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Sample records for single transcendental equation

  1. Roots of two transcendental equations involving spherical bessel functions

    International Nuclear Information System (INIS)

    Pexton, R.L.; Steiger, A.D.

    1977-01-01

    Roots of the transcendental equations j/sub l/(αlambda) y/sub l/(lambda) =j/sub l/(lambda) y/sub l/(αlambda) and [xj/sub l/(x)]'/sub x alphaeta yl-italic/(x)]'/sub x eta/=xj/sub l/(x)]'/sub x eta yl-italic/(x)]'/sub x alphaeta/for the spherical Bessel functions of the first and second kind, j/sub l/(z) and y/sub l/(z), have been computed. The ranges for the parameter α, the order l and the root index n are: α=0.1(0.1)0.7,l=1(1)15,n=1(1)30

  2. Transcendental smallness in singularly perturbed equations of volterra type

    International Nuclear Information System (INIS)

    Bijura, Angelina M.

    2003-11-01

    The application of different limit processes to a physical problem is an important tool in layer type techniques. Hence the study of initial layer correction functions is of central importance for understanding layer-type problems. It is shown that for singularly perturbed problems of Volterra type, the concept of transcendental smallness is an asymptotic one. Transcendentally small terms may be numerically important. (author)

  3. An Efficient Method to Find Solutions for Transcendental Equations with Several Roots

    Directory of Open Access Journals (Sweden)

    Rogelio Luck

    2015-01-01

    Full Text Available This paper presents a method for obtaining a solution for all the roots of a transcendental equation within a bounded region by finding a polynomial equation with the same roots as the transcendental equation. The proposed method is developed using Cauchy’s integral theorem for complex variables and transforms the problem of finding the roots of a transcendental equation into an equivalent problem of finding roots of a polynomial equation with exactly the same roots. The interesting result is that the coefficients of the polynomial form a vector which lies in the null space of a Hankel matrix made up of the Fourier series coefficients of the inverse of the original transcendental equation. Then the explicit solution can be readily obtained using the complex fast Fourier transform. To conclude, the authors present an example by solving for the first three eigenvalues of the 1D transient heat conduction problem.

  4. Transcendental equations in the Schwinger-Keldysh nonequilibrium theory and nonvanishing correlations

    Energy Technology Data Exchange (ETDEWEB)

    Giraldi, Filippo [School of Chemistry and Physics, University of KwaZulu-Natal and National Institute for Theoretical Physics (NITheP), KwaZulu-Natal, Westville Campus, Durban 4000, South Africa and Gruppo Nazionale per la Fisica Matematica (GNFM-INdAM), c/o Istituto Nazionale di Alta Matematica Francesco Severi, Città Universitaria, Piazza Aldo Moro 5, 00185 Roma (Italy)

    2015-09-15

    The Schwinger-Keldysh nonequilibrium theory allows the description of various transport phenomena involving bosons (fermions) embedded in bosonic (fermionic) environments. The retarded Green’s function obeys the Dyson equation and determines via its non-vanishing asymptotic behavior the dissipationless open dynamics. The appearance of this regime is conditioned by the existence of the solution of a general class of transcendental equations in complex domain that we study. Particular cases consist in transcendental equations containing exponential, hyperbolic, power law, logarithmic, and special functions. The present analysis provides an analytical description of the thermal and temporal correlation function of two general observables of a quantum system in terms of the corresponding spectral function. Special integral properties of the spectral function guarantee non-vanishing asymptotic behavior of the correlation function.

  5. Concerning an analytical solution of some families of Kepler’s transcendental equation

    Directory of Open Access Journals (Sweden)

    Slavica M. Perovich

    2016-03-01

    Full Text Available The problem of finding an analytical solution of some families of Kepler transcendental equation is studied in some detail, by the Special Trans Functions Theory – STFT. Thus, the STFT mathematical approach in the form of STFT iterative methods with a novel analytical solutions are presented. Structure of the STFT solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT. In addition, the obtained analytical results are compared with the calculated values of other analytical methods for alternative proving its significance. Undoubtedly, the proposed novel analytical approach implies qualitative improvement in comparison with conventional numerical and analytical methods.

  6. Roots of two transcendental equations determining the frequency spectra of standing spherical electromagnetic waves

    International Nuclear Information System (INIS)

    Pexton, R.L.; Steiger, A.D.

    1977-01-01

    Roots of the transcendental equations j/sub l/(lambda)/y/sub l/(lambda) =j/sub l/(αlambda) i/sub l/ (a)/i/sub j/(a)-j/sub l/(αlambda)/√vertical-barepsilonvertical-bar]/[y/sub l/ (αlambda) i/sub l/(a)/i/sub l/(a)-y/sub l/ (αlambda)/√vertical-barepsilonvertical-bar]/a=αlambda√vertical-barepsilonvertical-bar and [etaj/sub l/(eta)-lj/sub l/(eta)]/[etay/sub l/ (eta)-ly/sub l/(eta)]=vertical-barepsilonvertical-barβj/sub l/(β)/(1+vertical-barepsilonvertical-bar) -lj/sub l/(β)+√vertical-barepsilonvertical-barβj/sub l/(β) i/sub l/ (b)/(1+vertical-barepsilonvertical-bar) i/sub l/(b)]/[vertical-barepsilonvertical-barβy/sub l/ (β)/(1+vertical-barepsilonvertical-bar)-ly/sub l/(β)+√vertical-barepsilonvertical-barβy/sub l/(β) i/sub l/(b)/(1+vertical-barepsilonvertical-bar) i/sub l/(b)]/β =αeta/b=β√vertical-barepsilonvertical-bar for the spherical Bessel functions of the first and second kind, j/sub l/(x) and y/sub l/(x), and for the modified spherical Bessel functions of the first kind, i/sub l/(x), have been computed. The ranges for the parameters √vertical-barepsilonvertical-bar and α, the order l and the root index n are: √vertical-barepsilonvertical-bar=1.0, 10.0 100.0, 500.0; α=0.1(0.1)0.7; lambda=1(1)15; n=1(1)30

  7. The Transcendental Core of Correlationism

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    Paul J. Ennis

    2011-06-01

    Full Text Available In this paper I read Quentin Meillassoux’s critique of correlationism as truly a critique of transcendentalism and the transcendental method. I do so by considering the two correlationist rejoinders that occur in the English edition of Meillassoux’s After Finitude. The first rejoinder is from an idealist and relies on adumbrations for its defence. This reliance on adumbrations will be shown to be itself transcendentally implicated through Edmund Husserl’s Crisis of the European Sciences and Transcendental Phenomenology. I then turn to the explicit engagement with the transcendental method that arises from the transcendentalist’s rejoinder. Considered together I hope to convince the reader that the core of correlationism is transcendentalism.

  8. Honest Entertainment, Transcendental Jest

    DEFF Research Database (Denmark)

    Kluge, Sofie

    Through the centuries Don Quijote has delighted readers, inspired artists, stimulated thinkers, and helped form historians' perception of early modern Spain. It has, furthermore, played a major part in the development and theoretisation of one of the modern world’s most characteristic literary...... forms: the novel. In its own playful and non-systematic fashion, Honest Entertainment, Transcendental Jest. Six Essays on Don Quijote and Novelistic Theory explores the reception of Cervantes’ masterpiece with special attention to its significance for the theory of the novel. A book about books about...

  9. Transcendental Philosophy and its Transformations

    DEFF Research Database (Denmark)

    Ishihara, Yuko

    There is an interesting overlap between Heidegger and Nishida that has not gained attention in the literature. During the late 1920s, both philosophers looked to transcendental philosophy as a way to overcome the Western metaphysical tradition. Neither philosopher, however,simply accepted...... traditional forms of transcendental philosophy. Rather, both attempted to transform it from within. In this work, I aim to articulate the extent to which Heidegger and Nishidastill worked within a traditional transcendental framework and also the ways in which they attempt to transform transcendental...... philosophy. I argue that while Heidegger’s “hermeneutic” and Nishida’s “chorological” (I employ this term from Plato’s chōra) transformations have much in common, the latter is more radical than the former. Specifically, Nishida reveals the pre-reflective origin of transcendental reflection not in the pre...

  10. TRANSCENDENTAL ASPECTS OF GENDER

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    Volodymyr V. Khmel

    2014-06-01

    Full Text Available This paper aims to analyze the basic principles of gender philosophy applying methodological tools of communicative pragmatics; to demonstrate how gender construct can provide gender humanism formation as one of the ideals of democratic society; to specify gender glossary terms such as “gender democracy”, “gender equality” and “gender justice”. Methodology. In order to investigate a theoretical framework in feminist philosophy, methodological tools of communicative pragmatics and discursive ethics that were elaborated by modern German philosophers J. Habermas, K.-O. Apel for analyzing ethical gender principles and their legitimation ways have been used in this research. Scientific novelty. Based on methodological differences in concepts of J. Habermas and K.-O. Apel, two opposite approaches to gender concept analysis – rational and pragmatic (Habermas and transcendental conceptual (K.-O. Apel have been found out. The article helps to specify the framework of categories and concepts. According to the legitimation way of gender ethical theory it was discovered that such notions as “gender democracy”, “gender equality” and “gender justice” do not have the same meanings. According to the analysis of communicative action program and consensus, the “gender equality” concept by Habermas is an artificial social construct that is methodologically grounded in cognitivism and diminishes the possibilities of gender values legitimation. According to K.-O. Apel, the concept of “gender justice” is based on transcendental moral and ethical sense of opposite genders unity and does not discharge unequal distribution of responsibilities and any invasion as well as represents certain extent of their difference. Conclusions. Fast growing gender changes in the society face ageold drawbacks of moral and spiritual principles of communities, taking into account social and cultural, national and gender identity. Thorough understanding of

  11. Ballistic Limit Equation for Single Wall Titanium

    Science.gov (United States)

    Ratliff, J. M.; Christiansen, Eric L.; Bryant, C.

    2009-01-01

    Hypervelocity impact tests and hydrocode simulations were used to determine the ballistic limit equation (BLE) for perforation of a titanium wall, as a function of wall thickness. Two titanium alloys were considered, and separate BLEs were derived for each. Tested wall thicknesses ranged from 0.5mm to 2.0mm. The single-wall damage equation of Cour-Palais [ref. 1] was used to analyze the Ti wall's shielding effectiveness. It was concluded that the Cour-Palais single-wall equation produced a non-conservative prediction of the ballistic limit for the Ti shield. The inaccurate prediction was not a particularly surprising result; the Cour-Palais single-wall BLE contains shield material properties as parameters, but it was formulated only from tests of different aluminum alloys. Single-wall Ti shield tests were run (thicknesses of 2.0 mm, 1.5 mm, 1.0 mm, and 0.5 mm) on Ti 15-3-3-3 material custom cut from rod stock. Hypervelocity impact (HVI) tests were used to establish the failure threshold empirically, using the additional constraint that the damage scales with impact energy, as was indicated by hydrocode simulations. The criterion for shield failure was defined as no detached spall from the shield back surface during HVI. Based on the test results, which confirmed an approximately energy-dependent shield effectiveness, the Cour-Palais equation was modified.

  12. Intersubjetividad transcendental y mundo social

    OpenAIRE

    López Sáenz, Mª Carmen

    1994-01-01

    El tema de la intersubjetividad pone de relieve que las ciencias sociales necesitan a la filosofia, explica el origen de las relaciones sociales y ofrece una base para toda concepción de la subjetividad. La fenomenologia ha planteado esta cuestión desde sus raices; el solipsismo que se le atribuye es incompatible con el intento de Husserl de explicar la constitución del mundo por medio de la subjetividad transcendental. Husserl entendió la subjetividad transcendental como esencial a toda posi...

  13. Multigenre, Multiple Intelligences, and Transcendentalism.

    Science.gov (United States)

    Ruggieri, Colleen A.

    2002-01-01

    Explains an eleventh grade literature unit on Transcendentalism which employed a wide variety of supplemental materials and literary connections and which provided alternate assessment opportunities. Details how this unit revealed meaningful connections through comics, music, free reading, and multiple intelligences. Concludes that many students…

  14. Saha equation, single and two particle states

    Science.gov (United States)

    Kraeft, W. D.; Girardeau, M. D.; Strege, B.

    1990-01-01

    Single- and two-particle properties in a dense plasma are discussed in connection with their role in the mass action law for a partially ionized plasma. The two-particle-bound states are nearly density independent, while the continuum is essentially shifted. The single-particle states are damped, and their energy has a negative shift and a parabolic behavior for small momenta.

  15. Transcendental-function representation of Stark-modified hydrogenic states and atomic dipole polarizability

    Energy Technology Data Exchange (ETDEWEB)

    Bhattacharya, A.; Talukdar, B. [Department of Physics, Visva-Bharati University, Santiniketan (India); Banerji, G. [Mathematics Department, BU, Burdwan (India); Roy, U. [Theoretical Physics Department, IACS, Calcutta (India)

    1998-01-30

    A differential equation approach to the perturbation theoretic correction for excited hydrogenic states is introduced. The radial equations for the problem are solved in terms of known transcendental functions and the method to determine the complete primitive is discussed. The constructed perturbative correction to the wavefunction is adapted to evaluate the dipole polarizability of hydrogenic atoms. (author)

  16. Equilibration in Transcendental Meditation (TM

    Directory of Open Access Journals (Sweden)

    Hossein Bagheri

    2013-06-01

    Full Text Available Today in the realm of theoretical and applied humanities, the main concern is the ways to attain inner equilibrium than prosperity and the ways to discover it. Equilibrium, in some way, evokes the development of tolerance and a peaceful life which is mostly, a controversial issue in Christianity and with a few differences, in sophism controversies. The present meaning seeking human or modern and post-modern human is testing different anti-progress and prophetic theories for peace and inner equilibrium to end his adversary and outer contradictions. By the massive advertisement on meditation and Transcendental Meditation (TM and its effects on health and equanimity which has been started since 1960s in Europe and continued to spread everywhere with the help of global networks, it seems necessary to study the roots, vitality, necessity, levels and related techniques and compare it with Islamic religious and cultural concepts and investigate the positive and negative aspects of these practices. The present study aims at discovering whether the equilibrium or peace attained through TM is genuine and beatific.

  17. Isothermal equation of state of a lithium fluoride single crystal

    Energy Technology Data Exchange (ETDEWEB)

    Kim, K.Y.

    1975-01-01

    An isothermal equation of state of a LiF single crystal was determined from length change measurements of the specimen as a function of hydrostatic pressure up to approximately 7 kbars at 28 to 41/sup 0/C. The length change was measured with an accuracy of approximately 500 A by using a Fabry Perot type He--Ne laser interferometer for a 1-m long specimen at temperatures constant to less than 0.002/sup 0/C. Several two- and three-parameter equations of state were used in analyzing the measured pressure-volume data. The computer fit for each equation of state determines not only the value of its parameters but also the standard deviations associated with them and one dependent variable, either pressure or volume. With the parameters determined, the equations of state are extrapolated to approximately 5 megabars in order to see discrepancies. Using the Born model of ionic solids, two equations of state were derived both from a power law potential and from an exponential form for the repulsive energy of alkali metal halides and used to fit the pressure-volume data of a LiF single crystal. They are also extrapolated to approximately 5 megabars. The Birch's two-parameter equation and the Grover, Getting, and Kennedy equation are indistinguishable from the two equations of state derived from the Born model for pressures approximately equal to or less than 800 kbars within +-20 kbars. The above four equations of state also fit closely the Pagannone and Drickamer static compression data, the Christian shock wave data, and the Kormer et al. shock wave data. The isothermal bulk modulus and its first pressure derivative at atmospheric pressure and 28.83/sup 0/C are 664.5 +- 0.5 kbars and 5.40 +- 0.18, respectively, in close agreement with those values ultrasonically measured by R. A. Miller and C. S. Smith. (auth)

  18. Philosophy of biology: naturalistic or transcendental?

    Science.gov (United States)

    Kolen, Filip; Van de Vijver, Gertrudis

    2007-01-01

    The aim of this article is to clarify the meaning of a naturalistic position within philosophy of biology, against the background of an alternative view, founded on the basic insights of transcendental philosophy. It is argued that the apparently minimal and neutral constraints naturalism imposes on philosophy of science turn out to involve a quite heavily constraining metaphysics, due to the naturalism's fundamental neglect of its own perspective. Because of its intrinsic sensitivity to perspectivity and historicity, transcendental philosophy can avoid this type of hidden metaphysics.

  19. Semigroups of transcendental entire functions and their dynamics

    Indian Academy of Sciences (India)

    DINESH KUMAR

    Abstract. We investigate the dynamics of semigroups of transcendental entire func- tions using Fatou–Julia theory. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroups. We provide some condition for connectivity of the Julia set of the ...

  20. Husserl, Heidegger, and the Transcendental Dimension of ...

    African Journals Online (AJOL)

    denise

    intuition attaining the utmost significance in Husserl's phenomenology. In this regard, Husserl considers himself a Cartesian philosopher. For Husserl, “it was. Descartes rather than Kant who was the truly decisive thinker in modern philosophy; Kant had failed to fulfil even the promise of his own transcendental philosophy.

  1. Transcendental Dimension of the Reality and Systems

    Directory of Open Access Journals (Sweden)

    Miloš Vítek

    2017-06-01

    Full Text Available Transcend (origin Latin transcendere = climb means go beyond or exceed the limits of something abstract, esp. be beyond the range or grasp of human experience, reason, belief etc. Also be above and independence of, esp. of God exist apart from the limitations of the material universe. Surpass, excel or exceed in a special quality or attribute. Adjective transcendent denotes what is surpassing or excelling others of this kind, supreme beyond the range of human experience, reason, belief etc. In scholastic philosophy higher than included in any of ten Aristotle´s categories, in Kantian philosophy something not realizable in experience, in mathematics a transcendental expression is e.g. a non-algebraic function. Adjective transcendental chiefly in Kantian philosophy means presupposed in and necessary to experience, in modern sense superrational, superhuman, supernatural, metaphysical, vague, obscure; esp. in Emersonian thought regarding the divine as the guiding principle in humankind. Transcendentalism is the transcendental philosophy or thought, a system of this, esp. an exalted or visional language, a transcendent quality of character. These features are studied in context of the systems engineering.

  2. Delay-differential equations and the Painlevé transcendents

    Science.gov (United States)

    Grammaticos, B.; Ramani, A.; Moreira, I. C.

    1993-07-01

    We apply the recently proposed integrability criterion for differential-difference systems (that blends the classical Painlevé analysis with singularity confinement for discrete systems) to a class of first-order differential-delay equations. Our analysis singles out the family of bi-Riccati equations, as integrability candidates. Among these equations that pass the test some are integrable in a straightforward way (usually by reduction to a standard Riccati equation for some transformed variable) while the remaining ones define new hysterodifferential forms of the Painlevé transcendental equations.

  3. Transcendental Meditation and Assertive Training in the Treatment of Social Anxiety.

    Science.gov (United States)

    Wampler, Larry D.; Amira, Stephen B.

    Research indicates that transcendental meditation (TM) may provide relief from accumulated stress and render the meditator better able to cope with future stressful events. Single and combined TM and assertive training programs were compared for effectiveness in the treatment of socially anxious college students. A waiting-list group served as the…

  4. Kant's Transcendental Arguments as Conceptual Proofs | Stapleford ...

    African Journals Online (AJOL)

    The paper is an attempt to explain what a transcendental argument is for Kant. The interpretation is based on a reading of the “Discipline of Pure Reason,” sections 1 and 4, of the first Critique. The author first identifies several statements that Kant makes about the method of proof he followed in the “Analytic of Principles,” ...

  5. Do idealismo transcendental ao idealismo absoluto

    OpenAIRE

    Salvadori, Mateus

    2010-01-01

    Esta dissertação tem como objetivo investigar a superação do idealismo transcendental kantiano realizada pelo idealismo absoluto hegeliano. Os argumentos hegelianos em prol da superação do dualismo entre coisa-em-si e fenômeno serão detalhados e postos à prova. Enquanto Kant salienta que a metafísica como ciência é impossível, ou seja, os objetos que as Idéias transcendentais denotam estão além do espaço e do tempo, não existindo nenhum objeto no mundo sensível correspondentes a ela e, portan...

  6. Planck scale physics of the single-particle Schrödinger equation ...

    Indian Academy of Sciences (India)

    August 2002 physics pp. 375–383. Planck scale physics of the single-particle Schrödinger equation with gravitational self-interaction. VIKRAM SONI. National Physical Laboratory, K.S. Krishnan Marg, New Delhi 110 016, India. Abstract. We consider the modification of a single-particle Schrödinger equation by the inclusion.

  7. O transcendental encarnado: Merleau-Ponty e a Nouvelle Ontologie

    Directory of Open Access Journals (Sweden)

    Claudinei Aparecido de Freitas da Silva

    2011-06-01

    Full Text Available O fio condutor que perpassa o presente ensaio alinha o peculiar estatuto da problemática transcendental no horizonte aberto pela obra de Merleau-Ponty. Nessa direção, demarcaremos as linhas mestras desse novo discurso transcendental, isto é, sua inflexão ontologicamente decisiva enquanto crítica revisional das condições de todo conhecimento agenciada sob o enigma de nossa conaturalidade carnal e, portanto, corporal com o mundo e com o outro.The common thread running through this essay aligns the peculiar status of the transcendental problem on the horizon opened by the work of Merleau-Ponty. Along these lines, demarcating the guidelines of this new discourse transcendental, ie, its inflection ontologically decisive as revisional critical conditions of all knowledge brokered under the puzzle of our connaturality carnal, and therefore body with the world and each other.

  8. Scepticism & transcendental arguments: Some methodological reconsiderations

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    Westphal Kenneth R.

    2017-01-01

    Full Text Available Kant provided two parallel, sound proofs of mental content externalism; both prove this thesis: We human beings could not think of ourselves as persisting through apparent changes in what we (apparently experience - nor could we think of the apparent spatio-temporal world of objects, events and people - unless in fact we are conscious of some aspects of the actual spatio-temporal world and have at least some rudimentary knowledge of it. Such proofs turn, not on general facts about (or features of the world, but on appreciating various fundamental regards in which our finite human cognizance depends upon the world we inhabit. The ‘transcendental’ character of these analyses concerns identifying and appreciating various fundamental features of our finite form of human mindedness, and basic constraints upon, and prospects of, cognitive justification within the non-formal domain of human empirical knowledge. Such analyses and proofs have been developed in various ways, using distinctive strategies, not only by Kant, but also by Hegel, C.I. Lewis, Heidegger, Wittgenstein and Frederick Will. Here I examine and defend the methodological reflections required to understand, assess and appreciate such transcendental proofs, and why so few analytic epistemologists have found them persuasive or illuminating.

  9. A single model procedure for estimating tank calibration equations

    International Nuclear Information System (INIS)

    Liebetrau, A.M.

    1997-10-01

    A fundamental component of any accountability system for nuclear materials is a tank calibration equation that relates the height of liquid in a tank to its volume. Tank volume calibration equations are typically determined from pairs of height and volume measurements taken in a series of calibration runs. After raw calibration data are standardized to a fixed set of reference conditions, the calibration equation is typically fit by dividing the data into several segments--corresponding to regions in the tank--and independently fitting the data for each segment. The estimates obtained for individual segments must then be combined to obtain an estimate of the entire calibration function. This process is tedious and time-consuming. Moreover, uncertainty estimates may be misleading because it is difficult to properly model run-to-run variability and between-segment correlation. In this paper, the authors describe a model whose parameters can be estimated simultaneously for all segments of the calibration data, thereby eliminating the need for segment-by-segment estimation. The essence of the proposed model is to define a suitable polynomial to fit to each segment and then extend its definition to the domain of the entire calibration function, so that it (the entire calibration function) can be expressed as the sum of these extended polynomials. The model provides defensible estimates of between-run variability and yields a proper treatment of between-segment correlations. A portable software package, called TANCS, has been developed to facilitate the acquisition, standardization, and analysis of tank calibration data. The TANCS package was used for the calculations in an example presented to illustrate the unified modeling approach described in this paper. With TANCS, a trial calibration function can be estimated and evaluated in a matter of minutes

  10. Classification of All Single Travelling Wave Solutions to Calogero-Degasperis-Focas Equation

    International Nuclear Information System (INIS)

    Liu Chengshi

    2007-01-01

    Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation.

  11. A Study of Impulsive Multiterm Fractional Differential Equations with Single and Multiple Base Points and Applications

    Directory of Open Access Journals (Sweden)

    Yuji Liu

    2014-01-01

    Full Text Available We discuss the existence and uniqueness of solutions for initial value problems of nonlinear singular multiterm impulsive Caputo type fractional differential equations on the half line. Our study includes the cases for a single base point fractional differential equation as well as multiple base points fractional differential equation. The asymptotic behavior of solutions for the problems is also investigated. We demonstrate the utility of our work by applying the main results to fractional-order logistic models.

  12. Arqueology of the Transcendental Question. About Michel Foucault

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    Marco Díaz Marsá

    2013-07-01

    Full Text Available In the framework of a general analysis about the idea of «trascendental» in Foucault’s thought, and following an arqueological procedure, the aim will be to explain the general form of modern problematization, a form in whose framework a set of new questions could have been raised, one of them being the transcendental question, the subject of our study. We will try to show, first, the bond of necessity between the breaking of representation and the rising of the possibility of a transcendental questioning. Secondly, we will explore the transcendental area, which will be characterized, starting from a problematization of the articulation critique-metaphysics, as the transcendental field of a finite subject, as the region of critical facticity corresponding to a subject which is and, at the time, acts in a world. Finally we will present the closures of this dimension in two philosophical schematizations: the ones operating as «analytics of finitude» (anthropological schematization, and the ones as «metaphysics of the object» (reducing-objectifying layout of the transcendental question

  13. Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations.

    Science.gov (United States)

    Goings, Joshua J; Caricato, Marco; Frisch, Michael J; Li, Xiaosong

    2014-10-28

    Methods for fast and reliable computation of electronic excitation energies are in short supply, and little is known about their systematic performance. This work reports a comparison of several low-scaling approximations to the equation of motion coupled cluster singles and doubles (EOM-CCSD) and linear-response coupled cluster singles and doubles (LR-CCSD) equations with other single reference methods for computing the vertical electronic transition energies of 11 small organic molecules. The methods, including second order equation-of-motion many-body perturbation theory (EOM-MBPT2) and its partitioned variant, are compared to several valence and Rydberg singlet states. We find that the EOM-MBPT2 method was rarely more than a tenth of an eV from EOM-CCSD calculated energies, yet demonstrates a performance gain of nearly 30%. The partitioned equation-of-motion approach, P-EOM-MBPT2, which is an order of magnitude faster than EOM-CCSD, outperforms the CIS(D) and CC2 in the description of Rydberg states. CC2, on the other hand, excels at describing valence states where P-EOM-MBPT2 does not. The difference between the CC2 and P-EOM-MBPT2 can ultimately be traced back to how each method approximates EOM-CCSD and LR-CCSD. The results suggest that CC2 and P-EOM-MBPT2 are complementary: CC2 is best suited for the description of valence states while P-EOM-MBPT2 proves to be a superior O(N(5)) method for the description of Rydberg states.

  14. Intersubjectivitat transcendental i món social

    OpenAIRE

    López Sáenz, Mª Carmen

    1994-01-01

    El tema de la intersubjectivitat posa en relleu que les ciències socials necessiten a la filosofia, explica l'origen de les relacions socials i ofereix una base per a tota concepció de la subjectivitat.La fenomenologia ha plantejat aquesta qüestió des dels seus arrels; el solipsisme que se li atribueix és incompatible amb l'intent de Husserl d'explicar la constitució del món per mitjà de la subjectivitat transcendental.Husserl va entendre la subjectivitat transcendental com essencial a...

  15. Dynamics of certain class of critically bounded entire transcendental functions

    Science.gov (United States)

    Guru Prem Prasad, M.; Nayak, Tarakanta

    2007-05-01

    Let E denote the class of all transcendental entire functions for and an[greater-or-equal, slanted]0 for all n[greater-or-equal, slanted]0 such that f(x)>0 for x0. It is also shown that the Fatou set of f[lambda] is connected whenever it is an attracting basin and the immediate basin contains all the finite singular values of f[lambda]. Finally, a number of interesting examples of entire transcendental functions from the class E are discussed.

  16. A teoria do conhecimento de Kant : o idealismo transcendental

    OpenAIRE

    Silveira, Fernando Lang da

    2002-01-01

    A teoria do conhecimento de Kant - a filosofia transcendental ou idealismo transcendental - teve como objetivo justificar a possibilidade do conhecimento científico do século XVIII. Ela partiu da constatação de que nem o empirismo britânico, nem o racionalismo continental explicavam satisfatoriamente a ciência. Kant mostrou que apesar de o conhecimento se fundamentar na experiência, esta nunca se dá de maneira neutra, pois a ela são impostas as formas a priori da sensibilidade e do entendimen...

  17. A calderón-preconditioned single source combined field integral equation for analyzing scattering from homogeneous penetrable objects

    KAUST Repository

    Valdés, Felipe

    2011-06-01

    A new regularized single source equation for analyzing scattering from homogeneous penetrable objects is presented. The proposed equation is a linear combination of a Calderón-preconditioned single source electric field integral equation and a single source magnetic field integral equation. The equation is immune to low-frequency and dense-mesh breakdown, and free from spurious resonances. Unlike dual source formulations, this equation involves operator products that cannot be discretized using standard procedures for discretizing standalone electric, magnetic, and combined field operators. Instead, the single source equation proposed here is discretized using a recently developed technique that achieves a well-conditioned mapping from div- to curl-conforming function spaces, thereby fully respecting the space mapping properties of the operators involved, and guaranteeing accuracy and stability. Numerical results show that the proposed equation and discretization technique give rise to rapidly convergent solutions. They also validate the equation\\'s resonant free character. © 2006 IEEE.

  18. Inquiry-Based Learning of Transcendental Functions in Calculus

    Science.gov (United States)

    Ekici, Celil; Gard, Andrew

    2017-01-01

    In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for…

  19. The Effect of the Transcendental Meditation Technique on Anxiety Level

    Science.gov (United States)

    Dillbeck, Michael C.

    1977-01-01

    Two weeks of twice-daily practice of the Transcendental Meditation (TM) technique was compared with 2 weeks of twice-daily practice of passive relaxation as a means of reduction of anxiety, as measured by the Trait scale of the State-Trait Anxiety Inventory. (Editor)

  20. Is There a Need for Transcendental Arguments in Discourse Ethics?

    Science.gov (United States)

    Johnston, James Scott

    2016-01-01

    In this essay, James Scott Johnston examines Jürgen Habermas's transcendental justification of his discourse theory of morality. According to Johnston, the application of Habermas's theory to educational issues often assumes that this justification is a cogent one. However, if the theory is to provide reasoned and appropriate guidance for…

  1. Kant's 'Transcendental Exposition' of Space and Time in the ...

    African Journals Online (AJOL)

    DrNneka

    it does give us objective knowledge about the world of experience that science studies. The work considers ..... predicate form shows Kant's uncritical acceptance of Aristotelian logic and causes him to ignore statements that seem .... Kant holds that the “transcendental illusion” of pure reason rests on its dialectical inferences ...

  2. Semigroups of transcendental entire functions and their dynamics

    Indian Academy of Sciences (India)

    DINESH KUMAR

    realm of semigroups of rational and transcendental entire functions. The seminal work in this direction was done by Hinkkanen and Martin [10] related to semigroups of rational functions. In their paper, they extended the classical theory of the dynamics associated to the iteration of a rational function of one complex variable ...

