terms of the global error expansion of the solver in terms of its stepsize. In practical terms, a higher-order method with a larger stepsize can achieve the same level of accuracy as a lower-order method with a smaller one, potentially reducing the computational time of the system. RESULTS: By obtaining a global error expansion for a general weak first-order method, we prove that extrapolation can increase the weak order of convergence for the moments of the Euler and the midpoint τ-leap methods, from one to two. This is supported by numerical simulations of several chemical systems of biological importance using the Euler, midpoint and θ-trapezoidal τ-leap methods. In almost all cases, extrapolation results in an improvement of accuracy. As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations. CONCLUSIONS: Extrapolation is a general framework for increasing the order of accuracy of any fixed-step stochastic solver. This enables the simulation of complicated systems in less time, allowing for more realistic biochemical problems to be solved.
Future career intentions of higher specialist trainees in general Paediatrics.
Butler, Grainne; Breatnach, Colm; Harty, Sinead; Gavin, Patrick; O'Donnell, Colm; O'Grady, Michael J
2018-03-27
A survey of paediatric higher specialist trainees was carried out in 2002 assessing career intentions and perception of training. Fourteen years later, with increased numbers of trainees and a national model of care and a tertiary paediatric hospital on the horizon, we re-evaluated the career intentions of the current trainee workforce. To assess the career intentions of the current paediatric higher specialist trainees. A 28-item questionnaire was developed based on a previously validated instrument and distributed online using the Royal College of Physicians of Ireland trainee database. We distributed the questionnaire to 118 eligible trainees and received responses from 92 (78%). Seventy-nine (86%) respondents desire a consultant post in Ireland. Seventy-five (82%) indicated that their preferred consultant post location was in a tertiary paediatric centre. Sixty-two trainees (67%) intend to become subspecialists with 25 (27%) planning a career in general paediatrics. This contrasts with the 2002 survey when 76% wished to work in urban centres and 61% of trainees planned a career in general paediatrics. There appears to be a mismatch between the career goals of the future paediatric consultant workforce and the requirements for staffing paediatric units nationally. This has the potential to complicate the proposed expansion of general paediatricians in regional centres and result in a significant proportion of current trainees failing to secure a post in their desired location.
Robust fractional order differentiators using generalized modulating functions method
Liu, Dayan; Laleg-Kirati, Taous-Meriem
2015-01-01
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
Robust fractional order differentiators using generalized modulating functions method
Liu, Dayan
2015-02-01
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
Athanasios D. Karageorgos
2009-01-01
Full Text Available In many applications, and generally speaking in many dynamical differential systems, the problem of transferring the initial state of the system to a desired state in (almost zero-time time is desirable but difficult to achieve. Theoretically, this can be achieved by using a linear combination of Dirac -function and its derivatives. Obviously, such an input is physically unrealizable. However, we can think of it approximately as a combination of small pulses of very high magnitude and infinitely small duration. In this paper, the approximation process of the distributional behaviour of higher-order linear descriptor (regular differential systems is presented. Thus, new analytical formulae based on linear algebra methods and generalized inverses theory are provided. Our approach is quite general and some significant conditions are derived. Finally, a numerical example is presented and discussed.
A higher-order tensor vessel tractography for segmentation of vascular structures.
Cetin, Suheyla; Unal, Gozde
2015-10-01
A new vascular structure segmentation method, which is based on a cylindrical flux-based higher order tensor (HOT), is presented. On a vessel structure, the HOT naturally models branching points, which create challenges for vessel segmentation algorithms. In a general linear HOT model embedded in 3D, one has to work with an even order tensor due to an enforced antipodal-symmetry on the unit sphere. However, in scenarios such as in a bifurcation, the antipodally-symmetric tensor embedded in 3D will not be useful. In order to overcome that limitation, we embed the tensor in 4D and obtain a structure that can model asymmetric junction scenarios. During construction of a higher order tensor (e.g. third or fourth order) in 4D, the orientation vectors lie on the unit 3-sphere, in contrast to the unit 2-sphere in 3D tensor modeling. This 4D tensor is exploited in a seed-based vessel segmentation algorithm, where the principal directions of the 4D HOT is obtained by decomposition, and used in a HOT tractography approach. We demonstrate quantitative validation of the proposed algorithm on both synthetic complex tubular structures as well as real cerebral vasculature in Magnetic Resonance Angiography (MRA) datasets and coronary arteries from Computed Tomography Angiography (CTA) volumes.
Kim, Oleksiy S.; Jørgensen, Erik; Meincke, Peter
2004-01-01
An efficient higher-order method of moments (MoM) solution of volume integral equations is presented. The higher-order MoM solution is based on higher-order hierarchical Legendre basis functions and higher-order geometry modeling. An unstructured mesh composed of 8-node trilinear and/or curved 27...... of magnitude in comparison to existing higher-order hierarchical basis functions. Consequently, an iterative solver can be applied even for high expansion orders. Numerical results demonstrate excellent agreement with the analytical Mie series solution for a dielectric sphere as well as with results obtained...
On the expressiveness and decidability of higher-order process calculi
Lanese, Ivan; Perez, Jorge A.; Sangiorgi, Davide; Schmitt, Alan
In higher-order process calculi, the values exchanged in communications may contain processes. A core calculus of higher-order concurrency is studied; it has only the operators necessary to express higher-order communications: input prefix, process output, and parallel composition. By exhibiting a
A general first-order global sensitivity analysis method
Xu Chonggang; Gertner, George Zdzislaw
2008-01-01
Fourier amplitude sensitivity test (FAST) is one of the most popular global sensitivity analysis techniques. The main mechanism of FAST is to assign each parameter with a characteristic frequency through a search function. Then, for a specific parameter, the variance contribution can be singled out of the model output by the characteristic frequency. Although FAST has been widely applied, there are two limitations: (1) the aliasing effect among parameters by using integer characteristic frequencies and (2) the suitability for only models with independent parameters. In this paper, we synthesize the improvement to overcome the aliasing effect limitation [Tarantola S, Gatelli D, Mara TA. Random balance designs for the estimation of first order global sensitivity indices. Reliab Eng Syst Safety 2006; 91(6):717-27] and the improvement to overcome the independence limitation [Xu C, Gertner G. Extending a global sensitivity analysis technique to models with correlated parameters. Comput Stat Data Anal 2007, accepted for publication]. In this way, FAST can be a general first-order global sensitivity analysis method for linear/nonlinear models with as many correlated/uncorrelated parameters as the user specifies. We apply the general FAST to four test cases with correlated parameters. The results show that the sensitivity indices derived by the general FAST are in good agreement with the sensitivity indices derived by the correlation ratio method, which is a non-parametric method for models with correlated parameters
Liu, Qun; Jiang, Daqing
2018-04-01
In this paper, two stochastic predator-prey models with general functional response and higher-order perturbation are proposed and investigated. For the nonautonomous periodic case of the system, by using Khasminskii's theory of periodic solution, we show that the system admits a nontrivial positive T-periodic solution. For the system disturbed by both white and telegraph noises, sufficient conditions for positive recurrence and the existence of an ergodic stationary distribution to the solutions are established. The existence of stationary distribution implies stochastic weak stability to some extent.
Laitinen, Tommi; Nielsen, Jeppe Majlund; Pivnenko, Sergiy
2004-01-01
An investigation is performed to study the error of the far-field pattern determined from a spherical near-field antenna measurement in the case where a first-order (mu=+-1) probe correction scheme is applied to the near-field signal measured by a higher-order probe.......An investigation is performed to study the error of the far-field pattern determined from a spherical near-field antenna measurement in the case where a first-order (mu=+-1) probe correction scheme is applied to the near-field signal measured by a higher-order probe....
PRE-SERVICE MATHEMATICS TEACHERS’ CONCEPTION OF HIGHER-ORDER THINKING LEVEL IN BLOOM'S TAXONOMY
Damianus D Samo
2017-01-01
The purpose of this study is to explore pre-service mathematics teachers' conception of higher-order thinking in Bloom's Taxonomy, to explore pre-service mathematics teachers' ability in categorizing six cognitive levels of Bloom's Taxonomy as lower-order thinking and higher-order thinking, and pre-service mathematics teachers' ability in identifying some questionable items as lower-order and higher-order thinking. The higher-order thinking is the type of non-algorithm thinking which include ...
On a generalized fifth order KdV equations
Kaya, Dogan; El-Sayed, Salah M.
2003-01-01
In this Letter, we dealt with finding the solutions of a generalized fifth order KdV equation (for short, gfKdV) by using the Adomian decomposition method (for short, ADM). We prove the convergence of ADM applied to the gfKdV equation. Then we obtain the exact solitary-wave solutions and numerical solutions of the gfKdV equation for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are finally demonstrated for the gfKdV equation
SHARP: A Spatially Higher-order, Relativistic Particle-in-cell Code
Shalaby, Mohamad; Broderick, Avery E. [Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada); Chang, Philip [Department of Physics, University of Wisconsin-Milwaukee, 1900 E. Kenwood Boulevard, Milwaukee, WI 53211 (United States); Pfrommer, Christoph [Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam (Germany); Lamberts, Astrid [Theoretical Astrophysics, California Institute of Technology, Pasadena, CA 91125 (United States); Puchwein, Ewald, E-mail: mshalaby@live.ca [Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge, CB3 0HA (United Kingdom)
2017-05-20
Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially higher-order accurate relativistic PIC algorithm in one spatial dimension, which conserves charge and momentum exactly. We utilize the smoothness implied by the usage of higher-order interpolation functions to achieve a spatially higher-order accurate algorithm (up to the fifth order). We validate our algorithm against several test problems—thermal stability of stationary plasma, stability of linear plasma waves, and two-stream instability in the relativistic and non-relativistic regimes. Comparing our simulations to exact solutions of the dispersion relations, we demonstrate that SHARP can quantitatively reproduce important kinetic features of the linear regime. Our simulations have a superior ability to control energy non-conservation and avoid numerical heating in comparison to common second-order schemes. We provide a natural definition for convergence of a general PIC algorithm: the complement of physical modes captured by the simulation, i.e., those that lie above the Poisson noise, must grow commensurately with the resolution. This implies that it is necessary to simultaneously increase the number of particles per cell and decrease the cell size. We demonstrate that traditional ways for testing for convergence fail, leading to plateauing of the energy error. This new PIC code enables us to faithfully study the long-term evolution of plasma problems that require absolute control of the energy and momentum conservation.
De Sitter and scaling solutions in a higher-order modified teleparallel theory
Paliathanasis, Andronikos, E-mail: anpaliat@phys.uoa.gr [Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia (Chile)
2017-08-01
The existence and the stability conditions for some exact relativistic solutions of special interest are studied in a higher-order modified teleparallel gravitational theory. The theory with the use of a Lagrange multiplier is equivalent with that of General Relativity with a minimally coupled noncanonical field. The conditions for the existence of de Sitter solutions and ideal gas solutions in the case of vacuum are studied as also the stability criteria. Furthermore, in the presence of matter the behaviour of scaling solutions is given. Finally, we discuss the degrees of freedom of the field equations and we reduce the field equations in an algebraic equation, where in order to demonstrate our result we show how this noncanonical scalar field can reproduce the Hubble function of Λ-cosmology.
A Formalization of Newman's and Yokouchi's Lemmas in a Higher-Order Language
Andre Luiz Galdino
2008-12-01
Full Text Available This paper shows how a formalization for the theory of Abstract Reduction Systems (ARSs in which noetherianity was specified by the notion of well-foundness over binary relations is used in order to prove results such as the well-known Newman's and Yokouchi's Lemmas. The former is known as the diamond lemma and the latter states a property of commutation between ARSs. The theory ars was specified in the Prototype Verification System (PVS for which to the best of our knowledge there was no available theory for dealing with rewriting techniques in general before this development. In addition to proof techniques available in the higher-order specification language of PVS, the verification of these lemmas implies an elaborated use of natural and noetherian induction.
Higher-derivative boson field theories and constrained second-order theories
Urries, F.J. de [Departamento de Fisica, Universidad de Alcala de Henares, Madrid (Spain) and IMAFF, Consejo Superior de Investigaciones Cientificas, Madrid (Spain)]. E-mail: fernando.urries@uah.es; Julve, J. [IMAFF, Consejo Superior de Investigaciones Cientificas, Madrid (Spain)]. E-mail: julve@imaff.cfmac.csic.es; Sanchez, E.J. [IMAFF, Consejo Superior de Investigaciones Cientificas, Madrid (ES) and Departamento de Matematica, Universidad Europea, Madrid (Spain)]. E-mail: ejesus.sanchez@mat.ind.uem.es
2001-10-26
As an alternative to the covariant Ostrogradski method, we show that higher-derivative (HD) relativistic Lagrangian field theories can be reduced to second differential order by writing them directly as covariant two-derivative theories involving Lagrange multipliers and new fields. Despite the intrinsic non-covariance of the Dirac procedure used to deal with the constraints, the explicit Lorentz invariance is recovered at the end. We develop this new setting on the basis of a simple scalar model and then its applications to generalized electrodynamics and HD gravity are worked out. For a wide class of field theories this method is better suited than Ostrogradski's for a generalization to 2n-derivative theories. (author)
Spatio-chromatic adaptation via higher-order canonical correlation analysis of natural images.
Gutmann, Michael U; Laparra, Valero; Hyvärinen, Aapo; Malo, Jesús
2014-01-01
Independent component and canonical correlation analysis are two general-purpose statistical methods with wide applicability. In neuroscience, independent component analysis of chromatic natural images explains the spatio-chromatic structure of primary cortical receptive fields in terms of properties of the visual environment. Canonical correlation analysis explains similarly chromatic adaptation to different illuminations. But, as we show in this paper, neither of the two methods generalizes well to explain both spatio-chromatic processing and adaptation at the same time. We propose a statistical method which combines the desirable properties of independent component and canonical correlation analysis: It finds independent components in each data set which, across the two data sets, are related to each other via linear or higher-order correlations. The new method is as widely applicable as canonical correlation analysis, and also to more than two data sets. We call it higher-order canonical correlation analysis. When applied to chromatic natural images, we found that it provides a single (unified) statistical framework which accounts for both spatio-chromatic processing and adaptation. Filters with spatio-chromatic tuning properties as in the primary visual cortex emerged and corresponding-colors psychophysics was reproduced reasonably well. We used the new method to make a theory-driven testable prediction on how the neural response to colored patterns should change when the illumination changes. We predict shifts in the responses which are comparable to the shifts reported for chromatic contrast habituation.
Mixed hyperbolic-second-order-parabolic formulations of general relativity
Paschalidis, Vasileios
2008-01-01
Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt-Deser-Misner formulation and is derived by the addition of combinations of the constraints and their derivatives to the right-hand side of the Arnowitt-Deser-Misner evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic--second-order parabolic. The second formulation is a parabolization of the Kidder-Scheel-Teukolsky formulation and is a manifestly mixed strongly hyperbolic--second-order-parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint-violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.
Analysis and Improvement of the Generic Higher-Order Masking Scheme of FSE 2012
Roy, Arnab; Venkatesh, Srinivas Vivek
2013-01-01
Masking is a well-known technique used to prevent block cipher implementations from side-channel attacks. Higher-order side channel attacks (e.g. higher-order DPA attack) on widely used block cipher like AES have motivated the design of efficient higher-order masking schemes. Indeed, it is known that as the masking order increases, the difficulty of side-channel attack increases exponentially. However, the main problem in higher-order masking is to design an efficient and secure technique for...
Scott, Kristin M; Barbarin, Oscar A; Brown, Jeffrey M
2013-01-01
This study examines the relations of higher order (i.e., abstract) thinking (HOT) skills to specific domains of social competence in Black boys (n = 108) attending publicly sponsored prekindergarten (pre-K) programs. Data for the study were collected as part of the National Center for Early Development and Learning (NCEDL) Multi-State Study, a national, longitudinal study examining the quality and outcomes in a representative sample of publicly sponsored pre-K programs in six states (N = 240). Pre-K and kindergarten teachers rated randomly selected children on measures of abstract thinking, self-regulation, and social functioning at the beginning and end of each school year. Applying structural equation modeling, compared with earlier time points, HOT measured in the fall of kindergarten significantly predicted each of the domains of social competence in the spring of kindergarten, with the exception of peer social skills, while controlling for general cognitive ability. Results suggest that early intervention to improve HOT may be an effective and more focused approach to address concerns about Black boys' early social competencies in specific domains and potentially reduce the risk of later social difficulties. © 2013 American Orthopsychiatric Association.