  3. Strawson and Schaumann on the Metaphysics of Transcendental ...

    African Journals Online (AJOL)

    The paper is a limited defence of one of P. F. Strawson's least popular declarations about the nature of Kant's transcendental idealism. An attempt is made to relate Strawson's reading to an interpretative controversy that emerged in the years immediately following the publication of the first edition of the Critique of Pure ...

  4. Transcendental meditation for autism spectrum disorders? A perspective

    Directory of Open Access Journals (Sweden)

    David O. Black

    2015-12-01

    Full Text Available Anecdotal reports suggest that Transcendental Meditation (TM may be helpful for some children and young adults with autism spectrum disorders (ASDs. In this perspective piece, we present six carefully evaluated individuals with diagnosed ASDs, who appear to have benefitted from TM, and offer some thoughts as to how this technique might help such individuals.

  5. The vital role of transcendental truth in science.

    Science.gov (United States)

    Charlton, Bruce G

    2009-04-01

    I have come to believe that science depends for its long-term success on an explicit and pervasive pursuit of the ideal of transcendental truth. 'Transcendental' implies that a value is ideal and ultimate - it is aimed-at but can only imperfectly be known, achieved or measured. So, transcendental truth is located outside of science; beyond scientific methods, processes and peer consensus. Although the ultimate scientific authority of a transcendental value of truth was a view held almost universally by the greatest scientists throughout recorded history, modern science has all-but banished references to truth from professional scientific discourse - these being regarded as wishful, mystical and embarrassing at best, and hypocritical or manipulative at worst. With truth excluded, the highest remaining evaluation mechanism is 'professional consensus' or peer review - beyond which there is no higher court of appeal. Yet in Human accomplishment, Murray argues that cultures which foster great achievement need transcendental values (truth, beauty and virtue) to be a live presence in the culture; such that great artists and thinkers compete to come closer to the ideal. So a scientific system including truth as a live presence apparently performs better than a system which excludes truth. Transcendental truth therefore seems to be real in the pragmatic sense that it makes a difference. To restore the primacy of truth to science a necessary step would be to ensure that only truth-seekers were recruited to the key scientific positions, and to exclude from leadership those who are untruthful or exhibit insufficient devotion to the pursuit of truth. In sum, to remain anchored in its proper role, science should through 'truth talk' frequently be referencing normal professional practice to transcendental truth values. Ultimately, science should be conducted at every level, from top to bottom, on the basis of what Bronowski termed the 'habit of truth'. Such a situation currently

  6. Single-site Green function of the Dirac equation for full-potential electron scattering

    Energy Technology Data Exchange (ETDEWEB)

    Kordt, Pascal

    2012-05-30

    I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)

  7. Subspace Lang Conjecture and some Remarks on a transcendental ...

    Indian Academy of Sciences (India)

    24

    In 2004, Adamczewski, Bugeaud and Luca [2] provided a criterion for an irrational number to be a transcendental ... Though the answer is not as satisfactory as in the case of rational numbers, we do have some positive answer to ..... exists a subset T of S with |T| = ∞ such that jn = jm = j0 for all m, n ∈ T. Let n ∈ T be any ...

  8. Towards a Transcendental Critique of Feeling (A Response to Grenberg

    Directory of Open Access Journals (Sweden)

    Patrick Frierson

    2016-06-01

    Full Text Available This paper focuses on responding to Jeanine Grenberg’s claim that my discussion of Kant’s feeling of respect leaves no meaningful room for investigating feeling first-personally. I first make clear that I do think that feelings can be investigated first-personally, both in that they can be prospective reasons for action and in that – at least in Kant’s Critique of the Power of Judgment – there are feelings that we should have (for aesthetic reasons. I then show that at the time of writing the “Incentives” chapter of the second Critique, Kant had not yet determined an a priori basis for aesthetic (or affective normativity. On this basis, I argue that the “Incentives” chapter provides a sort of consolation prize for not (yet having an transcendental account of feeling. In that sense, it’s a properly transcendental analysis of feeling in which Kant examines feeling from within and a priori to show that there are good (moral reasons to have certain feelings. I end by acknowledging the extent to which, on this reading, I agree with Grenberg that Kant is doing a transcendentally significant form of phenomenology here, while I also highlight some remaining areas of disagreement.

  9. The free-electron laser - Maxwell's equations driven by single-particle currents

    Science.gov (United States)

    Colson, W. B.; Ride, S. K.

    1980-01-01

    It is shown that if single particle currents are coupled to Maxwell's equations, the resulting set of self-consistent nonlinear equations describes the evolution of the electron beam and the amplitude and phase of the free-electron-laser field. The formulation is based on the slowly varying amplitude and phase approximation, and the distinction between microscopic and macroscopic scales, which distinguishes the microscopic bunching from the macroscopic pulse propagation. The capabilities of this new theoretical approach become apparent when its predictions for the ultrashort pulse free-electron laser are compared to experimental data; the optical pulse evolution, determined simply and accurately, agrees well with observations.

  10. A single-equation study of US petroleum consumption: The role of model specificiation

    International Nuclear Information System (INIS)

    Jones, C.T.

    1993-01-01

    The price responsiveness of US petroleum consumption began to attract a great deal of attention following the unexpected and substantial oil price increases of 1973-74. There have been a number of large, multi-equation econometric studies of US energy demand since then which have focused primarily on estimating short run and long run price and income elasticities of individual energy resources (coal, oil, natural gas ampersand electricity) for various consumer sectors (residential, industrial, commercial). Following these early multi-equation studies there have been several single-equation studies of aggregate US petroleum consumption. When choosing an economic model specification for a single-equation study of aggregate US petroleum consumption, an easily estimated model that will provide unbiased price and income elasticity estimates and yield accurate forecasts is needed. Using Hendry's general-to-simple specification search technique and annual data to obtain a restricted, data-acceptable simplification of a general ADL model yielded GNP and short run price elasticities near the consensus estimates, but a long run price elasticity substantially smaller than existing estimates. Comparisons with three other seemingly acceptable simple-to-general models showed that popular model specifications often involve untested, unacceptable parameter restrictions. These models may also demonstrate poorer forecasting performance. Based on results, the general-to-simple approach appears to offer a more accurate methodology for generating superior forecast models of petroleum consumption and other energy use patterns

  11. Accurate analytic solution of chemical master equations for gene regulation networks in a single cell

    Science.gov (United States)

    Huang, Guan-Rong; Saakian, David B.; Hu, Chin-Kun

    2018-01-01

    Studying gene regulation networks in a single cell is an important, interesting, and hot research topic of molecular biology. Such process can be described by chemical master equations (CMEs). We propose a Hamilton-Jacobi equation method with finite-size corrections to solve such CMEs accurately at the intermediate region of switching, where switching rate is comparable to fast protein production rate. We applied this approach to a model of self-regulating proteins [H. Ge et al., Phys. Rev. Lett. 114, 078101 (2015), 10.1103/PhysRevLett.114.078101] and found that as a parameter related to inducer concentration increases the probability of protein production changes from unimodal to bimodal, then to unimodal, consistent with phenotype switching observed in a single cell.

  12. Single-cone finite difference scheme for the (2+1)D Dirac von Neumann equation

    Science.gov (United States)

    Pötz, Walter; Schreilechner, Magdalena

    2017-11-01

    An explicit finite difference scheme is presented for the von Neumann equation for (2+1)D Dirac fermions. It is founded upon a staggered space-time grid which ensures a single-cone energy dispersion and performs the time-derivative in one sweep using a three-step leap-frog procedure. It enables a space-time-resolved numerical treatment of the mixed-state dynamics of Dirac fermions within the effective single-particle density matrix formalism. Energy-momentum dispersion, stability and convergence properties are derived. Elementary numerical tests to demonstrate stability properties use parameters which pertain to topological insulator surface states. A method for the simulation of charge injection from an electric contact is presented and tested numerically. Potential extensions of the scheme to a Dirac-Lindblad equation, real-space-time Green's function formulations, and higher-order finite-difference schemes are discussed.

  13. On the difficulties of a single three-body Lippmann-Schwinger equation

    International Nuclear Information System (INIS)

    Sawada, Tatsuro; Miyagawa, Kazuya; Thushima, Kathuhide.

    1991-01-01

    First, we point out that the often quoted non-uniqueness argument on a single three-body Lippmann-Schwinger equation (the LS equation) is either not valid because the manipulation leading to it is not justifiable, or inconsequential because the non-uniqueness can easily be discerned and eliminated. Next, we discuss the property of the kernel with energy independent absorbing potentials (EIAP) of general forms. We find that the use of EIAP as in the CDCC approach dose not make the kernel compact. It remains non-compact no matter what we use for two-body potentials. Finally, we investigate in what sense the LS equation is solvable in terms of the CDCC approach. When the wave function inside the right-hand side (RHS) of the LS equation is restricted to a small CDCC model space, the difference between the RHS and the ordinary asymptotic form assumed in the approach is found to diverge asymptotically due to contributions from higher partial waves. We conclude that the CDCC solution cannot be claimed to be the solution to the LS equation, not unless it is restricted to a small model space. (author)

  14. Pseudospectral operational matrix for numerical solution of single and multiterm time fractional diffusion equation

    OpenAIRE

    GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD

    2016-01-01

    This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and fig...

  15. Time-domain single-source integral equations for analyzing scattering from homogeneous penetrable objects

    KAUST Repository

    Valdés, Felipe

    2013-03-01

    Single-source time-domain electric-and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis functions and a collocation testing procedure, thus allowing for a marching-on-in-time (MOT) solution scheme. Unlike dual-source formulations, single-source equations involve space-time domain operator products, for which spatial discretization techniques developed for standalone operators do not apply. Here, the spatial discretization of the single-source time-domain integral equations is achieved by using the high-order divergence-conforming basis functions developed by Graglia alongside the high-order divergence-and quasi curl-conforming (DQCC) basis functions of Valdés The combination of these two sets allows for a well-conditioned mapping from div-to curl-conforming function spaces that fully respects the space-mapping properties of the space-time operators involved. Numerical results corroborate the fact that the proposed procedure guarantees accuracy and stability of the MOT scheme. © 2012 IEEE.

  16. A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

    Science.gov (United States)

    Wapenaar, Kees

    2017-06-01

    A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.

  17. Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation

    International Nuclear Information System (INIS)

    Lim, S C; Teo, L P

    2009-01-01

    Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion

  18. Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation

    Science.gov (United States)

    Lim, S. C.; Teo, L. P.

    2009-08-01

    Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann-Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion.

  19. IBN ‘ARABI AND THE TRANSCENDENTAL UNITY OF RELIGIONS

    Directory of Open Access Journals (Sweden)

    Media Zainul Bahri

    2012-07-01

    Full Text Available This essay describes Ibn ‘Arabi’s comprehensive views, captured in his important Futuhat and Fusus, on the concept of wahdat al-adyan, the discrepancy of beliefs, and the Shari’ah as well as its juncture and its unity. Elaborated explanation in this paper is expected to result in a true understanding of this crucial issue, particularly the concept of religious pluralism in the discourse of Islamic studies. Ibn Arabi’ extensively  discusses religion in the sense of the “ideal” versus “historical” or “esoteric” versus “the exoteric”. Ibn ‘Arabi concludes that the absolute unity of religions may only occur within spiritual, ideal, or transcendental realm (or “esoteric”, which is beyond the formal form of religions. Hence, the transcendental unity of religions cannot be found in the formal form of religions nor in the shari’ah.[Artikel ini mengulas pandangan Ibn ‘Arabi’ mengenai wahdat al-adyan seperti dijelaskan dalam dua bukunya; Futuhat dan Fusus, dan perbedaan dan kesamaan antara iman dan shariah. Diharapkan diskusi artikel ini berkontribusi dalam kajian pluralisme, utamanya dalam disiplin studi Islam. Dalam diskusinya, Ibn Arabi’  menjelaskan perbedaan ‘ideal’ dan ‘historikal’ atau antara ‘esoterik’ dan ‘eksoterik’. Ibn ‘Arabi berpendapat bahwa kemanunggalan agama-agama dapat dicapai melalui spiritualitas, ideal, atau dimensi transcendental (esoterik yang ada di luar tampilan formal agama-agama. Dengan kata lain, kemanunggalan tersebut tidak akan ditemukan pada shari’ah.

  20. The embodied transcendental: a Kantian perspective on neurophenomenology

    Directory of Open Access Journals (Sweden)

    Omar Timothy Khachouf

    2013-09-01

    Full Text Available Neurophenomenology is a research programme aimed at bridging the explanatory gap between first-person subjective experience and neurophysiological third-person data, through an embodied and enactive approach to the biology of consciousness. The present proposal attempts to further characterize the bodily basis of the mind by adopting a naturalistic view of the phenomenological concept of intentionality as the a priori invariant character of any lived experience. Building on the Kantian definition of transcendentality as what concerns the a prioriformal structures of the subject’s mind and as a precondition for the very possibility of human knowledge, we will suggest that this transcendental core may in fact be rooted in biology and can be examined within an extension of the theory of autopoiesis. The argument will be first clarified by examining its application to previously proposed elementary autopoietic models, to the bacterium, and to the immune system; it will be then further substantiated and illustrated by examining the mirror-neuron system and the default mode network as biological instances exemplifying the enactive nature of knowledge, and by discussing the phenomenological aspects of selected neurological conditions (neglect, schizophrenia. In this context, the free-energy principle proposed recently by Karl Friston will be briefly introduced as a rigorous, neurally-plausible framework that seems to accomodate optimally these ideas. While our approach is biologically-inspired, we will maintain that lived first-person experience is still critical for a better understanding of brain function, based on our argument that the former and the latter share the same transcendental structure. Finally, the role that disciplined contemplative practices can play to this aim, and an interpretation of the cognitive processes taking place during meditation under this perspective, will be also discussed.

  1. The embodied transcendental: a Kantian perspective on neurophenomenology.

    Science.gov (United States)

    Khachouf, Omar T; Poletti, Stefano; Pagnoni, Giuseppe

    2013-01-01

    Neurophenomenology is a research programme aimed at bridging the explanatory gap between first-person subjective experience and neurophysiological third-person data, through an embodied and enactive approach to the biology of consciousness. The present proposal attempts to further characterize the bodily basis of the mind by adopting a naturalistic view of the phenomenological concept of intentionality as the a priori invariant character of any lived experience. Building on the Kantian definition of transcendentality as "what concerns the a priori formal structures of the subject's mind" and as a precondition for the very possibility of human knowledge, we will suggest that this transcendental core may in fact be rooted in biology and can be examined within an extension of the theory of autopoiesis. The argument will be first clarified by examining its application to previously proposed elementary autopoietic models, to the bacterium, and to the immune system; it will be then further substantiated and illustrated by examining the mirror-neuron system and the default mode network as biological instances exemplifying the enactive nature of knowledge, and by discussing the phenomenological aspects of selected neurological conditions (neglect, schizophrenia). In this context, the free-energy principle proposed recently by Karl Friston will be briefly introduced as a rigorous, neurally-plausible framework that seems to accomodate optimally these ideas. While our approach is biologically-inspired, we will maintain that lived first-person experience is still critical for a better understanding of brain function, based on our argument that the former and the latter share the same transcendental structure. Finally, the role that disciplined contemplative practices can play to this aim, and an interpretation of the cognitive processes taking place during meditation under this perspective, will be also discussed.

  2. Should researchers use single indicators, best indicators, or multiple indicators in structural equation models?

    Directory of Open Access Journals (Sweden)

    Hayduk Leslie A

    2012-10-01

    Full Text Available Abstract Background Structural equation modeling developed as a statistical melding of path analysis and factor analysis that obscured a fundamental tension between a factor preference for multiple indicators and path modeling’s openness to fewer indicators. Discussion Multiple indicators hamper theory by unnecessarily restricting the number of modeled latents. Using the few best indicators – possibly even the single best indicator of each latent – encourages development of theoretically sophisticated models. Additional latent variables permit stronger statistical control of potential confounders, and encourage detailed investigation of mediating causal mechanisms. Summary We recommend the use of the few best indicators. One or two indicators are often sufficient, but three indicators may occasionally be helpful. More than three indicators are rarely warranted because additional redundant indicators provide less research benefit than single indicators of additional latent variables. Scales created from multiple indicators can introduce additional problems, and are prone to being less desirable than either single or multiple indicators.

  3. The problems of typology of Transcendental Meditation movement (TM

    Directory of Open Access Journals (Sweden)

    Victoria Tikhonova

    2018-12-01

    Full Text Available One of the most important tasks of present-day religious studies is developing a united and detailed systematisation of new religious movements. With the aim of fi nding out what place the Transcendental Meditation movement could occupy in it, this article considers various characteristics of the theory, practice and social peculiarities of this movement, off ered by researchers of new religious movements and representatives of the organisation itself. This paper also reveals problems of typology, the main of which is that diff erent opinions about the relationship of ideas of Hinduism with the elements of modern science in the teachings of Maharishi Mahesh Yogi are designated in scientifi c and educational literature by diff erent terms, which, moreover, are ambiguous. In the conclusion of the article, variants of the stratifi ed typology are off ered, revealing a complete picture of the origin and transformation of the theories and practices of the Transcendental Meditation movement. The fi rst variant is aimed at inclusion in the unifi ed classifi cation of religions, which is supposed to be extended according to the principle applied by other scientifi c systems that take into account several levels of generalisation. The second variant can be employed in cataloguing new religious movements.

  4. Kramers-Moyal expansion for stochastic differential equations with single and multiple delays: Applications to financial physics and neurophysics

    International Nuclear Information System (INIS)

    Frank, T.D.

    2007-01-01

    We present a generalized Kramers-Moyal expansion for stochastic differential equations with single and multiple delays. In particular, we show that the delay Fokker-Planck equation derived earlier in the literature is a special case of the proposed Kramers-Moyal expansion. Applications for bond pricing and a self-inhibitory neuron model are discussed

  5. Parameter estimation in neuronal stochastic differential equation models from intracellular recordings of membrane potentials in single neurons

    DEFF Research Database (Denmark)

    Ditlevsen, Susanne; Samson, Adeline

    2016-01-01

    Dynamics of the membrane potential in a single neuron can be studied by estimating biophysical parameters from intracellular recordings. Diffusion processes, given as continuous solutions to stochastic differential equations, are widely applied as models for the neuronal membrane potential evolut...

  6. The effect of Transcendental Meditation on self-efficacy, perceived stress, and quality of life in mothers in Uganda.

    Science.gov (United States)

    Goldstein, Leslee; Nidich, Sanford I; Goodman, Rachel; Goodman, David

    2018-03-01

    Vulnerable women living in poverty in Uganda, who are primarily single, illiterate mothers, face high levels of physical and psychological stress. Our study assessed the impact of the Transcendental Meditation® (TM®) technique on self-efficacy, perceived stress, and mental and physical quality of life of these women. This single-blind controlled study involved eighty-one women who were assigned to either practice of the Transcendental Meditation program (n = 42) or wait-list (delayed start) control group (n = 39). Participants learned the Transcendental Meditation program over five sessions, then practiced at home for twenty minutes twice a day, and attended twice monthly group meetings over a three-month period. The primary outcome measure was self-efficacy using the General Self-Efficacy Scale (GSES). Perceived stress using Cohen's Perceived Stress Scale, and physical and mental quality of life using subscales of the Medical Outcomes Survey (MOS, HIV version) were secondary outcome measures. Significant improvements were shown in self-efficacy (p stress (p 88%. This is the first controlled study to demonstrate the effect of TM in the daily lives of mothers living in impoverished conditions. Further questionnaires were administered to participants at 8 months and at 36 months with questions about changes they may have experienced in their daily life since starting TM. "Yes", "No" self-reported answers suggested that the women experienced improved health, improved relationships with others, and increased employment rates. These findings taken as a whole have important implications for developing self-efficacy, improving mental and physical quality of life, and reducing stress in the lives of these vulnerable women.

  7. Finite state projection based bounds to compare chemical master equation models using single-cell data

    Energy Technology Data Exchange (ETDEWEB)

    Fox, Zachary [School of Biomedical Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States); Neuert, Gregor [Department of Molecular Physiology and Biophysics, Vanderbilt University School of Medicine, Nashville, Tennessee 37232 (United States); Department of Pharmacology, School of Medicine, Vanderbilt University, Nashville, Tennessee 37232 (United States); Department of Biomedical Engineering, Vanderbilt University School of Engineering, Nashville, Tennessee 37232 (United States); Munsky, Brian [School of Biomedical Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States); Department of Chemical and Biological Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States)

    2016-08-21

    Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value. These bounds allow one to discriminate rigorously between models and with a minimum level of computational effort. In practice, these bounds can be incorporated into stochastic model identification and parameter inference routines, which improve the accuracy and efficiency of endeavors to analyze and predict single-cell behavior. We demonstrate the applicability of our approach using simulated data for three example models as well as for experimental measurements of a time-varying stochastic transcriptional response in yeast.

  8. The effect of the Transcendental Meditation technique on anxiety level.

    Science.gov (United States)

    Dillbeck, M C

    1977-10-01

    Two weeks of twice-daily practice of the transcendental Meditation (TM) technique was compared with 2 weeks of twice-daily practice of passive relaxation as a means of reduction of anxiety, as measured by the Trait scale of the State-Trait Anxiety Inventory. Thirty-three graduate and undergraduate students were assigned randomly to a relaxation group and a TM group. After a 2-week experimental interval, the relaxation and meditation Ss, as well as between conditions of the relaxation-mediation group; TM was significantly more effective in reducing anxiety level. Thus, the anxiety-reducing effect of the practice of TM cannot be attributed merely to sitting quietly twice daily, although additional research must determine the extent to which S expectations for change contributed to this effect.

  9. Spin-curvature interaction from curved Dirac equation: Application to single-wall carbon nanotubes

    Science.gov (United States)

    Zhang, Kai; Zhang, Erhu; Chen, Huawei; Zhang, Shengli

    2017-06-01

    The spin-curvature interaction (SCI) and its effects are investigated based on curved Dirac equation. Through the low-energy approximation of curved Dirac equation, the Hamiltonian of SCI is obtained and depends on the geometry and spinor structure of manifold. We find that the curvature can be considered as field strength and couples with spin through Zeeman-like term. Then, we use dimension reduction to derive the local Hamiltonian of SCI for cylinder surface, which implies that the effective Hamiltonian of single-wall carbon nanotubes results from the geometry and spinor structure of lattice and includes two types of interactions: one does not break any symmetries of the lattice and only shifts the Dirac points for all nanotubes, while the other one does and opens the gaps except for armchair nanotubes. At last, analytical expressions of the band gaps and the shifts of their positions induced by curvature are given for metallic nanotubes. These results agree well with experiments and can be verified experimentally.

  10. THERMODYNAMIC PROPERTIES OF NONAQUEOUS SINGLE SALT SOLUTIONS USING THE Q-ELECTROLATTICE EQUATION OF STATE

    Directory of Open Access Journals (Sweden)

    A. Zuber

    2015-09-01

    Full Text Available AbstractThe correlation of thermodynamic properties of nonaqueous electrolyte solutions is relevant to design and operation of many chemical processes, as in fertilizer production and the pharmaceutical industry. In this work, the Q-electrolattice equation of state (EOS is used to model vapor pressure, mean ionic activity coefficient, osmotic coefficient, and liquid density of sixteen methanol and ten ethanol solutions containing single strong 1:1 and 2:1 salts. The Q-electrolattice comprises the lattice-based Mattedi-Tavares-Castier (MTC EOS, the Born term and the explicit MSA term. The model requires two adjustable parameters per ion, namely the ionic diameter and the solvent-ion interaction energy. Predictions of osmotic coefficient at 298.15 K and liquid density at different temperatures are also presented.

  11. Using Transcendental Phenomenology to Explore the “Ripple Effect” in a Leadership Mentoring Program

    Directory of Open Access Journals (Sweden)

    Tammy Moerer-Urdahl

    2004-06-01

    Full Text Available Several approaches exist for organizing and analyzing data in a phenomenological qualitative study. Transcendental phenomenology, based on principles identified by Husserl (1931 and translated into a qualitative method by Moustakas (1994, holds promise as a viable procedure for phenomenological research. However, to best understand the approach to transcendental phenomenology, the procedures need to be illustrated by a qualitative study that employs this approach. This article first discusses the procedures for organizing and analyzing data according to Moustakas (1994. Then it illustrates each step in the data analysis procedure of transcendental phenomenology using a study of reinvestment or the “ripple effect” for nine individuals who have participated in a youth leadership mentoring program from the 1970s to the present. Transcendental phenomenology works well for this study as this methodology provides logical, systematic, and coherent design elements that lead to an essential description of the experience.

  12. A new definition of a correlation equation for single collector efficiency

    Science.gov (United States)

    Messina, Francesca; Sethi, Rajandrea

    2014-05-01

    The transport and deposition of colloidal particles in porous media are important phenomena involved in many environmental and engineering problems as, for instance, the use of micro- and nanoscale zerovalent iron, a promising reagent in the field of groundwater remediation [1]. Particle transport and deposition in the proximity of injection or pumping wells and in porous media in general may also be relevant in other fields of chemical and petroleum engineering. Mathematical models able to predict particles transport and deposition in porous media are often needed in order to design field applications. The basic concept of these models is the single collector efficiency η, which predicts particles deposition onto a single grain of a complex porous medium in terms of probability that an approaching particle would be retained on a solid grain. Many different approaches and equations exist in the literature, however most of them are valid only under specific conditions (eg. specific range of flow rate, particle size, etc.), and predict, for certain parametric conditions, efficiency values exceeding unity, which is, for an efficiency concept, a contradiction [2][3]. The objectives of this study are to analyze the causes of the failure of the existing models in predicting the deposition rate in certain conditions and to modify the definition of collector efficiency in order to have a more general equation. The definition of collector efficiency, first proposed by Yao at al. [4], is based on the particles deposition onto a spherical grain (the collector) in an infinite domain. It is defined as the ration between the flux of particles that deposit on the grain and the total amount of particles that could reach the collector by advective flux from an area equal to the projection of the spherical grain itself. In the present work Yao's model has been implemented by COMSOL Multiphysics and solved with an Eulerian approach; particles deposition simulations were run. From

  13. Using Transcendental Phenomenology to Explore the “Ripple Effect” in a Leadership Mentoring Program

    OpenAIRE

    Tammy Moerer-Urdahl; John W. Creswell

    2004-01-01

    Several approaches exist for organizing and analyzing data in a phenomenological qualitative study. Transcendental phenomenology, based on principles identified by Husserl (1931) and translated into a qualitative method by Moustakas (1994), holds promise as a viable procedure for phenomenological research. However, to best understand the approach to transcendental phenomenology, the procedures need to be illustrated by a qualitative study that employs this approach. This article first discuss...

  14. Health technology assessment demonstrates efficient health promotion bu Transcendental Meditation (TM)

    DEFF Research Database (Denmark)

    Larsen, Torben

    2002-01-01

    BACKGROUND/OBJECTIVES: Health Technology Assessment of mantrameditation implemented as Transcendental Meditation (TM) METHODS: MEDLINE contains October 2001 335 titles on 'Transcendental Meditation' including various metaanalyses and a series of randomised, controlled trials: In summary...... mantrameditation (TM) is evidenced to produce a wakeful, hypometabolic state (in-depth-relaxation) independent of personality or individual mantras. A general metaanalysis summarizes the long-termed meditation effects as (1) a low baseline function; (2) release of stress and anxiety empowering self...

  15. Analysis and parameter identification for characteristic equations of single- and double-effect absorption chillers by means of multivariable regression

    DEFF Research Database (Denmark)

    Puig Arnavat, Maria; López-Villada, Jesús; Bruno, Joan Carles

    2010-01-01

    of the characteristic equation method developed by Kühn and Ziegler (2005) is the simplest and that it provides similar or better accuracy than the other approach. This selected approach has been used to fit catalogue and experimental data of single-effect chillers and has been extended to double-effect commercial......Two approaches to the characteristic equation method have been compared in order to find a simple model that best describes the performance of thermal chillers. After comparing the results obtained using experimental data from a single-effect absorption chiller, we concluded that the adaptation...

  16. Wave propagation speeds and source term influences in single and integral porosity shallow water equations

    Directory of Open Access Journals (Sweden)

    Ilhan Özgen

    2017-10-01

    Full Text Available In urban flood modeling, so-called porosity shallow water equations (PSWEs, which conceptually account for unresolved structures, e.g., buildings, are a promising approach to addressing high CPU times associated with state-of-the-art explicit numerical methods. The PSWE can be formulated with a single porosity term, referred to as the single porosity shallow water model (SP model, which accounts for both the reduced storage in the cell and the reduced conveyance, or with two porosity terms: one accounting for the reduced storage in the cell and another accounting for the reduced conveyance. The latter form is referred to as an integral or anisotropic porosity shallow water model (AP model. The aim of this study was to analyze the differences in wave propagation speeds of the SP model and the AP model and the implications of numerical model results. First, augmented Roe-type solutions were used to assess the influence of the source terms appearing in both models. It is shown that different source terms have different influences on the stability of the models. Second, four computational test cases were presented and the numerical models were compared. It is observed in the eigenvalue-based analysis as well as in the computational test cases that the models converge if the conveyance porosity in the AP model is close to the storage porosity. If the porosity values differ significantly, the AP model yields different wave propagation speeds and numerical fluxes from those of the BP model. In this study, the ratio between the conveyance and storage porosities was determined to be the most significant parameter.

  17. EEG microstates during different phases of Transcendental Meditation practice.

    Science.gov (United States)

    Faber, Pascal L; Travis, Frederick; Milz, Patricia; Parim, Niyazi

    2017-08-01

    Two phases of Transcendental Meditation (TM)-transcending and undirected mentation-were compared to each other and to task-free resting using multichannel EEG recorded from 20 TM practitioners. An EEG microstate analysis identified four classes of microstates which were labeled A, B, C and D, based on their similarity to previously published classes. For each class of microstates, mean duration, coverage and occurrence were computed. Resting and transcending differed from undirected mentation with decreased prominence of Class A and increased prominence of Class D microstates. In addition, transcending showed decreased prominence of Class C microstates compared to undirected mentation. Based on previous findings on the functional significance of the microstate classes, the results indicate an increased reference to reality and decreased visualization during resting and transcending compared to undirected mentation. Also, our results indicate decreased saliency of internally generated mentations during transcending compared to undirected mentation reflecting a more detached and less evaluative processing. It is proposed that the continuous cycling through these two phases of meditation during a TM session might facilitate and train the flexible modulation of the parameters of these microstates of these particular classes which are known to be altered in psychiatric disorders. This might promote beneficial stabilizing effects for the practitioner of TM.

  18. Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential

    Science.gov (United States)

    Cipolatti, R.; de Macedo Lira, Y.; Trallero-Giner, C.

    2018-03-01

    We consider a generalized nonlinear Schrödinger equation (GNLS) with a single power nonlinearity of the form λ ≤ft\\vert \\varphi \\right\\vert p , with p  >  0 and λ\\in{R} , in the presence of a harmonic confinement. We report the conditions that p and λ must fulfill for the existence and uniqueness of ground states of the GNLS. We discuss the Cauchy problem and summarize which conditions are required for the nonlinear term λ ≤ft\\vert \\varphi \\right\\vert p to render the ground state solutions orbitally stable. Based on a new variational method we provide exact formulæ for the minimum energy for each index p and the changing range of values of the nonlinear parameter λ. Also, we report an approximate close analytical expression for the ground state energy, performing a comparative analysis of the present variational calculations with those obtained by a generalized Thomas-Fermi approach, and soliton solutions for the respective ranges of p and λ where these solutions can be implemented to describe the minimum energy.

  19. Semiclassical dye-laser equations and the unidirectional single-frequency operation

    Science.gov (United States)

    Fu, Hong; Haken, H.

    1987-11-01

    A semiclassical description for dye lasers is proposed, where the energy-level diagram of the dye molecule is assumed to consist of a continuous bandlike ground state and an excited singlet state. Unidirectional single-frequency (s.f.) operation is discussed. The linear-stability analysis for this operation reveals a very low threshold instability, which may appear generally in practical lasers. The ratio of the instability threshold to the lasing threshold may be of any value greater than 1, depending mainly on the bandwidth and the distribution of the dipole moments on the band, but it is independent of the cavity loss. This instability may account for that observed in recent experiments by Hillman, Krasinki, Boyd, and Stroud [Phys. Rev. Lett. 52, 1605 (1984)]. A general approach to analyzing the linear stability of the s.f. operation of the Maxwell-Bloch equations is also proposed, which states that only the eigenvalues of a 2×2 matrix are relevant: one concerns the stability of the s.f. operation near the lasing threshold, the other determines the instability threshold of this operation.

  20. Orbital free DFT versus single density equation: a perspective through quantum domain behavior of a classically chaotic system.

    Science.gov (United States)

    Chakraborty, Debdutta; Kar, Susmita; Chattaraj, Pratim Kumar

    2015-12-21

    The orbital free density functional theory and the single density equation approach are formally equivalent. An orbital free density based quantum dynamical strategy is used to study the quantum-classical correspondence in both weakly and strongly coupled van der Pol and Duffing oscillators in the presence of an external electric field in one dimension. The resulting quantum hydrodynamic equations of motion are solved through an implicit Euler type real space method involving a moving weighted least square technique. The Lagrangian framework used here allows the numerical grid points to follow the wave packet trajectory. The associated classical equations of motion are solved using a sixth order Runge-Kutta method and the Ehrenfest dynamics is followed through the solution of the time dependent Schrodinger equation using a time dependent Fourier Grid Hamiltonian technique. Various diagnostics reveal a close parallelism between classical regular as well as chaotic dynamics and that obtained from the Bohmian mechanics.

  1. Empirical Equation Based Chirality (n, m Assignment of Semiconducting Single Wall Carbon Nanotubes from Resonant Raman Scattering Data

    Directory of Open Access Journals (Sweden)

    Md Shamsul Arefin

    2012-12-01

    Full Text Available This work presents a technique for the chirality (n, m assignment of semiconducting single wall carbon nanotubes by solving a set of empirical equations of the tight binding model parameters. The empirical equations of the nearest neighbor hopping parameters, relating the term (2n, m with the first and second optical transition energies of the semiconducting single wall carbon nanotubes, are also proposed. They provide almost the same level of accuracy for lower and higher diameter nanotubes. An algorithm is presented to determine the chiral index (n, m of any unknown semiconducting tube by solving these empirical equations using values of radial breathing mode frequency and the first or second optical transition energy from resonant Raman spectroscopy. In this paper, the chirality of 55 semiconducting nanotubes is assigned using the first and second optical transition energies. Unlike the existing methods of chirality assignment, this technique does not require graphical comparison or pattern recognition between existing experimental and theoretical Kataura plot.

  2. A note on Chudnovskyʼs Fuchsian equations

    Science.gov (United States)

    Brezhnev, Yurii V.

    We show that four exceptional Fuchsian equations, each determined by the four parabolic singularities, known as the Chudnovsky equations, are transformed into each other by algebraic transformations. We describe equivalence of these equations and their counterparts on tori. The latters are the Fuchsian equations on elliptic curves and their equivalence is characterized by transcendental transformations which are represented explicitly in terms of elliptic and theta functions.

  3. Planck scale physics of the single-particle Schrödinger equation ...

    Indian Academy of Sciences (India)

    ... t ) is the wave function and is the mass of the particle. This leads to a nonlinear equation, the 'Newton–Schrödinger' equation, which has been found to possess stationary self-bound solutions, whose energy can be determined using an asymptotic method. We find that such a particle strongly violates the superposition ...

  4. Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures

    Science.gov (United States)

    Pötz, Walter

    2017-11-01

    A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

  5. Real time quantitative phase microscopy based on single-shot transport of intensity equation (ssTIE) method

    Science.gov (United States)

    Yu, Wei; Tian, Xiaolin; He, Xiaoliang; Song, Xiaojun; Xue, Liang; Liu, Cheng; Wang, Shouyu

    2016-08-01

    Microscopy based on transport of intensity equation provides quantitative phase distributions which opens another perspective for cellular observations. However, it requires multi-focal image capturing while mechanical and electrical scanning limits its real time capacity in sample detections. Here, in order to break through this restriction, real time quantitative phase microscopy based on single-shot transport of the intensity equation method is proposed. A programmed phase mask is designed to realize simultaneous multi-focal image recording without any scanning; thus, phase distributions can be quantitatively retrieved in real time. It is believed the proposed method can be potentially applied in various biological and medical applications, especially for live cell imaging.

  6. Dynamics of single-bubble sonoluminescence. An alternative approach to the Rayleigh–Plesset equation

    Science.gov (United States)

    de Barros, Ana L. F.; Nogueira, Álvaro L. M. A.; Paschoal, Ricardo C.; Portes, Dirceu, Jr.; Rodrigues, Hilario

    2018-03-01

    Sonoluminescence is the phenomenon in which acoustic energy is (partially) transformed into light as a bubble of gas collapses inside a liquid medium. One particular model used to explain the motion of the bubble’s wall forced by acoustic pressure is expressed by the Rayleigh–Plesset equation, which can be obtained from the Navier–Stokes equation. In this article, we describe an alternative approach to derive the Rayleigh–Plesset equation based on Lagrangian mechanics. This work is addressed mainly to undergraduate students and teachers. It requires knowledge of calculus and of many concepts from various fields of physics at the intermediate level.

  7. New differential equations for on-shell loop integrals

    CERN Document Server

    Drummond, James M; Trnka, Jaroslav

    2011-01-01

    We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several infinite series of integrals satisfying such iterative differential equations. The differential operators we use are best written using momentum twistor space. The use of the latter was advocated in recent papers discussing loop integrals in N=4 super Yang-Mills. One of our motivations is to provide a tool for deriving analytical results for scattering amplitudes in this theory. We show that the integrals needed for planar MHV amplitudes up to two loops can be thought of as deriving from a single master topology. The master integral satisfies our differential equations, and so do most of the reduced integrals. A consequence of the differential equations is that the integrals we discuss are not arbitrarily complicated transcendental functions. For two specific two-loop integr...

  8. Mindfulness-Based Stress Reduction and Transcendental Meditation: Current State of Research

    Directory of Open Access Journals (Sweden)

    Adam Holt

    2015-04-01

    Full Text Available This article summarizes the current state of meditation research, specifically focusing on mindfulness-based stress reduction and transcendental meditation. Despite significant methodological problems with the studies reported to date on the subject, there is consistent evidence that meditation can produce changes in the nervous system and physiology of the meditator, and can help with various psychological markers of well-being. Regarding improvement in specific clinical diseases, research is generally mixed and preliminary. Strong recommendations cannot be made based on current evidence, and further studies are needed. In general, there is a stronger body of evidence supporting mindfulness-based stress reduction than for transcendental meditation.

  9. Modeling and analysis of surface potential of single gate fully depleted SOI MOSFET using 2D-Poisson's equation

    Science.gov (United States)

    Mani, Prashant; Tyagi, Chandra Shekhar; Srivastav, Nishant

    2016-03-01

    In this paper the analytical solution of the 2D Poisson's equation for single gate Fully Depleted SOI (FDSOI) MOSFET's is derived by using a Green's function solution technique. The surface potential is calculated and the threshold voltage of the device is minimized for the low power consumption. Due to minimization of threshold voltage the short channel effect of device is suppressed and after observation we obtain the device is kink free. The structure and characteristics of SingleGate FDSOI MOSFET were matched by using MathCAD and silvaco respectively.

  10. Single Peak Soliton and Periodic Cusp Wave of the Generalized Schrodinger-Boussinesq Equations

    Science.gov (United States)

    Qiao, Li-Jing; Tang, Sheng-Qiang; Zhao, Hai-Xia

    2015-06-01

    In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schrödinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schrödinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth soliton and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Supported by National Natural Science Foundation of China under Grant Nos. 11361017, 11161013 and Natural Science Foundation of Guangxi under Grant Nos. 2012GXNSFAA053003, 2013GXNSFAA019010, and Program for Innovative Research Team of Guilin University of Electronic Technology

  11. Psychotherapeutic Effects of Transcendental Meditation with Controls for Expectation of Relief and Daily Sitting

    Science.gov (United States)

    Smith, Jonathan C.

    1976-01-01

    Two experiments were conducted to isolate the trait-anxiety-reducing effects of transcendental meditation (TM) from expectation of relief and the concomitant ritual of sitting twice daily. The results strongly support the conclusion that the crucial therapeutic component of TM is not the TM exercise. (Author)

  12. Reclaiming the Power of Subversive Language in Romantic and Transcendental Literature

    Science.gov (United States)

    Nugent, Kelly Ann

    2004-01-01

    A high school teacher tries to eliminate the obstacles to subversive teaching in public schools by asking them to design schools that embodied the principles of learning suggested by the romantic and transcendental writers like Emily Dickinson, Ralph Waldo Emerson, Edgar Allan Poe, Henry David Thoreau, and Walt Whitman. It helps the students…

  13. The Effects of Behavior Therapy, Self-Relaxation, and Transcendental Meditation on Cardiovascular Stress Response.

    Science.gov (United States)

    Puente, Antonio E.; Beiman, Irving

    1980-01-01

    Compared Behavior Therapy (BT), self-relaxation (SR), transcendental meditation (TM), and a waiting-list control group (WL) on measures of cardiovascular and subjective stress response. Results indicate that BT and SR were more effective than either TM or WL in reducing cardiovascular stress response. (Author)

  14. Souvislost fenomenality a transcendentality v kontextu fenomenologické práce s polem

    Czech Academy of Sciences Publication Activity Database

    Nitsche, Martin

    2015-01-01

    Roč. 63, mimořádné číslo 1 (2015), s. 77-90 ISSN 0015-1831 R&D Projects: GA ČR(CZ) GA14-22586S Institutional support: RVO:67985955 Keywords : phenomenology * transcendentality Subject RIV: AA - Philosophy ; Religion

  15. Advanced Time Approach of FW-H Equations for Predicting Noise

    DEFF Research Database (Denmark)

    Haiqing, Si; Yan, Shi; Shen, Wen Zhong

    2013-01-01

    An advanced time approach of Ffowcs Williams-Hawkings (FW-H) acoustic analogy is developed, and the integral equations and integral solution of FW-H acoustic analogy are derived. Compared with the retarded time approach, the transcendental equation need not to be solved in the advanced time...

  16. A simple and consistent equation of state for sodium in the single phase and two phase regions

    International Nuclear Information System (INIS)

    Breton, J.P.

    1976-01-01

    An equation of state valid over an extended temperature and density range has been derived. Then, the following properties have been deduced : coefficient of thermal expansion, isothermal coefficient of bulk compressibility, thermal pressure coefficient, heat capacity at constant pressure, at constant volume, along the saturation curve for liquid, for vapor, heat of vaporization, speed of sound, and finally the Mollier diagram and the entropy diagram. All the obtained properties are thermodynamically consistent and satisfy the basic relations of thermodynamics for both single phase and two-phase regions. Experimental results were always used when available. (auth.)

  17. Michel Foucault e a Transposição arqueológica do sujeito transcendental Kantiano

    Directory of Open Access Journals (Sweden)

    Augusto Bach

    2017-01-01

    Full Text Available Este artigo pretende compreender a transposição arqueológica da questão crítica e a aporia do argumento transcendental. A crítica do transcendental nos primeiros escritos de Foucault revela-se essencial, desde que ela determina tanto as ilusões antropológicas da modernidade quanto o projeto de encontrar uma resposta válida para a questão das condições de possibilidade do conhecimento na renovação do argumento transcendental através do a priori histórico.

  18. Closure of the single fluid magnetohydrodynamic equations in presence of electron cyclotron current drive

    NARCIS (Netherlands)

    Westerhof, E.; Pratt, J.

    2014-01-01

    In the presence of electron cyclotron current drive (ECCD), the Ohm's law of single fluid magnetohydrodynamics is modified as E + v × B = η(J – J EC). This paper presents a new closure relation for the EC driven current density appearing in this modified Ohm's law. The new relation

  19. Negotiating Transcendentalism, Escaping « Paradise » : Herman Melville’s Moby-Dick.

    Directory of Open Access Journals (Sweden)

    Ramón Espejo Romero

    2010-06-01

    Full Text Available By reviewing the critical literature on Melville and Transcendentalism and then undertaking a close reading of Moby-Dick (1851, this paper argues that the novel reflects, among other things, an ongoing debate between the novelist and Transcendentalist philosophy. While in later works, Melville seems to express a more robust condemnation of the Concord movement and its dangerous idealism, Moby-Dick occupies less firmly-defined territory. The Transcendentalist urge of an Ahab to be himself is a counterpoint to Ishmael’s more idiosyncratic deployment of self-reliance, communion with the oversoul, and various other concepts easy to trace back to Emerson or Thoreau. The conclusion seems to be that a negotiation is necessary if Transcendentalism is to be heeded at all, precisely the kind of negotiation Ishmael undertakes throughout the novel, one which spares him from the maelstrom created by a more radical approach to self-acceptance and self-fashioning.

  20. The Role of Transcendental Idealism in Kant's Dialectic of Aesthetic Judgment

    OpenAIRE

    Ward, Andrew

    2007-01-01

    A defence of the view that the introduction of transendental idealism, in the Dialectic of Aesthetic Judgment, plays a central role in resolving the antinomy which, as Kant contends, exists in our pure judgments of taste. It is further argued that the link that he holds to exist between the realms of nature and morality (or freedom) can only be successfully made out if transcendental idealism is accepted as underpinning our judgments concerning the beauties of nature.

  1. An Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part one: Single Rigid Bodies

    Directory of Open Access Journals (Sweden)

    Pål Johan From

    2012-04-01

    Full Text Available This paper presents the explicit dynamic equations of a mechanical system. The equations are presented so that they can easily be implemented in a simulation software or controller environment and are also well suited for system and controller analysis. The dynamics of a general mechanical system consisting of one or more rigid bodies can be derived from the Lagrangian. We can then use several well known properties of Lie groups to guarantee that these equations are well defined. This will, however, often lead to rather abstract formulation of the dynamic equations that cannot be implemented in a simulation software directly. In this paper we close this gap and show what the explicit dynamic equations look like. These equations can then be implemented directly in a simulation software and no background knowledge on Lie theory and differential geometry on the practitioner's side is required. This is the first of two papers on this topic. In this paper we derive the dynamics for single rigid bodies, while in the second part we study multibody systems. In addition to making the equations more accessible to practitioners, a motivation behind the papers is to correct a few errors commonly found in literature. For the first time, we show the detailed derivations and how to arrive at the correct set of equations. We also show through some simple examples that these correspond with the classical formulations found from Lagrange's equations. The dynamics is derived from the Boltzmann--Hamel equations of motion in terms of local position and velocity variables and the mapping to the corresponding quasi-velocities. Finally we present a new theorem which states that the Boltzmann--Hamel formulation of the dynamics is valid for all transformations with a Lie group topology. This has previously only been indicated through examples, but here we also present the formal proof. The main motivation of these papers is to allow practitioners not familiar with

  2. Label-free nanoscale characterization of red blood cell structure and dynamics using single-shot transport of intensity equation

    Science.gov (United States)

    Poola, Praveen Kumar; John, Renu

    2017-10-01

    We report the results of characterization of red blood cell (RBC) structure and its dynamics with nanometric sensitivity using transport of intensity equation microscopy (TIEM). Conventional transport of intensity technique requires three intensity images and hence is not suitable for studying real-time dynamics of live biological samples. However, assuming the sample to be homogeneous, phase retrieval using transport of intensity equation has been demonstrated with single defocused measurement with x-rays. We adopt this technique for quantitative phase light microscopy of homogenous cells like RBCs. The main merits of this technique are its simplicity, cost-effectiveness, and ease of implementation on a conventional microscope. The phase information can be easily merged with regular bright-field and fluorescence images to provide multidimensional (three-dimensional spatial and temporal) information without any extra complexity in the setup. The phase measurement from the TIEM has been characterized using polymeric microbeads and the noise stability of the system has been analyzed. We explore the structure and real-time dynamics of RBCs and the subdomain membrane fluctuations using this technique.

  3. The singly averaged differential equations of satellite motion for e greater than or equal to 0 and less than 1

    Science.gov (United States)

    Dallas, S. S.; Khan, I.

    1976-01-01

    The singly-averaged differential equations of motion of a satellite are developed in terms of parameters valid for all eccentricities less than one. The perturbations included in the acceleration model are due to an aspherical central planet (zonal harmonics up to degree 20 and resonant harmonics up to degree and order 20), atmospheric drag for a time-varying atmosphere, third-body gravity (the sun and moon for an earth satellite), solar radiation pressure with shadowing, and impulsive maneuvers. Analytic averaging is used to remove short-period terms due to the aspherical central planet and third-body gravity. Numerical averaging is used to remove short-period terms due to atmospheric drag and solar radiation pressure.

  4. Remark on the nature of the spectrum of the Lame equation. A problem from transcendence theory

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.; Chudnovsky, G.V.

    1980-01-01

    Let #betta#(x) be Weierstrass elliptic function with algebraic invariant g 2 , g 3 . In the paper we prove that the degenerate point of spectrum for Lame equation having potential n(n-1)/2 #betta#(x) are transcendental, while non-degenerate points of the spectrum are algebraic. (author)

  5. Effects of Transcendental Meditation practice on brain functioning and stress reactivity in college students.

    Science.gov (United States)

    Travis, Fred; Haaga, David A F; Hagelin, John; Tanner, Melissa; Nidich, Sanford; Gaylord-King, Carolyn; Grosswald, Sarina; Rainforth, Maxwell; Schneider, Robert H

    2009-02-01

    This randomized controlled trial investigated effects of Transcendental Meditation (TM) practice on Brain Integration Scale scores (broadband frontal coherence, power ratios, and preparatory brain responses), electrodermal habituation to 85-dB tones, sleepiness, heart rate, respiratory sinus arrhythmia, and P300 latencies in 50 college students. After pretest, students were randomly assigned to learn TM immediately or learn after the 10-week posttest. There were no significant pretest group differences. A MANOVA of students with complete data (N=38) yielded significant group vs treatment interactions for Brain Integration Scale scores, sleepiness, and habituation rates (all pcollege students.

  6. Da revolução copernicana (do verdadeiro idealismo transcendental

    Directory of Open Access Journals (Sweden)

    Luiz Carlos Mariano da Rosa

    2017-02-01

    Full Text Available O artigo em questão se detém nas implicações epistemológicas da revolução copernicana de Immanuel Kant, cuja perspectiva, emergindo das fronteiras que inter-relacionam o racionalismo de Leibniz, o empirismo de Hume e a ciência positiva físico-matemática de Newton, instaura o horizonte do idealismo transcendental, estabelecendo a correlação fundamental envolvendo o sujeito e o objeto do conhecimento.

  7. The principle of maximal transcendentality and the four-loop collinear anomalous dimension

    Science.gov (United States)

    Dixon, Lance J.

    2018-01-01

    We use the principle of maximal transcendentality and the universal nature of subleading infrared poles to extract the analytic value of the four-loop collinear anomalous dimension in planar N = 4 super-Yang-Mills theory from recent QCD results, obtaining {\\widehatG}_0^{(4)}=-300{ζ}_7-256{ζ}_2{ζ}_5-384{ζ}_3{ζ}_4 . This value agrees with a previous numerical result to within 0.2%. It also provides the Regge trajectory, threshold soft anomalous dimension and rapidity anomalous dimension through four loops.

  8. On the existence and uniqueness problems of solutions for set-valued and single-valued nonlinear operator equations in probabilistic normed spaces

    Directory of Open Access Journals (Sweden)

    Shih-Sen Chang

    1994-01-01

    Full Text Available In this paper, we introduce the concept of more general probabilistic contractors in probabilistic normed spaces and show the existence and uniqueness of solutions for set-valued and single-valued nonlinear operator equations in Menger probabilistic normed spaces.

  9. Projected interaction picture of field operators and memory superoperators. A master equation for the single-particle Green's function in a Liouville space

    International Nuclear Information System (INIS)

    Grinberg, H.

    1983-11-01

    The projection operator method of Zwanzig and Feshbach is used to construct the time-dependent field operators in the interaction picture. The formula developed to describe the time dependence involves time-ordered cosine and sine projected evolution (memory) superoperators, from which a master equation for the interaction-picture single-particle Green's function in a Liouville space is derived. (author)

  10. Sobre o transcendental prático e a dialética da sociabilidade

    Directory of Open Access Journals (Sweden)

    Luiz Henrique Lopes dos Santos

    2011-07-01

    Full Text Available Ao escrever Apresentação do mundo: considerações sobre o pensamento de Ludwig Wittgenstein, as intenções de José Arthur Giannotti não eram principalmente exegéticas. Ele pretendia trilhar alguns caminhos abertos por Ludwig Wittgenstein no intuito de lidar com suas próprias obsessões filosóficas. Neste artigo, mostro por que e como algumas das linhas de pensamento de Wittgenstein ajudaram Giannotti a clarear logicamente alguns de seus próprios temas filosóficos obsessivos: o transcendental prático e a dialética da sociabilidade.In writing Presentation of the World: considerations on the thought of Ludwig Wittgenstein, Giannotti's intentions were not primarily exegetical. He aimed to follow some of Wittgenstein's conceptual pathways in order to deal with his own philosophical obsessions. In this paper, I show why and how some of Wittgenstein's lines of thought helped Giannotti to logically clarify a couple of his own obsessive philosophical themes: the practical transcendental and the dialectic of sociability.

  11. Conformity visa-vi transformational conversion in mission: Towards a self-transcendental mission agenda

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    Selaelo T. Kgatla

    2017-09-01

    Full Text Available In this article, the author discusses the concept of conversion as opposed to conformity to  a  religious tradition without internal self-assertiveness. A transcendental mission understanding as opposed to an immanent agenda for liberation is proposed as an alternative solution. He analyses the role played and the contributions made by missionary enterprise and the liberation theologies in South Africa as they shaped the path for liberation. The white churches and state theologies sought to produce black conformists to the system; liberation theologies resisted the conformity mentality and fought for an egalitarian and free society. Both movements failed to embrace a transcendental methodology that would go beyond the secular boundaries and bring about transformational and empowering spirituality. This article suggests new spirituality for life and affirmation that would work against self-hate among the previously oppressed and self-guilt among the previously oppressing ruling class. It seeks ways to heal broken relationships through authentic empowerment and transformation.

  12. Transcendental Meditation

    CERN Multimedia

    Wallace,K

    1971-01-01

    K.Wallace, qui vient des Etats Unis, parle des effects physiologiques de la méditation transcendantale. Il a fait son bachelor en physique à l'Université de Los Angeles et son doctorat en physiologie aussi à Los Angeles, mais à l'Institut de Recherche sur le cerveau. Il travaille maintenat à Harvard Medical School ou il continue des recherches biochimiques et physiologiques sur l'application médicale de la méditation transcendantale. Il s'occupe principalement des maladies cardiaques et de hypertension artérielle.

  13. Evaluation of total body water in canine breeds by single-frequency bioelectrical impedance analysis method: specific equations are needed for accuracy.

    Science.gov (United States)

    Yaguiyan-Colliard, Laurence; Daumas, Caroline; Nguyen, Patrick; Grandjean, Dominique; Cardot, Philippe; Priymenko, Nathalie; Roux, Françoise

    2015-08-06

    Equations based on single-frequency bioelectrical impedance analysis at 50 kHz for determination of total body water content (TBW) have been previously validated in healthy non-sedated beagle dogs. We investigated whether these equations are predictive of TBW in various canine breeds by comparing the results of these equations with TBW values evaluated directly by deuterium oxide (D2O) dilution. Total body water content of 13 healthy adult pet dogs of various breeds was determined directly using D2O dilution and indirectly using previous equations based on values obtained with a portable bioelectric impedance device. Paired Student's t-tests were used to compare TBW obtained by single-frequency bioelectrical impedance analysis and D2O dilution. A p-value of bioelectrical impedance analysis parameters validated at 50 kHz in healthy adult beagles need to be modified including morphological parameters such as body size and shape in a first approach. As in humans, morphological-specific equations have to be developed and validated.

  14. The Transcendental Meditation Program in the College Curriculum: A 4-Year Longitudinal Study of Effects on Cognitive and Affective Functioning.

    Science.gov (United States)

    Aron, Arthur; And Others

    1981-01-01

    Found participation in transcendental meditation classes produced significant freshman-senior increases on intelligence and increased social self-confidence, sociability, general psychological health, and social maturity. No change was observed on social desirability. Changes may reflect success of the Maharishi International University approach…

  15. Put Me in Coach: A Transcendental Phenomenological Study Examining School Wide Positive Behavior Support Coaches' Experience with Program Implementation

    Science.gov (United States)

    Rieffannacht, Kimberlie Beth

    2016-01-01

    The purpose of this transcendental phenomenological study was to describe lived experience during School Wide Positive Behavior Support (SWPBS) implementation for School Wide Positive Behavior coaches in Pennsylvania public schools. Participants, identified as co-researchers throughout this study, included 11 SWPBS coaches selected from seven…

  16. The Effects of Muslim Praying Meditation and Transcendental Meditation Programs on Mindfulness among the University of Nizwa Students

    Science.gov (United States)

    Aldahadha, Basim

    2013-01-01

    The aim of this study was to investigate the Effects of Muslim Praying Meditation (MPM) and Transcendental Meditation (TM) Program on Mindfulness among the University of Nizwa students. The sample of the study consisted of (354) students. The questionnaires of MPM (Al-Kushooa) and Kentucky Inventory of Mindfulness Skills (KIMS) were applied before…

  17. Can One Take the Logarithm or the Sine of a Dimensioned Quantity or a Unit? Dimensional Analysis Involving Transcendental Functions

    Science.gov (United States)

    Matta, Cherif F.; Massa, Lou; Gubskaya, Anna V.; Knoll, Eva

    2011-01-01

    The fate of dimensions of dimensioned quantities that are inserted into the argument of transcendental functions such as logarithms, exponentiation, trigonometric, and hyperbolic functions is discussed. Emphasis is placed on common misconceptions that are not often systematically examined in undergraduate courses of physical sciences. The argument…

  18. Numerical analysis of single pad of thrust bearing with the energy equation solved by the characteristic-based split method

    Directory of Open Access Journals (Sweden)

    Yaoyu Hu

    2015-09-01

    Full Text Available The solution of the energy equation of thermo-elasto-hydrodynamic analysis for bearings by the finite element method usually leads to convergence difficulties due to the presence of convection terms inherited from the Navier–Stokes equations. In this work, the numerical analysis is performed with finite element method universally by adopting the characteristic-based split method to solve the energy equation. Five case studies of fixed pad thrust bearings have been set up with different geometries, loads, and lubricants. The two-dimensional film pressure is obtained by solving the Reynolds equation with pre-defined axial load on the pad. The energy equation of the lubricant film and the heat transfer equation of the bearing pad are handled by characteristic-based split method and conventional finite element method in three-dimensional space, respectively. Hot oil carry-over effect and variable lubricant viscosity are considered in the simulations. The results of the temperature distributions in the lubricant film and the bearing pad are presented. The possible usability of characteristic-based split method for future thermo-elasto-hydrodynamic analysis is discussed.

  19. The legitimating fact in the transcendental deduction of the categories: on Dieter Henrich's reading of Kant

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    Christian Klotz

    Full Text Available This article reconstructs the principal moments of Dieter Henrich's work on Immanuel Kant's theoretical philosophy. Henrich seeks to clarify and regain the fundaments of Kant's theory of knowledge - from which his followers, according to him, have distanced themselves - based on the analysis of the "transcendental deduction of the categories". Firstly, Henrich investigates the proof structure of deduction, comparing the first and the second edition of Critique of Pure Reason. Secondly, he investigates, in the Kantian argument, the relationship between the identity principle of self-consciousness and objectivity. Finally, extending the comparison to Critique of Practical Reason, Henrich elucidates the program and methodology in deduction, showing that the idea of a legitimating fact, borrowed from the juridical notion of a deduction, becomes the fundamental element. We analyse the problems raised by the conception of a philosophical argument based on fundamental "facts".

  20. Comparing Indirect Effects in Different Groups in Single-Group and Multi-Group Structural Equation Models

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    Ehri Ryu

    2017-05-01

    Full Text Available In this article, we evaluated the performance of statistical methods in single-group and multi-group analysis approaches for testing group difference in indirect effects and for testing simple indirect effects in each group. We also investigated whether the performance of the methods in the single-group approach was affected when the assumption of equal variance was not satisfied. The assumption was critical for the performance of the two methods in the single-group analysis: the method using a product term for testing the group difference in a single path coefficient, and the Wald test for testing the group difference in the indirect effect. Bootstrap confidence intervals in the single-group approach and all methods in the multi-group approach were not affected by the violation of the assumption. We compared the performance of the methods and provided recommendations.

  1. What is the trouble with Dyson-Schwinger equations?

    International Nuclear Information System (INIS)

    Kreimer, D.

    2004-01-01

    We discuss similarities and differences between Green Functions in Quantum Field Theory and polylogarithms. Both can be obtained as solutions of fixpoint equations which originate from an underlying Hopf algebra structure. Typically, the equation is linear for the polylog, and non-linear for Green Functions. We argue though that the crucial difference lies not in the non-linearity of the latter, but in the appearance of non-trivial representation theory related to transcendental extensions of the number field which governs the linear solution. An example is studied to illuminate this point

  2. DISASTER RELIEF FOR THE JAPANESE EARTHQUAKE-TSUNAMI OF 2011: STRESS REDUCTION THROUGH THE TRANSCENDENTAL MEDITATION® TECHNIQUE.

    Science.gov (United States)

    Yoshimura, Mitsunobu; Kurokawa, Etsuko; Noda, Takayuki; Hineno, Koji; Tanaka, Yasuo; Kawai, Yuji; Dillbeck, Michael C

    2015-08-01

    This study examined changes in self-reported stress symptoms after instruction in the Transcendental Meditation(®) technique among 171 residents of two cities (Sendai and Ishinomaki) directly affected by the 2011 Japan earthquake and tsunami disaster compared with 326 non-disaster Tokyo participants previously tested before and after learning the technique and a no-treatment control group (n = 68). The participants completed a rating checklist of mental and physical symptoms. Disaster area participants who learned the Transcendental Meditation(®) technique in contrast to controls showed a significant drop in total symptom score from pre-test to post-test (effect size = -1.09). Results were comparable for an ordinal measure of symptom intensity. The findings suggest the potential value of this procedure for relief from disaster trauma.