Combining higher-order resummation with multiple NLO calculations and parton showers in GENEVA
Alioli, Simone; Bauer, Christian W.; Berggren, Calvin; Vermilion, Christopher K.; Walsh, Jonathan R.; Zuberi, Saba [California Univ., Berkeley, CA (United States). Ernest Orlando Lawrence Berkeley National Laboratory; Hornig, Andrew [Washington Univ., Seattle, WA (United States). Dept. of Physics; Tackmann, Frank J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie
2012-11-15
We extend the lowest-order matching of tree-level matrix elements with parton showers to give a complete description at the next higher perturbative accuracy in {alpha}{sub s} at both small and large jet resolutions, which has not been achieved so far. This requires the combination of the higher-order resummation of large Sudakov logarithms at small values of the jet resolution variable with the full next-to-leading order (NLO) matrix-element corrections at large values. As a by-product, this combination naturally leads to a smooth connection of the NLO calculations for different jet multiplicities. In this paper, we focus on the general construction of our method and discuss its application to e{sup +}e{sup -} and pp collisions. We present first results of the implementation in the GENEVA Monte Carlo framework. We employ N-jettiness as the jet resolution variable, combining its next-to-next-to-leading logarithmic resummation with fully exclusive NLO matrix elements, and PYTHIA 8 as the backend for further parton showering and hadronization. For hadronic collisions, we take Drell-Yan production as an example to apply our construction. For e{sup +}e{sup -} {yields} jets, taking {alpha}{sub s}(m{sub Z}) = 0.1135 from fits to LEP thrust data, together with the PYTHIA 8 hadronization model, we obtain good agreement with LEP data for a variety of 2-jet observables.
Higher-order ice-sheet modelling accelerated by multigrid on graphics cards
Brædstrup, Christian; Egholm, David
2013-04-01
Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.
Gamow-Jordan vectors and non-reducible density operators from higher-order S-matrix poles
Bohm, A.; Loewe, M.; Maxson, S.; Patuleanu, P.; Puentmann, C.; Gadella, M.
1997-01-01
In analogy to Gamow vectors that are obtained from first-order resonance poles of the S-matrix, one can also define higher-order Gamow vectors which are derived from higher-order poles of the S-matrix. An S-matrix pole of r-th order at z R =E R -iΓ/2 leads to r generalized eigenvectors of order k=0,1,hor-ellipsis,r-1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (E R -iΓ/2). The Gamow-Jordan vectors are elements of a generalized complex eigenvector expansion, whose form suggests the definition of a state operator (density matrix) for the microphysical decaying state of this higher-order pole. This microphysical state is a mixture of non-reducible components. In spite of the fact that the k-th order Gamow-Jordan vectors has the polynomial time-dependence which one always associates with higher-order poles, the microphysical state obeys a purely exponential decay law. copyright 1997 American Institute of Physics
Higher Order Thinking Skills among Secondary School Students in Science Learning
Saido, Gulistan Mohammed; Siraj, Saedah; Bin Nordin, Abu Bakar; Al Amedy, Omed Saadallah
2015-01-01
A central goal of science education is to help students to develop their higher order thinking skills to enable them to face the challenges of daily life. Enhancing students' higher order thinking skills is the main goal of the Kurdish Science Curriculum in the Iraqi-Kurdistan region. This study aimed at assessing 7th grade students' higher order…
The Higher Order Structure of Environmental Attitudes: A Cross-Cultural Examination
Taciano L. Milfont
2010-01-01
Full Text Available Past research has suggested that Preservation and Utilization are the two higher order dimensions forming the hierarchical structure of environmental attitudes. This means that these two higher order dimensions could group all kinds of perceptions or beliefs regarding the natural environment people have. A crosscultural study was conducted in Brazil, New Zealand, and South Africa to test this hierarchical structure of environmental attitudes. Results from single- and multi-group confirmatory factor analyses demonstrated that environmental attitudes are a multidimensional construct, and that their first-order factors associate to each other to form a vertical structure. However, the question whether the vertical structure comprise a single higher order factor or two higher order factors still remains unanswered. These results are discussed and directions for future research trying to demonstrate that Preservation and Utilization, taken as distinct second-order environmental attitudes factors, are more empirically meaningful than a single and generalised environmental attitudes higher order factor are presented.
Mathematics Teachers’ Interpretation of Higher-Order Thinking in Bloom’s Taxonomy
Tony Thompson
2008-01-01
This study investigated mathematics teachers’ interpretation of higher-order thinking in Bloom’s Taxonomy. Thirty-two high school mathematics teachers from the southeast U.S. were asked to (a) define lower- and higher-order thinking, (b) identify which thinking skills in Bloom’s Taxonomy represented lower- and higher-order thinking, and (c) create an Algebra I final exam item representative of each thinking skill. Results indicate that mathematics teachers have difficulty interpreting the thi...
Generalized Lee-Wick formulation from higher derivative field theories
Cho, Inyong; Kwon, O-Kab
2010-01-01
We study a higher derivative (HD) field theory with an arbitrary order of derivative for a real scalar field. The degree of freedom for the HD field can be converted to multiple fields with canonical kinetic terms up to the overall sign. The Lagrangian describing the dynamics of the multiple fields is known as the Lee-Wick (LW) form. The first step to obtain the LW form for a given HD Lagrangian is to find an auxiliary field (AF) Lagrangian which is equivalent to the original HD Lagrangian up to the quantum level. Until now, the AF Lagrangian has been studied only for N=2 and 3 cases, where N is the number of poles of the two-point function of the HD scalar field. We construct the AF Lagrangian for arbitrary N. By the linear combinations of AF fields, we also obtain the corresponding LW form. We find the explicit mapping matrices among the HD fields, the AF fields, and the LW fields. As an exercise of our construction, we calculate the relations among parameters and mapping matrices for N=2, 3, and 4 cases.
Analysis of Scattering by Inhomogeneous Dielectric Objects Using Higher-Order Hierarchical MoM
Kim, Oleksiy S.; Jørgensen, Erik; Meincke, Peter
2003-01-01
An efficient technique for the analysis of electromagnetic scattering by arbitrary shaped inhomogeneous dielectric objects is presented. The technique is based on a higher-order method of moments (MoM) solution of the volume integral equation. This higher-order MoM solution comprises recently...... that the condition number of the resulting MoM matrix is reduced by several orders of magnitude in comparison to existing higher-order hierarchical basis functions and, consequently, an iterative solver can be applied even for high expansion orders. Numerical results demonstrate excellent agreement...
Higher-order Multivariable Polynomial Regression to Estimate Human Affective States
Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin
2016-03-01
From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states.
Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time
Dhar, Amrit
2017-01-01
Abstract Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences. PMID:28177780
Jha, D.K.; Kant, Tarun; Srinivas, K.; Singh, R.K.
2013-01-01
Highlights: • We model through-thickness variation of material properties in functionally graded (FG) plates. • Effect of material grading index on deformations, stresses and natural frequency of FG plates is studied. • Effect of higher order terms in displacement models is studied for plate statics. • The benchmark solutions for the static analysis and free vibration of thick FG plates are presented. -- Abstract: Functionally graded materials (FGMs) are the potential candidates under consideration for designing the first wall of fusion reactors with a view to make best use of potential properties of available materials under severe thermo-mechanical loading conditions. A higher order shear and normal deformations plate theory is employed for stress and free vibration analyses of functionally graded (FG) elastic, rectangular, and simply (diaphragm) supported plates. Although FGMs are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to spatial coordinates. The material properties of FG plates are assumed here to vary through thickness of plate in a continuous manner. Young's modulii and material densities are considered to be varying continuously in thickness direction according to volume fraction of constituents which are mathematically modeled here as exponential and power law functions. The effects of variation of material properties in terms of material gradation index on deformations, stresses and natural frequency of FG plates are investigated. The accuracy of present numerical solutions has been established with respect to exact three-dimensional (3D) elasticity solutions and the other models’ solutions available in literature
Hwang, Jai-chan; Noh, Hyerim
2005-01-01
We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of φ v order higher than the second-order terms where φ v is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have δΦ∼(3/5)φ v to the linear order. Therefore, the pure general relativistic effects are of φ v order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropy of cosmic microwave background, we have (δT/T)∼(1/3)δΦ∼(1/5)φ v ∼10 -5 . Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon
Generalized Gödel universes in higher dimensions and pure Lovelock gravity
Dadhich, Naresh; Molina, Alfred; Pons, Josep M.
2017-10-01
The Gödel universe is a homogeneous rotating dust with negative Λ which is a direct product of a three-dimensional pure rotation metric with a line. We would generalize it to higher dimensions for Einstein and pure Lovelock gravity with only one N th-order term. For higher-dimensional generalization, we have to include more rotations in the metric, and hence we shall begin with the corresponding pure rotation odd (d =2 n +1 )-dimensional metric involving n rotations, which eventually can be extended by a direct product with a line or a space of constant curvature for yielding a higher-dimensional Gödel universe. The considerations of n rotations and also of constant curvature spaces is a new line of generalization and is being considered for the first time.
Gazzola, Filippo; Sweers, Guido
2010-01-01
This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the ﬁrst part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenbe...
Two-Photon or Higher-Order Absorbing Optical Materials for Generation of Reactive Species
Cumpston, Brian (Inventor); Lipson, Matthew (Inventor); Marder, Seth R. (Inventor); Perry, Joseph W. (Inventor)
2013-01-01
Disclosed are highly efficient multiphoton absorbing compounds and methods of their use. The compounds generally include a bridge of pi-conjugated bonds connecting electron donating groups or electron accepting groups. The bridge may be substituted with a variety of substituents as well. Solubility, lipophilicity, absorption maxima and other characteristics of the compounds may be tailored by changing the electron donating groups or electron accepting groups, the substituents attached to or the length of the pi-conjugated bridge. Numerous photophysical and photochemical methods are enabled by converting these compounds to electronically excited states upon simultaneous absorption of at least two photons of radiation. The compounds have large two-photon or higher-order absorptivities such that upon absorption, one or more Lewis acidic species, Lewis basic species, radical species or ionic species are formed.
Developing Instructional Design to Improve Mathematical Higher Order Thinking Skills of Students
Apino, E.; Retnawati, H.
2017-02-01
This study aimed to describe the instructional design to improve the Higher Order Thinking Skills (HOTS) of students in learning mathematics. This research is design research involving teachers and students of class X MIPA 1 MAN Yigyakarta III, Special Region of Yogyakarta, Indonesia. Data collected through focus group discussions and tests. Data analyzed by quantitative descriptive. The results showed that the instructional design developed is effective to improving students’ HOTS in learning mathematics. Instructional design developed generally include three main components: (1) involve students in the activities non-routine problem solving; (2) facilitating students to develop the ability to analyze and evaluate (critical thinking) and the ability to create (creative thinking); and (3) encourage students to construct their own knowledge.
Shi, L; Jones., R M
2014-01-01
erating cavities at FLASH linac, DESY, are equipped with electronics for beam position monitoring, which are based on HOM signals from special couplers. These monitors provide the beam position without additional vacuum components and at low cost. Moreover, they can be used to align the beam in the cavities to reduce the HOM effects on the beam. However, the HOMBPM (Higher Order Mode based Beam Position Monitor) shows an instability problem over time. In this paper, we will present the status of studies on this issue. Several methods are utilized to calibrate the HOMBPMs. These methods include DLR (Direct Linear Regression), and SVD (Singular Value Decomposition). We found that SVD generally is more suitable for HOMBPM calibration. We focus on the HOMBPMs at 1.3 GHz cavities. Techniques developed here are applicable to 3.9 ...
Recurrence approach and higher order polynomial algebras for superintegrable monopole systems
Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong
2018-05-01
We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a superintegrable monopole system in a generalized Taub-Newman-Unti-Tamburino (NUT) space. The Schrödinger equation of this model is solved in spherical coordinates in the framework of Stäckel transformation. It is shown that wave functions of the quantum system can be expressed in terms of the product of Laguerre and Jacobi polynomials. We construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas. By applying these recurrence relations, we construct higher order algebraically independent integrals of motion. We show that the integrals form a polynomial algebra. We construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model.
Authentic Instruction for 21st Century Learning: Higher Order Thinking in an Inclusive School
Preus, Betty
2012-01-01
The author studied a public junior high school identified as successfully implementing authentic instruction. Such instruction emphasizes higher order thinking, deep knowledge, substantive conversation, and value beyond school. To determine in what ways higher order thinking was fostered both for students with and without disabilities, the author…
Fischer, Christopher; Bol, Linda; Pribesh, Shana
2011-01-01
This study investigated the extent to which higher-order thinking skills are promoted in social studies classes in high schools that are implementing smaller learning communities (SLCs). Data collection in this mixed-methods study included classroom observations and in-depth interviews. Findings indicated that higher-order thinking was rarely…
From "Hello" to Higher-Order Thinking: The Effect of Coaching and Feedback on Online Chats
Stein, David S.; Wanstreet, Constance E.; Slagle, Paula; Trinko, Lynn A.; Lutz, Michelle
2013-01-01
This exploratory study examined the effect of a coaching and feedback intervention in teaching presence and social presence on higher-order thinking in an online community of inquiry. Coaching occurred before each chat, and feedback was provided immediately afterwards. The findings suggest that over time, the frequency of higher-order thinking…
Comparing higher order models for the EORTC QLQ-C30
Gundy, Chad M; Fayers, Peter M; Grønvold, Mogens
2012-01-01
To investigate the statistical fit of alternative higher order models for summarizing the health-related quality of life profile generated by the EORTC QLQ-C30 questionnaire.......To investigate the statistical fit of alternative higher order models for summarizing the health-related quality of life profile generated by the EORTC QLQ-C30 questionnaire....
Teaching Higher Order Thinking in the Introductory MIS Course: A Model-Directed Approach
Wang, Shouhong; Wang, Hai
2011-01-01
One vision of education evolution is to change the modes of thinking of students. Critical thinking, design thinking, and system thinking are higher order thinking paradigms that are specifically pertinent to business education. A model-directed approach to teaching and learning higher order thinking is proposed. An example of application of the…
Tanujaya, Benidiktus; Mumu, Jeinne; Margono, Gaguk
2017-01-01
Higher order thinking skills (HOTS) is one of important aspects in education. Students with high level of higher order thinking skills tend to be more successful. However, do this phenomenon also happen in the learning of Mathematics? To answer this question, this research aims to study the relationship between HOTS and students' academic…
Multi-domain, higher order level set scheme for 3D image segmentation on the GPU
Sharma, Ojaswa; Zhang, Qin; Anton, François
2010-01-01
to evaluate level set surfaces that are $C^2$ continuous, but are slow due to high computational burden. In this paper, we provide a higher order GPU based solver for fast and efficient segmentation of large volumetric images. We also extend the higher order method to multi-domain segmentation. Our streaming...
Higher-order blackhole solutions in N=2 supergravity and Calabi-Yau string backgrounds
Behrndt, K.; Cardoso, G.L.; de Wit, B.Q.P.J.; Lüst, D.; Mohaupt, T.; Sabra, W.A.
1998-01-01
Based on special geometry, we consider corrections to N=2 extremal black-hole solutions and their entropies originating from higher-order derivative terms in N=2 supergravity. These corrections are described by a holomorphic function, and the higher-order black-hole solutions can be expressed in
Higher order capacity statistics of multi-hop transmission systems over Rayleigh fading channels
Yilmaz, Ferkan
2012-03-01
In this paper, we present an exact analytical expression to evaluate the higher order statistics of the channel capacity for amplify and forward (AF) multihop transmission systems operating over Rayleigh fading channels. Furthermore, we present simple and efficient closed-form expression to the higher order moments of the channel capacity of dual hop transmission system with Rayleigh fading channels. In order to analyze the behavior of the higher order capacity statistics and investigate the usefulness of the mathematical analysis, some selected numerical and simulation results are presented. Our results are found to be in perfect agreement. © 2012 IEEE.
Zhai, Yi; Wang, Yan; Wang, Zhaoqi; Liu, Yongji; Zhang, Lin; He, Yuanqing; Chang, Shengjiang
2014-01-01
An achromatic element eliminating only longitudinal chromatic aberration (LCA) while maintaining transverse chromatic aberration (TCA) is established for the eye model, which involves the angle formed by the visual and optical axis. To investigate the impacts of higher-order aberrations on vision, the actual data of higher-order aberrations of human eyes with three typical levels are introduced into the eye model along visual axis. Moreover, three kinds of individual eye models are established to investigate the impacts of higher-order aberrations, chromatic aberration (LCA+TCA), LCA and TCA on vision under the photopic condition, respectively. Results show that for most human eyes, the impact of chromatic aberration on vision is much stronger than that of higher-order aberrations, and the impact of LCA in chromatic aberration dominates. The impact of TCA is approximately equal to that of normal level higher-order aberrations and it can be ignored when LCA exists.
Modular specification and verification for higher-order languages with state
Svendsen, Kasper
The overall topic of this thesis is modular reasoning for higher-order languages with state. The thesis consists of four mostly independent chapters that each deal with a different aspect of reasoning about higher-order languages with state. The unifying theme throughout all four chapters is higher....... The third chapter of the thesis is a case study of the C# joins library. What makes this library interesting as a case study is that it combines a lot of advanced features (higher-order code with effects, concurrency, recursion through the store, shared mutable state, and fine-grained synchronization...