  3. Einstein's ``Spooky Action at a Distance'' in the Light of Kant's Transcendental Doctrine of Space and Time

    Science.gov (United States)

    Hacyan, Shahen

    2006-11-01

    Since the famous Einstein-Podolsky-Rosen (EPR) paper, it is clear that there is a serious incompatibility between local realism and quantum mechanics. Einstein believed that a complete quantum theory should be free of what he once called "spooky actions at distance". However, all experiments in quantum optics and atomic physics performed in the last two decades confirm the existence of quantum correlations that seem to contradict local realism. According to Bohr, the apparent contradictions disclose only the inadequacy of our customary concepts for the description of the quantum world. Are space and time such customary concepts? In this presentation, I argue that the Copenhagen interpretation is compatible with Kant's transcendental idealism and that, in particular, EPR type paradoxes are consistent with Kant's transcendental aesthetics, according to which space and time have no objective reality but are pure forms of sensible intuition.

  4. Stability, bifurcation and a new chaos in the logistic differential equation with delay

    International Nuclear Information System (INIS)

    Jiang Minghui; Shen Yi; Jian Jigui; Liao Xiaoxin

    2006-01-01

    This Letter is concerned with bifurcation and chaos in the logistic delay differential equation with a parameter r. The linear stability of the logistic equation is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, the formula for determining the direction of Hopf bifurcation and the stability of bifurcation periodic solution in the first bifurcation values is obtained. By theoretical analysis and numerical simulation, we found a new chaos in the logistic delay differential equation

  5. Artificial Intelligence and Semantics through the Prism of Structural, Post-Structural and Transcendental Approaches.

    Science.gov (United States)

    Gasparyan, Diana

    2016-12-01

    There is a problem associated with contemporary studies of philosophy of mind, which focuses on the identification and convergence of human and machine intelligence. This is the problem of machine emulation of sense. In the present study, analysis of this problem is carried out based on concepts from structural and post-structural approaches that have been almost entirely overlooked by contemporary philosophy of mind. If we refer to the basic definitions of "sign" and "meaning" found in structuralism and post-structuralism, we see a fundamental difference between the capabilities of a machine and the human brain engaged in the processing of a sign. This research will exemplify and provide additional evidence to support distinctions between syntactic and semantic aspects of intelligence, an issue widely discussed by adepts of contemporary philosophy of mind. The research will demonstrate that some aspect of a number of ideas proposed in relation to semantics and semiosis in structuralism and post-structuralism are similar to those we find in contemporary analytical studies related to the theory and philosophy of artificial intelligence. The concluding part of the paper offers an interpretation of the problem of formalization of sense, connected to its metaphysical (transcendental) properties.

  6. Impact of Transcendental Meditation on Left Ventricular Mass in African American Adolescents

    Directory of Open Access Journals (Sweden)

    Vernon A. Barnes

    2012-01-01

    Full Text Available Background. An early sign of ventricular remodeling is increased left ventricular mass (LVM which over time may lead to left ventricular hypertrophy, the strongest predictor of cardiovascular morbidity and mortality, other than advancing age. Methods. 62 (30 TM; 32 CTL African American adolescents (age 16.2±1.3 years with high normal systolic BP were randomly assigned to either 4-month Transcendental Meditation (TM or health education control groups. The echocardiographic-derived measure of LVM index (LVMI = LVM/ht2.7 was measured before and after the 4-month TM study and at 4-month followup. 2D-guided M-mode echocardiography using a Hewlett Packard 5500 echosonograph was used to determine LVMI. Results. The TM group exhibited a greater decrease in LVMI at 4-month followup compared to the CTL group (−2.6 versus +0.3 gm/ht2.7, P<0.04. The TM group exhibited a lesser increase in BMI at 4-month follow-up compared to the CTL group (0.2±1.6 versus 1.1±1.4, P<0.03. Conclusion. These findings indicate that among a group of prehypertensive African American adolescents, 4 months of TM compared to heath education resulted in a significant decrease in LVMI, and these changes were maintained at 4-month follow-up.

  7. [An approach to bacteriological taxonomy by application of Immanuel Kant's transcendental dialectics (author's transl)].

    Science.gov (United States)

    Habs, H

    1981-01-01

    After having altered the name of International Committee for Bacteriological Nomenclature in International Committee on Systematic Bacteriology in 1970, the latter will also have to reflect upon the objects of taxonomy. An approach thereto is recognizable in the revision of the International Code of Nomenclature of Bacteria in 1975. Considerations are being made whether a classification of bacteria does justice to the laws of homogenicity, specification and continuity as laid down by Kant in his transcendental dialectic. Most important of all are definition and determination of the taxon species. As far as contents go the latter is not possible from the biological point of view but applicable to its range in application of the regulations of the code. Within the priorities of taxa the species adopts a preferential position because conceptions of applied bacteriology are contained therein. The variety of infra-subspecific subdivisions is taken into consideration; as far as the formae speciales are concerned considerations as made with regard to species apply.

  8. Beta-adrenergic receptor sensitivity, autonomic balance and serotonergic activity in practitioners of Transcendental Meditation

    International Nuclear Information System (INIS)

    Hill, D.A.

    1989-01-01

    The aim of this thesis was to investigate the acute autonomic effects of the Transcendental Meditation Program (TM) and resolve the conflict arising from discrepant neurochemical and psychophysiological data. Three experimental investigations were performed. The first examined beta 2 -adrenergic receptors (AR's) on peripheral blood lymphocytes, via [I 125 ]iodocyanopindolol binding, in 10 male mediating and 10 age matched non-meditating control subjects, to test the hypothesis that the long-term practice of TM and the TM Sidhi Program (TMSP) reduces end organ sensitivity to adrenergic agonists. The second investigated respiratory sinus arrhythmia (an indirect measure of cardiac Parasympathetic Nervous System tone), and skin resistance (a measure of Sympathetic Nervous System tone) during periods of spontaneous respiratory apneusis, a phenomenon occurring during TM that is known to mark the subjective experience of transcending. The third was within subject investigation of the acute effects of the TMSP on 5-hydroxytryptamine (5-HT) activity. Platelet 5-HT was assayed by high pressure liquid chromatography with electrochemical detection, plasma prolactin (PL) and lutenizing hormone (LH) by radioimmunoassay, tryptophan by spectrofluorimetry, and alpha-1-acid glycoprotein (AGP, a modulator of 5-HT uptake) by radial immunodiffusion assay

  9. Beta-adrenergic receptor sensitivity, autonomic balance and serotonergic activity in practitioners of Transcendental Meditation

    Energy Technology Data Exchange (ETDEWEB)

    Hill, D.A.

    1989-01-01

    The aim of this thesis was to investigate the acute autonomic effects of the Transcendental Meditation Program (TM) and resolve the conflict arising from discrepant neurochemical and psychophysiological data. Three experimental investigations were performed. The first examined beta{sub 2}-adrenergic receptors (AR's) on peripheral blood lymphocytes, via (I{sup 125})iodocyanopindolol binding, in 10 male mediating and 10 age matched non-meditating control subjects, to test the hypothesis that the long-term practice of TM and the TM Sidhi Program (TMSP) reduces end organ sensitivity to adrenergic agonists. The second investigated respiratory sinus arrhythmia (an indirect measure of cardiac Parasympathetic Nervous System tone), and skin resistance (a measure of Sympathetic Nervous System tone) during periods of spontaneous respiratory apneusis, a phenomenon occurring during TM that is known to mark the subjective experience of transcending. The third was within subject investigation of the acute effects of the TMSP on 5-hydroxytryptamine (5-HT) activity. Platelet 5-HT was assayed by high pressure liquid chromatography with electrochemical detection, plasma prolactin (PL) and lutenizing hormone (LH) by radioimmunoassay, tryptophan by spectrofluorimetry, and alpha-1-acid glycoprotein (AGP, a modulator of 5-HT uptake) by radial immunodiffusion assay.

  10. Primordial non-Gaussianities of gravitational waves in the most general single-field inflation model with second-order field equations.

    Science.gov (United States)

    Gao, Xian; Kobayashi, Tsutomu; Yamaguchi, Masahide; Yokoyama, Jun'ichi

    2011-11-18

    We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in the most general single-field inflation model with second-order field equations. It is shown that the most general cubic action for the tensor perturbation h(ij) is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each h(ij). The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct detection experiments.

  11. Solution of ODE u + p(u)(u')2 + q(u) = 0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations

    International Nuclear Information System (INIS)

    Liu Chengshi

    2008-01-01

    Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc, are reduced to an integrable ODE expressed by u + p(u)(u') 2 + q(u) = 0 whose general solution can be given. Furthermore, combining complete discrimination system for polynomial, the classifications of all single travelling wave solutions to these equations are obtained. The equation u + p(u)(u') 2 + q(u) = 0 includes the equation (u') 2 = f(u) as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.

  12. Introduction to differential equations

    CERN Document Server

    Taylor, Michael E

    2011-01-01

    The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen

  13. Dynamics of a family of transcendental meromorphic functions having rational Schwarzian derivative

    Science.gov (United States)

    Sajid, M.; Kapoor, G. P.

    2007-02-01

    In the present paper, a class of critically finite transcendental meromorphic functions having rational Schwarzian derivative is introduced and the dynamics of functions in one parameter family is investigated. It is found that there exist two parameter values [lambda]*=[phi](0)>0 and , where and is the real root of [phi]'(x)=0, such that the Fatou sets of f[lambda](z) for [lambda]=[lambda]* and [lambda]=[lambda]** contain parabolic domains. A computationally useful characterization of the Julia set of the function f[lambda](z) as the complement of the basin of attraction of an attracting real fixed point of f[lambda](z) is established and applied for the generation of the images of the Julia sets of f[lambda](z). Further, it is observed that the Julia set of explodes to whole complex plane for [lambda]>[lambda]**. Finally, our results found in the present paper are compared with the recent results on dynamics of one parameter families [lambda]tanz, [R.L. Devaney, L. Keen, Dynamics of meromorphic maps: Maps with polynomial Schwarzian derivative, Ann. Sci. Ecole Norm. Sup. 22 (4) (1989) 55-79; L. Keen, J. Kotus, Dynamics of the family [lambda]tan(z), Conform. Geom. Dynam. 1 (1997) 28-57; G.M. Stallard, The Hausdorff dimension of Julia sets of meromorphic functions, J. London Math. Soc. 49 (1994) 281-295] and , [lambda]>0 [G.P. Kapoor, M. Guru Prem Prasad, Dynamics of : The Julia set and bifurcation, Ergodic Theory Dynam. Systems 18 (1998) 1363-1383].

  14. La nueva Estética transcendental del Opus Postumum de Kant

    Directory of Open Access Journals (Sweden)

    Leopoldo Prieto López

    2014-11-01

    Full Text Available Este artículo presenta las razones de la transformación de la teoría kantiana de la sensilibilidad,es decir, de la estética trascendental. La estética trascendental de la Crítica de la razón pura contenía una clara aporía: por un lado, la cosa en sí era entendida como la causa de la sensación, pero, por otro, la categoría de causa no era de legítima aplicación a la cosa en sí. Este insatisfactorio estatuto epistemológico de la estética trascendental y de la afección sensible fue vivamente discutido y criticado, ya en tiempos de Kant, en lo que se conoce con el nombre de disputa en torno a la cosa en sí,en la que intervinieron, entre otros, Jacobi, Reinhold, Beck y Schelling. De este modo Kant, sea para hacer más coherente el propio sistema, sea incluso por ser de algún modo influenciado por tales críticas,llevó a cabo en el Opus Postumum una profunda reforma de la teoría de la sensibilidad, que se fundará sobre dos principios: la transformación de la vieja afección transcendente en la nueva teoría de la autoafección (Selbstaffizierung, y consecuentemente, la disolución de la cosa en sí dentro de la potencia sintética del yo, que ahora no es afectado por la cosa, sino por sí mismo

  15. The experience of transcendental meditation in middle school students: a qualitative report.

    Science.gov (United States)

    Rosaen, Cara; Benn, Rita

    2006-01-01

    Transcendental Meditation (TM), a sitting meditation technique designed to quiet the mind and induce physical and mental relaxation, has been widely studied in adults. Our objective was to explore systematically the first-person experience of young adolescents who practice TM. A descriptive, qualitative study using semistructured interviews. Middle school setting. Participants included 10 seventh grade students who have practiced TM for a one-year period of time. Themes described by students resulting from meditation included the following: (1) an increasing state of restful alertness; (2) improvement in skills indicative of emotional intelligence (self-control, self-reflection/awareness, and flexibility in emotional response); and (3) improvement in academic performance. The state of restful alertness induced by meditation appeared central to facilitating growth in social-emotional capacities, academic performance, and flexibility in emotional response. The inner state of restful alertness provided students with greater capacity to expand their ways of looking inwardly at themselves and their relationships with others (emotional intelligence) as well as focusing their attention on controlling their behavior and keeping on task in school. Students described beneficial effects of TM: an increased state of restful alertness and greater capacity for self-reflection, self-control, and flexibility as well as improved academic performance. The state of restful alertness induced by meditation may facilitate the growth of social-emotional capacities necessary for regulating the emotional labiality and interpersonal stress of adolescence. Future empirical validation is needed to analyze systematically the impact of this practice on students' social-emotional and cognitive development and to determine whether its practice can serve as a protective function for helping students successfully meet the challenges of adolescence.

  16. Emphaty as the foundation of the social sciences and of social life: a reading of Husserl's phenomenology of transcendental intersubjectivity

    Directory of Open Access Journals (Sweden)

    Frédéric Vandenberghe

    2002-12-01

    Full Text Available Starting with an overview of possible solutions to the problem of social order, the author presents a non-acritical reconstruction of Edmund Husserl's transcendental phenomenology of intersubjectivity as a sympathetic alternative to Habermas's theory of communicative action. By means of a detailed analysis of the concept of empathy (Einfühlung, he shows that Husserl's phenomenology of intersubjectivity offers a triple foundation of the sciences. As a warrant of the objectivity of the world, it grounds the natural sciences; as a presupposition of sociality, it founds the social sciences; as mediated by culture, it grounds the social sciences as human sciences.

  17. ECOLOGIA NA ÓTICA DO NIILISMO: POR UMA ECOLOGIA ABERTA AO TRANSCENDENTE

    Directory of Open Access Journals (Sweden)

    Clodovis Boff

    2010-01-01

    Full Text Available Aborda-se aqui a questão ecológica numa perspectiva pouco comum: a do niilismo moderno. Este é aqui entendido, em geral, como vida sem sentido e, em particular, como falta de um sentido último e transcendente para a vida. A falta de sentido estaria na raiz da falta de respeito e de amor à natureza. Pois, se a vida humana não tem sentido, como o teria a natureza? A crise ecológica seria, pois, um aspecto de uma crise mais ampla e mais profunda: a crise do sentido. Mas de onde provém a crise de sentido? Provém, no fundo, de uma visão secularista do mundo. Tal visão, radicalmente antropocentrista e prescindindo de Deus, acaba entregando o mundo à vontade de potência do ser humano, inclusive na forma de niilismo ativo ou destrutivo. A “ecologia profunda”, enquanto se quer “biocêntrica” ou “ecocêntrica”, não é uma verdadeira alternativa, por manter-se ainda presa, como o antropocentrismo, a uma perspectiva fundamentalmente imanentista do mundo. A verdadeira saída se dá “por cima”: consiste em reconhecer a “criaturalidade” das coisas, enquanto dependentes do Criador e possuindo, por isso mesmo, um valor próprio, que o ser humano é chamado a respeitar e de que deve dar conta. ABSTRACT: This article treats the question of ecology in a not so common perspective: that of modern nihilism. This perspective is understood, in general, as life without meaning, and in particular, as a lack of an ultimate and transcendent meaning for life. The lack of meaning would be the root of the lack of respect and love for nature. Therefore, if human life does not have meaning, how would nature have meaning? The ecological crisis would be, therefore, an aspect of a larger and deeper crisis: the crisis of meaning. But where does the crisis of meaning come from? It comes from, in depth, a secularist vision of the world. Such a vision, radically anthropocentrist and dispensing with God, ends up delivering the world to the potent will

  18. Use of the Transcendental Meditation Technique to Reduce Symptoms of Attention Deficit Hyperactivity Disorder (ADHD) by Reducing Stress and Anxiety: An Exploratory Study

    Science.gov (United States)

    Grosswald, Sarina J.; Stixrud, William R.; Travis, Fred; Bateh, Mark A.

    2008-01-01

    This exploratory study tested the feasibility of using the Transcendental Meditation[R] technique to reduce stress and anxiety as a means of reducing symptoms of ADHD. Students ages 11-14 were taught the technique, and practiced it twice daily in school. Common ADHD inventories and performance measures of executive function were administered at…

  19. Effect of the Transcendental Meditation Program on Graduation, College Acceptance and Dropout Rates for Students Attending an Urban Public High School

    Science.gov (United States)

    Colbert, Robert D.

    2013-01-01

    High school graduation rates nationally have declined in recent years, despite public and private efforts. The purpose of the current study was to determine whether practice of the Quiet Time/Transcendental Meditation® program at a medium-size urban school results in higher school graduation rates compared to students who do not receive training…

  20. Soliton multidimensional equations and integrable evolutions preserving Laplace's equation

    International Nuclear Information System (INIS)

    Fokas, A.S.

    2008-01-01

    The KP equation, which is an integrable nonlinear evolution equation in 2+1, i.e., two spatial and one temporal dimensions, is a physically significant generalization of the KdV equation. The question of constructing an integrable generalization of the KP equation in 3+1, has been one of the central open problems in the field of integrability. By complexifying the independent variables of the KP equation, I obtain an integrable nonlinear evolution equation in 4+2. The requirement that real initial conditions remain real under this evolution, implies that the dependent variable satisfies a nonlinear evolution equation in 3+1 coupled with Laplace's equation. A reduction of this system of equations to a single equation in 2+1 contains as particular cases certain singular integro-differential equations which appear in the theory of water waves

  1. Impact of Transcendental Meditation on Psychotropic Medication Use Among Active Duty Military Service Members With Anxiety and PTSD.

    Science.gov (United States)

    Barnes, Vernon A; Monto, Andrea; Williams, Jennifer J; Rigg, John L

    2016-01-01

    The purpose of the study was to determine whether the regular practice of Transcendental Meditation (TM) decreased the need for psychotropic medications required for anxiety and post-traumatic stress disorder (PTSD) management and increased psychological wellbeing. The sample included 74 military Service Members with documented PTSD or anxiety disorder not otherwise specified (ADNOS), 37 that practiced TM and 37 that did not. At 1 month, 83.7% of the TM group stabilized, decreased, or ceased medications and 10.8% increased medication dosage; compared with 59.4% of controls that showed stabilizations, decreases, or cessations; and 40.5% that increased medications (p reducing PTSD and ADNOS psychological symptoms and associated medication use. Reprint & Copyright © 2016 Association of Military Surgeons of the U.S.

  2. Physiological patterns during practice of the Transcendental Meditation technique compared with patterns while reading Sanskrit and a modern language.

    Science.gov (United States)

    Travis, F; Olson, T; Egenes, T; Gupta, H K

    2001-07-01

    This study tested the prediction that reading Vedic Sanskrit texts, without knowledge of their meaning, produces a distinct physiological state. We measured EEG, breath rate, heart rate, and skin conductance during: (1) 15-min Transcendental Meditation (TM) practice; (2) 15-min reading verses of the Bhagavad Gita in Sanskrit; and (3) 15-min reading the same verses translated in German, Spanish, or French. The two reading conditions were randomly counterbalanced, and subjects filled out experience forms between each block to reduce carryover effects. Skin conductance levels significantly decreased during both reading Sanskrit and TM practice, and increased slightly during reading a modern language. Alpha power and coherence were significantly higher when reading Sanskrit and during TM practice, compared to reading modern languages. Similar physiological patterns when reading Sanskrit and during practice of the TM technique suggests that the state gained during TM practice may be integrated with active mental processes by reading Sanskrit.

  3. Dieter Henrich, leitor de Kant: sobre o fato legitimador na dedução transcendental das categorias

    Directory of Open Access Journals (Sweden)

    Christian Klotz

    2007-01-01

    Full Text Available Este artigo reconstrói os momentos principais dos trabalhos de Dieter Henrich sobre a filosofia teórica de Immanuel Kant. Henrich procura esclarecer e recuperar os fundamentos da teoria do conhecimento de Kant, dos quais seus seguidores teriam se distanciado, a partir da análise da dedução transcendental das categorias. De início, Henrich investiga a estrutura da prova na dedução, comparando a primeira e a segunda edição da Crítica da Razão Pura. Em seguida, Henrich investiga no argumento kantiano a relação entre o princípio de identidade da consciência de si, por um lado, e objetividade, por outro. Por fim, estendendo a comparação à Crítica da Razão Prática, Henrich elucida o programa e a metodologia na dedução, mostrando como o "fato" legitimador se torna o elemento fundamental.This article reconstructs the principal moments of Dieter Henrich's work on Immanuel Kant's theoretical philosophy. Henrich tries to clarify and recover the foundations of Kant's theory of knowledge, from which his followers would have taken distance, based on the analysis of the "transcendental deduction of categories". Firstly, Henrich investigates the proof structure in the deduction, comparing the first and the second edition of the Critique of Pure Reason. Secondly, he investigates, inside Kantian argument, the relationship between the identity principle of self-consciousness and objectivity. Finally, extending the comparison to the Critique of Practical Reason, Henrich elucidates the program and methodology of deduction, showing how the legitimating fact becomes the fundamental element.

  4. Successfully Transitioning to Linear Equations

    Science.gov (United States)

    Colton, Connie; Smith, Wendy M.

    2014-01-01

    The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…

  5. Coesão discursiva nos Estudos de execução transcendental de Liszt: as últimas sete peças Discourse cohesion in Liszt's Transcendental studies: the last seven pieces

    Directory of Open Access Journals (Sweden)

    Daniel Bento

    2010-01-01

    Full Text Available Parece urgente a investigação dos processos de coesão nos Estudos de execução transcendental de Franz Liszt: a emergência de um todo unificado é sugerida já no plano tonal que os coordena. O exame de outros aspectos que pudessem garantir unidade - vinculados aos materiais específicos das composições - constitui o foco do presente trabalho. Seu recorte é o subconjunto formado pelas últimas sete peças do grupo, justificado pelo fato de elas demonstrarem uma afinidade particular, o salto de sexta ascendente antecedido por diferentes formas de ênfase. O fundamento teórico adotado é uma adaptação do conceito de subtematismo de Dahlhaus, que nutre o procedimento metodológico: a abordagem analítica. Os resultados mostram conexões baseadas não apenas em fenômenos harmônicos, mas também na recorrência de materiais flexíveis que sofrem transformações. Com isso, confirma-se a coesão dos recortes e a pertinência dos processos de integração no volume de Liszt.It seems to be urgent the investigation upon the cohesive processes in the Transcendental studies by Franz Liszt: the emergence of a unified whole is already suggested in the tonal plan that coordinates them. The examination of other aspects that could guarantee unity - related to specific materials of the compositions - is this text's main concern. Its focus is the subset formed by the last seven pieces of the group, and that is justified by the fact that they show a particular affiliation, the ascending leap of sixth preceded by different forms of emphasis. The theoretical basis adopted is an adaptation of Dahlhaus' concept of subthematicism, which supports the methodological procedure: the analytical approach. The results show connections based not only on harmonic phenomena, but also on the recurrence of flexible materials that are object of transformations. Hence, it is possible to substantiate the cohesion of the selected pieces and the relevance of the

  6. Analysis of the neutron slowing down equation

    International Nuclear Information System (INIS)

    Sengupta, A.; Karnick, H.

    1978-01-01

    The infinite series solution of the elementary neutron slowing down equation is studied using the theory of entire functions of exponential type and nonharmonic Fourier series. It is shown from Muntz--Szasz and Paley--Wiener theorems, that the set of exponentials ]exp(ilambda/sub n/u) ]/sup infinity//sub n/=-infinity, where ]lambda/sub n/]/sup infinity//sub n/=-infinity are the roots of the transcendental equation in slowing down theory, is complete and forms a basis in a lethargy interval epsilon. This distinctive role of the maximum lethargy change per collision is due to the Fredholm character of the slowing down operator which need not be quasinilpotent. The discontinuities in the derivatives of the collision density are examined by treating the slowing down equation in its differential-difference form. The solution (Hilbert) space is the union of a countable number of subspaces L 2 (-epsilon/2, epsilon/2) over each of which the exponential functions are complete

  7. Understanding the Relationships between Gender Inequitable Behaviours, Childhood Trauma and Socio-Economic Status in Single and Multiple Perpetrator Rape in Rural South Africa: Structural Equation Modelling.

    Directory of Open Access Journals (Sweden)

    Rachel Jewkes

    Full Text Available Interventions to prevent rape perpetration must be designed to address its drivers. This paper seeks to extend understanding of drivers of single and multiple perpetrator rape (referred to here as SPR and MPR respectively and the relationships between socio-economic status, childhood trauma, peer pressure, other masculine behaviours and rape.1370 young men aged 15 to 26 were interviewed as part of the randomised controlled trial evaluation of Stepping Stones in the rural Eastern Cape. We used multinomial to compare the characteristics of men who reported rape perpetration at baseline. We used structural equation modelling (SEM to examine pathways to rape perpetration.76.1% of young men had never raped, 10.0% had perpetrated SPR and 13.9% MPR. The factors associated with both MPR and SPR (compared to never having raped were indicators of socio-economic status (SES, childhood trauma, sexual coercion by a woman, drug and alcohol use, peer pressure susceptibility, having had transactional sex, multiple sexual partners and being physically violent towards a partner. The SEM showed the relationship between SES and rape perpetration to be mediated by gender inequitable masculinity. It was complex as there was a direct path indicating that SES correlated with the masculinity variable directly such that men of higher SES had more gender inequitable masculinities, and indirect path mediated by peer pressure resistance indicated that the former pertained so long as men lacked peer pressure resistance. Having a higher SES conveyed greater resistance for some men. There was also a path mediated through childhood trauma, such that men of lower SES were more likely to have a higher childhood trauma exposure and this correlated with a higher likelihood of having the gender inequitable masculinity (with or without the mediating effect of peer pressure resistance.Both higher and lower socio-economic status were associated with raping. Prevention of rape

  8. Understanding the Relationships between Gender Inequitable Behaviours, Childhood Trauma and Socio-Economic Status in Single and Multiple Perpetrator Rape in Rural South Africa: Structural Equation Modelling

    Science.gov (United States)

    Jewkes, Rachel; Nduna, Mzikazi; Jama-Shai, Nwabisa; Chirwa, Esnat; Dunkle, Kristin

    2016-01-01

    Background Interventions to prevent rape perpetration must be designed to address its drivers. This paper seeks to extend understanding of drivers of single and multiple perpetrator rape (referred to here as SPR and MPR respectively) and the relationships between socio-economic status, childhood trauma, peer pressure, other masculine behaviours and rape. Method 1370 young men aged 15 to 26 were interviewed as part of the randomised controlled trial evaluation of Stepping Stones in the rural Eastern Cape. We used multinomial to compare the characteristics of men who reported rape perpetration at baseline. We used structural equation modelling (SEM) to examine pathways to rape perpetration. Results 76.1% of young men had never raped, 10.0% had perpetrated SPR and 13.9% MPR. The factors associated with both MPR and SPR (compared to never having raped) were indicators of socio-economic status (SES), childhood trauma, sexual coercion by a woman, drug and alcohol use, peer pressure susceptibility, having had transactional sex, multiple sexual partners and being physically violent towards a partner. The SEM showed the relationship between SES and rape perpetration to be mediated by gender inequitable masculinity. It was complex as there was a direct path indicating that SES correlated with the masculinity variable directly such that men of higher SES had more gender inequitable masculinities, and indirect path mediated by peer pressure resistance indicated that the former pertained so long as men lacked peer pressure resistance. Having a higher SES conveyed greater resistance for some men. There was also a path mediated through childhood trauma, such that men of lower SES were more likely to have a higher childhood trauma exposure and this correlated with a higher likelihood of having the gender inequitable masculinity (with or without the mediating effect of peer pressure resistance). Discussion Both higher and lower socio-economic status were associated with raping

  9. Understanding the Relationships between Gender Inequitable Behaviours, Childhood Trauma and Socio-Economic Status in Single and Multiple Perpetrator Rape in Rural South Africa: Structural Equation Modelling.

    Science.gov (United States)

    Jewkes, Rachel; Nduna, Mzikazi; Jama-Shai, Nwabisa; Chirwa, Esnat; Dunkle, Kristin

    2016-01-01

    Interventions to prevent rape perpetration must be designed to address its drivers. This paper seeks to extend understanding of drivers of single and multiple perpetrator rape (referred to here as SPR and MPR respectively) and the relationships between socio-economic status, childhood trauma, peer pressure, other masculine behaviours and rape. 1370 young men aged 15 to 26 were interviewed as part of the randomised controlled trial evaluation of Stepping Stones in the rural Eastern Cape. We used multinomial to compare the characteristics of men who reported rape perpetration at baseline. We used structural equation modelling (SEM) to examine pathways to rape perpetration. 76.1% of young men had never raped, 10.0% had perpetrated SPR and 13.9% MPR. The factors associated with both MPR and SPR (compared to never having raped) were indicators of socio-economic status (SES), childhood trauma, sexual coercion by a woman, drug and alcohol use, peer pressure susceptibility, having had transactional sex, multiple sexual partners and being physically violent towards a partner. The SEM showed the relationship between SES and rape perpetration to be mediated by gender inequitable masculinity. It was complex as there was a direct path indicating that SES correlated with the masculinity variable directly such that men of higher SES had more gender inequitable masculinities, and indirect path mediated by peer pressure resistance indicated that the former pertained so long as men lacked peer pressure resistance. Having a higher SES conveyed greater resistance for some men. There was also a path mediated through childhood trauma, such that men of lower SES were more likely to have a higher childhood trauma exposure and this correlated with a higher likelihood of having the gender inequitable masculinity (with or without the mediating effect of peer pressure resistance). Both higher and lower socio-economic status were associated with raping. Prevention of rape perpetration must

  10. Use of prediction equations to determine the accuracy of whole-body fat and fat-free mass and appendicular skeletal muscle mass measurements from a single abdominal image using computed tomography in advanced cancer patients.

    Science.gov (United States)

    Kilgour, Robert D; Cardiff, Katrina; Rosenthall, Leonard; Lucar, Enriqueta; Trutschnigg, Barbara; Vigano, Antonio

    2016-01-01

    Measurements of body composition using dual-energy X-ray absorptiometry (DXA) and single abdominal images from computed tomography (CT) in advanced cancer patients (ACP) have important diagnostic and prognostic value. The question arises as to whether CT scans can serve as surrogates for DXA in terms of whole-body fat-free mass (FFM), whole-body fat mass (FM), and appendicular skeletal muscle (ASM) mass. Predictive equations to estimate body composition for ACP from CT images have been proposed (Mourtzakis et al. 2008; Appl. Physiol. Nutr. Metabol. 33(5): 997-1006); however, these equations have yet to be validated in an independent cohort of ACP. Thus, this study evaluated the accuracy of these equations in estimating FFM, FM, and ASM mass using CT images at the level of the third lumbar vertebrae and compared these values with DXA measurements. FFM, FM, and ASM mass were estimated from the prediction equations proposed by Mourtzakis and colleagues (2008) using single abdominal CT images from 43 ACP and were compared with whole-body DXA scans using Spearman correlations and Bland-Altman analyses. Despite a moderate to high correlation between the actual (DXA) and predicted (CT) values for FM (rho = 0.93; p ≤ 0.001), FFM (rho = 0.78; p ≤ 0.001), and ASM mass (rho = 0.70; p ≤ 0.001), Bland-Altman analyses revealed large range-of-agreement differences between the 2 methods (29.39 kg for FFM, 15.47 kg for FM, and 3.99 kg for ASM mass). Based on the magnitude of these differences, we concluded that prediction equations using single abdominal CT images have poor accuracy, cannot be considered as surrogates for DXA, and may have limited clinical utility.

  11. Penetration equations

    Energy Technology Data Exchange (ETDEWEB)

    Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)

    1997-10-01

    In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.

  12. Transcendental Trinitarian: James Marsh, the Free Will Problem, and the American Intellectual Context of Coleridge’s Aids to Reflection

    Directory of Open Access Journals (Sweden)

    Jonathan Koefoed

    2017-08-01

    Full Text Available Historians of American religion and Transcendentalism have long known of James Marsh as a catalyst for the Concord Transcendentalist movement. The standard narrative suggests that the Congregationalist Marsh naively imported Samuel Taylor Coleridge's Aids to Reflection (Am. ed. 1829 hoping to revivify orthodoxy in America. By providing a “Preliminary Essay” to explain Coleridge’s abstruse theology, Marsh injected Coleridge’s hijacked Kantian epistemology—with its distinction between Reason and Understanding—into American discourse. This epistemology inspired Transcendentalists such as Ralph Waldo Emerson and Bronson Alcott, and it helped spark the Transcendentalists’ largely post-Christian religious convictions. This article provides a re-evaluation of Marsh’s philosophical theology by attending to the precise historical moment that Marsh chose to publish the Aids to Reflection and his “Preliminary Essay.” By the late 1820s, the philosophical problem of free will lurked in American religious discourse—Unitarian as well as Trinitarian—and Marsh sought to exploit the problem as a way to explain how aspects of Trinitarian Christianity might be rational and yet unexplainable. Attending carefully to the numerous philosophical and religious discourses of the moment—including Unitarianism, Trinitarianism, Kant, Coleridge, and Scottish Common Sense—and providing close readings of the historical philosophers Marsh engaged, this article shows how James Marsh laid the epistemological groundwork for a new romanticized Christianity that was distinct from the Concord Transcendentalists, but nonetheless part of its historical lineage.

  13. Reduced Trauma Symptoms and Perceived Stress in Male Prison Inmates through the Transcendental Meditation Program: A Randomized Controlled Trial

    Science.gov (United States)

    Nidich, Sanford; O’Connor, Tom; Rutledge, Thomas; Duncan, Jeff; Compton, Blaze; Seng, Angela; Nidich, Randi

    2016-01-01

    Context Trauma events are four times more prevalent in inmates than in the general public and are associated with increased recidivism and other mental and physical health issues. Objective To evaluate the effects of Transcendental Meditationa (TM) on trauma symptoms in male inmates. Design One hundred eighty-one inmates with a moderate- to high-risk criminal profile were randomly assigned to either the TM program or to a usual care control group. Main Outcome Measures The Trauma Symptom Checklist and the Perceived Stress Scale were administered at baseline and four-month posttest. Results Significant reductions in total trauma symptoms, anxiety, depression, dissociation, and sleep disturbance subscales, and perceived stress in the TM group were found compared with controls (all p values < 0.001). The high-trauma subgroup analysis further showed a higher magnitude of effects in the TM group compared with controls on all outcomes, with Cohen effect sizes ranging from 0.67 to 0.89. Conclusion Results are consistent with those of prior studies of the TM program in other populations and its effects on trauma symptoms and perceived stress. PMID:27723444

  14. Intentionality and Presence: On the Intrinsic Of-ness of Consciousness from a Transcendental-Phenomenological Perspective.

    Science.gov (United States)

    Fasching, Wolfgang

    This paper discusses the nature of consciousness' intrinsic intentionality from a transcendental-phenomenological viewpoint. In recent philosophy of mind the essentially intentional character of consciousness has become obscured because the latter is predominantly understood in terms of "qualia" or the "what-it-is-like-ness" of mental states and it is hard to see why such subjective "feels", of all things, could bestow states with objective reference. As the paper attempts to demonstrate, this is an inadequate understanding of consciousness, which should instead be defined in terms of presence. Consciousness essentially takes place as presence-of, i.e., consists in something coming to appearance. This presence-of is not only a fundamental, irreducible phenomenon, but also in a radical sense un-naturalisable. Naturalism only knows "nature", as the world of objects, and the question of intentionality then seems to be how certain inner-worldly objects can be "representations" of other inner-worldly objects. In fact, no object is ever intrinsically "about" anything. This is exclusively the nature of subjectivity qua consciousness, which is not an object alongside other objects but rather exists as the manifestation of objects.

  15. Changes in trait brainwave power and coherence, state and trait anxiety after three-month transcendental meditation (TM) practice.

    Science.gov (United States)

    Tomljenović, Helena; Begić, Dražen; Maštrović, Zora

    2016-03-01

    The amount of studies showing different benefits of practicing meditation is growing. EEG brainwave patterns objectively reflect both the cognitive processes and objects of meditation. This study aimed to examine the effects of transcendental meditation (TM) practice on baseline EEG brainwave patterns (outside of meditation) and to examine weather TM reduces state and trait anxiety. Standard EEG recordings were conducted on volunteer participants (N=12), all students or younger employed people, before and after a three-month meditation training. Artifact-free 100-second epochs were selected and analyzed by Fast Fourier Transformation (FFT) analysis. Endlers Multidimensional Anxiety Scales (EMAS) were used to assess anxiety levels. Power (μV(2)) and coherence levels were compared in the alpha, beta, theta and delta frequency band. Changes in EEG patterns after meditation practice were found mostly in the theta band. An interaction effect was found on the left hemisphere (pmeditation practice. Most of the changes were found in the occipital and temporal areas, less in the central and frontal areas. State anxiety decreased after TM practice. Findings suggest TM practice could be helpful in treating different kinds of disorders, especially anxiety disorders.

  16. Differential equations

    CERN Document Server

    Tricomi, FG

    2013-01-01

    Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff

  17. Some Properties on Complex Functional Difference Equations

    Directory of Open Access Journals (Sweden)

    Zhi-Bo Huang

    2014-01-01

    Full Text Available We obtain some results on the transcendental meromorphic solutions of complex functional difference equations of the form ∑λ∈Iαλ(z(∏j=0nf(z+cjλj=R(z,f∘p=((a0(z+a1(z(f∘p+ ⋯ +as(z (f∘ps/(b0(z+b1(z(f∘p+ ⋯ +bt(z(f∘pt, where I is a finite set of multi-indexes λ=(λ0,λ1,…,λn, c0=0,cj∈ℂ∖{0} (j=1,2,…,n are distinct complex constants, p(z is a polynomial, and αλ(z  (λ∈I, ai(z  (i=0,1,…,s, and bj(z  (j=0,1,…,t are small meromorphic functions relative to f(z. We further investigate the above functional difference equation which has special type if its solution has Borel exceptional zero and pole.

  18. The Lived Experiences of Single Hispanic Mothers Raising Gang-Affiliated Male Youth Released from Texas Juvenile Justice Department State Facilities: A Phenomenological Study

    Science.gov (United States)

    Rodriguez-Almendarez, Ruby

    2013-01-01

    Purpose of the Study: The purpose of this transcendental phenomenological study (Moustakas, 1994) was to describe the experiences that single Hispanic mothers of gang-affiliated male juveniles face during their sons' reentry process after being released from a Texas Juvenile Justice Department state facility. Methods: After an extensive review of…

  19. Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation

    Science.gov (United States)

    Pulkkinen, Otto; Metzler, Ralf

    2015-12-01

    Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.

  20. Psicanálise lacaniana e estruturalismo: a condução do desejo como função pura a um plano transcendental

    Directory of Open Access Journals (Sweden)

    Léa Silveira Sales

    2009-12-01

    Full Text Available Há, na fase mais estruturalista da obra de Lacan - aquela que se desdobra durante o início dos anos 50 -, uma insistência na dissociação entre desejo e objeto que resulta não apenas da abordagem que Kojève havia providenciado para o tema, mas agora, sobretudo, dos instrumentos disponibilizados pela ideia de estrutura. O artigo investiga os detalhes desse processo e indica em que sentido ele conduz o desejo a um plano transcendental.

  1. equate: An R Package for Observed-Score Linking and Equating

    Directory of Open Access Journals (Sweden)

    Anthony D. Albano

    2016-10-01

    Full Text Available The R package equate contains functions for observed-score linking and equating under single-group, equivalent-groups, and nonequivalent-groups with anchor test(s designs. This paper introduces these designs and provides an overview of observed-score equating with details about each of the supported methods. Examples demonstrate the basic functionality of the equate package.

  2. On Transcendental Functions

    Indian Academy of Sciences (India)

    Functions like loge X, eX, x real, and eZ loge Z, Z complex are very important in mathematics and physics. The re- sults in this article are not new, but they are presented in a very natural way. It is observed that eZ is the one and only one complex analytic extension of the real analytic function eX with the preservation of ...

  3. Transcendental niche construction.

    Science.gov (United States)

    Callebaut, Werner

    2007-01-01

    I discuss various reactions to my article "Again, what the philosophy of science is not" [Callebaut (Acta Biotheor 53:92-122 (2005a))], most of which concern the naturalism issue, the place of the philosophy of biology within philosophy of science and philosophy at large, and the proper tasks of the philosophy of biology.

  4. Stochastic partial differential equations

    CERN Document Server

    Chow, Pao-Liu

    2014-01-01

    Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad

  5. General method of analysis of kinetic equations for multistep reversible mechanisms in the single-exponential regime: application to kinetics of open complex formation between Esigma70 RNA polymerase and lambdaP(R) promoter DNA.

    Science.gov (United States)

    Tsodikov, O V; Record, M T

    1999-03-01

    A novel analytical method based on the exact solution of equations of kinetics of unbranched first- and pseudofirst-order mechanisms is developed for application to the process of Esigma70 RNA polymerase (R)-lambdaPR promoter (P) open complex formation, which is described by the minimal three-step mechanism with two kinetically significant intermediates (I1, I2), [equation: see text], where the final product is an open complex RPo. The kinetics of reversible and irreversible association (pseudofirst order, [R] > [P]) to form long-lived complexes (RPo and I2) and the kinetics of dissociation of long-lived complexes both exhibit single exponential behavior. In this situation, the analytical method provides explicit expressions relating observed rate constants to the microscopic rate constants of mechanism steps without use of rapid equilibrium or steady-state approximations, and thereby provides a basis for interpreting the composite rate constants of association (ka), isomerization (ki), and dissociation (kd) obtained from experiment for this or any other sequential mechanism of any number of steps. In subsequent papers, we apply this formalism to analyze kinetic data obtained in the reversible and irreversible binding regimes of Esigma70 RNA polymerase (R)-lambdaP(R) promoter (P) open complex formation.

  6. Singular multiparameter dynamic equations with distributional ...

    African Journals Online (AJOL)

    In this paper, we consider both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-innite time scales. At rst we construct Weyl's theory for the single singular multiparameter dynamic equation with distributional potentials and we prove that the forward jump of at ...

  7. About the solvability of matrix polynomial equations

    OpenAIRE

    Netzer, Tim; Thom, Andreas

    2016-01-01

    We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.

  8. Feynman integrals and difference equations

    International Nuclear Information System (INIS)

    Moch, S.; Schneider, C.

    2007-09-01

    We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)

  9. Consciência moral transcendente e experiência religiosa na obra de Viktor Frankl = Transcendent moral conscience and religious experience in the work of Viktor Frankl

    Directory of Open Access Journals (Sweden)

    Pereira, Ivo Studart

    2014-01-01

    Full Text Available No presente trabalho, avaliamos como a tese de Viktor Emil Frankl sobre o caráter transcendente da consciência moral [Gewissen] constitui um argumento-chave para elucidar sua visão de experiência religiosa. Trata-se de um debate que toca, de maneira singular, o pensamento teológico do filósofo e psiquiatra vienense, na medida em que, partindo de uma análise do fenômeno da responsabilidade humana, chega-se a uma peculiar noção de relacionamento entre homem e Deus. Nesse sentido, paralelamente, vislumbramos como o pensador em questão refuta as leituras psicológicas sobre a moralidade, ao mesmo tempo em que objeta contra teses centrais da psicanálise sobre o tema

  10. Soliton equations and Hamiltonian systems

    CERN Document Server

    Dickey, L A

    2002-01-01

    The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau

  11. Extended rate equations

    International Nuclear Information System (INIS)

    Shore, B.W.

    1981-01-01

    The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence

  12. Explicit frequency equations of free vibration of a nonlocal Timoshenko beam with surface effects

    Science.gov (United States)

    Zhao, Hai-Sheng; Zhang, Yao; Lie, Seng-Tjhen

    2018-02-01

    Considerations of nonlocal elasticity and surface effects in micro- and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions: hinged-hinged, clamped-clamped and clamped-hinged ends. For a hinged-hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped-clamped and clamped-hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short, explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.

  13. Equations for formally real meadows

    NARCIS (Netherlands)

    Bergstra, J.A.; Bethke, I.; Ponse, A.

    2015-01-01

    We consider the signatures Σm = (0,1,−,+,⋅,−1)  of meadows and (Σm,s)  of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom

  14. Partial Differential Equations

    CERN Document Server

    1988-01-01

    The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

  15. Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations

    Directory of Open Access Journals (Sweden)

    Maamar Andasmas

    2016-04-01

    Full Text Available The main purpose of this article is to investigate the growth of meromorphic solutions to homogeneous and non-homogeneous second order linear differential equations f00+Af0+Bf = F, where A(z, B (z and F (z are meromorphic functions with finite order having only finitely many poles. We show that, if there exist a positive constants σ > 0, α > 0 such that |A(z| ≥ eα|z|σ as |z| → +∞, z ∈ H, where dens{|z| : z ∈ H} > 0 and ρ = max{ρ(B, ρ(F} < σ, then every transcendental meromorphic solution f has an infinite order. Further, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros.

  16. A self-referential default brain state: patterns of coherence, power, and eLORETA sources during eyes-closed rest and Transcendental Meditation practice.

    Science.gov (United States)

    Travis, Fred; Haaga, David A F; Hagelin, John; Tanner, Melissa; Arenander, Alaric; Nidich, Sanford; Gaylord-King, Carolyn; Grosswald, Sarina; Rainforth, Maxwell; Schneider, Robert H

    2010-02-01

    Activation of a default mode network (DMN) including frontal and parietal midline structures varies with cognitive load, being more active during low-load tasks and less active during high-load tasks requiring executive control. Meditation practices entail various degrees of cognitive control. Thus, DMN activation patterns could give insight into the nature of meditation practices. This 10-week random assignment study compared theta2, alpha1, alpha2, beta1, beta2 and gamma EEG coherence, power, and eLORETA cortical sources during eyes-closed rest and Transcendental Meditation (TM) practice in 38 male and female college students, average age 23.7 years. Significant brainwave differences were seen between groups. Compared to eyes-closed rest, TM practice led to higher alpha1 frontal log-power, and lower beta1 and gamma frontal and parietal log-power; higher frontal and parietal alpha1 interhemispheric coherence and higher frontal and frontal-central beta2 intrahemispheric coherence. eLORETA analysis identified sources of alpha1 activity in midline cortical regions that overlapped with the DMN. Greater activation in areas that overlap the DMN during TM practice suggests that meditation practice may lead to a foundational or 'ground' state of cerebral functioning that may underlie eyes-closed rest and more focused cognitive processes.

  17. The effects of the transcendental mediation technique and progressive muscle relaxation on EEG coherence, stress reactivity, and mental health in black adults.

    Science.gov (United States)

    Gaylord, C; Orme-Johnson, D; Travis, F

    1989-05-01

    Eighty-three black college students, staff and adults were pretested on EEG coherence, skin potential (SP) habituation to a series of loud tones, psychometric measures of mental health (Tennessee Self-Concept Empirical Scales and Spielberger State-Trait Anxiety Inventory) and IQ. They were then randomly assigned to one of the three treatment groups: the Transcendental Meditation technique (TM); Progressive Muscle Relaxation (PR); or cognitive-behavioral strategies (C). Approximately one year later, they were posttested. TM and PR increased significantly on an overall mental health factor (p less than .036) and anxiety (p less than .0006). TM showed a greater reduction in neuroticism than PR and C (p less than .032). TM also showed global increases in alpha and theta coherence among frontal and central leads during the TM period compared to eyes closed (p less than .016), whereas PR and C did not show EEG state changes. The coherence increases during TM were most marked in the right hemisphere (F4C4). TM showed faster SP habituation at posttest compared to pretest (p less than .047) whereas PR did not (data was missing for C). None of the groups showed longitudinal changes in EEG, perhaps due to lack of regularity of participation in the treatment programs.

  18. Difference equations by differential equation methods

    CERN Document Server

    Hydon, Peter E

    2014-01-01

    Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.

  19. Parabolized stability equations

    Science.gov (United States)

    Herbert, Thorwald

    1994-01-01

    The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.

  20. Handbook of integral equations

    CERN Document Server

    Polyanin, Andrei D

    2008-01-01

    This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.

  1. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N

    1995-01-01

    This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

  2. A randomized controlled trial on effects of the Transcendental Meditation program on blood pressure, psychological distress, and coping in young adults.

    Science.gov (United States)

    Nidich, Sanford I; Rainforth, Maxwell V; Haaga, David A F; Hagelin, John; Salerno, John W; Travis, Fred; Tanner, Melissa; Gaylord-King, Carolyn; Grosswald, Sarina; Schneider, Robert H

    2009-12-01

    Psychological distress contributes to the development of hypertension in young adults. This trial assessed the effects of a mind-body intervention on blood pressure (BP), psychological distress, and coping in college students. This was a randomized controlled trial (RCT) of 298 university students randomly allocated to either the Transcendental Meditation (TM) program or wait-list control. At baseline and after 3 months, BP, psychological distress, and coping ability were assessed. A subgroup of 159 subjects at risk for hypertension was analyzed similarly. Changes in systolic BP (SBP)/diastolic BP (DBP) for the overall sample were -2.0/-1.2 mm Hg for the TM group compared to +0.4/+0.5 mm Hg for controls (P = 0.15, P = 0.15, respectively). Changes in SBP/DBP for the hypertension risk subgroup were -5.0/-2.8 mm Hg for the TM group compared to +1.3/+1.2 mm Hg for controls (P = 0.014, P = 0.028, respectively). Significant improvements were found in total psychological distress, anxiety, depression, anger/hostility, and coping (P values < 0.05). Changes in psychological distress and coping correlated with changes in SBP (P values < 0.05) and DBP (P values < 0.08). This is the first RCT to demonstrate that a selected mind-body intervention, the TM program, decreased BP in association with decreased psychological distress, and increased coping in young adults at risk for hypertension. This mind-body program may reduce the risk for future development of hypertension in young adults.

  3. Pseudodifferential equations over non-Archimedean spaces

    CERN Document Server

    Zúñiga-Galindo, W A

    2016-01-01

    Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applica...

  4. Particle methods for Boltzmann equation

    International Nuclear Information System (INIS)

    Hermeline, F.

    1985-05-01

    This work is aimed at showing how to discretize an equation such as Boltzmann equation in its most general form, by particle methods. Then method is applied to some equations of plasma physics which appear as peculiar cases of Boltzmann equation, such as Vlasov equation, Bhatnager-Gross-Krook equation, Fokker-Planck equation and neutron transport equation [fr

  5. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2014-01-01

    A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or

  6. Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  7. The Pendulum Equation

    Science.gov (United States)

    Fay, Temple H.

    2002-01-01

    We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…

  8. A Comparison of IRT Equating and Beta 4 Equating

    Science.gov (United States)

    Kim, Dong-In; Brennan, Robert; Kolen, Michael

    2005-01-01

    Four equating methods (3PL true score equating, 3PL observed score equating, beta 4 true score equating, and beta 4 observed score equating) were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional-mean-squared-error (CMSE) difference, and the equi-percentile equating property. True score…

  9. Constitutive equations for two-phase flows

    International Nuclear Information System (INIS)

    Boure, J.A.

    1974-12-01

    The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr

  10. On solution of Lame equations in axisymmetric domains with conical points

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-10-01

    Partial Fourier series expansion is applied to the Dirichlet problem for the Lame equations in axisymmetric domains Ω-circumflex is a subset of R 3 with conical points on the rotation axis. This leads to dimension reduction of the three-dimensional boundary value problem resulting to an infinite sequence of two-dimensional boundary value problems on the plane meridian domain Ω a is a subset of R + 2 of Ω-circumflex with solutions u n (n = 0,1,2, ...) being the Fourier coefficients of the solution u-circumflex of the 3D BVP. The asymptotic behavior of the Fourier coefficients u n (n = 0,1,2, ...) near the angular points of the meridian domain Ω a is fully described by singular vector-functions which are related to the zeros α n of some transcendental equations involving Legendre functions of the first kind. Equations which determine the values of α n are given and a numerical algorithm for the computation of α n is proposed with some plots of values obtained presented. The singular vector functions for the solution of the 3D BVP is obtained by Fourier synthesis. (author)

  11. On separable Pauli equations

    International Nuclear Information System (INIS)

    Zhalij, Alexander

    2002-01-01

    We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

  12. Functional equations with causal operators

    CERN Document Server

    Corduneanu, C

    2003-01-01

    Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.

  13. Elliptic partial differential equations

    CERN Document Server

    Volpert, Vitaly

    If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equ...

  14. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  15. Partial differential equations

    CERN Document Server

    Evans, Lawrence C

    2010-01-01

    This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

  16. Differential equations for dummies

    CERN Document Server

    Holzner, Steven

    2008-01-01

    The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

  17. Degenerate nonlinear diffusion equations

    CERN Document Server

    Favini, Angelo

    2012-01-01

    The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

  18. Reactimeter dispersion equation

    OpenAIRE

    A.G. Yuferov

    2016-01-01

    The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...

  19. Differential equations I essentials

    CERN Document Server

    REA, Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.

  20. The 'golden' algebraic equations

    International Nuclear Information System (INIS)

    Stakhov, A.; Rozin, B.

    2006-01-01

    The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1, 2, 3, ?) is researched in the present article. For the case p = 1, the given equation is reduced to the well-known Golden Proportion equation x 2 = x + 1. These equations are called the golden algebraic equations because the golden p-proportions τ p , special irrational numbers that follow from Pascal's triangle, are their roots. A research on the general properties of the roots of the golden algebraic equations is carried out in this article. In particular, formulas are derived for the golden algebraic equations that have degree greater than p + 1. There is reason to suppose that algebraic equations derived by the authors in the present article will interest theoretical physicists. For example, these algebraic equations could be found in the research of the energy relationships within the structures of many compounds and physical particles. For the case of butadiene (C 4 H 6 ), this fact is proved by the famous physicist Richard Feynman

  1. Ordinary differential equations

    CERN Document Server

    Pontryagin, Lev Semenovich

    1962-01-01

    Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.

  2. fractional differential equations

    Indian Academy of Sciences (India)

    We apply this method for solving space–time fractional Cahn--Allen equation and space--time fractional Klein–Gordon equation. The fractional derivatives are described in the sense of modified Riemann--Lioville. As a result of some exact solution in the form of hyperbolic, trigonometric and rational solutions are deduced.

  3. Navier-Stokes equation

    Directory of Open Access Journals (Sweden)

    Hannelore Breckner

    2000-01-01

    Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.

  4. dimensional Fokas equation

    Indian Academy of Sciences (India)

    role in converting the Fokas equation into Hirota's bilinear form. Keywords. Bilinearization; multisoliton solution; Fokas equation; Hirota's bilinear method. PACS Nos 05.45.Yv; 04.20.Jb; 02.30.Jr. 1. Introduction. As pointed out by Drazin and Johnson [1], it is not easy to give a comprehensive and precise definition of a soliton.

  5. The Wouthuysen equation

    NARCIS (Netherlands)

    M. Hazewinkel (Michiel)

    1995-01-01

    textabstractDedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an

  6. Elliptic Quadratic Operator Equations

    OpenAIRE

    Ganikhodjaev, Rasul; Mukhamedov, Farrukh; Saburov, Mansoor

    2017-01-01

    In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method is also presented for stable solutions.

  7. Differential Equation of Equilibrium

    African Journals Online (AJOL)

    user

    differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the ... tedious and more time saving than the classical method in the solution of the aforementioned differential equation. ... silos, pipelines, bridge arches or wind turbine towers [3]. The objective of this ...

  8. Partial differential equations

    Indian Academy of Sciences (India)

    been a regular stream of high quality work done in these areas. Talking of elliptic partial differen- tial equations, important contributions have been made in the ...... [6] Evans L C 1992 Periodic homogenisation of certain fully nonlinear partial differential equations; Proc. Roy. Soc. Edinburgh Sect. A 120 No. 3–4, 245–265.

  9. Reduced Braginskii equations

    Energy Technology Data Exchange (ETDEWEB)

    Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies

    1993-11-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.

  10. Reduced Braginskii equations

    International Nuclear Information System (INIS)

    Yagi, M.; Horton, W.

    1993-11-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0

  11. Alternative equations of gravitation

    International Nuclear Information System (INIS)

    Pinto Neto, N.

    1983-01-01

    It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt

  12. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2004-01-01

    This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

  13. A constituição do sujeito no tempo empírico e a memória transcendental: Deleuze leitor de Hume e Proust / The constitution of the subject in empirical time and the transcendental memory: Deleuze reader of Hume and Proust

    Directory of Open Access Journals (Sweden)

    Sandro Kobol Fornazari

    2010-12-01

    Full Text Available Partindo da interpretação deleuziana do empirismo de Hume, o artigo visa a apreender a elaboração por Deleuze da primeira síntese do tempo, a síntese do hábito, a partir da constituição de um sujeito que contempla e contrai as percepções sensíveis, ultrapassando o dado a partir da ação de princípios que lhe são exteriores. A contração do passado e a expectativa em relação ao futuro são as duas dimensões do mesmo presente vivido. É pela contração pelo hábito que a repetição produz uma diferença no espírito e assim nos produz como sujeitos. Sobre a síntese passiva do hábito virão desdobrar-se as sínteses ativas da memória e da reflexão. Desde a análise da obra de Proust, Deleuze desenvolve, então, o tema desse encontro com o fora como a produção no sujeito de uma capacidade de explicitar o sentido do que se apresenta como um signo, o que implica ultrapassar as ilusões objetivistas e subjetivistas e a busca do sentido numa diferença interiorizada que é o próprio ser em si do passado. Daí decorre ir para além da dimensão empírica do tempo e encontrar uma nova síntese do tempo, a síntese transcendental da memória, em que o passado não sucede ao presente, mas coexiste com ele.AbstractBased on Deleuzian interpretation of Hume's empiricism, this article seeks to understand the development of Deleuze's first synthesis of time, the synthesis of habit, from the constitution of a subject who contemplates and contracts sensitive perceptions, surpassing the data from de action of principles that are external to him. The contraction of the past and the expectations regarding the future are two dimensions of this lived present. Through the contraction by the habit, repetition produces a difference in the spirit and then produces us as subjects. On the passive synthesis of habit will unfold the active synthesis of memory and reflection. From analysis of the work of Proust, Deleuze develops, then, the theme of

  14. Accurate analytical periodic solution of the elliptical Kepler equation using the Adomian decomposition method

    Science.gov (United States)

    Alshaery, Aisha; Ebaid, Abdelhalim

    2017-11-01

    Kepler's equation is one of the fundamental equations in orbital mechanics. It is a transcendental equation in terms of the eccentric anomaly of a planet which orbits the Sun. Determining the position of a planet in its orbit around the Sun at a given time depends upon the solution of Kepler's equation, which we will solve in this paper by the Adomian decomposition method (ADM). Several properties of the periodicity of the obtained approximate solutions have been proved in lemmas. Our calculations demonstrated a rapid convergence of the obtained approximate solutions which are displayed in tables and graphs. Also, it has been shown in this paper that only a few terms of the Adomian decomposition series are sufficient to achieve highly accurate numerical results for any number of revolutions of the Earth around the Sun as a consequence of the periodicity property. Numerically, the four-term approximate solution coincides with the Bessel-Fourier series solution in the literature up to seven decimal places at some values of the time parameter and nine decimal places at other values. Moreover, the absolute error approaches zero using the nine term approximate Adomian solution. In addition, the approximate Adomian solutions for the eccentric anomaly have been used to show the convergence of the approximate radial distances of the Earth from the Sun for any number of revolutions. The minimal distance (perihelion) and maximal distance (aphelion) approach 147 million kilometers and 152.505 million kilometers, respectively, and these coincide with the well known results in astronomical physics. Therefore, the Adomian decomposition method is validated as an effective tool to solve Kepler's equation for elliptical orbits.

  15. Ordinary differential equations

    CERN Document Server

    Ince, Edward Lindsay

    1956-01-01

    The theory of ordinary differential equations in real and complex domains is here clearly explained and analyzed. Not only classical theory, but also the main developments of modern times are covered. Exhaustive sections on the existence and nature of solutions, continuous transformation groups, the algebraic theory of linear differential systems, and the solution of differential equations by contour integration are as valuable to the pure mathematician as the fine treatment of the equations of Legendre, Bessel, and Mathieu, the conditions for the oscillatory character of solutions of a diffe

  16. Uncertain differential equations

    CERN Document Server

    Yao, Kai

    2016-01-01

    This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

  17. Hyperbolic partial differential equations

    CERN Document Server

    Witten, Matthew

    1986-01-01

    Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M

  18. Nonlinear diffusion equations

    CERN Document Server

    Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning

    2001-01-01

    Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which

  19. Ordinary differential equations

    CERN Document Server

    Miller, Richard K

    1982-01-01

    Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,

  20. Differential equations problem solver

    CERN Document Server

    Arterburn, David R

    2012-01-01

    REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and

  1. Fully nonlinear elliptic equations

    CERN Document Server

    Caffarelli, Luis A

    1995-01-01

    The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equa

  2. Partial differential equations

    CERN Document Server

    Friedman, Avner

    2008-01-01

    This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we

  3. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2011-01-01

    A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres

  4. The Minimum-Mass Surface Density of the Solar Nebula using the Disk Evolution Equation

    Science.gov (United States)

    Davis, Sanford S.

    2005-01-01

    The Hayashi minimum-mass power law representation of the pre-solar nebula (Hayashi 1981, Prog. Theo. Phys.70,35) is revisited using analytic solutions of the disk evolution equation. A new cumulative-planetary-mass-model (an integrated form of the surface density) is shown to predict a smoother surface density compared with methods based on direct estimates of surface density from planetary data. First, a best-fit transcendental function is applied directly to the cumulative planetary mass data with the surface density obtained by direct differentiation. Next a solution to the time-dependent disk evolution equation is parametrically adapted to the planetary data. The latter model indicates a decay rate of r -1/2 in the inner disk followed by a rapid decay which results in a sharper outer boundary than predicted by the minimum mass model. The model is shown to be a good approximation to the finite-size early Solar Nebula and by extension to extra solar protoplanetary disks.

  5. Partial differential equations mathematical techniques for engineers

    CERN Document Server

    Epstein, Marcelo

    2017-01-01

    This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate s...

  6. Modern nonlinear equations

    CERN Document Server

    Saaty, Thomas L

    1981-01-01

    Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.

  7. Equations For Rotary Transformers

    Science.gov (United States)

    Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.

    1988-01-01

    Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.

  8. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  9. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2015-01-01

    This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...

  10. Applied partial differential equations

    CERN Document Server

    DuChateau, Paul

    2012-01-01

    Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.

  11. dimensional nonlinear evolution equations

    Indian Academy of Sciences (India)

    –. (4)) by applying the exp-function method. The computer symbolic systems such as. Maple and Mathematica allow us to perform complicated and tedious calculations. 2. Solutions of (N + 1)-dimensional generalized Boussinesq equation.