Erkinjon Karimov
2017-10-01
Full Text Available In this work we discuss higher order multi-term partial differential equation (PDE with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
Erkinjon Karimov; Sardor Pirnafasov
2017-01-01
In this work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
Cer, Erkan
2018-01-01
Purpose: The purpose of the current study is to reveal general qualities of the objectives in the mother-tongue curricula of Hong Kong and Shanghai-China, South Korea, Singapore, and Turkey in terms of higher-order thinking processes specified by PISA tests. Research Methods: In this study, the researcher used a qualitative research design.…
The geometry of higher-order Lagrange spaces applications to mechanics and physics
Miron, Radu
1997-01-01
This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1 A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with Applications to higher-order analytical mechanics and theoretical physics are included as well Audience This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology
Application of Higher-Order Cumulant in Fault Diagnosis of Rolling Bearing
Shen, Yongjun; Yang, Shaopu; Wang, Junfeng
2013-01-01
In this paper a new method of pattern recognition based on higher-order cumulant and envelope analysis is presented. The core of this new method is to construct analytical signals from the given signals and obtain the envelope signals firstly, then compute and compare the higher-order cumulants of the envelope signals. The higher-order cumulants could be used as a characteristic quantity to distinguish these given signals. As an example, this method is applied in fault diagnosis for 197726 rolling bearing of freight locomotive. The comparisons of the second-order, third-order and fourth-order cumulants of the envelope signals from different vibration signals of rolling bearing show this new method could discriminate the normal and two fault signals distinctly
Higher-order Peregrine combs and Peregrine walls for the variable-coefficient Lenells-Fokas equation
Wang, Zi-Qi; Wang, Xin; Wang, Lei; Sun, Wen-Rong; Qi, Feng-Hua
2017-02-01
In this paper, we study the variable-coefficient Lenells-Fokas (LF) model. Under large periodic modulations in the variable coefficients of the LF model, the generalized Akhmediev breathers develop into the breather multiple births (BMBs) from which we obtain the Peregrine combs (PCs). The PCs can be considered as the limiting case of the BMBs and be transformed into the Peregrine walls (PWs) with a specific amplitude of periodic modulation. We further investigate the spatiotemporal characteristics of the PCs and PWs analytically. Based on the second-order breather and rogue-wave solutions, we derive the corresponding higher-order structures (higher-order PCs and PWs) under proper periodic modulations. What is particularly noteworthy is that the second-order PC can be converted into the Peregrine pyramid which exhibits the higher amplitude and thickness. Our results could be helpful for the design of experiments in the optical fiber communications.
A novel algebraic procedure for solving non-linear evolution equations of higher order
Huber, Alfred
2007-01-01
We report here a systematic approach that can easily be used for solving non-linear partial differential equations (nPDE), especially of higher order. We restrict the analysis to the so called evolution equations describing any wave propagation. The proposed new algebraic approach leads us to traveling wave solutions and moreover, new class of solution can be obtained. The crucial step of our method is the basic assumption that the solutions satisfy an ordinary differential equation (ODE) of first order that can be easily integrated. The validity and reliability of the method is tested by its application to some non-linear evolution equations. The important aspect of this paper however is the fact that we are able to calculate distinctive class of solutions which cannot be found in the current literature. In other words, using this new algebraic method the solution manifold is augmented to new class of solution functions. Simultaneously we would like to stress the necessity of such sophisticated methods since a general theory of nPDE does not exist. Otherwise, for practical use the algebraic construction of new class of solutions is of fundamental interest
Higher-Order Fermi-Liquid Corrections for an Anderson Impurity Away from Half Filling
Oguri, Akira; Hewson, A. C.
2018-03-01
We study the higher-order Fermi-liquid relations of Kondo systems for arbitrary impurity-electron fillings, extending the many-body quantum theoretical approach of Yamada and Yosida. It includes, partly, a microscopic clarification of the related achievements based on Nozières' phenomenological description: Filippone, Moca, von Delft, and Mora [Phys. Rev. B 95, 165404 (2017), 10.1103/PhysRevB.95.165404]. In our formulation, the Fermi-liquid parameters such as the quasiparticle energy, damping, and transport coefficients are related to each other through the total vertex Γσ σ';σ'σ(ω ,ω';ω',ω ), which may be regarded as a generalized Landau quasiparticle interaction. We obtain exactly this function up to linear order with respect to the frequencies ω and ω' using the antisymmetry and analytic properties. The coefficients acquire additional contributions of three-body fluctuations away from half filling through the nonlinear susceptibilities. We also apply the formulation to nonequilibrium transport through a quantum dot, and clarify how the zero-bias peak evolves in a magnetic field.
Higher-Order Fermi-Liquid Corrections for an Anderson Impurity Away from Half Filling.
Oguri, Akira; Hewson, A C
2018-03-23
We study the higher-order Fermi-liquid relations of Kondo systems for arbitrary impurity-electron fillings, extending the many-body quantum theoretical approach of Yamada and Yosida. It includes, partly, a microscopic clarification of the related achievements based on Nozières' phenomenological description: Filippone, Moca, von Delft, and Mora [Phys. Rev. B 95, 165404 (2017)PRBMDO2469-995010.1103/PhysRevB.95.165404]. In our formulation, the Fermi-liquid parameters such as the quasiparticle energy, damping, and transport coefficients are related to each other through the total vertex Γ_{σσ^{'};σ^{'}σ}(ω,ω^{'};ω^{'},ω), which may be regarded as a generalized Landau quasiparticle interaction. We obtain exactly this function up to linear order with respect to the frequencies ω and ω^{'} using the antisymmetry and analytic properties. The coefficients acquire additional contributions of three-body fluctuations away from half filling through the nonlinear susceptibilities. We also apply the formulation to nonequilibrium transport through a quantum dot, and clarify how the zero-bias peak evolves in a magnetic field.
Recirculating beam-breakup thresholds for polarized higher-order modes with optical coupling
Georg H. Hoffstaetter
2007-04-01
Full Text Available Here we will derive the general theory of the beam-breakup (BBU instability in recirculating linear accelerators with coupled beam optics and with polarized higher-order dipole modes. The bunches do not have to be at the same radio-frequency phase during each recirculation turn. This is important for the description of energy recovery linacs (ERLs where beam currents become very large and coupled optics are used on purpose to increase the threshold current. This theory can be used for the analysis of phase errors of recirculated bunches, and of errors in the optical coupling arrangement. It is shown how the threshold current for a given linac can be computed and a remarkable agreement with tracking data is demonstrated. General formulas are then analyzed for several analytically solvable problems: (a Why can different higher order modes (HOM in one cavity couple and why can they then not be considered individually, even when their frequencies are separated by much more than the resonance widths of the HOMs? For the Cornell ERL as an example, it is noted that optimum advantage is taken of coupled optics when the cavities are designed with an x-y HOM frequency splitting of above 50 MHz. The simulated threshold current is then far above the design current of this accelerator. To justify that the simulation can represent an actual accelerator, we simulate cavities with 1 to 8 modes and show that using a limited number of modes is reasonable. (b How does the x-y coupling in the particle optics determine when modes can be considered separately? (c How much of an increase in threshold current can be obtained by coupled optics and why does the threshold current for polarized modes diminish roughly with the square root of the HOMs’ quality factors. Because of this square root scaling, polarized modes with coupled optics increase the threshold current more effectively for cavities that have rather large HOM quality factors, e.g. those without very
Verifying object-oriented programs with higher-order separation logic in Coq
Bengtson, Jesper; Jensen, Jonas Braband; Sieczkowski, Filip
2011-01-01
We present a shallow Coq embedding of a higher-order separation logic with nested triples for an object-oriented programming language. Moreover, we develop novel specification and proof patterns for reasoning in higher-order separation logic with nested triples about programs that use interfaces...... and interface inheritance. In particular, we show how to use the higher-order features of the Coq formalisation to specify and reason modularly about programs that (1) depend on some unknown code satisfying a specification or that (2) return objects conforming to a certain specification. All of our results have...
Modeling 3D PCMI using the Extended Finite Element Method with higher order elements
Jiang, W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Spencer, Benjamin W. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2017-03-31
This report documents the recent development to enable XFEM to work with higher order elements. It also demonstrates the application of higher order (quadratic) elements to both 2D and 3D models of PCMI problems, where discrete fractures in the fuel are represented using XFEM. The modeling results demonstrate the ability of the higher order XFEM to accurately capture the effects of a crack on the response in the vicinity of the intersecting surfaces of cracked fuel and cladding, as well as represent smooth responses in the regions away from the crack.
Transformation of general binary MRF minimization to the first-order case.
Ishikawa, Hiroshi
2011-06-01
We introduce a transformation of general higher-order Markov random field with binary labels into a first-order one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higher-order multi-label MRF energies that combines the new reduction with the fusion-move and QPBO algorithms. While many computer vision problems today are formulated as energy minimization problems, they have mostly been limited to using first-order energies, which consist of unary and pairwise clique potentials, with a few exceptions that consider triples. This is because of the lack of efficient algorithms to optimize energies with higher-order interactions. Our algorithm challenges this restriction that limits the representational power of the models so that higher-order energies can be used to capture the rich statistics of natural scenes. We also show that some minimization methods can be considered special cases of the present framework, as well as comparing the new method experimentally with other such techniques.
Higher time derivatives of the generalized Liapunov function
Schieve, W.C.; Bulsara, A.R.
1975-01-01
Using the generalized N-body expression for a Liapunov functional developed by Prigogine and coworkers, a condition is obtained whereby the successive time derivatives of this function alternate in sign for weakly coupled systems. This generalized Liapunov function contains contributions from the diagonal as well as off-diagonal (correlation) components of the density matrix. The alternating sign condition is applied (and seen to hold true) for the cases of elastic phonon scattering in a lattice, three-phonon scattering (the anharmonic lattice), and the quantum electron gas. It is also proved simply for the Friedrichs model
Defining Higher-Order Turbulent Moment Closures with an Artificial Neural Network and Random Forest
McGibbon, J.; Bretherton, C. S.
2017-12-01
Unresolved turbulent advection and clouds must be parameterized in atmospheric models. Modern higher-order closure schemes depend on analytic moment closure assumptions that diagnose higher-order moments in terms of lower-order ones. These are then tested against Large-Eddy Simulation (LES) higher-order moment relations. However, these relations may not be neatly analytic in nature. Rather than rely on an analytic higher-order moment closure, can we use machine learning on LES data itself to define a higher-order moment closure?We assess the ability of a deep artificial neural network (NN) and random forest (RF) to perform this task using a set of observationally-based LES runs from the MAGIC field campaign. By training on a subset of 12 simulations and testing on remaining simulations, we avoid over-fitting the training data.Performance of the NN and RF will be assessed and compared to the Analytic Double Gaussian 1 (ADG1) closure assumed by Cloudy Layers Unified By Binormals (CLUBB), a higher-order turbulence closure currently used in the Community Atmosphere Model (CAM). We will show that the RF outperforms the NN and the ADG1 closure for the MAGIC cases within this diagnostic framework. Progress and challenges in using a diagnostic machine learning closure within a prognostic cloud and turbulence parameterization will also be discussed.
Jha, D.K., E-mail: dkjha@barc.gov.in [Civil Engineering Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085 (India); Kant, Tarun [Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076 (India); Srinivas, K. [Civil Engineering Division, Bhabha Atomic Research Centre, Mumbai 400 085 (India); Singh, R.K. [Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai 400 085 (India)
2013-12-15
Highlights: • We model through-thickness variation of material properties in functionally graded (FG) plates. • Effect of material grading index on deformations, stresses and natural frequency of FG plates is studied. • Effect of higher order terms in displacement models is studied for plate statics. • The benchmark solutions for the static analysis and free vibration of thick FG plates are presented. -- Abstract: Functionally graded materials (FGMs) are the potential candidates under consideration for designing the first wall of fusion reactors with a view to make best use of potential properties of available materials under severe thermo-mechanical loading conditions. A higher order shear and normal deformations plate theory is employed for stress and free vibration analyses of functionally graded (FG) elastic, rectangular, and simply (diaphragm) supported plates. Although FGMs are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to spatial coordinates. The material properties of FG plates are assumed here to vary through thickness of plate in a continuous manner. Young's modulii and material densities are considered to be varying continuously in thickness direction according to volume fraction of constituents which are mathematically modeled here as exponential and power law functions. The effects of variation of material properties in terms of material gradation index on deformations, stresses and natural frequency of FG plates are investigated. The accuracy of present numerical solutions has been established with respect to exact three-dimensional (3D) elasticity solutions and the other models’ solutions available in literature.
Measuring higher order optical aberrations of the human eye: techniques and applications
L. Alberto V. Carvalho
2002-11-01
Full Text Available In the present paper we discuss the development of "wave-front", an instrument for determining the lower and higher optical aberrations of the human eye. We also discuss the advantages that such instrumentation and techniques might bring to the ophthalmology professional of the 21st century. By shining a small light spot on the retina of subjects and observing the light that is reflected back from within the eye, we are able to quantitatively determine the amount of lower order aberrations (astigmatism, myopia, hyperopia and higher order aberrations (coma, spherical aberration, etc.. We have measured artificial eyes with calibrated ametropia ranging from +5 to -5 D, with and without 2 D astigmatism with axis at 45º and 90º. We used a device known as the Hartmann-Shack (HS sensor, originally developed for measuring the optical aberrations of optical instruments and general refracting surfaces in astronomical telescopes. The HS sensor sends information to a computer software for decomposition of wave-front aberrations into a set of Zernike polynomials. These polynomials have special mathematical properties and are more suitable in this case than the traditional Seidel polynomials. We have demonstrated that this technique is more precise than conventional autorefraction, with a root mean square error (RMSE of less than 0.1 µm for a 4-mm diameter pupil. In terms of dioptric power this represents an RMSE error of less than 0.04 D and 5º for the axis. This precision is sufficient for customized corneal ablations, among other applications.
Color-motion feature-binding errors are mediated by a higher-order chromatic representation.
Shevell, Steven K; Wang, Wei
2016-03-01
Peripheral and central moving objects of the same color may be perceived to move in the same direction even though peripheral objects have a different true direction of motion [Nature429, 262 (2004)10.1038/429262a]. The perceived, illusory direction of peripheral motion is a color-motion feature-binding error. Recent work shows that such binding errors occur even without an exact color match between central and peripheral objects, and, moreover, the frequency of the binding errors in the periphery declines as the chromatic difference increases between the central and peripheral objects [J. Opt. Soc. Am. A31, A60 (2014)JOAOD60740-323210.1364/JOSAA.31.000A60]. This change in the frequency of binding errors with the chromatic difference raises the general question of the chromatic representation from which the difference is determined. Here, basic properties of the chromatic representation are tested to discover whether it depends on independent chromatic differences on the l and the s cardinal axes or, alternatively, on a more specific higher-order chromatic representation. Experimental tests compared the rate of feature-binding errors when the central and peripheral colors had the identical s chromaticity (so zero difference in s) and a fixed magnitude of l difference, while varying the identical s level in center and periphery (thus always keeping the s difference at zero). A chromatic representation based on independent l and s differences would result in the same frequency of color-motion binding errors at everyslevel. The results are contrary to this prediction, thus showing that the chromatic representation at the level of color-motion feature binding depends on a higher-order chromatic mechanism.
Higher Order Loess Terracettes and Related Ungulate Activities in Western Pottawattamie County, Iowa
Weihs, B. J.
2009-12-01
Terracettes are small, quasi-parallel, staircase-like, stepped landforms. They are generally less than a meter in tread width and riser height and as long as 300 meters, located transversely along slopes. Many theories purport to explain the mechanisms that cause them, including animal disturbance, soil creep, solifluction (gelifluction), slumping and rotational slippage, regolith control, vegetation control, subsidence, and anthropogenic or tectonic activities. This thesis was aimed at morphologically characterizing terracettes in the western Iowa Loess Hills, with an emphasis on further classifying the forms morphogenetically. Onsite observations suggest that terracettes in this area are highly associated with anthropogenically induced grazing of domestic ungulates such as cattle, horses, and sheep, as well as deer. A new class of terracette (higher order or mega-terracette) is proposed that characterizes (and differentiates) the study area forms based on size, in that the study area contains terracettes that are an order above those discussed by other authors (sub-meter). This new addition to the current standard (tear terracettes-risers bare of vegetation, and normal terracettes-normal to the slope), as suggested by Anderson (1972), will add to the local understanding of the forms, and especially to the theory of polygenesis in which terracettes can result from a host of processes. This new class of terracette (mega) is higher magnitude, and directly related to ungulate activities such as geophagy, soil transport (from hooves), compaction, smearing, pawing, and wallowing (dust bathing) as well as the effects of variable soil moisture on erosion of the forms used by the animals. High magnitude terracettes in western Pottawattamie County, Iowa
Simplicial models for trace spaces II: General higher dimensional automata
Raussen, Martin
of directed paths with given end points in a pre-cubical complex as the nerve of a particular category. The paper generalizes the results from Raussen [19, 18] in which we had to assume that the HDA in question arises from a semaphore model. In particular, important for applications, it allows for models...
Generalized monotonicity from global minimization in fourth-order ODEs
M.A. Peletier (Mark)
2000-01-01
textabstractWe consider solutions of the stationary Extended Fisher-Kolmogorov equation with general potential that are global minimizers of an associated variational problem. We present results that relate the global minimization property to a generalized concept of monotonicity of the solutions.