  12. Problems in differential equations

    CERN Document Server

    Brenner, J L

    2013-01-01

    More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.

  13. Regularized Structural Equation Modeling

    Science.gov (United States)

    Jacobucci, Ross; Grimm, Kevin J.; McArdle, John J.

    2016-01-01

    A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM’s utility. PMID:27398019

  14. Complex nonlinear Lagrangian for the Hasegawa-Mima equation

    International Nuclear Information System (INIS)

    Dewar, R.L.; Abdullatif, R.F.; Sangeetha, G.G.

    2005-01-01

    The Hasegawa-Mima equation is the simplest nonlinear single-field model equation that captures the essence of drift wave dynamics. Like the Schroedinger equation it is first order in time. However its coefficients are real, so if the potential φ is initially real it remains real. However, by embedding φ in the space of complex functions a simple Lagrangian is found from which the Hasegawa-Mima equation may be derived from Hamilton's Principle. This Lagrangian is used to derive an action conservation equation which agrees with that of Biskamp and Horton. (author)

  15. General solution of the scattering equations

    Energy Technology Data Exchange (ETDEWEB)

    Dolan, Louise [Department of Physics, University of North Carolina,Chapel Hill, NC 27599 (United States); Goddard, Peter [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States)

    2016-10-26

    The scattering equations, originally introduced by Fairlie and Roberts in 1972 and more recently shown by Cachazo, He and Yuan to provide a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension, have been reformulated in polynomial form. The scattering equations for N particles are equivalent to N−3 polynomial equations h{sub m}=0, 1≤m≤N−3, in N−3 variables, where h{sub m} has degree m and is linear in the individual variables. Facilitated by this linearity, elimination theory is used to construct a single variable polynomial equation, Δ{sub N}=0, of degree (N−3)! determining the solutions. Δ{sub N} is the sparse resultant of the system of polynomial scattering equations and it can be identified as the hyperdeterminant of a multidimensional matrix of border format within the terminology of Gel’fand, Kapranov and Zelevinsky. Macaulay’s Unmixedness Theorem is used to show that the polynomials of the scattering equations constitute a regular sequence, enabling the Hilbert series of the variety determined by the scattering equations to be calculated, independently showing that they have (N−3)! solutions.

  16. Ordinary differential equations.

    Science.gov (United States)

    Lebl, Jiří

    2013-01-01

    In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice. As an example, we work out the equations arising in Michaelis-Menten kinetics and give a short introduction to using Matlab for their numerical solution.

  17. On the Raychaudhuri equation

    Indian Academy of Sciences (India)

    continuous medium is μgrav ≡ μ + 3p/c2. Particular versions of this equation had been obtained earlier, at centers of symmetry by Tolman and Synge (see Raychaud- .... (8) by l ˙l and integrate to find. 3( ˙l)2 − κμl2 − Λl2 = const. (10). This is just the Friedmann equation which governs the time evolution of FLRW universe ...

  18. Equations of radiation hydrodynamics

    International Nuclear Information System (INIS)

    Mihalas, D.

    1982-01-01

    The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented

  19. The Bernoulli-Poiseuille Equation.

    Science.gov (United States)

    Badeer, Henry S.; Synolakis, Costas E.

    1989-01-01

    Describes Bernoulli's equation and Poiseuille's equation for fluid dynamics. Discusses the application of the combined Bernoulli-Poiseuille equation in real flows, such as viscous flows under gravity and acceleration. (YP)

  20. Introduction to partial differential equations

    CERN Document Server

    Greenspan, Donald

    2000-01-01

    Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

  1. Jacobi equations as Lagrange equations of the deformed Lagrangian

    International Nuclear Information System (INIS)

    Casciaro, B.

    1995-03-01

    We study higher-order variational derivatives of a generic Lagrangian L 0 = L 0 (t,q,q). We introduce two new Lagrangians, L 1 and L 2 , associated to the first and second-order deformations of the original Lagrangian L 0 . In terms of these Lagrangians, we are able to establish simple relations between the variational derivatives of different orders of a Lagrangian. As a consequence of these relations the Euler-Lagrange and the Jacobi equations are obtained from a single variational principle based on L 1 . We can furthermore introduce an associated Hamiltonian H 1 = H 1 (t,q,q radical,η,η radical) with η equivalent to δq. If L 0 is independent of time then H 1 is a conserved quantity. (author). 15 refs

  2. Boussinesq evolution equations

    DEFF Research Database (Denmark)

    Bredmose, Henrik; Schaffer, H.; Madsen, Per A.

    2004-01-01

    This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...

  3. Quadratic Diophantine equations

    CERN Document Server

    Andreescu, Titu

    2015-01-01

    This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

  4. Stochastic porous media equations

    CERN Document Server

    Barbu, Viorel; Röckner, Michael

    2016-01-01

    Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.

  5. Equations of mathematical physics

    CERN Document Server

    Tikhonov, A N

    2011-01-01

    Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri

  6. Partial differential equations

    CERN Document Server

    Agranovich, M S

    2002-01-01

    Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener

  7. Generalized estimating equations

    CERN Document Server

    Hardin, James W

    2002-01-01

    Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th

  8. Nonlinear wave equations

    CERN Document Server

    Li, Tatsien

    2017-01-01

    This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

  9. Systematic Equation Formulation

    DEFF Research Database (Denmark)

    Lindberg, Erik

    2007-01-01

    A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....

  10. Test equating methods and practices

    CERN Document Server

    Kolen, Michael J

    1995-01-01

    In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...

  11. Conservation laws for equations related to soil water equations

    OpenAIRE

    C. M. Khalique; F. M. Mahomed

    2005-01-01

    We obtain all nontrivial conservation laws for a class of ( 2+1 ) nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.

  12. Conservation laws for equations related to soil water equations

    Directory of Open Access Journals (Sweden)

    Khalique C. M.

    2005-01-01

    Full Text Available We obtain all nontrivial conservation laws for a class of ( 2+1 nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.

  13. Coupled Higgs field equation and Hamiltonian amplitude equation ...

    Indian Academy of Sciences (India)

    Abstract. In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the ...

  14. Coupled Higgs field equation and Hamiltonian amplitude equation ...

    Indian Academy of Sciences (India)

    In this paper, coupled Higgs field equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian ...

  15. CALL FOR PAPERS: Special issue: One hundred years of PVI, the Fuchs Painlevé equation

    Science.gov (United States)

    Clarkson, P. A.; Joshi, N.; Mazzocco, M.; Nijhoff, F. W.; Noumi, M.

    2005-10-01

    This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `One hundred years of Painlevé VI, the Fuchs Painlevé equation'. The motivation behind this special issue is to celebrate the centenary of the discovery of this famous differential equation. The Editorial Board has invited P A Clarkson, N Joshi, M Mazzocco, F W Nijhoff and M Noumi to serve as Guest Editors for the issue. The nonlinear ordinary differential equation, which is nowadays known as the Painlevé VI (PVI) equation, is one of the most important differential equations in mathematical physics. It was discovered 100 years ago by Richard Fuchs (son of the famous mathematician Lazarus Fuchs) and reported for the first time in Comptes Rendus de l'Academie des Sciences Paris 141 555 8 (1905). Gambier, in his seminal paper of 1906, included this equation as the top equation in the list of what are now known as the six Painlevé transcendental equations. The Painlevé list emerged from the work on the classification of all ordinary second-order differential equations whose general solution are `uniform', in the sense that there are no movable (i.e. as a function of the initial data) singularities (meaning branch points) worse than poles. The latter is known as the Painlevé property. As the top equation in the Painlevé list of transcendental equations, the importance of PVI can be appreciated by recognizing that this is a universal differential equation, which is the most general (in terms of number of free parameters) of the known second order ODEs defining nonlinear special functions. As such, parallels can be drawn between the role played by PVI transcendents in the nonlinear case and the hypergeometric functions at the linear level. In fact, the monograph From Gauss to Painlevé by K Iwasaki, H Kimura, S Shimomura and M Yoshida (Vieweg, 1991), draws very clearly the line stretching over more than 150 years of special function theory in which PVI is

  16. First-order partial differential equations in classical dynamics

    Science.gov (United States)

    Smith, B. R.

    2009-12-01

    Carathèodory's classic work on the calculus of variations explores in depth the connection between ordinary differential equations and first-order partial differential equations. The n second-order ordinary differential equations of a classical dynamical system reduce to a single first-order differential equation in 2n independent variables. The general solution of first-order partial differential equations touches on many concepts central to graduate-level courses in analytical dynamics including the Hamiltonian, Lagrange and Poisson brackets, and the Hamilton-Jacobi equation. For all but the simplest dynamical systems the solution requires one or more of these techniques. Three elementary dynamical problems (uniform acceleration, harmonic motion, and cyclotron motion) can be solved directly from the appropriate first-order partial differential equation without the use of advanced methods. The process offers an unusual perspective on classical dynamics, which is readily accessible to intermediate students who are not yet fully conversant with advanced approaches.

  17. The Maxwell equations in a uniformly accelerated frame

    International Nuclear Information System (INIS)

    Torres del Castillo, G.F.; Perez S, C.I.

    2007-01-01

    The solution of the source-free Maxwell equations in a uniformly accelerated frame of reference is expressed in terms of a single complex scalar potential that obeys a second-order equation. The field of a static electric charge is obtained as an example of a stationary axisymmetric field. (Author)

  18. Reduction of structured population models to threshold-type delay equations and functional differential equations: A case study

    Energy Technology Data Exchange (ETDEWEB)

    Smith, H.L. (Arizona State Univ., Tempe (United States))

    1993-01-01

    It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability. 28 refs., 2 figs.

  19. A simultaneous equations model of fiscal policy interactions

    NARCIS (Netherlands)

    Allers, Maarten A.; Elhorst, J. Paul

    Existing studies of fiscal policy interactions are based on single equation (SE) models of either taxation or expenditures, without specifying the underlying social welfare function, without taking account of budget constraints and without allowing for cost differences between jurisdictions. Taking

  20. Model Compaction Equation

    African Journals Online (AJOL)

    Petrophysical, Decompaction and Linear Regression techniques were used to investigate overpressure, degree of compaction and to derive a model compaction equation for. -1. -1 hydrostatic sandstones. Compaction coefficients obtained range from 0.0003 - 0.0005 m (averaging 0.0004 m ) and percentage compaction ...

  1. Structural Equation Model Trees

    Science.gov (United States)

    Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

    2013-01-01

    In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…

  2. The Freudenstein Equation

    Indian Academy of Sciences (India)

    Design of Four-Link Mechanisms. Ashitava Ghosal. Ashitava Ghosal is a. Professor in the Depart- ment of Mechanical. Engineering and Centre for Product Design, IISc,. Bangalore. His research interests are in the areas of analysis and design of mechanisms and ... Freudenstein's thesis and the equation named af- ter him.

  3. On the Raychaudhuri equation

    Indian Academy of Sciences (India)

    Amalkumar Raychaudhuri's remarkable paper [1] for the first time gave a general derivation of the fundamental equation of gravitational attraction for pressure- free matter, showing the repulsive nature of a positive cosmological constant, and underlying the basic singularity theorem (see below). He used special coordinates.

  4. Solving Equations Applet Project

    OpenAIRE

    Thatcher, Kimberly

    2011-01-01

    The purpose of this paper is to summarize a Masters Project for the MMath Degree. The purpose of the project was to create and evaluate an applet that maintains the advantages of the existent manipulatives (Hands-On Equations® and the NLVM applet) while also overcoming the limitations of each. Another product of this project is accompanying lesson plans for teachers.

  5. Differential Equations as Actions

    DEFF Research Database (Denmark)

    Ronkko, Mauno; Ravn, Anders P.

    1997-01-01

    We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...

  6. Stochastic nonlinear beam equations

    Czech Academy of Sciences Publication Activity Database

    Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan

    2005-01-01

    Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005

  7. A Quadratic Spring Equation

    Science.gov (United States)

    Fay, Temple H.

    2010-01-01

    Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

  8. Differential Equation of Equilibrium

    African Journals Online (AJOL)

    user

    Department of Civil Engineering. University of Nigeria Nsukka. ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak.

  9. The Freudenstein Equation

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 8. The Freudenstein Equation - Design of Four-Link Mechanisms. Ashitava Ghosal. General Article Volume 15 Issue 8 August 2010 pp 699-710. Fulltext. Click here to view fulltext PDF. Permanent link:

  10. Equational binary decision diagrams

    NARCIS (Netherlands)

    J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)

    2000-01-01

    textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and

  11. An invariance of CDF equation

    International Nuclear Information System (INIS)

    Tian Chou.

    1991-05-01

    It is important but difficult to find the invariant groups for the differential equations. We found a new invariant group for the MKdV equation. In this paper, we present a new invariance for the CDF equation. By using this invariance, we obtain some new solutions of CDF equation. (author). 5 refs

  12. Lectures on partial differential equations

    CERN Document Server

    Petrovsky, I G

    1992-01-01

    Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.

  13. Quantum equations from Brownian motions

    International Nuclear Information System (INIS)

    Rajput, B.S.

    2011-01-01

    Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)

  14. Anticipated backward stochastic differential equations

    OpenAIRE

    Peng, Shige; Yang, Zhe

    2007-01-01

    In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.

  15. Elements of partial differential equations

    CERN Document Server

    Sneddon, Ian Naismith

    1957-01-01

    Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st

  16. Elimination of variables in simple laser equations

    Energy Technology Data Exchange (ETDEWEB)

    Ning, C.Z.; Haken, H. (Stuttgart Univ. (Germany). Inst. fuer Theoretische Physik)

    1992-08-01

    The usual way of obtaining rate equations (RE) and a single equation for the field amplitude (EFA) from the semiclassical laser equations (Lorentz-Haken model) is reexamined by undertaking a systematic elimination procedure developed in synergetics. The RE and EFA are justified in the case 1 ({gamma}{sub perpendicular} {sub to}>> {gamma}{sub parallel}, {kappa}) and case 2 ({gamma}{sub perpendicular} {sub to}, {gamma}{sub parallel}>>{kappa}), respectively. We show that, because the eliminated variable happens to contain a considerable contribution from an unstable mode, the usual elimination technique in the case 3 ({gamma}{sub perpendicular} {sub to}, {kappa}>>{gamma}{sub parallel}) leads to an inconsistency. As important by-products we obtain the RE and EFA for arbitrary cavity relaxation constant ({kappa}). Some remarks are given on the direct elimination technique in the non-diagonal representation in the study of instabilities. (orig.).

  17. Crank-Nicolson - Differential quadrature algorithms for the Kawahara equation

    Energy Technology Data Exchange (ETDEWEB)

    Korkmaz, Alper [Anadolu Guzel Sanatlar Lisesi, Eskisehir Osmangazi University, Kuetahya (Turkey)], E-mail: alperkorkmaz7@gmail.com; Dag, Idris [Computer Engineering Department, Eskisehir Osmangazi University, Eskisehir (Turkey)], E-mail: idag@ogu.edu.tr

    2009-10-15

    The Kawahara equation is solved numerically using both Lagrange interpolation polynomials based differential quadrature method and cosine expansion based differential quadrature method. The travelling single solitary wave simulation is pictured. Maximum and discrete mean square error norms, lowest three conserved quantities are computed. Height, peak position and velocity of single solitary wave at various times are also computed for both methods. Breakup of an arbitrary single solitary wave into solitons and oscillatory shock wave generation from single solitary wave are studied.

  18. Crank-Nicolson - Differential quadrature algorithms for the Kawahara equation

    International Nuclear Information System (INIS)

    Korkmaz, Alper; Dag, Idris

    2009-01-01

    The Kawahara equation is solved numerically using both Lagrange interpolation polynomials based differential quadrature method and cosine expansion based differential quadrature method. The travelling single solitary wave simulation is pictured. Maximum and discrete mean square error norms, lowest three conserved quantities are computed. Height, peak position and velocity of single solitary wave at various times are also computed for both methods. Breakup of an arbitrary single solitary wave into solitons and oscillatory shock wave generation from single solitary wave are studied.

  19. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

    Directory of Open Access Journals (Sweden)

    Hamidreza Rezazadeh

    2014-05-01

    Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

  20. Derivation of stable Burnett equations for rarefied gas flows.

    Science.gov (United States)

    Singh, Narendra; Jadhav, Ravi Sudam; Agrawal, Amit

    2017-07-01

    A set of constitutive relations for the stress tensor and heat flux vector for the hydrodynamic description of rarefied gas flows is derived in this work. A phase density function consistent with Onsager's reciprocity principle and H theorem is utilized to capture nonequilibrium thermodynamics effects. The phase density function satisfies the linearized Boltzmann equation and the collision invariance property. Our formulation provides the correct value of the Prandtl number as it involves two different relaxation times for momentum and energy transport by diffusion. Generalized three-dimensional constitutive equations for different kinds of molecules are derived using the phase density function. The derived constitutive equations involve cross single derivatives of field variables such as temperature and velocity, with no higher-order derivative in higher-order terms. This is remarkable feature of the equations as the number of boundary conditions required is the same as needed for conventional Navier-Stokes equations. Linear stability analysis of the equations is performed, which shows that the derived equations are unconditionally stable. A comparison of the derived equations with existing Burnett-type equations is presented and salient features of our equations are outlined. The classic internal flow problem, force-driven compressible plane Poiseuille flow, is chosen to verify the stable Burnett equations and the results for equilibrium variables are presented.

  1. Multiscale functions, scale dynamics, and applications to partial differential equations

    Science.gov (United States)

    Cresson, Jacky; Pierret, Frédéric

    2016-05-01

    Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

  2. Classical Diophantine equations

    CERN Document Server

    1993-01-01

    The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...

  3. Energy master equation

    DEFF Research Database (Denmark)

    Dyre, Jeppe

    1995-01-01

    energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk model—the energy master equation...... (EME)—is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...

  4. Damped nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Nicholson, D.R.; Goldman, M.V.

    1976-01-01

    High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time

  5. Differential equations with Mathematica

    CERN Document Server

    Abell, Martha L

    2004-01-01

    The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica

  6. Fun with Differential Equations

    Indian Academy of Sciences (India)

    IAS Admin

    tion of ® with ¼=2. One can use the uniqueness of solutions of differential equations to prove the addition formulae for sin(t1 +t2), etc. But instead of continuing with this thought process, let us do something more interesting. Now we shall consider another system. Fix 0 < < 1. I am looking for three real-valued functions x(t), ...

  7. Generalized reduced MHD equations

    International Nuclear Information System (INIS)

    Kruger, S.E.; Hegna, C.C.; Callen, J.D.

    1998-07-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson

  8. Mathematics and Maxwell's equations

    International Nuclear Information System (INIS)

    Boozer, Allen H

    2010-01-01

    The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.

  9. Action principles for the Vlasov equation

    International Nuclear Information System (INIS)

    Ye, H.; Morrison, P.J.

    1992-01-01

    Five action principles for the Vlasov--Poisson and Vlasov--Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov--Maxwell equations are altered so as to produce the Vlasov--Poisson equation upon variation with respect to only the particle variables, and one action principle previously known for the Vlasov--Poisson equation is altered to produce the Vlasov--Maxwell equations upon variations with respect to particle and field variables independently. Also, a new action principle for both systems, which is called the leaf action, is presented. This new action has the desirable features of using only a single generating function as the dynamical variable for describing the particle distribution, and manifestly preserving invariants of the system known as Casimir invariants. The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables

  10. Single Electrode Heat Effects

    DEFF Research Database (Denmark)

    Jacobsen, Torben; Broers, G. H. J.

    1977-01-01

    The heat evolution at a single irreversibly working electrode is treated onthe basis of the Brønsted heat principle. The resulting equation is analogous to the expression for the total heat evolution in a galvanic cellwith the exception that –DeltaS is substituted by the Peltier entropy, Delta......SP, of theelectrode reaction. eta is the overvoltage at the electrode. This equation is appliedto a high temperature carbonate fuel cell. It is shown that the Peltier entropyterm by far exceeds the heat production due to the irreversible losses, and thatthe main part of heat evolved at the cathode is reabsorbed...

  11. Computing generalized Langevin equations and generalized Fokker-Planck equations.

    Science.gov (United States)

    Darve, Eric; Solomon, Jose; Kia, Amirali

    2009-07-07

    The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

  12. Equations of the mixed type

    CERN Document Server

    Bitsadze, A V

    1963-01-01

    Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parab

  13. Non-oscillation domains of differential equations with two parameters

    CERN Document Server

    Mingarelli, Angelo B

    1988-01-01

    This research monograph is an introduction to single linear differential equations (systems) with two parameters and extensions to difference equations and Stieltjes integral equations. The scope is a study of the values of the parameters for which the equation has one solution(s) having one (finitely many) zeros. The prototype is Hill's equation or Mathieu's equation. For the most part no periodicity assumptions are used and when such are made, more general notions such as almost periodic functions are introduced, extending many classical and introducing many new results. Many of the proofs in the first part are variational thus allowing for natural extensions to more general settings later. The book should be accessible to graduate students and researchers alike and the proofs are, for the most part, self-contained.

  14. Soliton solutions for ABS lattice equations: I. Cauchy matrix approach

    Science.gov (United States)

    Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo

    2009-10-01

    In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.

  15. Inferring Mathematical Equations Using Crowdsourcing.

    Directory of Open Access Journals (Sweden)

    Szymon Wasik

    Full Text Available Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players.

  16. Inferring Mathematical Equations Using Crowdsourcing.

    Science.gov (United States)

    Wasik, Szymon; Fratczak, Filip; Krzyskow, Jakub; Wulnikowski, Jaroslaw

    2015-01-01

    Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players.

  17. Ordinary differential equations

    CERN Document Server

    Cox, William

    1995-01-01

    Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further

  18. Partial differential equations

    CERN Document Server

    Sloan, D; Süli, E

    2001-01-01

    /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in

  19. Elliptic partial differential equations

    CERN Document Server

    Han, Qing

    2011-01-01

    Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo

  20. Hyperbolic partial differential equations

    CERN Document Server

    Lax, Peter D

    2006-01-01

    The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of soluti

  1. Partial differential equations

    CERN Document Server

    Levine, Harold

    1997-01-01

    The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.

  2. Nonelliptic Partial Differential Equations

    CERN Document Server

    Tartakoff, David S

    2011-01-01

    This book provides a very readable description of a technique, developed by the author years ago but as current as ever, for proving that solutions to certain (non-elliptic) partial differential equations only have real analytic solutions when the data are real analytic (locally). The technique is completely elementary but relies on a construction, a kind of a non-commutative power series, to localize the analysis of high powers of derivatives in the so-called bad direction. It is hoped that this work will permit a far greater audience of researchers to come to a deep understanding of this tec

  3. Kuznetsov equation with variable coefficients

    Indian Academy of Sciences (India)

    like solutions of the PDE in (2+1) dimension with variable coefficients. ... Shivamoggi [12] gives only four polynomial conservation laws of the ZK equation ..... [3] P J Olver, Application of Lie group to differential equation (Springer, New York,.

  4. Conservational PDF Equations of Turbulence

    Science.gov (United States)

    Shih, Tsan-Hsing; Liu, Nan-Suey

    2010-01-01

    Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application

  5. Functional equations for Feynman integrals

    International Nuclear Information System (INIS)

    Tarasov, O.V.

    2011-01-01

    New types of equations for Feynman integrals are found. It is shown that Feynman integrals satisfy functional equations connecting integrals with different kinematics. A regular method is proposed for obtaining such relations. The derivation of functional equations for one-loop two-, three- and four-point functions with arbitrary masses and external momenta is given. It is demonstrated that functional equations can be used for the analytic continuation of Feynman integrals to different kinematic domains

  6. Classical solutions of quasielliptic equations

    International Nuclear Information System (INIS)

    Belonosov, V S

    1999-01-01

    Fundamental solutions of quasielliptic equations are constructed; this allows the author to develop a relevant theory of volume potentials, establish estimates for the Holder norms of solutions of equations with constant coefficients, and extend them after that to equations with variable coefficients. As a result, sharp Schauder-type interior estimates are obtained, of which the well-known classical results for elliptic and parabolic equations are special cases

  7. Solution of Finite Element Equations

    DEFF Research Database (Denmark)

    Krenk, Steen

    An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...... features that justify the development of specialized solution algorithms....

  8. Singularity: Raychaudhuri equation once again

    Indian Academy of Sciences (India)

    quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity. Keywords. Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity; loop quantum cosmology. PACS Nos 04.20.Jb; 04.2 ...

  9. Equation with the many fathers

    DEFF Research Database (Denmark)

    Kragh, Helge

    1984-01-01

    In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...

  10. Completely integrable operator evolutionary equations

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.

    1979-01-01

    The authors present natural generalizations of classical completely integrable equations where the functions are replaced by arbitrary operators. Among these equations are the non-linear Schroedinger, the Korteweg-de Vries, and the modified KdV equations. The Lax representation and the Baecklund transformations are presented. (Auth.)

  11. On the Saha Ionization Equation

    Indian Academy of Sciences (India)

    Abstract. We revisit the Saha Ionization Equation in order to highlightthe rich interdisciplinary content of the equation thatstraddles distinct areas of spectroscopy, thermodynamics andchemical reactions. In a self-contained discussion, relegatedto an appendix, we delve further into the hidden message ofthe equation in terms ...

  12. Czy neopragmatyzm jest transcendentalizmem? Rozważania na tle filozofii Richarda Rorty’ego i Roberta Brandoma [Is Neopragmatism Transcendentalism? Considerations in the Background of the Philosophy of Robert Brandom and Richard Rorty

    Directory of Open Access Journals (Sweden)

    Daniel Żuromski

    2012-12-01

    Full Text Available The subject of this paper is one of the central problems of philosophy, which isaptly stated by Hilary Putnam: “How does mind/language hook on to the world?”.This question presupposes a model of knowledge which may be called “the subject--object model of knowledge”. However, contemporary philosophers such as WilfridSellars, Hilary Putnam, Donald Davidson, Richard Rorty, John McDowell, JohnHaugeland and Robert Brandom criticize this traditional model of knowledge. I claimthat at least some versions of neopragmatism look at this problem implicitly assum-ing a transcendental point of view. This istranscendentalism without transcendentalstandpointand can be found in Marek Siemek’s works. This transcendentalismcan be considered in two ways. First, as a therapy – a standpoint that is characteristicof Rorty, who demonstrated that the subject-object model of knowledge is optionaland contingent. Second, as constructivism – this standpoint is represented by Bran-dom, who tries to show that this traditional model is not autonomus.

  13. Reduction of infinite dimensional equations

    Directory of Open Access Journals (Sweden)

    Zhongding Li

    2006-02-01

    Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.

  14. Discovering evolution equations with applications

    CERN Document Server

    McKibben, Mark

    2011-01-01

    Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochast

  15. Two Approaches for Using Multiple Anchors in NEAT Equating: A Description and Demonstration

    Science.gov (United States)

    Moses, Tim; Deng, Weiling; Zhang, Yu-Li

    2011-01-01

    Nonequivalent groups with anchor test (NEAT) equating functions that use a single anchor can have accuracy problems when the groups are extremely different and/or when the anchor weakly correlates with the tests being equated. Proposals have been made to address these issues by incorporating more than one anchor into NEAT equating functions. These…

  16. On the helix equation

    Directory of Open Access Journals (Sweden)

    Taouil Hajer

    2012-08-01

    Full Text Available This paper is devoted to the helices processes, i.e. the solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω of the helix equation egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,oonumber end{eqnarray} H ( 0 ,ω = 0 ;   H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω where Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω is a dynamical system on a measurable space (Ω, ℱ. More precisely, we investigate dominated solutions and non differentiable solutions of the helix equation. For the last case, the Wiener helix plays a fundamental role. Moreover, some relations with the cocycle equation defined by Φ, are investigated. Ce papier est consacré aux hélices, c’est-à-dire les solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω de l’équation fonctionnelle egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,o onumber end{eqnarray} H ( 0 ,ω = 0 ;   H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω où Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω est un système dynamique défini sur un espace mesurable (Ω, ℱ. Plus présisément, nous déterminons d’abord les hélices dominées puis nous caractérisons les hélices non différentiables. Dans ce dernier cas, l’hélice de Wiener joue un rôle important. Nous précisons aussi quelques relations des hélices avec les cocycles définis par Φ.

  17. p-Euler equations and p-Navier-Stokes equations

    Science.gov (United States)

    Li, Lei; Liu, Jian-Guo

    2018-04-01

    We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

  18. Generalized quantal equation of motion

    International Nuclear Information System (INIS)

    Morsy, M.W.; Embaby, M.

    1986-07-01

    In the present paper, an attempt is made for establishing a generalized equation of motion for quantal objects, in which intrinsic self adjointness is naturally built in, independently of any prescribed representation. This is accomplished by adopting Hamilton's principle of least action, after incorporating, properly, the quantal features and employing the generalized calculus of variations, without being restricted to fixed end points representation. It turns out that our proposed equation of motion is an intrinsically self-adjoint Euler-Lagrange's differential equation that ensures extremization of the quantal action as required by Hamilton's principle. Time dependence is introduced and the corresponding equation of motion is derived, in which intrinsic self adjointness is also achieved. Reducibility of the proposed equation of motion to the conventional Schroedinger equation is examined. The corresponding continuity equation is established, and both of the probability density and the probability current density are identified. (author)

  19. Structural Equation Model Trees

    Science.gov (United States)

    Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

    2015-01-01

    In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model. PMID:22984789

  20. Elliptic scattering equations

    Energy Technology Data Exchange (ETDEWEB)

    Cardona, Carlos [Physics Division, National Center for Theoretical Sciences, National Tsing-Hua University,Hsinchu, Taiwan 30013 (China); Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)

    2016-06-16

    Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a ℂP{sup 2} space. We show that for the simplest integrand, namely the n−gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ−algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.

  1. Λ scattering equations

    Energy Technology Data Exchange (ETDEWEB)

    Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)

    2016-06-17

    The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.

  2. Scaling of differential equations

    CERN Document Server

    Langtangen, Hans Petter

    2016-01-01

    The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...

  3. Differential equations with involutions

    CERN Document Server

    Cabada, Alberto

    2015-01-01

    This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.

  4. Single-Photon Optomechanics

    Science.gov (United States)

    Nunnenkamp, A.; Børkje, K.; Girvin, S. M.

    2011-08-01

    Optomechanics experiments are rapidly approaching the regime where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. We show that in this limit the power spectrum has multiple sidebands and that the cavity response has several resonances in the resolved-sideband limit. Using master-equation simulations, we also study the crossover from the weak-coupling many-photon to the single-photon strong-coupling regime. Finally, we find non-Gaussian steady states of the mechanical oscillator when multiphoton transitions are resonant. Our study provides the tools to detect and take advantage of this novel regime of optomechanics.

  5. Mode decomposition evolution equations.

    Science.gov (United States)

    Wang, Yang; Wei, Guo-Wei; Yang, Siyang

    2012-03-01

    Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be

  6. Integrability of two coupled Kadomtsev–Petviashvili equations

    Indian Academy of Sciences (India)

    2011-08-02

    Aug 2, 2011 ... (5) where K is the amplitude of the wave, into the linear terms of the evolution equation, to determine the dispersion relation between k,r and c. We then substitute the single-soliton solution u(x, y, t) = R(ln f (x, y, t))xx ,. (6) where R is a constant, into the given equation, where the auxiliary function f (x, y, t) is.