Higher-Order Blind Signal Feature Separation: An Enabling Technology for Battlefield Awareness
Su, Wei; Kosinski, John A
2006-01-01
Higher-order transform blind signal feature classification is discussed for separating bar-shaped, circular, squared, circular-squared, and offset-diamonded constellation patterns of digital linear signals...
Higher-Order Wavefront Aberrations for Populations of Young Emmetropes and Myopes
Jinhua Bao
2009-01-01
Conclusions: Human eyes have systematical higher order aberrations in population, and factors that cause bilateral symmetry of wavefront aberrations between the right and left eyes made important contribution to the systematical aberrations.
The Need to Deliver Higher-Order Skills in the Context of Marketing in SMEs
Copley, Paul
2013-01-01
It is argued that the delivery of learning and the development of skills and competences are central to SME success; and there appears to be a requirement for higher-order education and training that can deliver a
Higher-order asymptotic homogenization of periodic materials with low scale separation
Ameen, M.M.; Peerlings, R.H.J.; Geers, M.G.D
2016-01-01
In this work, we investigate the limits of classical homogenization theories pertaining to homogenization of periodic linear elastic composite materials at low scale separations and demonstrate the effectiveness of higher-order periodic homogenization in alleviating this limitation. Classical
Non-Poisson Dichotomous Noise: Higher-Order Correlation Functions and Aging
Allegrini, Paolo; Grigolini, Paolo; Palatella, Luigi; West, Bruce J
2004-01-01
.... The transition of psi(tau) from the exponential to the nonexponential condition yields the breakdown of the usual factorization condition of higher-order correlation functions, as well as the birth of aging effects...
Jaber, Nizar; Ramini, Abdallah; Carreno, Armando Arpys Arevalo; Younis, Mohammad I.
2016-01-01
© 2016 IOP Publishing Ltd. In this study, we demonstrate analytically and experimentally the excitations of the higher order modes of vibrations in electrostatically actuated clamped-clamped microbeam resonators. The concept is based on using
A stable higher order space time Galerkin marching-on-in-time scheme
Pray, Andrew J.; Shanker, Balasubramaniam; Bagci, Hakan
2013-01-01
We present a method for the stable solution of time-domain integral equations. The method uses a technique developed in [1] to accurately evaluate matrix elements. As opposed to existing stabilization schemes, the method presented uses higher order
Connection between weighted LPC and higher-order statistics for AR model estimation
Kamp, Y.; Ma, C.
1993-01-01
This paper establishes the relationship between a weighted linear prediction method used for robust analysis of voiced speech and the autoregressive modelling based on higher-order statistics, known as cumulants
Deformation from symmetry for Schrodinger equations of higher order on unbounded domains
Addolorata Salvatore
2003-06-01
Full Text Available By means of a perturbation method recently introduced by Bolle, we discuss the existence of infinitely many solutions for a class of perturbed symmetric higher order Schrodinger equations with non-homogeneous boundary data on unbounded domains.
Dynamics of massless higher spins in the second order in curvatures
Vasiliev, M.A.
1989-08-01
The consistent equations of motion of interacting fields of all spins s=0,1/2,1...∞ are constructed explicitly to the second order of the expansion in powers of the higher spin strengths. (author). 14 refs
Dynamics of massless higher spins in the second order in curvatures
Vasiliev, M A [International Centre for Theoretical Physics, Trieste (Italy)
1990-04-05
The consistent equations of motion of interacting massless fields of all spins s=0, 1/2, 1, ..., {infinity} are constructed explicitly to the second order of the expansion in powers of the higher spin strengths. (orig.).
Visualization and processing of higher order descriptors for multi-valued data
Schultz, Thomas
2015-01-01
Modern imaging techniques and computational simulations yield complex multi-valued data that require higher-order mathematical descriptors. This book addresses topics of importance when dealing with such data, including frameworks for image processing, visualization, and statistical analysis of higher-order descriptors. It also provides examples of the successful use of higher-order descriptors in specific applications and a glimpse of the next generation of diffusion MRI. To do so, it combines contributions on new developments, current challenges in this area, and state-of-the-art surveys. Compared to the increasing importance of higher-order descriptors in a range of applications, tools for analysis and processing are still relatively hard to come by. Even though application areas such as medical imaging, fluid dynamics, and structural mechanics are very different in nature they face many shared challenges. This book provides an interdisciplinary perspective on this topic with contributions from key rese...
Higher order capacity statistics of multi-hop transmission systems over Rayleigh fading channels
Yilmaz, Ferkan; Tabassum, Hina; Alouini, Mohamed-Slim
2012-01-01
In this paper, we present an exact analytical expression to evaluate the higher order statistics of the channel capacity for amplify and forward (AF) multihop transmission systems operating over Rayleigh fading channels. Furthermore, we present
HIGHER EDUCATION AND GENERAL STUDIES IN NIGERIA: A ...
JONATHAN
This is evidenced by the fact that, above all, the good number of graduates from this ... It is the act of methodic development or training of the mind ..... comprised of universities, polytechnics, and colleges offering programmes in ... or higher education, through its normative roles of teaching, research and community service to.
Impact and Implementation of Higher-Order Ionospheric Effects on Precise GNSS Applications
Hadas, T.; Krypiak-Gregorczyk, A.; Hernández-Pajares, M.; Kaplon, J.; Paziewski, J.; Wielgosz, P.; Garcia-Rigo, A.; Kazmierski, K.; Sosnica, K.; Kwasniak, D.; Sierny, J.; Bosy, J.; Pucilowski, M.; Szyszko, R.; Portasiak, K.; Olivares-Pulido, G.; Gulyaeva, T.; Orus-Perez, R.
2017-11-01
High precision Global Navigation Satellite Systems (GNSS) positioning and time transfer require correcting signal delays, in particular higher-order ionospheric (I2+) terms. We present a consolidated model to correct second- and third-order terms, geometric bending and differential STEC bending effects in GNSS data. The model has been implemented in an online service correcting observations from submitted RINEX files for I2+ effects. We performed GNSS data processing with and without including I2+ corrections, in order to investigate the impact of I2+ corrections on GNSS products. We selected three time periods representing different ionospheric conditions. We used GPS and GLONASS observations from a global network and two regional networks in Poland and Brazil. We estimated satellite orbits, satellite clock corrections, Earth rotation parameters, troposphere delays, horizontal gradients, and receiver positions using global GNSS solution, Real-Time Kinematic (RTK), and Precise Point Positioning (PPP) techniques. The satellite-related products captured most of the impact of I2+ corrections, with the magnitude up to 2 cm for clock corrections, 1 cm for the along- and cross-track orbit components, and below 5 mm for the radial component. The impact of I2+ on troposphere products turned out to be insignificant in general. I2+ corrections had limited influence on the performance of ambiguity resolution and the reliability of RTK positioning. Finally, we found that I2+ corrections caused a systematic shift in the coordinate domain that was time- and region-dependent and reached up to -11 mm for the north component of the Brazilian stations during the most active ionospheric conditions.
Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav
2007-01-01
The problem of electromagnetic scattering by composite metallic and dielectric objects is solved using the coupled volume-surface integral equation (VSIE). The method of moments (MoM) based on higher-order hierarchical Legendre basis functions and higher-order curvilinear geometrical elements...... with the analytical Mie series solution. Scattering by more complex metal-dielectric objects are also considered to compare the presented technique with other numerical methods....
Ultra-compact Higher-Order-Mode Pass Filter in a Silicon Waveguide
Guan, Xiaowei; Frandsen, Lars Hagedorn; Ding, Yunhong
2015-01-01
An 3.7 μm long higher-order-mode pass filter with an extinction ratio larger than 20 dB is demonstrated in a 1D corrugated silicon multimode waveguide......An 3.7 μm long higher-order-mode pass filter with an extinction ratio larger than 20 dB is demonstrated in a 1D corrugated silicon multimode waveguide...
Higher order mode of a microstripline fed cylindrical dielectric resonator antenna
Kumar, A. V. Praveen, E-mail: praveen.kumar@pilani.bits-pilani.ac.in [Department of Electrical and Electronics Engineering, BITS Pilani, Pilani, Rajasthan-333 031 (India)
2016-03-09
A microstrip transmission line can be used to excite the broadside radiating mode of a cylindrical dielectric resonator antenna (CDRA). The same is found to excite considerably well a higher order mode (HOM) as well. However unlike the broadside mode, the higher order mode gives distorted radiation pattern which makes this mode less useful for practical applications. The cause of distortion in the HOM radiation and the dependence of HOM coupling on the microstrip feed line are explored using HFSS simulations.
Holographic Dark Energy with Generalized Chaplygin Gas in Higher Dimensions
Ghose, S.; Saha, A.; Paul, B. C.
2014-11-01
We investigate holographic dark energy (HDE) correspondence of interacting Generalized Chaplygin Gas (GCG) in the framework of compact Kaluza-Klein (KK) cosmology. The evolution of the modified HDE with corresponding equation of state is obtained here. Considering the present value of the density parameter a stable configuration is found which accommodates Dark Energy (DE). We note a connection between DE and Phantom fields. It reveals that the DE might have evolved from a Phantom state in the past.
Higher order aberrations in amblyopic children and their role in refractory amblyopia
Arnaldo Dias-Santos
2014-12-01
Full Text Available Objective: Some studies have hypothesized that an unfavourable higher order aberrometric profile could act as an amblyogenic mechanism and may be responsible for some amblyopic cases that are refractory to conventional treatment or cases of “idiopathic” amblyopia. This study compared the aberrometric profile in amblyopic children to that of children with normal visual development and compared the aberrometric profile in corrected amblyopic eyes and refractory amblyopic eyes with that of healthy eyes. Methods: Cross-sectional study with three groups of children – the CA group (22 eyes of 11 children with unilateral corrected amblyopia, the RA group (24 eyes of 13 children with unilateral refractory amblyopia and the C group (28 eyes of 14 children with normal visual development. Higher order aberrations were evaluated using an OPD-Scan III (NIDEK. Comparisons of the aberrometric profile were made between these groups as well as between the amblyopic and healthy eyes within the CA and RA groups. Results: Higher order aberrations with greater impact in visual quality were not significantly higher in the CA and RA groups when compared with the C group. Moreover, there were no statistically significant differences in the higher order aberrometric profile between the amblyopic and healthy eyes within the CA and RA groups. Conclusions: Contrary to lower order aberrations (e.g., myopia, hyperopia, primary astigmatism, higher order aberrations do not seem to be involved in the etiopathogenesis of amblyopia. Therefore, these are likely not the cause of most cases of refractory amblyopia.
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
Iwashige, Kengo; Ikeda, Takashi [Hitachi, Ltd. (Japan)
1995-09-01
A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.
The power of non-determinism in higher-order implicit complexity
Kop, Cynthia Louisa Martina; Simonsen, Jakob Grue
2017-01-01
We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we consider cons-free programs of varying data orders, equipped with explicit non-deterministic choice. Cons-freeness roughly means that data constructors cannot occur...... in function bodies and all manipulation of storage space thus has to happen indirectly using the call stack. While cons-free programs have previously been used by several authors to characterise complexity classes, the work on non-deterministic programs has almost exclusively considered programs of data order...... 0. Previous work has shown that adding explicit non-determinism to consfree programs taking data of order 0 does not increase expressivity; we prove that this—dramatically—is not the case for higher data orders: adding non-determinism to programs with data order at least 1 allows...
29 CFR 1205.3 - General Order No. 1.
2010-07-01
... order prescribes that such notices are to be standard as to contents, dimensions of sheet, and size of... may be necessary to make them accessible to all employees. Such notices must not be hidden by other...
In-Service Teacher Education: Asking Questions for Higher Order Thinking in Visual Literacy
Moodley, Visvaganthie
2013-01-01
The kinds of questions teachers ask may thwart or promote learner high-order thinking; teachers themselves must have expertise in questioning skills to promote higher order cognition among learners. Drawing on experiential knowledge of assessment, and as an English-teaching professional development programme (PDP) facilitator, I demonstrate that…
On realization of nonlinear systems described by higher-order differential equations
van der Schaft, Arjan
1987-01-01
We consider systems of smooth nonlinear differential and algebraic equations in which some of the variables are distinguished as “external variables.” The realization problem is to replace the higher-order implicit differential equations by first-order explicit differential equations and the
Contribution of higher order terms in the reductive perturbation theory, 2
Ichikawa, Y.H.; Mitsuhashi, Teruo; Konno, Kimiaki.
1977-01-01
Contribution of higher order terms in the reductive perturbation theory has been investigated for nonlinear propagation of strongly dispersive ion plasma wave. The basic set of fluid equation is reduced to a coupled set of the nonlinear Schroedinger equation for the first order perturbed potential and a linear inhomogeneous equation for the second order perturbed potential. A steady state solution of the coupled set of equations has been solved analytically in the asymptotic limit of small wave number. (auth.)
A stable higher order space time Galerkin marching-on-in-time scheme
Pray, Andrew J.
2013-07-01
We present a method for the stable solution of time-domain integral equations. The method uses a technique developed in [1] to accurately evaluate matrix elements. As opposed to existing stabilization schemes, the method presented uses higher order basis functions in time to improve the accuracy of the solver. The method is validated by showing convergence in temporal basis function order, time step size, and geometric discretization order. © 2013 IEEE.
Gamino, Jacquelyn F.; Chapman, Sandra B.; Cook, Lori G.
2009-01-01
Little is known about strategic learning ability in preteens and adolescents with traumatic brain injury (TBI). Strategic learning is the ability to combine and synthesize details to form abstracted gist-based meanings, a higher-order cognitive skill associated with frontal lobe functions and higher classroom performance. Summarization tasks were…
Ram Verma
2016-02-01
Full Text Available This paper deals with mainly establishing numerous sets of generalized second order paramertic sufficient optimality conditions for a semiinfinite discrete minmax fractional programming problem, while the results on semiinfinite discrete minmax fractional programming problem achieved based on some partitioning schemes under various types of generalized second order univexity assumptions.
QCD sum rules for D mesons. In-medium effects, chiral symmetry aspects and higher orders
Buchheim, Thomas
2017-04-11
Heavy open flavor mesons can serve as probes of hot and dense, strongly interacting matter in heavy-ion collisions suitable to mimic the extreme conditions shortly after the big-bang or in compact stars. Thus, the thorough theoretical investigation of medium modifications of D mesons is of utmost importance for the interpretation of the experimental data. Even at finite thermodynamic parameters, such as temperature and density, the non-perturbative framework of QCD sum rules allows for the determination of hadronic properties which are not accessible in perturbative quantum chromodynamics (QCD). By virtue of the separation of scales, long-range effects of hadrons are related to quark and gluon degrees of freedom, where features of the hadron spectrum are linked to condensates parameterizing the complex QCD ground state. This thesis furnishes the conception and calculus of QCD sum rules with emphasis on in-medium effects which are inevitable when addressing such effects in higher order contributions. In this regard, the notion and implications of medium-specific condensates are elucidated. Motivated by the significant numerical impact of four-quark condensates to the ρ meson sum rule we evaluate, for the first time, the corresponding in-medium mass-dimension 6 terms for D mesons tentatively employing the factorization hypothesis. Four-quark condensates containing heavy-quark operators may be included into the sum rule analysis utilizing the in-medium heavy-quark expansion made available here. Particular quark condensates are potential order parameters of chiral symmetry breaking, which is the mass generating mechanism of QCD giving the essential mass fraction to light hadrons. The interplay of altered spectral properties with changing in-medium QCD condensates, i. e. the chiral order parameters, can be studied with chiral partner sum rules. Although, introduced for light spin-1 mesons we foster their generalization to spin-0 open charm mesons demonstrating their
QCD sum rules for D mesons. In-medium effects, chiral symmetry aspects and higher orders
Buchheim, Thomas
2017-01-01
Heavy open flavor mesons can serve as probes of hot and dense, strongly interacting matter in heavy-ion collisions suitable to mimic the extreme conditions shortly after the big-bang or in compact stars. Thus, the thorough theoretical investigation of medium modifications of D mesons is of utmost importance for the interpretation of the experimental data. Even at finite thermodynamic parameters, such as temperature and density, the non-perturbative framework of QCD sum rules allows for the determination of hadronic properties which are not accessible in perturbative quantum chromodynamics (QCD). By virtue of the separation of scales, long-range effects of hadrons are related to quark and gluon degrees of freedom, where features of the hadron spectrum are linked to condensates parameterizing the complex QCD ground state. This thesis furnishes the conception and calculus of QCD sum rules with emphasis on in-medium effects which are inevitable when addressing such effects in higher order contributions. In this regard, the notion and implications of medium-specific condensates are elucidated. Motivated by the significant numerical impact of four-quark condensates to the ρ meson sum rule we evaluate, for the first time, the corresponding in-medium mass-dimension 6 terms for D mesons tentatively employing the factorization hypothesis. Four-quark condensates containing heavy-quark operators may be included into the sum rule analysis utilizing the in-medium heavy-quark expansion made available here. Particular quark condensates are potential order parameters of chiral symmetry breaking, which is the mass generating mechanism of QCD giving the essential mass fraction to light hadrons. The interplay of altered spectral properties with changing in-medium QCD condensates, i. e. the chiral order parameters, can be studied with chiral partner sum rules. Although, introduced for light spin-1 mesons we foster their generalization to spin-0 open charm mesons demonstrating their
Vilanova, Anna; Burgeth, Bernhard; Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data
2014-01-01
Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and...
Higher- and Lower-Order Factor Analyses of the Temperament in Middle Childhood Questionnaire
Kotelnikova, Yuliya; Olino, Thomas M.; Klein, Daniel N.; Mackrell, Sarah V.M.; Hayden, Elizabeth P.
2017-01-01
The Temperament in Middle Childhood Questionnaire (TMCQ; Simonds & Rothbart, 2004) is a widely used parent-report measure of temperament. However, neither its lower- nor higher-order structures have been tested via a bottom-up, empirically based approach. We conducted higher- and lower-order exploratory factor analyses (EFAs) of the TMCQ in a large (N = 654) sample of 9-year-olds. Item-level EFAs identified 92 items as suitable (i.e., with loadings ≥.40) for constructing lower-order factors, only half of which resembled a TMCQ scale posited by the measure’s authors. Higher-order EFAs of the lower-order factors showed that a three-factor structure (Impulsivity/Negative Affectivity, Negative Affectivity, and Openness/Assertiveness) was the only admissible solution. Overall, many TMCQ items did not load well onto a lower-order factor. In addition, only three factors, which did not show a clear resemblance to Rothbart’s four-factor model of temperament in middle childhood, were needed to account for the higher-order structure of the TMCQ. PMID:27002124
More LNG ship orders for GD (General Dynamics Corp. )
1977-09-01
General Dynamics Corp. has been awarded a contract for two LNG tankers to transport LNG from Algeria to Lake Charles, La., with the U.S. Maritime Administration funding 25.5% of the $155 million cost of each vessel. The two ships are being built for Lachmar Inc., of Delaware, a partnership composed of Morgas Inc., Pantheon Inc., and Pelmar Inc., subsidiaries respectively of Moore-McCormack Bulk Transport Inc., General Dynamics Corp., and Panhandle Eastern Pipe Line Co. Upon completion in Dec. 1979 and Mar. 1980, the ships will be operated by Gastrans Inc. of Delaware, which is also a subsidiary of Moore-McCormack.
Stability analysis of fractional-order generalized chaotic susceptible ...
susceptible–infected–recovered epidemic model and its ... engineering and biology have already been studied by a number of ... In contrast to integer-order ... sures the inhibitory effect, β is the transmission or contact rate, γ is the rate of ...
Reformulation of the symmetries of first-order general relativity
Montesinos, Merced; González, Diego; Celada, Mariano; Díaz, Bogar
2017-10-01
We report a new internal gauge symmetry of the n-dimensional Palatini action with cosmological term (n>3 ) that is the generalization of three-dimensional local translations. This symmetry is obtained through the direct application of the converse of Noether’s second theorem on the theory under consideration. We show that diffeomorphisms can be expressed as linear combinations of it and local Lorentz transformations with field-dependent parameters up to terms involving the variational derivatives of the action. As a result, the new internal symmetry together with local Lorentz transformations can be adopted as the fundamental gauge symmetries of general relativity. Although their gauge algebra is open in general, it allows us to recover, without resorting to the equations of motion, the very well-known Lie algebra satisfied by translations and Lorentz transformations in three dimensions. We also report the analog of the new gauge symmetry for the Holst action with cosmological term, finding that it explicitly depends on the Immirzi parameter. The same result concerning its relation to diffeomorphisms and the open character of the gauge algebra also hold in this case. Finally, we consider the non-minimal coupling of a scalar field to gravity in n dimensions and establish that the new gauge symmetry is affected by this matter field. Our results indicate that general relativity in dimension greater than three can be thought of as a gauge theory.
Neurodevelopmental outcomes of triplets or higher-order extremely low birth weight infants.
Wadhawan, Rajan; Oh, William; Vohr, Betty R; Wrage, Lisa; Das, Abhik; Bell, Edward F; Laptook, Abbot R; Shankaran, Seetha; Stoll, Barbara J; Walsh, Michele C; Higgins, Rosemary D
2011-03-01
Extremely low birth weight twins have a higher rate of death or neurodevelopmental impairment than singletons. Higher-order extremely low birth weight multiple births may have an even higher rate of death or neurodevelopmental impairment. Extremely low birth weight (birth weight 401-1000 g) multiple births born in participating centers of the Neonatal Research Network between 1996 and 2005 were assessed for death or neurodevelopmental impairment at 18 to 22 months' corrected age. Neurodevelopmental impairment was defined by the presence of 1 or more of the following: moderate to severe cerebral palsy; mental developmental index score or psychomotor developmental index score less than 70; severe bilateral deafness; or blindness. Infants who died within 12 hours of birth were excluded. Maternal and infant demographic and clinical variables were compared among singleton, twin, and triplet or higher-order infants. Logistic regression analysis was performed to establish the association between singletons, twins, and triplet or higher-order multiples and death or neurodevelopmental impairment, controlling for confounding variables that may affect death or neurodevelopmental impairment. Our cohort consisted of 8296 singleton, 2164 twin, and 521 triplet or higher-order infants. The risk of death or neurodevelopmental impairment was increased in triplets or higher-order multiples when compared with singletons (adjusted odds ratio: 1.7 [95% confidence interval: 1.29-2.24]), and there was a trend toward an increased risk when compared with twins (adjusted odds ratio: 1.27 [95% confidence: 0.95-1.71]). Triplet or higher-order births are associated with an increased risk of death or neurodevelopmental impairment at 18 to 22 months' corrected age when compared with extremely low birth weight singleton infants, and there was a trend toward an increased risk when compared with twins.
The Effect of Higher Order Thinking Skill Instruction on EFL Reading Ability
Nava Nourdad
2018-05-01
Full Text Available This quantitative and quasi-experimental study dealt with the effect of the teaching higher order thinking (HOT on the reading comprehension ability of foreign language learners. Since reading ability plays a crucial role in learners’ education, it is language teachers’ mission to be aware of the useful and beneficial strategies to improve their students’ reading comprehension ability. Considering the fruitful results of applying HOT skills in education, the present study was conducted to investigate the effect of their instruction on students’ reading comprehension ability. To achieve the objectives of the study, a group of 236 male and female university students majoring in various fields but all taking General English course was selected by convenience sampling. They were randomly assigned into two groups of control and experimental. PET test was applied to homogenize the participants of the two study groups. The study followed pre-test, treatment, post-test design. While the experimental group followed a nine-session treatment on strategies of HOT, the control group was instructed through conventional method determined by the course book. The results of independent samples t-test revealed the positive effect of teaching HOT skills on improving reading comprehension ability of adult EFL learners. Pedagogical implications of these findings for language learners, language teachers, course book developers, and educational policy makers are discussed.
Higher order visual input to the mushroom bodies in the bee, Bombus impatiens.
Paulk, Angelique C; Gronenberg, Wulfila
2008-11-01
To produce appropriate behaviors based on biologically relevant associations, sensory pathways conveying different modalities are integrated by higher-order central brain structures, such as insect mushroom bodies. To address this function of sensory integration, we characterized the structure and response of optic lobe (OL) neurons projecting to the calyces of the mushroom bodies in bees. Bees are well known for their visual learning and memory capabilities and their brains possess major direct visual input from the optic lobes to the mushroom bodies. To functionally characterize these visual inputs to the mushroom bodies, we recorded intracellularly from neurons in bumblebees (Apidae: Bombus impatiens) and a single neuron in a honeybee (Apidae: Apis mellifera) while presenting color and motion stimuli. All of the mushroom body input neurons were color sensitive while a subset was motion sensitive. Additionally, most of the mushroom body input neurons would respond to the first, but not to subsequent, presentations of repeated stimuli. In general, the medulla or lobula neurons projecting to the calyx signaled specific chromatic, temporal, and motion features of the visual world to the mushroom bodies, which included sensory information required for the biologically relevant associations bees form during foraging tasks.
Triangular Alignment (TAME). A Tensor-based Approach for Higher-order Network Alignment
Mohammadi, Shahin [Purdue Univ., West Lafayette, IN (United States); Gleich, David F. [Purdue Univ., West Lafayette, IN (United States); Kolda, Tamara G. [Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Grama, Ananth [Purdue Univ., West Lafayette, IN (United States)
2015-11-01
Network alignment is an important tool with extensive applications in comparative interactomics. Traditional approaches aim to simultaneously maximize the number of conserved edges and the underlying similarity of aligned entities. We propose a novel formulation of the network alignment problem that extends topological similarity to higher-order structures and provide a new objective function that maximizes the number of aligned substructures. This objective function corresponds to an integer programming problem, which is NP-hard. Consequently, we approximate this objective function as a surrogate function whose maximization results in a tensor eigenvalue problem. Based on this formulation, we present an algorithm called Triangular AlignMEnt (TAME), which attempts to maximize the number of aligned triangles across networks. We focus on alignment of triangles because of their enrichment in complex networks; however, our formulation and resulting algorithms can be applied to general motifs. Using a case study on the NAPABench dataset, we show that TAME is capable of producing alignments with up to 99% accuracy in terms of aligned nodes. We further evaluate our method by aligning yeast and human interactomes. Our results indicate that TAME outperforms the state-of-art alignment methods both in terms of biological and topological quality of the alignments.
Higher moments method for generalized Pareto distribution in flood frequency analysis
Zhou, C. R.; Chen, Y. F.; Huang, Q.; Gu, S. H.
2017-08-01
The generalized Pareto distribution (GPD) has proven to be the ideal distribution in fitting with the peak over threshold series in flood frequency analysis. Several moments-based estimators are applied to estimating the parameters of GPD. Higher linear moments (LH moments) and higher probability weighted moments (HPWM) are the linear combinations of Probability Weighted Moments (PWM). In this study, the relationship between them will be explored. A series of statistical experiments and a case study are used to compare their performances. The results show that if the same PWM are used in LH moments and HPWM methods, the parameter estimated by these two methods is unbiased. Particularly, when the same PWM are used, the PWM method (or the HPWM method when the order equals 0) shows identical results in parameter estimation with the linear Moments (L-Moments) method. Additionally, this phenomenon is significant when r ≥ 1 that the same order PWM are used in HPWM and LH moments method.
Generality of a congruity effect in judgements of relative order.
Liu, Yang S; Chan, Michelle; Caplan, Jeremy B
2014-10-01
The judgement of relative order (JOR) procedure is used to investigate serial-order memory. Measuring response times, the wording of the instructions (whether the earlier or the later item was designated as the target) reversed the direction of search in subspan lists (Chan, Ross, Earle, & Caplan Psychonomic Bulletin & Review, 16(5), 945-951, 2009). If a similar congruity effect applied to above-span lists and, furthermore, with error rate as the measure, this could suggest how to model order memory across scales. Participants performed JORs on lists of nouns (Experiment 1: list lengths = 4, 6, 8, 10) or consonants (Experiment 2: list lengths = 4, 8). In addition to the usual distance, primacy, and recency effects, instructions interacted with serial position of the later probe in both experiments, not only in response time, but also in error rate, suggesting that availability, not just accessibility, is affected by instructions. The congruity effect challenges current memory models. We fitted Hacker's (Journal of Experimental Psychology: Human Learning and Memory, 6(6), 651-675, 1980) self-terminating search model to our data and found that a switch in search direction could explain the congruity effect for short lists, but not longer lists. This suggests that JORs may need to be understood via direct-access models, adapted to produce a congruity effect, or a mix of mechanisms.
Perturbative theory of higher-order collision-enhanced wave mixing
Trebino, R.; Rahn, L.A.
1989-01-01
This paper reports on collision-enhanced resonances which represent an interesting class of nonlinear- optical processes. They occur because collisional dephasing can rephase quantum-mechanical amplitudes that ordinarily cancel out exactly, thereby allowing otherwise unobservable wave-mixing resonances to be seen. This is an especially interesting phenomenon because these resonances are coherent effects that are induced by an incoherent process (collisional dephasing). First predicted in the late 1970s and eventually observed in 1981, these novel effects have now been seen in a wide variety of four-wave-mixing experiments, ranging from self-focusing to coherent anti-Stokes Raman spectroscopy. Recently, the authors have extended these observations to higher order, where the authors have shown both experimentally and theoretically the higher-order, collision-enhanced effects exist in nonlinear optics, appearing as subharmonics of two-photon resonances. Indeed, the authors have found that collision-enhanced processes are ideal systems for studying higher-order, nonlinear-optical effects because very high orders can be made to contribute with little or no saturation braodening. Experiments on sodium in a flame using six- and eight-wave-mixing geometries have revealed still higher-order effects (at least as high- order as χ (13) )
A general solution strategy of modified power method for higher mode solutions
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.
Analysis of warping deformation modes using higher order ANCF beam element
Orzechowski, Grzegorz; Shabana, Ahmed A.
2016-02-01
Most classical beam theories assume that the beam cross section remains a rigid surface under an arbitrary loading condition. However, in the absolute nodal coordinate formulation (ANCF) continuum-based beams, this assumption can be relaxed allowing for capturing deformation modes that couple the cross-section deformation and beam bending, torsion, and/or elongation. The deformation modes captured by ANCF finite elements depend on the interpolating polynomials used. The most widely used spatial ANCF beam element employs linear approximation in the transverse direction, thereby restricting the cross section deformation and leading to locking problems. The objective of this investigation is to examine the behavior of a higher order ANCF beam element that includes quadratic interpolation in the transverse directions. This higher order element allows capturing warping and non-uniform stretching distribution. Furthermore, this higher order element allows for increasing the degree of continuity at the element interface. It is shown in this paper that the higher order ANCF beam element can be used effectively to capture warping and eliminate Poisson locking that characterizes lower order ANCF finite elements. It is also shown that increasing the degree of continuity requires a special attention in order to have acceptable results. Because higher order elements can be more computationally expensive than the lower order elements, the use of reduced integration for evaluating the stress forces and the use of explicit and implicit numerical integrations to solve the nonlinear dynamic equations of motion are investigated in this paper. It is shown that the use of some of these integration methods can be very effective in reducing the CPU time without adversely affecting the solution accuracy.
Higher order terms of the nonlinear forces in plasmas with collisions at laser interaction
Kentwell, G.W.; Hora, H.
1980-01-01
The evaluation of the general expression of the nonlinear force of laser-plasma interaction showed discrepancies depending on the assumptions of the phase and collisions in the expressions used for E and H. While the first order terms of the derivations are remaining unchanged, new third order terms are found for the case of perpendicular incidence without collisions. With collisions, the additional non-pondermotive terms are derived to be more general than known before. It is then possible to evaluate the forces for oblique incidence with collisions and find an absorption caused force in the plane of the plasma surface. (author)
Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction
Barth, Timothy J.; Frederickson, Paul O.
1990-01-01
High order accurate finite-volume schemes for solving the Euler equations of gasdynamics are developed. Central to the development of these methods are the construction of a k-exact reconstruction operator given cell-averaged quantities and the use of high order flux quadrature formulas. General polygonal control volumes (with curved boundary edges) are considered. The formulations presented make no explicit assumption as to complexity or convexity of control volumes. Numerical examples are presented for Ringleb flow to validate the methodology.
Study of higher order cumulant expansion of U(1) lattice gauge model at finite temperature
Zheng Xite; Lei Chunhong; Li Yuliang; Chen Hong
1993-01-01
The order parameter, Polyakov line , of the U(1) gauge model on N σ 3 x N τ (N τ = 1) lattice by using the cumulant expansion is calculated to the 5-th order. The emphasis is put on the behaviour of the cumulant expansion in the intermediate coupling region. The necessity of higher order expansion is clarified from the connection between the cumulant expansion and the correlation length. The variational parameter in the n-th order calculation is determined by the requirement that corrections of the n-th order expansion to the zeroth order expansion finish. The agreement with the Monte Carlo simulation is obtained not only in the weak and strong coupling regions, but also in the intermediate coupling region except in the very vicinity of the phase transition point
MIMO processing based on higher-order Poincaré spheres
Fernandes, Gil M.; Muga, Nelson J.; Pinto, Armando N.
2017-08-01
A multi-input multi-output (MIMO) algorithm based on higher-order Poincaré spheres is demonstrated for space-division multiplexing (SDM) systems. The MIMO algorithm is modulation format agnostic, robust to frequency offset and does not require training sequences. In this approach, the space-multiplexed signal is decomposed in sets of two tributary signals, with each set represented in a higher-order Poincaré sphere. For any arbitrary complex modulation format, the samples of two tributaries can be represented in a given higher-order Poincaré sphere with a symmetry plane. The crosstalk along propagation changes the spatial orientation of this plane and, therefore, it can be compensated by computing and realigning the best fit plane. We show how the transmitted signal can be successfully recovered using this procedure for all possible combinations of tributaries. Moreover, we analyze the convergence speed for the MIMO technique considering several optical-to-noise ratios.