  7. Novel loop-like solitons for the generalized Vakhnenko equation

    International Nuclear Information System (INIS)

    Zhang Min; Ma Yu-Lan; Li Bang-Qing

    2013-01-01

    A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method. The solution includes an arbitrary function of an independent variable. Based on the solution, two hyperbolic functions are chosen to construct new solitons. Novel single-loop-like and double-loop-like solitons are found for the equation

  8. Lectures on differential equations for Feynman integrals

    International Nuclear Information System (INIS)

    Henn, Johannes M

    2015-01-01

    Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations (DE). These lectures give a review of these developments, while not assuming any prior knowledge of the subject. After an introduction to DE for Feynman integrals, we point out how they can be simplified using algorithms available in the mathematical literature. We discuss how this is related to a recent conjecture for a canonical form of the equations. We also discuss a complementary approach that is based on properties of the space–time loop integrands, and explain how the ideas of leading singularities and d-log representations can be used to find an optimal basis for the DE. Finally, as an application of these ideas we show how single-scale integrals can be bootstrapped using the Drinfeld associator of a DE. (topical review)

  9. Equations for studies of feedback stabilization

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1998-01-01

    Important ideal magnetohydrodynamic (MHD) instabilities grow slowly when a conducting wall surrounds a toroidal plasma. Feedback stabilization of these instabilities may be required for tokamaks and other magnetic confinement concepts to achieve adequate plasma pressure and self-driven current for practical fusion power. Equations are derived for simulating feedback stabilization, which require the minimum information about an ideal plasma for an exact analysis. The equations are solved in the approximation of one unstable mode, one wall circuit, one feedback circuit, and one sensor circuit. The analysis based on a single unstable mode is shown to be mathematically equivalent to the standard analysis of feedback of the axisymmetric vertical instability of tokamaks. Unlike that analysis, the method presented here applies to multiple modes that are coupled by the wall and to arbitrary toroidal mode numbers. copyright 1998 American Institute of Physics

  10. Integral equations and their applications

    CERN Document Server

    Rahman, M

    2007-01-01

    For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of integral equations governing the physical situation of the problems. It also contains elegant analytical and numerical methods, and an important topic of the variational principles. Primarily intended for senior undergraduate students and first year postgraduate students of engineering and science courses, students of mathematical and physical sciences will also find many sections of direct relevance. The book contains eig...

  11. Differential equations methods and applications

    CERN Document Server

    Said-Houari, Belkacem

    2015-01-01

    This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .

  12. Introduction to partial differential equations

    CERN Document Server

    Borthwick, David

    2016-01-01

    This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.

  13. Equations Holding in Hilbert Lattices

    Science.gov (United States)

    Mayet, René

    2006-07-01

    We produce and study several sequences of equations, in the language of orthomodular lattices, which hold in the ortholattice of closed subspaces of any classical Hilbert space, but not in all orthomodular lattices. Most of these equations hold in any orthomodular lattice admitting a strong set of states whose values are in a real Hilbert space. For some of these equations, we give conditions under which they hold in the ortholattice of closed subspaces of a generalised Hilbert space. These conditions are relative to the dimension of the Hilbert space and to the characteristic of its division ring of scalars. In some cases, we show that these equations cannot be deduced from the already known equations, and we study their mutual independence. To conclude, we suggest a new method for obtaining such equations, using the tensorial product.

  14. Stochastic partial differential equations

    CERN Document Server

    Lototsky, Sergey V

    2017-01-01

    Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...

  15. JWL Equation of State

    Energy Technology Data Exchange (ETDEWEB)

    Menikoff, Ralph [Los Alamos National Laboratory

    2015-12-15

    The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.

  16. Hyperbolic Methods for Einstein's Equations

    Directory of Open Access Journals (Sweden)

    Reula Oscar

    1998-01-01

    Full Text Available I review evolutionary aspects of general relativity, in particular those related to the hyperbolic character of the field equations and to the applications or consequences that this property entails. I look at several approaches to obtaining symmetric hyperbolic systems of equations out of Einstein's equations by either removing some gauge freedoms from them, or by considering certain linear combinations of a subset of them.

  17. The generalized Airy diffusion equation

    Directory of Open Access Journals (Sweden)

    Frank M. Cholewinski

    2003-08-01

    Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.

  18. An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Moh’d Khier Al-Srihin

    2017-01-01

    Full Text Available In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to multiterm fractional differential equations, where we overcome the difficulty of computing iterated fractional derivatives, which are difficult to be computed in general. The terms of the series are obtained sequentially using a closed formula, where only integer derivatives have to be computed. Several examples are presented to illustrate the efficiency of the new approach and comparison with the Adomian decomposition method is performed.

  19. Peaked and Smooth Solitons for K*(4,1 Equation

    Directory of Open Access Journals (Sweden)

    Yongan Xie

    2013-01-01

    Full Text Available This paper is contributed to explore all possible single peak solutions for the K*(4,1 equation ut=uxu2+2α(uuxxx+2uxuxx. Our procedure shows that the K*(4,1 equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal limξ→±∞u=A≠0 or possesses compacton solutions only when limξ→±∞u=A=0. We present a new smooth soliton solution in an explicit form. Mathematical analysis and numeric graphs are provided for those soliton solutions of the K*(4,1 equation.

  20. Correct Linearization of Einstein's Equations

    Directory of Open Access Journals (Sweden)

    Rabounski D.

    2006-06-01

    Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.

  1. Half-linear differential equations

    CERN Document Server

    Dosly, Ondrej

    2005-01-01

    The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations and var

  2. The forced nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Kaup, D.J.; Hansen, P.J.

    1985-01-01

    The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

  3. Equations of motion for cross term modified gravitational field equations

    Energy Technology Data Exchange (ETDEWEB)

    Mueller, V. (Akademie der Wissenschaften der DDR, Potsdam-Babelsberg. Zentralinstitut fuer Astrophysik)

    1982-01-01

    As proposed by Treder, possible consequences of a unitary field theory may be described phenomenologically by additional cross terms in Einstein's equations. The violation of the weak principle of equivalence and potential observable effects are discussed in deriving hydrodynamic EIH equations. Conclusions on gravitational instabilities follow in the quasistatic approximation.

  4. Difference equations theory, applications and advanced topics

    CERN Document Server

    Mickens, Ronald E

    2015-01-01

    THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...

  5. An equation of state for sodium

    International Nuclear Information System (INIS)

    Browning, P.

    1981-03-01

    The equation of state (EOS) for sodium which has been employed in assessments of hypothetical accidents in liquid metal cooled fast breeder nuclear reactors has been in use for some years in the British programme. During this time some important experimental reference data, upon which the EOS is based, have been revised. The purpose of this report is primarily to update the sodium EOS by incorporating these revised data. In addition, a number of improvements have been made in the calculational technique used in deriving properties in the single phase. These refinements, which have indicated numerical errors in the earlier EOS output, have improved the precision of the reported data. (author)

  6. Short equational bases for ortholattices : proofs and countermodels.

    Energy Technology Data Exchange (ETDEWEB)

    McCune, W.; Padmanabhan, R.; Rose, M. A.; Veroff, R.

    2004-01-09

    This document contains proofs and countermodels in support of the paper ''Short Equational Bases for Ortholattices'', by the same set of authors. In that paper, short single axioms for ortholattices, orthomodular lattices, and modular ortholattices are presented, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. Other equational bases in terms of the Sheffer stroke and in terms of join, meet, and complement are presented. Computers were used extensively to find candidates, reject candidates, and search for proofs that candidates are single axioms.

  7. Solutions to Arithmetic Convolution Equations

    Czech Academy of Sciences Publication Activity Database

    Glöckner, H.; Lucht, L.G.; Porubský, Štefan

    2007-01-01

    Roč. 135, č. 6 (2007), s. 1619-1629 ISSN 0002-9939 R&D Projects: GA ČR GA201/04/0381 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic functions * Dirichlet convolution * polynomial equations * analytic equations * topological algebras * holomorphic functional calculus Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007

  8. Introduction to nonlinear dispersive equations

    CERN Document Server

    Linares, Felipe

    2015-01-01

    This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...

  9. Averaging of multivalued differential equations

    Directory of Open Access Journals (Sweden)

    G. Grammel

    2003-04-01

    Full Text Available Nonlinear multivalued differential equations with slow and fast subsystems are considered. Under transitivity conditions on the fast subsystem, the slow subsystem can be approximated by an averaged multivalued differential equation. The approximation in the Hausdorff sense is of order O(ϵ1/3 as ϵ→0.

  10. Fractals and the Kepler equation

    Science.gov (United States)

    Kasten, Volker

    1992-09-01

    The application of fractal mathematics to Kepler's equation is addressed. Complex solutions to Kepler's equation are considered along with methods to determine them. The roles of regions of attraction and their boundaries, Julia quantities, Fatou quantities, and fractal quantities in these methods are discussed.

  11. Enclosing Solutions of Integral Equations

    DEFF Research Database (Denmark)

    Madsen, Kaj; NA NA NA Caprani, Ole; Stauning, Ole

    1996-01-01

    We present a method for enclosing the solution of an integral equation. It is assumed that a solution exists and that the corresponding integral operator T is a contraction near y. When solving the integral equation by iteration we obtain a result which is normally different from y because...

  12. On asymptotics for difference equations

    NARCIS (Netherlands)

    Rafei, M.

    2012-01-01

    In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the

  13. Students' Understanding of Quadratic Equations

    Science.gov (United States)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  14. On the Saha Ionization Equation

    Indian Academy of Sciences (India)

    An example of the soci- etal impact of the famous equation can be discerned in a .... gaseous state and they behaved like a dilute classical gas, as in. Maxwell's kinetic theory. That is to say, the atoms do .... the Sackur–Tetrode equation for the entropy of an ideal gas at high temperatures, that Saha was quite aware of [13].

  15. Higher order equations of motion

    International Nuclear Information System (INIS)

    Bollini, C.G.; Giambiagi, J.J.

    1989-01-01

    The possibility that the motion of elementary particles be described by higher order differential equations induced by supersymmetry in higher dimensional space-time is discussed. The specific example of six dimensions writing the corresponding Lagrangian and equations of motion, is presented. (author) [pt

  16. Solving equations by topological methods

    Directory of Open Access Journals (Sweden)

    Lech Górniewicz

    2005-01-01

    Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.

  17. The relativistic electron wave equation

    International Nuclear Information System (INIS)

    Dirac, P.A.M.

    1977-08-01

    The paper was presented at the European Conference on Particle Physics held in Budapest between the 4th and 9th July of 1977. A short review is given on the birth of the relativistic electron wave equation. After Schroedinger has shown the equivalence of his wave mechanics and the matrix mechanics of Heisenberg, a general transformation theory was developed by the author. This theory required a relativistic wave equation linear in delta/delta t. As the Klein--Gordon equation available at this time did not satisfy this condition the development of a new equation became necessary. The equation which was found gave the value of the electron spin and magnetic moment automatically. (D.P.)

  18. Discovering Evolution Equations with Applications, 1 Deterministic Equations

    CERN Document Server

    McKibben, Mark A

    2010-01-01

    Most books written on evolution equations either provide a thorough in-depth treatment of a particular class of equations for beginners or present an assimilation of materials devoted to a very particular timely research direction. This volume offers an engaging, accessible account of a rudimentary core of theoretical results that should be understood by anyone studying evolution equations. The text gradually builds readers' intuition and the material culminates in a discussion of an area of active research. The author's conversational style sets the stage for the next step of theoretical deve

  19. Modeling and Prediction Using Stochastic Differential Equations

    DEFF Research Database (Denmark)

    Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp

    2016-01-01

    deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs......) for modeling and forecasting. It is argued that this gives models and predictions which better reflect reality. The SDE approach also offers a more adequate framework for modeling and a number of efficient tools for model building. A software package (CTSM-R) for SDE-based modeling is briefly described....... that describes the variation between subjects. The ODE setup implies that the variation for a single subject is described by a single parameter (or vector), namely the variance (covariance) of the residuals. Furthermore the prediction of the states is given as the solution to the ODEs and hence assumed...

  20. Extremophile Diatoms: Implications to the Drake Equation

    Science.gov (United States)

    Sterrenburg, Frithjof A. S.; Hoover, Richard B.

    2011-01-01

    Diatoms are unicellular Eukaryotes that (as a group and phylogenetically) are not strictly regarded as extremophiles , since the vast majority of diatoms are mesophilic photoautotrophs. However, among the terrestrial Eukaryotes, diatoms are by far the single group of organisms with the ability to inhabit the greatest range of hostile environments on Earth. They are the dominant eukaryotes in the polar regions; in fumaroles, hot springs and geysers; and in hypersaline and hyperalkaline lakes and pools. Cryophilic species such as Fragilaria sublinearis and Chaetoceras fragilis are able to carry out respiration at extremely low rates at low temperatures in darkness. The Drake Equation refers to the likelihood of there being intelligent life at the technological level of electromagnetic communication. However, consideration of the range of conditions suitable for the habitability of eukaryotic diatoms and prokaryotic extremophiles, the likelihood that life exists elsewhere in the cosmos becomes many orders of magnitude greater than that predicted by the classical Drake Equation. In this paper we review the characteristics of diatoms as eukaryotic extremophiles and consider the implications to adjustments needed to the Drake Equation to assess the possibility that life exists elsewhere in the Universe.

  1. Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

    Science.gov (United States)

    Ozdemir, Burhanettin

    2017-01-01

    The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

  2. Neoclassical MHD equations for tokamaks

    International Nuclear Information System (INIS)

    Callen, J.D.; Shaing, K.C.

    1986-03-01

    The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion

  3. Stochastic differential equations, backward SDEs, partial differential equations

    CERN Document Server

    Pardoux, Etienne

    2014-01-01

    This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the theory of reflected SDEs in the above mentioned framework and include exercises at the end of each chapter. Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Itô in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has...

  4. Fractional delayed damped Mathieu equation

    Science.gov (United States)

    Mesbahi, Afshin; Haeri, Mohammad; Nazari, Morad; Butcher, Eric A.

    2015-03-01

    This paper investigates the dynamical behaviour of the fractional delayed damped Mathieu equation. This system includes three different phenomena (fractional order, time delay, parametric resonance). The method of harmonic balance is employed to achieve approximate expressions for the transition curves in the parameter plane. The n = 0 and n = 1 transition curves (both lower and higher order approximations) are obtained. The dependencies of these curves on the system parameters and fractional orders are determined. Previous results for the transition curves reported for the damped Mathieu equation, delayed second-order oscillator, and fractional Mathieu equation are confirmed as special cases of the results for the current system.

  5. Soliton equations and pseudospherical surfaces

    International Nuclear Information System (INIS)

    Sasaki, R.

    1979-03-01

    All the soliton equations in 1+1 dimensions that can be solved by the AKNS 2x2 inverse scattering method (for example, the sine-Gordon, KdV or Modified KdV equations) are shown to describe pseudospherical surfaces, i.e. surfaces of constant negative Gaussian curvature. This result provides a unified picture of all these soliton equations. Geometrical interpretations of characteristic properties like infinite numbers of conservation laws, and Baecklund transformations and of the soliton solutions themselves are presented. The important role of scale transformations as generating one parameter families of pseudospherical surfaces is pointed out. (Auth.)

  6. Galois theory of difference equations

    CERN Document Server

    Put, Marius

    1997-01-01

    This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.

  7. Integral equation methods for electromagnetics

    CERN Document Server

    Volakis, John

    2012-01-01

    This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the mo

  8. Elliptic Yang-Mills equation.

    Science.gov (United States)

    Tian, Gang

    2002-11-26

    We discuss some recent progress on the regularity theory of the elliptic Yang-Mills equation. We start with some basic properties of the elliptic Yang-Mills equation, such as Coulomb gauges, monotonicity, and curvature estimates. Next we discuss singularity of stationary Yang-Mills connections and compactness theorems on Yang-Mills connections with bounded L(2) norm of curvature. We also discuss in some detail self-dual solutions of the Yang-Mills equation and describe a compactification of their moduli space.

  9. Elliptic Yang–Mills equation

    OpenAIRE

    Tian, Gang

    2002-01-01

    We discuss some recent progress on the regularity theory of the elliptic Yang–Mills equation. We start with some basic properties of the elliptic Yang–Mills equation, such as Coulomb gauges, monotonicity, and curvature estimates. Next we discuss singularity of stationary Yang–Mills connections and compactness theorems on Yang–Mills connections with bounded L2 norm of curvature. We also discuss in some detail self-dual solutions of the Yang–Mills equation and describe a compactification of the...

  10. Lectures on ordinary differential equations

    CERN Document Server

    Hurewicz, Witold

    1958-01-01

    Hailed by The American Mathematical Monthly as ""a rigorous and lively introduction,"" this text explores a topic of perennial interest in mathematics. The author, a distinguished mathematician and formulator of the Hurewicz theorem, presents a clear and lucid treatment that emphasizes geometric methods. Topics include first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. Suitable for senior mathematics students, the text begins with an examination of differential equations of the first order in one unknown funct

  11. Iterative Splitting Methods for Differential Equations

    CERN Document Server

    Geiser, Juergen

    2011-01-01

    Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential

  12. Nonlinear integrodifferential equations as discrete systems

    Science.gov (United States)

    Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.

    1999-06-01

    We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.

  13. Direct 'delay' reductions of the Toda equation

    International Nuclear Information System (INIS)

    Joshi, Nalini

    2009-01-01

    A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference equations, sometimes referred to as delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painleve equations. The Lax pair associated with this equation is obtained, also by reduction. (fast track communication)

  14. Anthropometric predictive equations for estimating body composition

    Science.gov (United States)

    Salamat, Mohammad Reza; Shanei, Ahmad; Salamat, Amir Hossein; Khoshhali, Mehri; Asgari, Mahdi

    2015-01-01

    Background: Precise and accurate measurements of body composition are useful in achieving a greater understanding of human energy metabolism in physiology and in different clinical conditions, such as, cardiovascular disease and overall mortality. Dual-energy x-ray absorptiometry (DXA) can be used to measure body composition, but the easiest method to assess body composition is the use of anthropometric indices. This study has been designed to evaluate the accuracy and precision of body composition prediction equations by various anthropometric measures instead of a whole body DXA scan. Materials and Methods: We identified 143 adult patients underwent DXA evaluation of the whole body. The anthropometric indices were also measured. Datasets were split randomly into two parts. Multiple regression analysis with a backward stepwise elimination procedure was used as the derivation set and then the estimates were compared with the actual measurements from the whole-body scans for a validation set. The SPSS version 20 for Windows software was used in multiple regression and data analysis. Results: Using multiple linear regression analyses, the best equation for predicting the whole-body fat mass (R2 = 0.808) included the body mass index (BMI) and gender; the best equation for predicting whole-body lean mass (R2 = 0.780) included BMI, WC, gender, and age; and the best equation for predicting trunk fat mass (R2 = 0.759) included BMI, WC, and gender. Conclusions: Combinations of anthropometric measurements predict whole-body lean mass and trunk fat mass better than any of these single anthropometric indices. Therefore, the findings of the present study may be used to verify the results in patients with various diseases or diets. PMID:25709999

  15. Localization transition in one dimension using Wegner flow equations

    Science.gov (United States)

    Quito, Victor L.; Titum, Paraj; Pekker, David; Refael, Gil

    2016-09-01

    The flow-equation method was proposed by Wegner as a technique for studying interacting systems in one dimension. Here, we apply this method to a disordered one-dimensional model with power-law decaying hoppings. This model presents a transition as function of the decaying exponent α . We derive the flow equations and the evolution of single-particle operators. The flow equation reveals the delocalized nature of the states for α 1/2 , we present a strong-bond renormalization group structure based on iterating the three-site clusters, where we solve the flow equations perturbatively. This renormalization group approach allows us to probe the critical point (α =1 ). This method correctly reproduces the critical level-spacing statistics and the fractal dimensionality of the eigenfunctions.

  16. Fitting of a multiphase equation of state with swarm intelligence

    International Nuclear Information System (INIS)

    Cox, G A; Christie, M A

    2015-01-01

    Hydrocode calculations require knowledge of the variation of pressure of a material with density and temperature, which is given by the equation of state. An accurate model needs to account for discontinuities in energy, density and properties of a material across a phase boundary. When generating a multiphase equation of state the modeller attempts to balance the agreement between the available data for compression, expansion and phase boundary location. However, this can prove difficult because minor adjustments in the equation of state for a single phase can have a large impact on the overall phase diagram. This paper describes how combining statistical-mechanics-based condensed matter physics models with a stochastic analysis technique called particle swarm optimisation, yields multiphase equations of state which give good agreement with experiment over a wide range of pressure–temperature space. Aluminium and tin are used as test cases in the proof of principle described in this paper. (paper)

  17. Fitting of a multiphase equation of state with swarm intelligence.

    Science.gov (United States)

    Cox, G A; Christie, M A

    2015-10-14

    Hydrocode calculations require knowledge of the variation of pressure of a material with density and temperature, which is given by the equation of state. An accurate model needs to account for discontinuities in energy, density and properties of a material across a phase boundary. When generating a multiphase equation of state the modeller attempts to balance the agreement between the available data for compression, expansion and phase boundary location. However, this can prove difficult because minor adjustments in the equation of state for a single phase can have a large impact on the overall phase diagram. This paper describes how combining statistical-mechanics-based condensed matter physics models with a stochastic analysis technique called particle swarm optimisation, yields multiphase equations of state which give good agreement with experiment over a wide range of pressure-temperature space. Aluminium and tin are used as test cases in the proof of principle described in this paper.

  18. Reduction of the state vector by a nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Pearle, P.

    1976-01-01

    It is hypothesized that the state vector describes the physical state of a single system in nature. Then it is necessary that the state vector of a macroscopic apparatus not assume the form of a superposition of macroscopically distinguishable state vectors. To prevent this, it is suggested that a nonlinear term be added to the Schrodinger equation, which rapidly drives the amplitude of one or another of the state vectors in such a superposition to one, and the rest to zero. It is proposed that it is the phase angles of the amplitudes immediately after a measurement which determine which amplitude is driven to one. A diffusion equation is arrived at to describe the reduction of an ensemble of state vectors corresponding to an ensemble of macroscopically identically prepared experiments. Then a nonlinear term to add to the Schrodinger equation is presented, and it is shown that this leads to the diffusion equation in a weak-coupling approximation

  19. Analytical Solution of Mathieu Equation

    OpenAIRE

    Yerchuck, Dmitri; Dovlatova, Alla; Yerchak, Yauhen; Borovik, Felix

    2014-01-01

    The general solution of the homogeneous damped Mathieu equation in the analytical form, allowing its practical using in many applications, including superconductivity studies, without numerical calculations has been found.

  20. Kinks and the Dirac equation

    International Nuclear Information System (INIS)

    Skyrme, T.H.R.

    1994-01-01

    In a model quantum theory of interacting mesons, the motion of certain conserved particle-like structures is discussed. It is shown how collective coordinates may be introduced to describe them, leading, in lowest approximation, to a Dirac equation. (author)

  1. Saha equation in Rindler space

    Indian Academy of Sciences (India)

    The Saha equations for the photoionization process of hydrogen atoms and the creation of electron–positron pairs at high temperature are investigated in a reference frame undergoing a uniform accelerated motion. It is known as the Rindler space.

  2. An Investigation on Quadratic Equations.

    Science.gov (United States)

    Hirst, Keith

    1988-01-01

    Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)

  3. Solutions of Nonlocal -Laplacian Equations

    Directory of Open Access Journals (Sweden)

    Mustafa Avci

    2013-01-01

    Full Text Available In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.

  4. The quasilinear parabolic kirchhoff equation

    Directory of Open Access Journals (Sweden)

    Dawidowski Łukasz

    2017-04-01

    Full Text Available In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.

  5. Singularity: Raychaudhuri equation once again

    Indian Academy of Sciences (India)

    2015-11-27

    Keywords. Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quantum gravity; loop quantum cosmology. ... Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science (IWCCMP-2015). Posted on November 27, 2015. Guest Editors: Anurag ...

  6. Geophysical interpretation using integral equations

    CERN Document Server

    Eskola, L

    1992-01-01

    Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu­ med to have a back...

  7. Peakon–antipeakon interaction in the Dullin–Gottwald–Holm equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhou, Jiangbo, E-mail: zhoujiangbo@yahoo.cn [Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013 (China); Tian, Lixin [Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013 (China); Zhang, Wenbin [Taizhou Institute of Science and Technology, NUST, Taizhou, Jiangsu 225300 (China); Kumar, Sunil [Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand 831014 (India)

    2013-08-01

    In this Letter, we obtain a two-peakon solution to a special Dullin–Gottwald–Holm equation explicitly by direct computation, and then discuss the peakon–antipeakon interaction in this equation. Our results show that, like the Camassa–Holm equation, during the soliton absorption time, the peakon–antipeakon in this equation is essentially a single-peaked, double-cornered wave. However, the two corners may travel in opposite direction for some ω, which is different from that in the Camassa–Holm equation.

  8. Hidden Statistics of Schroedinger Equation

    Science.gov (United States)

    Zak, Michail

    2011-01-01

    Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

  9. Wave equations for pulse propagation

    Energy Technology Data Exchange (ETDEWEB)

    Shore, B.W.

    1987-06-24

    Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation.

  10. Geometrical Solutions of Quadratic Equations.

    Science.gov (United States)

    Grewal, A. S.; Godloza, L.

    1999-01-01

    Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)

  11. Single-dopant resonance in a single-electron transistor

    Science.gov (United States)

    Golovach, V. N.; Jehl, X.; Houzet, M.; Pierre, M.; Roche, B.; Sanquer, M.; Glazman, L. I.

    2011-02-01

    Single dopants in semiconductor nanostructures have been studied in great detail recently as they are good candidates for quantum bits, provided they are coupled to a detector. Here we report the coupling of a single As donor atom to a single-electron transistor (SET) in a silicon nanowire field-effect transistor. Both capacitive and tunnel coupling are achieved, the latter resulting in a dramatic increase of the conductance through the SET, by up to one order of magnitude. The experimental results are well explained by the rate-equation theory developed in parallel with the experiment.

  12. Analytical solutions of coupled-mode equations for microring ...

    Indian Academy of Sciences (India)

    equivalent to waveguide and single microring coupled system. The 3 × 3 coupled system is equivalent to waveguide and double microring coupled system. In this paper, we adopt a novel approach for obtaining coupled-mode equations for linearly distributed and circularly distributed multiwaveguide systems with different ...

  13. Meson Spectra: Power Law Potential Model in the Dirac Equation ...

    African Journals Online (AJOL)

    A single mass-spectra potential model has been used to predict the spectra of both light and heavy mesons (including leptonic decay-widths) in the Dirac equation. In fact a power law potential has been proposed with effective power where is the mass of the constituent quarks (in GeV) of the mesons considered.

  14. A Sesame Equation of State for Dense Ce

    Energy Technology Data Exchange (ETDEWEB)

    Greeff, Carl William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Crockett, Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2016-03-15

    We generated a new Sesame equation of state table for Ce. It is a single effective phase table for the high density phases α, α ', ϵ and liquid. Also, the EOS is meant to be used with a ramp to represent the initial low density γ phase.

  15. Computational partial differential equations using Matlab

    CERN Document Server

    Li, Jichun

    2008-01-01

    Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE

  16. Determination of the optical constants of a thin film supported on a ...

    African Journals Online (AJOL)

    The full expression for the minima of transmission and reflection spectra of a thin absorbing film are unwieldy transcendental functions of wavelength. Exact solutions of these equations for optical constants are, therefore, not single valued but can be uniquely determined at the extrema of the spectra instead. The solutions ...

  17. Equationally Compact Acts : Coproducts / Peeter Normak

    Index Scriptorium Estoniae

    Normak, Peeter

    1998-01-01

    In this article equational compactness of acts and its generalizations are discussed. As equational compactness does not carry over to coproducts a slight generalization of c-equational campactness is introduced. It is proved that a coproduct of acts is c-equationally compact if and only if all components are c-equationally campact

  18. The soil moisture velocity equation

    Science.gov (United States)

    Ogden, Fred L.; Allen, Myron B.; Lai, Wencong; Zhu, Jianting; Seo, Mookwon; Douglas, Craig C.; Talbot, Cary A.

    2017-06-01

    Numerical solution of the one-dimensional Richards' equation is the recommended method for coupling groundwater to the atmosphere through the vadose zone in hyperresolution Earth system models, but requires fine spatial discretization, is computationally expensive, and may not converge due to mathematical degeneracy or when sharp wetting fronts occur. We transformed the one-dimensional Richards' equation into a new equation that describes the velocity of moisture content values in an unsaturated soil under the actions of capillarity and gravity. We call this new equation the Soil Moisture Velocity Equation (SMVE). The SMVE consists of two terms: an advection-like term that accounts for gravity and the integrated capillary drive of the wetting front, and a diffusion-like term that describes the flux due to the shape of the wetting front capillarity profile divided by the vertical gradient of the capillary pressure head. The SMVE advection-like term can be converted to a relatively easy to solve ordinary differential equation (ODE) using the method of lines and solved using a finite moisture-content discretization. Comparing against analytical solutions of Richards' equation shows that the SMVE advection-like term is >99% accurate for calculating infiltration fluxes neglecting the diffusion-like term. The ODE solution of the SMVE advection-like term is accurate, computationally efficient and reliable for calculating one-dimensional vadose zone fluxes in Earth system and large-scale coupled models of land-atmosphere interaction. It is also well suited for use in inverse problems such as when repeat remote sensing observations are used to infer soil hydraulic properties or soil moisture.type="synopsis">type="main">Plain Language SummarySince its original publication in 1922, the so-called Richards' equation has been the only rigorous way to couple groundwater to the land surface through the unsaturated zone that lies between the water table and land surface. The soil

  19. The Use of Two Anchors in Nonequivalent Groups with Anchor Test (NEAT) Equating. Research Report. ETS RR-10-23

    Science.gov (United States)

    Moses, Tim; Deng, Weiling; Zhang, Yu-Li

    2010-01-01

    In the equating literature, a recurring concern is that equating functions that utilize a single anchor to account for examinee groups' nonequivalence are biased when the groups are extremely different and/or when the anchor only weakly measures what the tests measure. Several proposals have been made to address this equating bias by incorporating…

  20. Symmetry reductions of a particular set of equations of associativity in two-dimensional topological field theory

    Science.gov (United States)

    Conte, Robert; Gandarias, Maria Luz

    2005-02-01

    The WDVV equations of associativity arising in two-dimensional topological field theory can be represented, in the simplest nontrivial case, by a single third-order equation of the Monge-Ampère type. By investigating its Lie point symmetries, we reduce it to various nonlinear ordinary differential equations, and obtain several new explicit solutions.

  1. Exact results for the Boltzmann equation and Smoluchowski's coagulation equation

    International Nuclear Information System (INIS)

    Hendriks, E.M.

    1983-01-01

    Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)

  2. Approximations of Stochastic Partial Differential Equations

    OpenAIRE

    Di Nunno, Giulia; Zhang, Tusheng

    2014-01-01

    In this paper we show that solutions of stochastic partial differ- ential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic Burgers equations are discussed.

  3. Linear integral equations and soliton systems

    International Nuclear Information System (INIS)

    Quispel, G.R.W.

    1983-01-01

    A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

  4. Abstract methods in partial differential equations

    CERN Document Server

    Carroll, Robert W

    2012-01-01

    Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.

  5. How to obtain the covariant form of Maxwell's equations from the continuity equation

    International Nuclear Information System (INIS)

    Heras, Jose A

    2009-01-01

    The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations

  6. Extraction of dynamical equations from chaotic data

    International Nuclear Information System (INIS)

    Rowlands, G.; Sprott, J.C.