Recurrent activity in higher order, modality non-specific brain regions
Lou, Hans Olav Christensen; Joensson, Morten; Biermann-Ruben, Katja
2011-01-01
It has been proposed that the workings of the brain are mainly intrinsically generated recurrent neuronal activity, with sensory inputs as modifiers of such activity in both sensory and higher order modality non-specific regions. This is supported by the demonstration of recurrent neuronal activity...... in the visual system as a response to visual stimulation. In contrast recurrent activity has never been demonstrated before in higher order modality non-specific regions. Using magneto-encephalography and Granger causality analysis, we tested in a paralimbic network the hypothesis that stimulation may enhance...... causal recurrent interaction between higher-order, modality non-specific regions. The network includes anterior cingulate/medial prefrontal and posterior cingulate/medial parietal cortices together with pulvinar thalami, a network known to be effective in autobiographic memory retrieval and self...
Higher order polynomial expansion nodal method for hexagonal core neutronics analysis
Jin, Young Cho; Chang, Hyo Kim
1998-01-01
A higher-order polynomial expansion nodal(PEN) method is newly formulated as a means to improve the accuracy of the conventional PEN method solutions to multi-group diffusion equations in hexagonal core geometry. The new method is applied to solving various hexagonal core neutronics benchmark problems. The computational accuracy of the higher order PEN method is then compared with that of the conventional PEN method, the analytic function expansion nodal (AFEN) method, and the ANC-H method. It is demonstrated that the higher order PEN method improves the accuracy of the conventional PEN method and that it compares very well with the other nodal methods like the AFEN and ANC-H methods in accuracy
FitzPatrick, Beverly; Hawboldt, John; Doyle, Daniel; Genge, Terri
2015-02-17
To determine whether national educational outcomes, course objectives, and classroom assessments for 2 therapeutics courses were aligned for curricular content and cognitive processes, and if they included higher-order thinking. Document analysis and student focus groups were used. Outcomes, objectives, and assessment tasks were matched for specific therapeutics content and cognitive processes. Anderson and Krathwohl's Taxonomy was used to define higher-order thinking. Students discussed whether assessments tested objectives and described their thinking when responding to assessments. There were 7 outcomes, 31 objectives, and 412 assessment tasks. The alignment for content and cognitive processes was not satisfactory. Twelve students participated in the focus groups. Students thought more short-answer questions than multiple choice questions matched the objectives for content and required higher-order thinking. The alignment analysis provided data that could be used to reveal and strengthen the enacted curriculum and improve student learning.
A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation
Diosady, Laslo T.; Murman, Scott M.
2018-01-01
A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.
Collocated electrodynamic FDTD schemes using overlapping Yee grids and higher-order Hodge duals
Deimert, C.; Potter, M. E.; Okoniewski, M.
2016-12-01
The collocated Lebedev grid has previously been proposed as an alternative to the Yee grid for electromagnetic finite-difference time-domain (FDTD) simulations. While it performs better in anisotropic media, it performs poorly in isotropic media because it is equivalent to four overlapping, uncoupled Yee grids. We propose to couple the four Yee grids and fix the Lebedev method using discrete exterior calculus (DEC) with higher-order Hodge duals. We find that higher-order Hodge duals do improve the performance of the Lebedev grid, but they also improve the Yee grid by a similar amount. The effectiveness of coupling overlapping Yee grids with a higher-order Hodge dual is thus questionable. However, the theoretical foundations developed to derive these methods may be of interest in other problems.
Kawano, S.
2003-01-01
Magnetic materials consisting of rare earth ions form modulation structures such as a helical or sinusoidal structure caused by the oscillating magnetic interaction between rare earth ions due to RKKY magnetic interaction. These modulation structures, in some cases, develop further to higher order modulation structures by additional modulations caused by higher order crystalline electric field, magnetic interactions such as spin-lattice interaction, external magnetic field and pressure. The higher order modulation structures are observed in a spin-slip structure or a helifan structure in Ho, and a tilt helix structure in a TbEr alloy. Paramagnetic ions originated from frustration generate many magnetic phases under applied external magnetic field. KUR neutron diffraction groups have performed the development and adjustment of high-pressure instruments and external magnetic fields for neutron diffraction spectrometers. The studies of 'neutron diffraction under extreme conditions' by the seven groups are described in this report. (Y. Kazumata)
Development of a Higher Order Laminate Theory for Modeling Composites with Induced Strain Actuators
Chattopadhyay, Aditi; Seeley, Charles E.
1996-01-01
A refined higher order plate theory is developed to investigate the actuation mechanism of piezoelectric materials surface bonded or embedded in composite laminates. The current analysis uses a displacement field which accurately accounts for transverse shear stresses. Some higher order terms are identified by using the conditions that shear stresses vanish at all free surfaces. Therefore, all boundary conditions for displacements and stresses are satisfied in the present theory. The analysis is implemented using the finite element method which provides a convenient means to construct a numerical solution due to the discrete nature of the actuators. The higher order theory is computationally less expensive than a full three dimensional analysis. The theory is also shown to agree well with published experimental results. Numerical examples are presented for composite plates with thicknesses ranging from thin to very thick.
A higher order space-time Galerkin scheme for time domain integral equations
Pray, Andrew J.; Beghein, Yves; Nair, Naveen V.; Cools, Kristof; Bagci, Hakan; Shanker, Balasubramaniam
2014-01-01
Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.
Higher-order fluctuation-dissipation relations in plasma physics: Binary Coulomb systems
Golden, Kenneth I.
2018-05-01
A recent approach that led to compact frequency domain formulations of the cubic and quartic fluctuation-dissipation theorems (FDTs) for the classical one-component plasma (OCP) [Golden and Heath, J. Stat. Phys. 162, 199 (2016), 10.1007/s10955-015-1395-6] is generalized to accommodate binary ionic mixtures. Paralleling the procedure followed for the OCP, the basic premise underlying the present approach is that a (k ,ω ) 4-vector rotational symmetry, known to be a pivotal feature in the frequency domain architectures of the linear and quadratic fluctuation-dissipation relations for a variety of Coulomb plasmas [Golden et al., J. Stat. Phys. 6, 87 (1972), 10.1007/BF01023681; J. Stat. Phys. 29, 281 (1982), 10.1007/BF01020787; Golden, Phys. Rev. E 59, 228 (1999), 10.1103/PhysRevE.59.228], is expected to be a pivotal feature of the frequency domain architectures of the higher-order members of the FDT hierarchy. On this premise, each member, in its most tractable form, connects a single (p +1 )-point dynamical structure function to a linear combination of (p +1 )-order p density response functions; by definition, such a combination must also remain invariant under rotation of their (k1,ω1) ,(k2,ω2) ,...,(kp,ωp) , (k1+k2+⋯+kp,ω1+ω2+⋯+ωp) 4-vector arguments. Assigned to each 4-vector is a species index that corotates in lock step. Consistency is assured by matching the static limits of the resulting frequency domain cubic and quartic FDTs to their exact static counterparts independently derived in the present work via a conventional time-independent perturbation expansion of the Liouville distribution function in its macrocanonical form. The proposed procedure entirely circumvents the daunting issues of entangled Liouville space paths and nested Poisson brackets that one would encounter if one attempted to use the conventional time-dependent perturbation-theoretic Kubo approach to establish the frequency domain FDTs beyond quadratic order.
Massless second-order tetradic spin-3 and higher-helicity bosons
Aragone, C; La Roche, H [Universidad Simon Bolivar, Caracas (Venezuela) Dept. de Fisica
1982-11-21
The unique, uniform, second-order formulation of massless bosons of helicity >=3 is presented here in terms of tetradic fields. The actions we find are shown to coincide both with the first-order (tetradic) formulation of Vasiliev and with the symmetric second-order description of Fronsdal. We carefully analyse the gravitational coupling of the spin-3 field and find that tetradic spin-3 matter presents the same translational consistency problem as symmetric matter does. Furthermore, in the curved tetradic case the generalized Lorentz invariance can be restored by the addition of nominimal terms.
Shimizu, Kenji
2017-10-01
The 2nd-order Korteweg-de Vries (KdV) equation and the Gardner (or extended KdV) equation are often used to investigate internal solitary waves, commonly observed in oceans and lakes. However, application of these KdV-type equations for continuously stratified fluids to geophysical problems is hindered by nonuniqueness of the higher-order coefficients and the associated correction functions to the wave fields. This study proposes to reduce arbitrariness of the higher-order KdV theory by considering its uniqueness in the following three physical senses: (i) consistency of the nonlinear higher-order coefficients and correction functions with the corresponding phase speeds, (ii) wavenumber-independence of the vertically integrated available potential energy, and (iii) its positive definiteness. The spectral (or generalized Fourier) approach based on vertical modes in the isopycnal coordinate is shown to enable an alternative derivation of the 2nd-order KdV equation, without encountering nonuniqueness. Comparison with previous theories shows that Parseval's theorem naturally yields a unique set of special conditions for (ii) and (iii). Hydrostatic fully nonlinear solutions, derived by combining the spectral approach and simple-wave analysis, reveal that both proposed and previous 2nd-order theories satisfy (i), provided that consistent definitions are used for the wave amplitude and the nonlinear correction. This condition reduces the arbitrariness when higher-order KdV-type theories are compared with observations or numerical simulations. The coefficients and correction functions that satisfy (i)-(iii) are given by explicit formulae to 2nd order and by algebraic recurrence relationships to arbitrary order for hydrostatic fully nonlinear and linear fully nonhydrostatic effects.
A finite deformation theory of higher-order gradient crystal plasticity
Kuroda, Mitsutoshi; Tvergaard, Viggo
2008-01-01
crystal plasticity that is based on an assumption of the existence of higher-order stresses. Furthermore, a boundary-value problem for simple shear of a constrained thin strip is studied numerically, and some characteristic features of finite deformation are demonstrated through a comparison to a solution......For higher-order gradient crystal plasticity, a finite deformation formulation is presented. The theory does not deviate much from the conventional crystal plasticity theory. Only a back stress effect and additional differential equations for evolution of the geometrically necessary dislocation...
Higher-order resonant electronic recombination as a manifestation of configuration interaction
Beilmann, C; Amaro, P; Tashenov, S; Bekker, H; Harman, Z; Crespo López-Urrutia, J R
2013-01-01
Theoretical and experimental investigations of higher-order electron–ion recombination resonances including inter-shell excitations are presented for L-shell ions of Kr with the aim of examining details of atomic structure calculations. The particular importance of electron–electron interaction and configuration mixing effects for these recombination processes enables their use for detailed tests of electron correlation effects. A test of the required level of considered mixing configurations is presented and further experiments involving higher-order recombination channels are motivated. (paper)
McKechan, David J. A.
2010-11-01
This thesis concerns the use, in gravitational wave data analysis, of higher order wave form models of the gravitational radiation emitted by compact binary coalescences. We begin with an introductory chapter that includes an overview of the theory of general relativity, gravitational radiation and ground-based interferometric gravitational wave detectors. We then discuss, in Chapter 2, the gravitational waves emitted by compact binary coalescences, with an explanation of higher order waveforms and how they differ from leading order waveforms we also introduce the post-Newtonian formalism. In Chapter 3 the method and results of a gravitational wave search for low mass compact binary coalescences using a subset of LIGO's 5th science run data are presented and in the subsequent chapter we examine how one could use higher order waveforms in such analyses. We follow the development of a new search algorithm that incorporates higher order waveforms with promising results for detection efficiency and parameter estimation. In Chapter 5, a new method of windowing time-domain waveforms that offers benefit to gravitational wave searches is presented. The final chapter covers the development of a game designed as an outreach project to raise public awareness and understanding of the search for gravitational waves.
Higher-order radiative corrections for b b ¯→H-W+
Kidonakis, Nikolaos
2018-02-01
I present higher-order radiative corrections from collinear and soft-gluon emission for the associated production of a charged Higgs boson with a W boson. The calculation uses expressions from resummation at next-to-leading-logarithm accuracy. From the resummed cross section I derive analytical formulas at approximate next-to-next-to-leading order and next-to-next-to-next-to-leading order. Total cross sections are presented for the process b b ¯→H-W+ at various LHC energies. The transverse momentum and rapidity distributions of the charged Higgs boson are also calculated.
Higher-order schemes for the Laplace transformation method for parabolic problems
Douglas, C.
2011-01-01
In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely high order convergent. Second, higher-order compact schemes of order four and six are used for the the spatial discretization. Finally, the discretized linear algebraic systems are solved using multigrid to show the actual convergence rate for numerical examples, which are compared to other numerical solution methods. © 2011 Springer-Verlag.
Higher-order threshold resummation for semi-inclusive e+e- annihilation
Moch, S.; Vogt, A.
2009-08-01
The complete soft-enhanced and virtual-gluon contributions are derived for the quark coefficient functions in semi-inclusive e + e - annihilation to the third order in massless perturbative QCD. These terms enable us to extend the soft-gluon resummation for the fragmentation functions by two orders to the next-to-next-to-next-to-leading logarithmic (N 3 LL) accuracy. The resummation exponent is found to be the same as for the structure functions in inclusive deep-inelastic scattering. This finding, together with known results on the higher-order quark form factor, facilitates the determination of all soft and virtual contributions of the fourth-order difference of the coefficient functions for these two processes. Unlike the previous (N 2 LL) order in the exponentiation, the numerical effect of the N 3 LL contributions turns out to be negligible at LEP energies. (orig.)
Analyzes of students’ higher-order thinking skills of heat and temperature concept
Slamet Budiarti, Indah; Suparmi, A.; Sarwanto; Harjana
2017-11-01
High order thinking skills refer to three highest domains of the revised Bloom Taxonomy. The aims of the research were to analyze the student’s higher-order thinking skills of heat and temperature concept. The samples were taken by purposive random sampling technique consisted of 85 high school students from 3 senior high schools in Jayapura city. The descriptive qualitative method was employed in this study. The data were collected by using tests and interviews regarding the subject matters of heat and temperature. Based on the results of data analysis, it was concluded that 68.24% of the students have a high order thinking skills in the analysis, 3.53% of the students have a high order thinking skills in evaluating, and 0% of the students have a high order thinking skills in creation.
Abdel-Ouahab Boudraa
2005-10-01
Full Text Available In white-light interference microscopy, measurement of surface shape generally requires peak extraction of the fringe function envelope. In this paper the Teager-Kaiser energy and higher-order energy operators are proposed for efficient extraction of the fringe envelope. These energy operators are compared in terms of precision, robustness to noise, and subsampling. Flexible energy operators, depending on order and lag parameters, can be obtained. Results show that smoothing and interpolation of envelope approximation using spline model performs better than Gaussian-based approach.
Toward an Understanding of Higher-Order Thinking among Minority Students.
Armour-Thomas, Eleanor; And Others
1992-01-01
Used principal-factors extraction with varimax rotation analysis to clarify nature and function of higher-order thinking among minority high school students (n=107) from economically disadvantaged backgrounds. Results allowed for specification of mental processes associated with the construct and the extent to which students reported awareness and…
Saragih, Sahat; Napitupulu, E. Elvis; Fauzi, Amin
2017-01-01
This research aims to develop a student-centered learning model based on local culture and instrument of mathematical higher order thinking of junior high school students in the frame of the 2013-Curriculum in North Sumatra, Indonesia. The subjects of the research are seventh graders which are taken proportionally random consisted of three public…
Tanujaya, Benidiktus
2016-01-01
The purpose of this research was to develop an instrument that can be used to measure higher-order thinking skills (HOTS) in mathematics instruction of high school students. This research was conducted using a standard procedure of instrument development, from the development of conceptual definitions, development of operational definitions,…
The Higher Order Factor Structure and Gender Invariance of the Pathological Narcissism Inventory
Wright, Aidan G. C.; Lukowitsky, Mark R.; Pincus, Aaron L.; Conroy, David E.
2010-01-01
The Pathological Narcissism Inventory (PNI) is a recently developed multidimensional inventory for the assessment of pathological narcissism. The authors describe and report the results of two studies that investigate the higher order factor structure and gender invariance of the PNI. The results of the first study indicate that the PNI has a…
Method of applying single higher order polynomial basis function over multiple domains
Lysko, AA
2010-03-01
Full Text Available A novel method has been devised where one set of higher order polynomial-based basis functions can be applied over several wire segments, thus permitting to decouple the number of unknowns from the number of segments, and so from the geometrical...
Impedance Eduction in Large Ducts Containing Higher-Order Modes and Grazing Flow
Watson, Willie R.; Jones, Michael G.
2017-01-01
Impedance eduction test data are acquired in ducts with small and large cross-sectional areas at the NASA Langley Research Center. An improved data acquisition system in the large duct has resulted in increased control of the acoustic energy in source modes and more accurate resolution of higher-order duct modes compared to previous tests. Two impedance eduction methods that take advantage of the improved data acquisition to educe the liner impedance in grazing flow are presented. One method measures the axial propagation constant of a dominant mode in the liner test section (by implementing the Kumarsean and Tufts algorithm) and educes the impedance from an exact analytical expression. The second method solves numerically the convected Helmholtz equation and minimizes an objective function to obtain the liner impedance. The two methods are tested first on data synthesized from an exact mode solution and then on measured data. Results show that when the methods are applied to data acquired in the larger duct with a dominant higher-order mode, the same impedance spectra are educed as that obtained in the small duct where only the plane wave mode propagates. This result holds for each higher-order mode in the large duct provided that the higher-order mode is sufficiently attenuated by the liner.
Controlled generation of higher-order Poincaré sphere beams from a laser
Naidoo, Darryl
2016-03-01
Full Text Available . 10: 327-332 Controlled generation of higher-order Poincaré sphere beams from a laser Naidoo D Roux FS Dudley A Litvin I Piccirillo B Marrucci L Forbes A ABSTRACT: The angular momentum of light can be described by positions on a...
Superpositions of higher-order bessel beams and nondiffracting speckle fields
Dudley, Angela L
2009-08-01
Full Text Available speckle fields. The paper reports on illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the phase dependence of the light...
EXISTENCE OF PERIODIC SOLUTION TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT
无
2009-01-01
In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of periodic solutions to the equations are obtained. In addition,we give an example to illustrate the main results.
Dori, Yehudit J.; Tal, Revital T.; Tsaushu, Masha
2003-01-01
Teaching nonscience majors topics in biotechnology through case studies is the focus of this research. Our "Biotechnology, Environment, and Related Issues" module, developed within the "Science for All" framework, is aimed at elevating the level of students' scientific and technological literacy and their higher order thinking…
Oscillation of certain higher-order neutral partial functional differential equations.
Li, Wei Nian; Sheng, Weihong
2016-01-01
In this paper, we study the oscillation of certain higher-order neutral partial functional differential equations with the Robin boundary conditions. Some oscillation criteria are established. Two examples are given to illustrate the main results in the end of this paper.
McGill, Ryan J.; Canivez, Gary L.
2016-01-01
As recommended by Carroll, the present study examined the factor structure of the Wechsler Intelligence Scale for Children-Fourth Edition Spanish (WISC-IV Spanish) normative sample using higher order exploratory factor analytic techniques not included in the WISC-IV Spanish Technical Manual. Results indicated that the WISC-IV Spanish subtests were…
A review of higher order strain gradient theories of plasticity: Origins ...
require higher order boundary conditions that enable us to model effects of disloca- ..... where ǫ0 is a reference strain, σ0 the yield stress and n the strain hardening exponent. The ...... Petch N J 1953 J. Iron Steel Inst. London 173: 25. Pantleon ...
Foundational (co)datatypes and (co)recursion for higher-order logic
Biendarra, Julian; Blanchette, Jasmin Christian; Bouzy, Aymeric; Desharnais, Martin; Fleury, Mathias; Hölzl, Johannes; Kunčar, Ondřej; Lochbihler, Andreas; Meier, Fabian; Panny, Lorenz; Popescu, Andrei; Sternagel, Christian; Thiemann, René; Traytel, Dmitriy; Dixon, C.; Finger, M.
2017-01-01
We describe a line of work that started in 2011 towards enriching Isabelle/HOL’s language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive datatype than previously supported by any system based on higher-order logic. These (co)datatypes are
Higher-order QCD corrections to inclusive particle production in panti p collisions
Borzumati, F.M.; Kniehl, B.A.; Kramer, G.
1992-10-01
Inclusive single-particle production cross sections have been calculated including higher-order QCD corrections. Transverse-momentum and rapidity distributions are presented and the scale dependence is studied. The results are compared with experimental data from the CERN Spanti pS Collider and the Fermilab Tevatron. (orig.)
Stabilization of solutions to higher-order nonlinear Schrodinger equation with localized damping
Eleni Bisognin
2007-01-01
Full Text Available We study the stabilization of solutions to higher-order nonlinear Schrodinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.
Wang, Chao; Yang, Chuan-sheng
2017-09-01
In this paper, we present a simplified parsimonious higher-order multivariate Markov chain model with new convergence condition. (TPHOMMCM-NCC). Moreover, estimation method of the parameters in TPHOMMCM-NCC is give. Numerical experiments illustrate the effectiveness of TPHOMMCM-NCC.
Brady, Timothy F.; Tenenbaum, Joshua B.
2013-01-01
When remembering a real-world scene, people encode both detailed information about specific objects and higher order information like the overall gist of the scene. However, formal models of change detection, like those used to estimate visual working memory capacity, assume observers encode only a simple memory representation that includes no…
Higher order hierarchical discretization scheme for surface integral equations for layered media
Jørgensen, Erik; Kim, Oleksiy S.; Meincke, Peter
2004-01-01
This paper presents an efficient technique for the analysis of electromagnetic scattering by arbitrarily shaped perfectly conducting objects in layered media. The technique is based on a higher order method of moments (MoM) solution of the electric field, magnetic field, or combined-field integra...
Shape invariant higher-order Bessel-like beams carrying orbital angular momentum
Ismail, Y
2012-09-01
Full Text Available -1 Journal of Optics September 2012/ Vol. 14 Shape invariant higher-order Bessel-like beams carrying orbital angular momentum Y Ismail1,2, N Khilo3, V Belyi3 and A Forbes1,2 1 School of Physics, University of KwaZulu-Natal, Private Bag X54001...
Lim, Cher Ping; Tay, Lee Yong
2003-01-01
Based on a case study of an elementary school in Singapore, this article describes and analyzes how different types of ICT tools (informative, situating, constructive, and communicative tools) are used to engage students in higher-order thinking. The discussion emphasizes that the objective of the lesson and the orienting activities, rather than…
Second- and Higher-Order Virial Coefficients Derived from Equations of State for Real Gases
Parkinson, William A.
2009-01-01
Derivation of the second- and higher-order virial coefficients for models of the gaseous state is demonstrated by employing a direct differential method and subsequent term-by-term comparison to power series expansions. This communication demonstrates the application of this technique to van der Waals representations of virial coefficients.…
Quantum Noether identities for non-local transformations in higher-order derivatives theories
Li, Z.P.; Long, Z.W.
2003-01-01
Based on the phase-space generating functional of the Green function for a system with a regular/singular higher-order Lagrangian, the quantum canonical Noether identities (NIs) under a local and non-local transformation in phase space have been deduced, respectively. For a singular higher-order Lagrangian, one must use an effective canonical action I eff P in quantum canonical NIs instead of the classical I P in classical canonical NIs. The quantum NIs under a local and non-local transformation in configuration space for a gauge-invariant system with a higher-order Lagrangian have also been derived. The above results hold true whether or not the Jacobian of the transformation is equal to unity or not. It has been pointed out that in certain cases the quantum NIs may be converted to conservation laws at the quantum level. This algorithm to derive the quantum conservation laws is significantly different from the quantum first Noether theorem. The applications of our formulation to the Yang-Mills fields and non-Abelian Chern-Simons (CS) theories with higher-order derivatives are given, and the conserved quantities at the quantum level for local and non-local transformations are found, respectively. (orig.)
Tularam, Gurudeo Anand
2013-01-01
This paper addresses the importance of teaching mathematics in business and finance schools of tertiary institutions of Australia. The paper explores the nature of thinking and reasoning required for advancement financial or economic studies involves the use of higher order thinking and creativity skills (HOTS) for teaching in mathematics classes.…
Performance-Based Task Assessment of Higher-Order Proficiencies in Redesigned STEM High Schools
Ernst, Jeremy V.; Glennie, Elizabeth; Li, Songze
2017-01-01
This study explored student abilities in applying conceptual knowledge when presented with structured performance tasks. Specifically, the study gauged proficiency in higher-order applications of students enrolled in earth and environmental science or biology. The student sample was drawn from a Redesigned STEM high school model where a tested…
Breinbjerg, Olav
1992-01-01
An approach for including higher order edge diffraction in the equivalent edge current (EEC) method is proposed. This approach, which applies to monostatic as well as bistatic radar configurations with perfectly conducting polygonal plates, involves three distinct sets of EECs. All of these sets...
Superpositions of higher-order bessel beams and nondiffracting speckle fields - (SAIP 2009)
Dudley, Angela L
2009-07-01
Full Text Available speckle fields. The paper reports on illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the phase dependence of the light...
H2O2-induced higher order chromatin degradation: A novel ...
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mediator of oxidative stress, can also cause genomic damage indirectly. Thus, H2O2 at pathologically relevant concentrations rapidly induces higher order chromatin degradation (HOCD), i.e. enzymatic ... clease works through a single strand scission mechanism ... a great mutagenic risk to the surviving cells, because en-.
A Hybrid PO - Higher-Order Hierarchical MoM Formulation using Curvilinear Geometry Modeling
Jørgensen, E.; Meincke, Peter; Breinbjerg, Olav
2003-01-01
which implies a very modest memory requirement. Nevertheless, the hierarchical feature of the basis functions maintains the ability to treat small geometrical details efficiently. In addition, the scatterer is modelled with higher-order curved patches which allows accurate modelling of curved surfaces...
Higher-order multipole amplitude measurement in psi ' -> gamma chi(c2)
Ablikim, M.; Achasov, M. N.; Alberto, D.; An, F. F.; An, Q.; An, Z. H.; Bai, J. Z.; Baldini, R.; Ban, Y.; Becker, J.; Berger, N.; Bertani, M.; Bian, J. M.; Boger, E.; Bondarenko, O.; Boyko, I.; Briere, R. A.; Bytev, V.; Cai, X.; Calcaterra, A. C.; Cao, G. F.; Chang, J. F.; Chelkov, G.; Chen, G.; Chen, H. S.; Chen, J. C.; Chen, M. L.; Chen, S. J.; Chen, Y.; Chen, Y. B.; Cheng, H. P.; Chu, Y. P.; Cronin-Hennessy, D.; Dai, H. L.; Dai, J. P.; Dedovich, D.; Deng, Z. Y.; Denysenko, I.; Destefanis, M.; Ding, Y.; Dong, L. Y.; Dong, M. Y.; Du, S. X.; Fang, J.; Fang, S. S.; Feng, C. Q.; Fu, C. D.; Fu, J. L.; Gao, Y.; Geng, C.; Goetzen, K.; Gong, W. X.; Greco, M.; Gu, M. H.; Gu, Y. T.; Guan, Y. H.; Guo, A. Q.; Guo, L. B.; Guo, Y. P.; Han, Y. L.; Hao, X. Q.; Harris, F. A.; He, K. L.; He, M.; He, Z. Y.; Heng, Y. K.; Hou, Z. L.; Hu, H. M.; Hu, J. F.; Hu, T.; Huang, B.; Huang, G. M.; Huang, J. S.; Huang, X. T.; Huang, Y. P.; Hussain, T.; Ji, C. S.; Ji, Q.; Ji, X. B.; Ji, X. L.; Jia, L. K.; Jiang, L. L.; Jiang, X. S.; Jiao, J. B.; Jiao, Z.; Jin, D. P.; Jin, S.; Jing, F. F.; Kalantar-Nayestanaki, N.; Kavatsyuk, M.; Kuehn, W.; Lai, W.; Lange, J. S.; Leung, J. K. C.; Li, C. H.; Li, Cheng; Li, Cui; Li, D. M.; Li, F.; Li, G.; Li, H. B.; Li, J. C.; Li, K.; Li, Lei; Li, N. B.; Li, Q. J.; Li, S. L.; Li, W. D.; Li, W. G.; Li, X. L.; Li, X. N.; Li, X. Q.; Li, X. R.; Li, Z. B.; Liang, H.; Liang, Y. F.; Liang, Y. T.; Liao, X. T.; Liu, B. J.; Liu, C. L.; Liu, C. X.; Liu, C. Y.; Liu, F. H.; Liu, Fang; Liu, Feng; Liu, H.; Liu, H. B.; Liu, H. H.; Liu, H. M.; Liu, H. W.; Liu, J. P.; Liu, K.; Liu, K.; Liu, K. Y.; Liu, Q.; Liu, S. B.; Liu, X.; Liu, X. H.; Liu, Y. B.; Liu, Y. W.; Liu, Yong; Liu, Z. A.; Liu, Zhiqiang; Liu, Zhiqing; Loehner, H.; Lu, G. R.; Lu, H. J.; Lu, J. G.; Lu, Q. W.; Lu, X. R.; Lu, Y. P.; Luo, C. L.; Luo, M. X.; Luo, T.; Luo, X. L.; Lv, M.; Ma, C. L.; Ma, F. C.; Ma, H. L.; Ma, Q. M.; Ma, S.; Ma, T.; Ma, X.; Ma, X. Y.; Maggiora, M.; Malik, Q. A.; Mao, H.; Mao, Y. J.; Mao, Z. P.; Messchendorp, J. G.; Min, J.; Min, T. J.; Mitchell, R. E.; Mo, X. H.; Muchnoi, N. Yu; Nefedov, Y.; Nikolaev, I. B.; Ning, Z.; Olsen, S. L.; Ouyang, Q.; Pacetti, S.; Park, J. W.; Pelizaeus, M.; Peters, K.; Ping, J. L.; Ping, R. G.; Poling, R.; Pun, C. S. J.; Qi, M.; Qian, S.; Qiao, C. F.; Qin, X. S.; Qiu, J. F.; Rashid, K. H.; Rong, G.; Ruan, X. D.; Sarantsev, A.; Schulze, J.; Shao, M.; Shen, C. P.; Shen, X. Y.; Sheng, H. Y.; Shepherd, M. R.; Song, X. Y.; Spataro, S.; Spruck, B.; Sun, D. H.; Sun, G. X.; Sun, J. F.; Sun, S. S.; Sun, X. D.; Sun, Y. J.; Sun, Y. Z.; Sun, Z. J.; Sun, Z. T.; Tang, C. J.; Tang, X.; Tian, H. L.; Toth, D.; Varner, G. S.; Wang, B.; Wang, B. Q.; Wang, K.; Wang, L. L.; Wang, L. S.; Wang, M.; Wang, P.; Wang, P. L.; Wang, Q.; Wang, Q. J.; Wang, S. G.; Wang, X. L.; Wang, Y. D.; Wang, Y. F.; Wang, Y. Q.; Wang, Z.; Wang, Z. G.; Wang, Z. Y.; Wei, D. H.; Wen, Q. G.; Wen, S. P.; Wiedner, U.; Wu, L. H.; Wu, N.; Wu, W.; Wu, Z.; Xiao, Z. J.; Xie, Y. G.; Xiu, Q. L.; Xu, G. F.; Xu, G. M.; Xu, H.; Xu, Q. J.; Xu, X. P.; Xu, Y.; Xu, Z. R.; Xu, Z. Z.; Xue, Z.; Yan, L.; Yan, W. B.; Yan, Y. H.; Yang, H. X.; Yang, T.; Yang, Y.; Yang, Y. X.; Ye, H.; Ye, M.; Ye, M. H.; Yu, B. X.; Yu, C. X.; Yu, S. P.; Yuan, C. Z.; Yuan, W. L.; Yuan, Y.; Zafar, A. A.; Zallo, A.; Zeng, Y.; Zhang, B. X.; Zhang, B. Y.; Zhang, C.; Zhang, C. C.; Zhang, D. H.; Zhang, H. H.; Zhang, H. Y.; Zhang, J.; Zhang, J. Q.; Zhang, J. W.; Zhang, J. Y.; Zhang, J. Z.; Zhang, L.; Zhang, S. H.; Zhang, T. R.; Zhang, X. J.; Zhang, X. Y.; Zhang, Y.; Zhang, Y. H.; Zhang, Y. S.; Zhang, Z. P.; Zhang, Z. Y.; Zhao, G.; Zhao, H. S.; Zhao, Jiawei; Zhao, Jingwei; Zhao, Lei; Zhao, Ling; Zhao, M. G.; Zhao, Q.; Zhao, S. J.; Zhao, T. C.; Zhao, X. H.; Zhao, Y. B.; Zhao, Z. G.; Zhao, Z. L.; Zhemchugov, A.; Zheng, B.; Zheng, J. P.; Zheng, Y. H.; Zheng, Z. P.; Zhong, B.; Zhong, J.; Zhong, L.; Zhou, L.; Zhou, X. K.; Zhou, X. R.; Zhu, C.; Zhu, K.; Zhu, K. J.; Zhu, S. H.; Zhu, X. L.; Zhu, X. W.; Zhu, Y. S.; Zhu, Z. A.; Zhuang, J.; Zou, B. S.; Zou, J. H.; Zuo, J. X.
2011-01-01
Using 106 x 10(6) psi' events collected with the BESIII detector at the BEPCII storage ring, the higher-order multipole amplitudes in the radiative transition psi' -> gamma chi(c2) -> gamma pi(+)pi(-)/gamma K+K- are measured. A fit to the chi(c2) production and decay angular distributions yields M2
Unifying refinement and hoare-style reasoning in a logic for higher-order concurrency
Turon, Aaron; Dreyer, Derek; Birkedal, Lars
2013-01-01
Modular programming and modular verification go hand in hand, but most existing logics for concurrency ignore two crucial forms of modularity: *higher-order functions*, which are essential for building reusable components, and *granularity abstraction*, a key technique for hiding the intricacies ...
Evidence for higher-order effects in L-shell ionization by proton impact
Sarkadi, L.; Mukoyama, T.
1988-01-01
It is widely believed that higher order processes of ion-atom collisions are negligible in cases of light projectiles like proton. Recent refined experiments tried to prove that the existence of such effects were comperable with the experimental errors, and they showed the unexpected relative importance of the higher order processes. Thus a new coupled channel calculation was performed for proton-gold atom collision in the energy range of 0.15-3.0 MeV, including dynamical subshell coupling effects. The results show that the deviations from the first order cross sections reach 40% at low collision energy. This result made necessary to correct the calculations of L-shell X-ray production cross sections. (D.G.) 6 refs
Coaxial higher-order mode damper employing a high-pass filter
Kang, Y.W.; Jiang, X.
1997-01-01
Two different types of coaxial higher-order mode (HOM) dampers have been investigated for the Advanced Photon Source (APS) storage ring cavities: e-probe dampers and h-loop dampers. Realization of the h-loop dampers has been difficult because the loop antenna couples not only to the HOMs but also to the accelerating mode and results in loss of Q at the fundamental frequency. Previously, a first-order fundamental rejection filter was tested with unsatisfactory rejection characteristics. This problem can be overcome by using a higher-order high-pass filter between the loop and the matched load. Prototype dampers have been fabricated and tested in a storage ring single-cell cavity and the damping characteristic was analyzed
Sapriadil, S.; Setiawan, A.; Suhandi, A.; Malik, A.; Safitri, D.; Lisdiani, S. A. S.; Hermita, N.
2018-05-01
Communication skill is one skill that is very needed in this 21st century. Preparing and teaching this skill in teaching physics is relatively important. The focus of this research is to optimizing of students’ scientific communication skills after the applied higher order thinking virtual laboratory (HOTVL) on topic electric circuit. This research then employed experimental study particularly posttest-only control group design. The subject in this research involved thirty senior high school students which were taken using purposive sampling. A sample of seventy (70) students participated in the research. An equivalent number of thirty five (35) students were assigned to the control and experimental group. The results of this study found that students using higher order thinking virtual laboratory (HOTVL) in laboratory activities had higher scientific communication skills than students who used the verification virtual lab.
On higher-order flavour-singlet splitting and coefficient functions at large x
Vogt, A.; Soar, G.; Vermaseren, J.A.M.
2010-08-01
We discuss the large-x behaviour of the splitting functions P qg and P gq and of flavour-singlet coefficient functions, such as the gluon contributions C 2,g and C L,g to the structure functions F 2,L , in massless perturbative QCD. These quantities are suppressed by one or two powers of (1-x) with respect to the (1-x) -1 terms which are the subject of the well-known threshold exponentiation. We show that the double-logarithmic contributions to P qg , P gq and C L at order α s 4 can be predicted from known third-order results and present, as a first step towards a full all-order generalization, the leading-logarithmic large-x behaviour of P qg , P gq and C 2,g at all orders in α s . (orig.)
General order of the origin of life in the Universe
Kompanichenko, V. N.
2007-08-01
covers not only to Earth, but to processes in the vast explored Universe too. The used key notions "free energy" and "entropy" are universal and characterize ability or disability of a natural system to carry out work elsewhere. For instance, outbreak of ash by active volcanoes on Earth and Jupiter's satellite Io is the same kind of work that can be approximately evaluated in terms of the spent free energy. The opposite spontaneous and non-spontaneous processes are universal as well. They are described the transition of a natural system to more or less probable state correspondingly. Cooling of a lava flow on Earth and cooling of the entire Mars planet are similar processes related with the spontaneous process - heat conductivity. All stars, planets and other space bodies in the Universe are composed of about one hundred elements systematized in the Periodic Table. In this context behaviour of chemical systems elsewhere in the explored Universe should comply with the fundamental laws determined on Earth, in particular with the Le Chatelier principle, Onsager theorem and the theory of dissipative structures used in this work. For example, outflow of matter from a star occurs simultaneously with outflow of heat energy (i.e. they are interdependent processes) as it follows of the Onsager theorem. The organic microsystems, which are considered as prebiotic for the early Earth, composed of diverse organic compounds that were detected in the space and meteorites (from simple hydrocarbons up to amino acids). Taking these reasons into account, the distinguished three stages in principle can be considered in the context of a general scenario of the origin of life in the Universe. Some new ways of the experimental research in the origin of life field are suggested. The first of them is laboratory experimental research of diverse prebiotic models at the state of bifurcate transition and under oscillating conditions in the experimental chamber. The goal of the experiments is to
Symbolic Algebra Development for Higher-Order Electron Propagator Formulation and Implementation.
Tamayo-Mendoza, Teresa; Flores-Moreno, Roberto
2014-06-10
Through the use of symbolic algebra, implemented in a program, the algebraic expression of the elements of the self-energy matrix for the electron propagator to different orders were obtained. In addition, a module for the software package Lowdin was automatically generated. Second- and third-order electron propagator results have been calculated to test the correct operation of the program. It was found that the Fortran 90 modules obtained automatically with our algorithm succeeded in calculating ionization energies with the second- and third-order electron propagator in the diagonal approximation. The strategy for the development of this symbolic algebra program is described in detail. This represents a solid starting point for the automatic derivation and implementation of higher-order electron propagator methods.
A Frank mixture copula family for modeling higher-order correlations of neural spike counts
Onken, Arno; Obermayer, Klaus
2009-01-01
In order to evaluate the importance of higher-order correlations in neural spike count codes, flexible statistical models of dependent multivariate spike counts are required. Copula families, parametric multivariate distributions that represent dependencies, can be applied to construct such models. We introduce the Frank mixture family as a new copula family that has separate parameters for all pairwise and higher-order correlations. In contrast to the Farlie-Gumbel-Morgenstern copula family that shares this property, the Frank mixture copula can model strong correlations. We apply spike count models based on the Frank mixture copula to data generated by a network of leaky integrate-and-fire neurons and compare the goodness of fit to distributions based on the Farlie-Gumbel-Morgenstern family. Finally, we evaluate the importance of using proper single neuron spike count distributions on the Shannon information. We find notable deviations in the entropy that increase with decreasing firing rates. Moreover, we find that the Frank mixture family increases the log likelihood of the fit significantly compared to the Farlie-Gumbel-Morgenstern family. This shows that the Frank mixture copula is a useful tool to assess the importance of higher-order correlations in spike count codes.
Symmetries, invariants and generating functions: higher-order statistics of biased tracers
Munshi, Dipak
2018-01-01
Gravitationally collapsed objects are known to be biased tracers of an underlying density contrast. Using symmetry arguments, generalised biasing schemes have recently been developed to relate the halo density contrast δh with the underlying density contrast δ, divergence of velocity θ and their higher-order derivatives. This is done by constructing invariants such as s, t, ψ,η. We show how the generating function formalism in Eulerian standard perturbation theory (SPT) can be used to show that many of the additional terms based on extended Galilean and Lifshitz symmetry actually do not make any contribution to the higher-order statistics of biased tracers. Other terms can also be drastically simplified allowing us to write the vertices associated with δh in terms of the vertices of δ and θ, the higher-order derivatives and the bias coefficients. We also compute the cumulant correlators (CCs) for two different tracer populations. These perturbative results are valid for tree-level contributions but at an arbitrary order. We also take into account the stochastic nature bias in our analysis. Extending previous results of a local polynomial model of bias, we express the one-point cumulants Script SN and their two-point counterparts, the CCs i.e. Script Cpq, of biased tracers in terms of that of their underlying density contrast counterparts. As a by-product of our calculation we also discuss the results using approximations based on Lagrangian perturbation theory (LPT).
Higher-order neural network software for distortion invariant object recognition
Reid, Max B.; Spirkovska, Lilly
1991-01-01
The state-of-the-art in pattern recognition for such applications as automatic target recognition and industrial robotic vision relies on digital image processing. We present a higher-order neural network model and software which performs the complete feature extraction-pattern classification paradigm required for automatic pattern recognition. Using a third-order neural network, we demonstrate complete, 100 percent accurate invariance to distortions of scale, position, and in-plate rotation. In a higher-order neural network, feature extraction is built into the network, and does not have to be learned. Only the relatively simple classification step must be learned. This is key to achieving very rapid training. The training set is much smaller than with standard neural network software because the higher-order network only has to be shown one view of each object to be learned, not every possible view. The software and graphical user interface run on any Sun workstation. Results of the use of the neural software in autonomous robotic vision systems are presented. Such a system could have extensive application in robotic manufacturing.
Nejad, Bijan Chokoufe
2017-07-12
In this thesis, we present detailed studies of top-pair production with (t anti tH) and without association of a Higgs boson (t anti t) in e{sup +}e{sup -} collisions. These processes are of utmost interest for the top physics program of future lepton colliders. They allow in particular a precise measurement of the top quark mass and the Yukawa coupling. For this purpose, we present predictions for off-shell t anti t and t anti tH production including non-resonant and interference contributions up to next-to-leading order (NLO) in perturbative quantum chromodynamics (QCD). This allows for top-quark phenomenology in the continuum at an unprecedented level of accuracy. We show that off-shell effects and NLO QCD corrections for these processes do not factorize in general. In particular, we present the Yukawa coupling dependence of the cross section, which receives negative corrections due to sizable interference terms. We also add a discussion of p{sub T} resummation in the form of combining the NLO prediction via POWHEG matching with the parton shower and the associated uncertainties. To handle large Coulomb singularities at threshold, we include the next-to-leading log (NLL) threshold resummation derived in nonrelativistic QCD (NRQCD) for t anti t production. This results in a form factor that we incorporate in a fully relativistic cross section, which is factorized within an extended double-pole approximation. Fixed-order QCD corrections are included, hereby, for the top decay. We combine this calculation with the full fixed-order QCD results at NLO for W{sup +}W{sup -}b anti b production to obtain a computation that is not only valid at threshold but smoothly interpolates to the continuum. This allows us to present the first prediction for exclusive W{sup +}W{sup -}b anti b production at a lepton collider with a consistent matching between the top-antitop threshold and continuum regions. This computation is not only required to describe the intermediate energy
Nejad, Bijan Chokoufe
2017-01-01
In this thesis, we present detailed studies of top-pair production with (t anti tH) and without association of a Higgs boson (t anti t) in e"+e"- collisions. These processes are of utmost interest for the top physics program of future lepton colliders. They allow in particular a precise measurement of the top quark mass and the Yukawa coupling. For this purpose, we present predictions for off-shell t anti t and t anti tH production including non-resonant and interference contributions up to next-to-leading order (NLO) in perturbative quantum chromodynamics (QCD). This allows for top-quark phenomenology in the continuum at an unprecedented level of accuracy. We show that off-shell effects and NLO QCD corrections for these processes do not factorize in general. In particular, we present the Yukawa coupling dependence of the cross section, which receives negative corrections due to sizable interference terms. We also add a discussion of p_T resummation in the form of combining the NLO prediction via POWHEG matching with the parton shower and the associated uncertainties. To handle large Coulomb singularities at threshold, we include the next-to-leading log (NLL) threshold resummation derived in nonrelativistic QCD (NRQCD) for t anti t production. This results in a form factor that we incorporate in a fully relativistic cross section, which is factorized within an extended double-pole approximation. Fixed-order QCD corrections are included, hereby, for the top decay. We combine this calculation with the full fixed-order QCD results at NLO for W"+W"-b anti b production to obtain a computation that is not only valid at threshold but smoothly interpolates to the continuum. This allows us to present the first prediction for exclusive W"+W"-b anti b production at a lepton collider with a consistent matching between the top-antitop threshold and continuum regions. This computation is not only required to describe the intermediate energy region but also allows to study
Higher order and heavy quark mass effects in the determination of parton distribution functions
Bertone, Valerio
2013-07-01
The present thesis was devoted to the study of the inclusion of higher-order corrections and heavy quark mass effects in a PDF determination. This has been carried out in the NNPDF framework resulting originally in the NNPDF2.1 sets, which were at a later stage supplemented by the first LHC data leading to the most recent NNPDF2.3 sets. In Chapter 1 the concept of Parton Distribution Function (PDF) was introduced. We have shown how the analytical computation of the Deep-Inelastic-Scattering (DIS) process at order α{sub s} in QCD leads to initial-stale collinear divergences which, using the factorization theorem, can be reabsorbed into the PDFs. The energy dependence of PDFs is fully determined and the task is then reduced to the determination of the x (Bjorken variable) dependence. In Chapter 2 a detailed discussion of the factorization schemes presently available to include heavy quark mass effects into DIS structure functions has been given. It emerged that there are two possible basic approaches to the calculation of the DIS structure functions. In the first approach, the so-called Fixed-Flavour-Number Scheme (FFNS), the calculation is performed retaining the quark mass of the heavy flavours which provide a ''natural'' regulator for the infrared divergences. In the second approach, called Zero-Mass Variable-Flavour-Number Scheme (ZM-VFNS), the heavy quark masses are instead set to zero and this gives rise to the usual final-state collinear divergences that are absorbed into the PDFs. In addition, in the ZM-VFNS, the number of active flavours is assumed to increase by one unity as the energy of the process crosses the energy threshold of a given heavy quark. In order to obtain a factorization scheme that is accurate both at large and low energies, several prescriptions that interpolate between FFNS at low energy and ZM-VFNS at large energy have been proposed and implemented in as many PDF fits. In Chapter 2 they have been described showing how they behave for
Higher order and heavy quark mass effects in the determination of parton distribution functions
Bertone, Valerio
2013-07-01
The present thesis was devoted to the study of the inclusion of higher-order corrections and heavy quark mass effects in a PDF determination. This has been carried out in the NNPDF framework resulting originally in the NNPDF2.1 sets, which were at a later stage supplemented by the first LHC data leading to the most recent NNPDF2.3 sets. In Chapter 1 the concept of Parton Distribution Function (PDF) was introduced. We have shown how the analytical computation of the Deep-Inelastic-Scattering (DIS) process at order α{sub s} in QCD leads to initial-stale collinear divergences which, using the factorization theorem, can be reabsorbed into the PDFs. The energy dependence of PDFs is fully determined and the task is then reduced to the determination of the x (Bjorken variable) dependence. In Chapter 2 a detailed discussion of the factorization schemes presently available to include heavy quark mass effects into DIS structure functions has been given. It emerged that there are two possible basic approaches to the calculation of the DIS structure functions. In the first approach, the so-called Fixed-Flavour-Number Scheme (FFNS), the calculation is performed retaining the quark mass of the heavy flavours which provide a ''natural'' regulator for the infrared divergences. In the second approach, called Zero-Mass Variable-Flavour-Number Scheme (ZM-VFNS), the heavy quark masses are instead set to zero and this gives rise to the usual final-state collinear divergences that are absorbed into the PDFs. In addition, in the ZM-VFNS, the number of active flavours is assumed to increase by one unity as the energy of the process crosses the energy threshold of a given heavy quark. In order to obtain a factorization scheme that is accurate both at large and low energies, several prescriptions that interpolate between FFNS at low energy and ZM-VFNS at large energy have been proposed and implemented in as many PDF fits. In Chapter 2 they have been described showing
Higher order and heavy quark mass effects in the determination of parton distribution functions
Bertone, Valerio
2013-01-01
The present thesis was devoted to the study of the inclusion of higher-order corrections and heavy quark mass effects in a PDF determination. This has been carried out in the NNPDF framework resulting originally in the NNPDF2.1 sets, which were at a later stage supplemented by the first LHC data leading to the most recent NNPDF2.3 sets. In Chapter 1 the concept of Parton Distribution Function (PDF) was introduced. We have shown how the analytical computation of the Deep-Inelastic-Scattering (DIS) process at order α s in QCD leads to initial-stale collinear divergences which, using the factorization theorem, can be reabsorbed into the PDFs. The energy dependence of PDFs is fully determined and the task is then reduced to the determination of the x (Bjorken variable) dependence. In Chapter 2 a detailed discussion of the factorization schemes presently available to include heavy quark mass effects into DIS structure functions has been given. It emerged that there are two possible basic approaches to the calculation of the DIS structure functions. In the first approach, the so-called Fixed-Flavour-Number Scheme (FFNS), the calculation is performed retaining the quark mass of the heavy flavours which provide a ''natural'' regulator for the infrared divergences. In the second approach, called Zero-Mass Variable-Flavour-Number Scheme (ZM-VFNS), the heavy quark masses are instead set to zero and this gives rise to the usual final-state collinear divergences that are absorbed into the PDFs. In addition, in the ZM-VFNS, the number of active flavours is assumed to increase by one unity as the energy of the process crosses the energy threshold of a given heavy quark. In order to obtain a factorization scheme that is accurate both at large and low energies, several prescriptions that interpolate between FFNS at low energy and ZM-VFNS at large energy have been proposed and implemented in as many PDF fits. In Chapter 2 they have been described showing how