    1991-02-01

    A method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise. The equations facilitate calculation of fractal dimension, Lyapunov exponents and short-term predictions. The method is applied to data derived from numerical solutions of the Logistic equation, the Henon equations, the Lorenz equations and the Roessler equations. 10 refs., 5 figs

  7. First-order partial differential equations

    CERN Document Server

    Rhee, Hyun-Ku; Amundson, Neal R

    2001-01-01

    This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo

  8. Moduli of Riemann surfaces, transcendental aspects

    International Nuclear Information System (INIS)

    Hain, R.

    2000-01-01

    These notes are an informal introduction to moduli spaces of compact Riemann surfaces via complex analysis, topology and Hodge Theory. The prerequisites for the first lecture are just basic complex variables, basic Riemann surface theory up to at least the Riemann-Roch formula, and some algebraic topology, especially covering space theory. The first lecture covers moduli in genus 0 and genus 1 as these can be understood using relatively elementary methods, but illustrate many of the points which arise in higher genus. The notes cover more material than was covered in the lectures, and sometimes the order of topics in the notes differs from that in the lectures. We have seen in genus 1 case that M 1 is the quotient Γ 1 /X 1 of a contractible complex manifold X 1 = H by a discrete group Γ 1 = SL 2 (Z). The action of Γ 1 on X 1 is said to be virtually free - that is, Γ 1 has a finite index subgroup which acts (fixed point) freely on X 1 . In this section we will generalize this to all g >= 1 - we will sketch a proof that there is a contractible complex manifold Xg, called Teichmueller space, and a group Γ g , called the mapping class group, which acts virtually freely on X g . The moduli space of genus g compact Riemann surfaces is the quotient: M g = Γ g /X g . This will imply that M g has the structure of a complex analytic variety with finite quotient singularities. Teichmueller theory is a difficult and technical subject. Because of this, it is only possible to give an overview. In this lecture, we compute the orbifold Picard group of M g for all g >= 1. Recall that an orbifold line bundle over M g is a holomorphic line bundle L over Teichmueller space X g together with an action of the mapping class group Γ g on it such that the projection L → X g is Γ g -equivariant. An orbifold section of this line bundle is a holomorphic Γ g -equivariant section X g → L of L. This is easily seen to be equivalent to fixing a level l>= 3 and considering holomorphic line bundles over M g [l] with an Sp g (Z/lZ)-actionsuch that the projection is Sp g (Z/lZ)-equivariant. Working on M g [l] has the advantage that we can talk about algebraic line bundles more easily. An algebraic orbifold line bundle over M g is an algebraic line bundle over Mg[l] for some l equipped with an action of Sp g (Z/lZ) such that the projection to M g [l] is Sp g (Z/lZ) equivariant. A section of such a line bundle is simply an Sp g (Z/lZ)-equivariant section defined over M g [l]. Isomorphism of such orbifold line bundles is defined in the obvious way. Let Pic orb M g denote the group of isomorphisms classes of algebraic orbifold line bundles over M g . Our goal in this lecture is to compute this group. It is first useful to review some facts about the Picard group of a smooth projective variety

  9. Transcendental Political Systems and the Gravity Model

    Science.gov (United States)

    Lock, Connor

    2012-01-01

    This summer I have been working on an Army Deep Futures Model project named Themis. Themis is a JPL based modeling framework that anticipates possible future states for the world within the next 25 years. The goal of this framework is to determine the likelihood that the US Army will need to intervene on behalf of the US strategic interests. Key elements that are modeled within this tool include the world structure and major decisions that are made by key actors. Each actor makes decisions based on their goals and within the constraints of the structure of the system in which they are located. In my research I have focused primarily on the effects of structures upon the decision-making processes of the actors within them. This research is a natural extension of my major program at Georgetown University, where I am studying the International Political Economy and the structures that make it up. My basic goal for this summer project was to be a helpful asset to the Themis modeling team, with any research done or processes learned constituting a bonus.

  10. On the Transcendental Properties of Real Beings

    OpenAIRE

    Andrzej Maryniarczyk

    2016-01-01

    The article analyzes the metaphysical approach to the rational cognition of the world of persons and things. It shows the way in which metaphysicians reveal the essential and universal properties of the world and the laws that govern their being. Among these properties, the most important are as follows: to be a thing (that is, to have a concretely determined essence), to be one (that is, to be non-contradictory in itself), to be separate or distinct (that is, to be sovereign in being), and a...

  11. On the Transcendental Properties of Real Beings

    Directory of Open Access Journals (Sweden)

    Andrzej Maryniarczyk

    2016-06-01

    Full Text Available The article analyzes the metaphysical approach to the rational cognition of the world of persons and things. It shows the way in which metaphysicians reveal the essential and universal properties of the world and the laws that govern their being. Among these properties, the most important are as follows: to be a thing (that is, to have a concretely determined essence, to be one (that is, to be non-contradictory in itself, to be separate or distinct (that is, to be sovereign in being, and also to be a vehicle of truth, good, and beauty. Among the laws of being, in turn, the article indicates the law of identity, the law of non-contradiction, the law of the excluded middle, the law of the reason of being, the law of finality, and the law of perfection. These laws primarily show the source and foundation of the rational order.

  12. Tuukka Kaidesoja on Critical Realist Transcendental Realism

    Directory of Open Access Journals (Sweden)

    Groff Ruth

    2015-09-01

    Full Text Available I argue that critical realists think pretty much what Tukka Kaidesoja says that he himself thinks, but also that Kaidesoja’s objections to the views that he attributes to critical realists are not persuasive.

  13. Constituting objectivity: Transcendental perspectives on modern physics

    Science.gov (United States)

    Everett, Jonathan

    2012-05-01

    There is increasing interest in exploring Kantian approaches in the study of the history and philosophy of physics. The most well-known examples of this trend-Friedman's (2001), Ryckman's (2005) and DiSalle's (2006)-focus on Kantianism in the context of the development of the general theory of relativity. The edited collection Constituting Objectivity seeks to develop key Kantian insights-in the most part-in the context of later developments in physics: as well as discussing relativity the volume also provides Kantian interpretations of Bohr's development of quantum theory and continues to provide Kantian insight from later interpretations of quantum mechanics all the way through to considering noncommutative geometry and loop quantum gravity. The volume contains papers on a wide variety of subjects and offers an essential introduction to the breadth of Kantian trends in modern physics.

  14. Constructing Morality : Transcendental Arguments in Ethics

    NARCIS (Netherlands)

    de Maagt, S.

    2017-01-01

    How are moral claims justified? And is there an objective basis for morality? These fundamental questions of ethics are the central questions of this thesis. I explore and offer a partial defense of a so-called Kantian constructivist account of morality. I define Kantian constructivism as the

  15. On extension of solutions of a simultaneous system of iterative functional equations

    Directory of Open Access Journals (Sweden)

    Janusz Matkowski

    2009-01-01

    Full Text Available Some sufficient conditions which allow to extend every local solution of a simultaneous system of equations in a single variable of the form \\[ \\varphi(x = h (x, \\varphi[f_1(x],\\ldots,\\varphi[f_m(x],\\] \\[\\varphi(x = H (x, \\varphi[F_1(x],\\ldots,\\varphi[F_m(x],\\] to a global one are presented. Extensions of solutions of functional equations, both in single and in several variables, play important role (cf. for instance [M. Kuczma, Functional equations in a single variable, Monografie Mat. 46, Polish Scientific Publishers, Warsaw, 1968, M. Kuczma, B. Choczewski, R. Ger, Iterative functional equations, Encyclopedia of Mathematics and Its Applications v. 32, Cambridge, 1990, J. Matkowski, Iteration groups, commuting functions and simultaneous systems of linear functional equations, Opuscula Math. 28 (2008 4, 531-541].

  16. Hypergeometric solutions to Schr\\"odinger equations for the quantum Painlev\\'e equations

    OpenAIRE

    Nagoya, Hajime

    2011-01-01

    We consider Schr\\"odinger equations for the quantum Painlev\\'e equations. We present hypergeometric solutions of the Schr\\"odinger equations for the quantum Painlev\\'e equations, as particular solutions. We also give a representation theoretic correspondence between Hamiltonians of the Schr\\"odinger equations for the quantum Painlev\\'e equations and those of the KZ equation or the confluent KZ equations.

  17. Developing Semi-Analytical solutions for Saint-Venant Equations in the Uniform Flow Region

    Directory of Open Access Journals (Sweden)

    M.M. Heidari

    2016-09-01

    -Venant equations. The got transcendental function can then be simplified using various methods to get a model expressed as a rational function of s (the Laplace variable, possibly including a time delay. It is therefore important to develop simple analytical models able to accurately reproduce the dynamic behavior of the system in realistic conditions. Materials and Methods: Changes in water demand can create transient flow in irrigation networks. The Saint Venant equations are the equations governing open channel flow when unsteady flow propagates. In this research, the finite volume method using the time splitting scheme was employed to develop a computer code for solving the one dimensional unsteady flow equations. Considering stationary regime and small variations around it, the Saint-Venant equations around initial condition was linearized. The Laplace transform is applied to the linearized saint venant equations, leading to an ordinary differential equation in the space variable x and parameterized by the Laplace variable s. The integration of this equation lead to a transfer matrix, and gives the discharge Q*(x, s at any location with respect for the upstream discharge. This matrix is coupled with the downstream boundary condition and developed an equation that solved using Simpson integration algorithm. It should be noted numerical solution of developed equation is easier than solving fully dynamic saint venant and is less sensitive to the spatial step and the researcher simply writing code. Results and Discussion: Froud Number (F, variation of inflow discharge (ΔQ/Q, and dimensionless parameter of KF2 in which K is the kinematic flow number, are effective factors on accuracy of developed equation. In order to determine the effect of the factors on accuracy of presenting formula, several simulations were performed using numerical model. The presented formula and numerical model were compared for 10, 20 and 30 percent discharge variation and error calculated, the maximum

  18. Students' understanding of quadratic equations

    Science.gov (United States)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-05-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.

  19. Integration of quantum hydrodynamical equation

    Science.gov (United States)

    Ulyanova, Vera G.; Sanin, Andrey L.

    2007-04-01

    Quantum hydrodynamics equations describing the dynamics of quantum fluid are a subject of this report (QFD).These equations can be used to decide the wide class of problem. But there are the calculated difficulties for the equations, which take place for nonlinear hyperbolic systems. In this connection, It is necessary to impose the additional restrictions which assure the existence and unique of solutions. As test sample, we use the free wave packet and study its behavior at the different initial and boundary conditions. The calculations of wave packet propagation cause in numerical algorithm the division. In numerical algorithm at the calculations of wave packet propagation, there arises the problem of division by zero. To overcome this problem we have to sew together discrete numerical and analytical continuous solutions on the boundary. We demonstrate here for the free wave packet that the numerical solution corresponds to the analytical solution.

  20. Dynamics of partial differential equations

    CERN Document Server

    Wayne, C Eugene

    2015-01-01

    This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation.   The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...

  1. Introductory course on differential equations

    CERN Document Server

    Gorain, Ganesh C

    2014-01-01

    Introductory Course on DIFFERENTIAL EQUATIONS provides an excellent exposition of the fundamentals of ordinary and partial differential equations and is ideally suited for a first course of undergraduate students of mathematics, physics and engineering. The aim of this book is to present the elementary theories of differential equations in the forms suitable for use of those students whose main interest in the subject are based on simple mathematical ideas. KEY FEATURES: Discusses the subject in a systematic manner without sacrificing mathematical rigour. A variety of exercises drill the students in problem solving in view of the mathematical theories explained in the book. Worked out examples illustrated according to the theories developed in the book with possible alternatives. Exhaustive collection of problems and the simplicity of presentation differentiate this book from several others. Material contained will help teachers as well as aspiring students of different competitive examinations.

  2. Integration rules for scattering equations

    Energy Technology Data Exchange (ETDEWEB)

    Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H. [Niels Bohr International Academy and Discovery Center,Niels Bohr Institute, University of Copenhagen,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)

    2015-09-21

    As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.

  3. Numerical integration of variational equations.

    Science.gov (United States)

    Skokos, Ch; Gerlach, E

    2010-09-01

    We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom and investigate their efficiency in accurately reproducing well-known properties of chaos indicators such as the Lyapunov characteristic exponents and the generalized alignment indices. We find that the best numerical performance is exhibited by the "tangent map method," a scheme based on symplectic integration techniques which proves to be optimal in speed and accuracy. According to this method, a symplectic integrator is used to approximate the solution of the Hamilton equations of motion by the repeated action of a symplectic map S , while the corresponding tangent map TS is used for the integration of the variational equations. A simple and systematic technique to construct TS is also presented.

  4. Integration rules for scattering equations

    International Nuclear Information System (INIS)

    Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H.

    2015-01-01

    As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.

  5. The respiratory system in equations

    CERN Document Server

    Maury, Bertrand

    2013-01-01

    The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.

  6. Quantum Gross-Pitaevskii Equation

    Directory of Open Access Journals (Sweden)

    Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete

    2017-07-01

    Full Text Available We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

  7. Complete Mie-Gruneisen Equation of State

    Energy Technology Data Exchange (ETDEWEB)

    Menikoff, Ralph [Los Alamos National Laboratory

    2012-06-28

    The Mie-Gruneisen equation of state (EOS) is frequently used in hydro simulations to model solids at high pressure (up to a few Mb). It is an incomplete EOS characterized by a Gruneisen coefficient, {Lambda} = -V({partial_derivative}{sub e}P){sub V}, that is a function of only V. Expressions are derived for isentropes and isotherms. This enables the extension to a complete EOS. Thermodynamic consistency requires that the specific heat is a function of a single scaled temperature. A complete extension is uniquely determined by the temperature dependence of the specific heat at a fixed reference density. In addition we show that if the domain of the EOS extends to T = 0 and the specific heat vanishes on the zero isotherm then {Lambda} a function of only V is equivalent to a specific heat with a single temperature scale. If the EOS domain does not include the zero isotherm, then a specific heat with a single temperature scale leads to a generalization of the Mie-Gruneisen EOS in which the pressure is linear in both the specific energy and the temperature. Such an EOS has previously been used to model liquid nitromethane.

  8. Estimates for a general fractional relaxation equation and application to an inverse source problem

    OpenAIRE

    Bazhlekova, Emilia

    2018-01-01

    A general fractional relaxation equation is considered with a convolutional derivative in time introduced by A. Kochubei (Integr. Equ. Oper. Theory 71 (2011), 583-600). This equation generalizes the single-term, multi-term and distributed-order fractional relaxation equations. The fundamental and the impulse-response solutions are studied in detail. Properties such as analyticity and subordination identities are established and employed in the proof of an upper and a lower bound. The obtained...

  9. Coupled Higgs field equation and Hamiltonian amplitude equation ...

    Indian Academy of Sciences (India)

    (G /G)-expansion method for finding exact travelling wave solutions of Higgs field equa- tion. Section 3.2 is devoted to find travelling wave solutions of Hamiltonian amplitude equation. In §4, some conclusions are given. 2. Lie symmetry analysis. Lie's method [8–10] is an effective method and is the simplest among group ...

  10. FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...

    African Journals Online (AJOL)

    eobe

    rived equation based on the concept of specific resistance, was used to i was used to i drying bed as a slud ... the sludge, it was observed that the specific resistance decreases with incr ng results: D ng results: Dosage increase of 10g, ..... Assessment of the Suitability of Anaerobic Digestion. Effluent for Direct Application as ...

  11. Coupled Higgs field equation and Hamiltonian amplitude equation ...

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 79; Issue 1. Coupled Higgs field equation and ... School of Mathematics and Computer Applications, Thapar University, Patiala 147 004, India; Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Distt. Solan 173 234, India ...

  12. Stability theory of differential equations

    CERN Document Server

    Bellman, Richard Ernest

    1953-01-01

    Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from

  13. Fundamentals of equations of state

    CERN Document Server

    Eliezer, Shalom; Hora, Heinrich

    2002-01-01

    The equation of state was originally developed for ideal gases, and proved central to the development of early molecular and atomic physics. Increasingly sophisticated equations of state have been developed to take into account molecular interactions, quantization, relativistic effects, etc. Extreme conditions of matter are encountered both in nature and in the laboratory, for example in the centres of stars, in relativistic collisions of heavy nuclei, in inertial confinement fusion (where a temperature of 10 9 K and a pressure exceeding a billion atmospheres can be achieved). A sound knowledg

  14. Nielsen number and differential equations

    Directory of Open Access Journals (Sweden)

    Andres Jan

    2005-01-01

    Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.

  15. The nuclear equation of state

    International Nuclear Information System (INIS)

    Kahana, S.

    1986-01-01

    The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab

  16. The nuclear equation of state

    Energy Technology Data Exchange (ETDEWEB)

    Kahana, S.

    1986-01-01

    The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab.

  17. Applied analysis and differential equations

    CERN Document Server

    Cârj, Ovidiu

    2007-01-01

    This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.

  18. Group analysis of differential equations

    CERN Document Server

    Ovsiannikov, L V

    1982-01-01

    Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations.This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the g

  19. Partial differential equations an introduction

    CERN Document Server

    Colton, David

    2004-01-01

    Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of

  20. Basic linear partial differential equations

    CERN Document Server

    Treves, Francois

    1975-01-01

    Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their

  1. Einstein Equations from Varying Complexity

    Science.gov (United States)

    Czech, Bartłomiej

    2018-01-01

    A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by varying complexity. I present such a derivation for vacuum solutions of pure Einstein gravity in three-dimensional asymptotically anti-de Sitter space. The argument relies on known facts about holography and on properties of tensor network renormalization, an algorithm for coarse-graining (and optimizing) tensor networks.

  2. Sequent Calculus and Equational Programming

    Directory of Open Access Journals (Sweden)

    Nicolas Guenot

    2015-07-01

    Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.

  3. Radar equations for modern radar

    CERN Document Server

    Barton, David K

    2012-01-01

    Based on the classic Radar Range-Performance Analysis from 1980, this practical volume extends that work to ensure applicability of radar equations to the design and analysis of modern radars. This unique book helps you identify what information on the radar and its environment is needed to predict detection range. Moreover, it provides equations and data to improve the accuracy of range calculations. You find detailed information on propagation effects, methods of range calculation in environments that include clutter, jamming and thermal noise, as well as loss factors that reduce radar perfo

  4. On the non-stationary generalized Langevin equation

    Science.gov (United States)

    Meyer, Hugues; Voigtmann, Thomas; Schilling, Tanja

    2017-12-01

    In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.

  5. Prediction Equations for Spirometry for Children from Northern India.

    Science.gov (United States)

    Chhabra, Sunil K; Kumar, Rajeev; Mittal, Vikas

    2016-09-08

    To develop prediction equations for spirometry for children from northern India using current international guidelines for standardization. Re-analysis of cross-sectional data from a single school. 670 normal children (age 6-17 y; 365 boys) of northern Indian parentage. After screening for normal health, we carried out spirometry with recommended quality assurance according to current guidelines. We developed linear and nonlinear prediction equations using multiple regression analysis. We selected the final models on the basis of the highest coefficient of multiple determination (R2) and statistical validity. Spirometry parameters: FVC, FEV1, PEFR, FEF50, FEF75 and FEF25-75. The equations for the main parameters were as follows: Boys, Ln FVC = -1.687+0.016*height +0.022*age; Ln FEV1 = -1.748+0.015*height+0.031*age. Girls, Ln FVC = -9.989 +(2.018*Ln(height)) + (0.324*Ln(age)); Ln FEV1 = -10.055 +(1.990*Ln(height))+(0.358*Ln(age)). Nonlinear regression yielded substantially greater R2 values compared to linear models except for FEF50 for girls. Height and age were found to be the significant explanatory variables for all parameters on multiple regression with weight making no significant contribution. We developed prediction equations for spirometry for children from northern India. Nonlinear equations were superior to linear equations.

  6. A Method for Solving the Voltage and Torque Equations of the Split ...

    African Journals Online (AJOL)

    Single phase induction machines have been the subject of many researches in recent times. The voltage and torque equations which describe the dynamic characteristics of these machines have been quoted in many papers, including the papers that present the simulation results of these model equations. The way and ...

  7. Biomass equations for shrub species of Tamualipan thornscrub of North-Eastern Mexico

    Science.gov (United States)

    J. Navar; E. Mendez; A. Najera; J. Graciano; V. Dale; B. Parresol

    2004-01-01

    Nine additive allometric equations for computing above-ground, standing biomass were developed for the plant community and for each of 18 single species typical of the Tamaulipan thornscrub of north-eastern Mexico. Equations developed using additive procedures in seemingly unrelated linear regression provided statistical efficiency in total biomass estimates at the...

  8. New approach to solve fully fuzzy system of linear equations using ...

    Indian Academy of Sciences (India)

    This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and applied ...

  9. Applications of the Peng-Robinson Equation of State Using MATLAB[R

    Science.gov (United States)

    Nasri, Zakia; Binous, Housam

    2009-01-01

    A single equation of state (EOS) such as the Peng-Robinson (PR) EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state, including estimation of pure component properties and computation of the vapor-liquid equilibrium (VLE) diagram for binary mixtures. We perform high-pressure…

  10. New approach to solve fully fuzzy system of linear equations using ...

    Indian Academy of Sciences (India)

    Abstract. This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and.

  11. Validation of the Korean coefficient for the modification of diet in renal disease study equation.

    Science.gov (United States)

    Oh, Yun Jung; Cha, Ran-Hui; Lee, Seung Hwan; Yu, Kyung Sang; Kim, Satbyul Estella; Kim, Ho; Kim, Yon Su

    2016-03-01

    Race and ethnicity are important determinants when estimatingglomerular filtration rate (GFR). The Korean coefficients for the isotope dilution mass spectrometry (IDMS) Modification of Diet in Renal Disease (MDRD) Study equations were developed in 2010. However, the coefficients have not been validated. The aim of this study was to validate the performance of the Korean coefficients for the IDMS MDRD Study equations. Equation development and validation were performed in separate groups (development group, n = 147 from 2008 to 2009; validation group, n = 125 from 2010 to 2012). We compared the performance of the original IDMS MDRD equations and modified equations with Korean coefficients. Performance was assessed by comparing correlation coefficients, bias, and accuracy between estimated GFR and measured GFR, with systemic inulin clearance using a single injection method. The Korean coefficients for the IDMS MDRD equations developed previously showed good performance in the validation group. The new Korean coefficients for the four- and six-variable IDMS MDRD equations using both the development and validation cohorts were 1.02046 and 0.97300, respectively. No significant difference was detected for the new Korean coefficients, in terms of estimating GFR, between the original and modified IDMS MDRD Study equations. The modified equations with Korean coefficients for the IDMS MDRD Study equations were not superior to the original equations for estimating GFR. Therefore, we recommend using the original IDMS MDRD Study equation without ethnic adjustment in the Korean population.

  12. Solving the Linear 1D Thermoelasticity Equations with Pure Delay

    Directory of Open Access Journals (Sweden)

    Denys Ya. Khusainov

    2015-01-01

    Full Text Available We propose a system of partial differential equations with a single constant delay τ>0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R1. For an initial-boundary value problem associated with this system, we prove a well-posedness result in a certain topology under appropriate regularity conditions on the data. Further, we show the solution of our delayed model to converge to the solution of the classical equations of thermoelasticity as τ→0. Finally, we deduce an explicit solution representation for the delay problem.

  13. Multiparameter extrapolation and deflation methods for solving equation systems

    Directory of Open Access Journals (Sweden)

    A. J. Hughes Hallett

    1984-01-01

    Full Text Available Most models in economics and the applied sciences are solved by first order iterative techniques, usually those based on the Gauss-Seidel algorithm. This paper examines the convergence of multiparameter extrapolations (accelerations of first order iterations, as an improved approximation to the Newton method for solving arbitrary nonlinear equation systems. It generalises my earlier results on single parameter extrapolations. Richardson's generalised method and the deflation method for detecting successive solutions in nonlinear equation systems are also presented as multiparameter extrapolations of first order iterations. New convergence results are obtained for those methods.

  14. Resonance tongues in the linear Sitnikov equation

    Science.gov (United States)

    Misquero, Mauricio

    2018-04-01

    In this paper, we deal with a Hill's equation, depending on two parameters e\\in [0,1) and Λ >0, that has applications to some problems in Celestial Mechanics of the Sitnikov type. Due to the nonlinearity of the eccentricity parameter e and the coexistence problem, the stability diagram in the (e,Λ )-plane presents unusual resonance tongues emerging from points (0,(n/2)^2), n=1,2,\\ldots The tongues bounded by curves of eigenvalues corresponding to 2π -periodic solutions collapse into a single curve of coexistence (for which there exist two independent 2π -periodic eigenfunctions), whereas the remaining tongues have no pockets and are very thin. Unlike most of the literature related to resonance tongues and Sitnikov-type problems, the study of the tongues is made from a global point of view in the whole range of e\\in [0,1). Indeed, an interesting behavior of the tongues is found: almost all of them concentrate in a small Λ -interval [1, 9 / 8] as e→ 1^-. We apply the stability diagram of our equation to determine the regions for which the equilibrium of a Sitnikov (N+1)-body problem is stable in the sense of Lyapunov and the regions having symmetric periodic solutions with a given number of zeros. We also study the Lyapunov stability of the equilibrium in the center of mass of a curved Sitnikov problem.

  15. On the commutator of C^{\\infty}} -symmetries and the reduction of Euler-Lagrange equations

    Science.gov (United States)

    Ruiz, A.; Muriel, C.; Olver, P. J.

    2018-04-01

    A novel procedure to reduce by four the order of Euler-Lagrange equations associated to nth order variational problems involving single variable integrals is presented. In preparation, a new formula for the commutator of two \

  16. Meta-analytic structural equation modelling

    CERN Document Server

    Jak, Suzanne

    2015-01-01

    This book explains how to employ MASEM, the combination of meta-analysis (MA) and structural equation modelling (SEM). It shows how by using MASEM, a single model can be tested to explain the relationships between a set of variables in several studies. This book gives an introduction to MASEM, with a focus on the state of the art approach: the two stage approach of Cheung and Cheung & Chan. Both, the fixed and the random approach to MASEM are illustrated with two applications to real data. All steps that have to be taken to perform the analyses are discussed extensively. All data and syntax files are available online, so that readers can imitate all analyses. By using SEM for meta-analysis, this book shows how to benefit from all available information from all available studies, even if few or none of the studies report about all relationships that feature in the full model of interest.

  17. dimensional KdV equation

    Indian Academy of Sciences (India)

    is to study the interaction properties between the periodic waves. Here, we take the (2+1)-dimensional KdV equation .... In fact, such limit for the present family of doubly periodic waves is especially rich, since one can proceed with the long .... ematical Society, Providence, 1997). [11] K Chandrasekharan, Elliptic functions ...

  18. Stability of Functional Differential Equations

    CERN Document Server

    Lemm, Jeffrey M

    1986-01-01

    This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.

  19. Sonar equations for planetary exploration.

    Science.gov (United States)

    Ainslie, Michael A; Leighton, Timothy G

    2016-08-01

    The set of formulations commonly known as "the sonar equations" have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and localize objects submerged in seawater. The efficacy of the sonar equations, with individual terms evaluated in decibels, is well established in Earth's oceans. The sonar equations have been used in the past for missions to other planets and moons in the solar system, for which they are shown to be less suitable. While it would be preferable to undertake high-fidelity acoustical calculations to support planning, execution, and interpretation of acoustic data from planetary probes, to avoid possible errors for planned missions to such extraterrestrial bodies in future, doing so requires awareness of the pitfalls pointed out in this paper. There is a need to reexamine the assumptions, practices, and calibrations that work well for Earth to ensure that the sonar equations can be accurately applied in combination with the decibel to extraterrestrial scenarios. Examples are given for icy oceans such as exist on Europa and Ganymede, Titan's hydrocarbon lakes, and for the gaseous atmospheres of (for example) Jupiter and Venus.

  20. Sonar equations for planetary exploration

    NARCIS (Netherlands)

    Ainslie, M.A.; Leighton, T.G.

    2016-01-01

    The set of formulations commonly known as “the sonar equations” have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and ocalize objects submerged in seawater. The efficacy of the sonar equations, with individualterms evaluated in decibels,

  1. Saha equation in Rindler space

    Indian Academy of Sciences (India)

    Sanchari De

    MS received 21 October 2016; revised 3 January 2017; accepted 25 January 2017; published online 31 May 2017. Abstract. The Saha equations for the photoionization process of hydrogen atoms .... [3] C W Misner, Kip S Thorne and J A Wheeler, Gravitation (W.H.. Freeman and Company, New York, 1972). [4] W Rindler ...

  2. On the Saha Ionization Equation

    Indian Academy of Sciences (India)

    On the Saha Ionization Equation. Sushanta Dattagupta. General Article Volume 23 Issue 1 January 2018 pp 41-55. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/023/01/0041-0055. Keywords. Ionization, astrophysics, spectroscopy, chemical reaction, transition state. Abstract.

  3. Pendulum Motion and Differential Equations

    Science.gov (United States)

    Reid, Thomas F.; King, Stephen C.

    2009-01-01

    A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a…

  4. Wave-equation dispersion inversion

    KAUST Repository

    Li, Jing

    2016-12-08

    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

  5. Transport equation and shock waves

    International Nuclear Information System (INIS)

    Besnard, D.

    1981-04-01

    A multi-group method is derived from a one dimensional transport equation for the slowing down and spatial transport of energetic positive ions in a plasma. This method is used to calculate the behaviour of energetic charged particles in non homogeneous and non stationary plasma, and the effect of energy deposition of the particles on the heating of the plasma. In that purpose, an equation for the density of fast ions is obtained from the Fokker-Planck equation, and a closure condition for the second moment of this equation is deduced from phenomenological considerations. This method leads to a numerical method, simple and very efficient, which doesn't require much computer storage. Two types of numerical results are obtained. First, results on the slowing down of 3.5 MeV alpha particles in a 50 keV plasma plublished by Corman and al and Moses are compared with the results obtained with both our method and a Monte Carlo type method. Good agreement was obtained, even for energy deposition on the ions of the plasma. Secondly, we have calculated propagation of alpha particles heating a cold plasma. These results are in very good agreement with those given by an accurate Monte Carlo method, for both the thermal velocity, and the energy deposition in the plasma

  6. Benjamin–Bona–Mahony equation

    Indian Academy of Sciences (India)

    Abstract. By applying the bifurcation theory of dynamical system to the generalized. KP–BBM equation, the phase portraits of the travelling wave system are obtained. It can be shown that singular straight line in the travelling wave system is the reason why smooth periodic waves converge to periodic cusp waves.

  7. Singularity: Raychaudhuri equation once again

    Indian Academy of Sciences (India)

    birth of the Universe in a Big Bang. Nothing could be happier and more persuasive than the observation verifying the prediction of theory. This gave rise to a general belief that singularities were inevitable in general relativity (GR) so long as the dynamics were governed by Einstein's equations and more over positive energy ...

  8. Renaissance Learning Equating Study. Report

    Science.gov (United States)

    Sewell, Julie; Sainsbury, Marian; Pyle, Katie; Keogh, Nikki; Styles, Ben

    2007-01-01

    An equating study was carried out in autumn 2006 by the National Foundation for Educational Research (NFER) on behalf of Renaissance Learning, to provide validation evidence for the use of the Renaissance Star Reading and Star Mathematics tests in English schools. The study investigated the correlation between the Star tests and established tests.…

  9. A generalized advection dispersion equation

    Indian Academy of Sciences (India)

    This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.

  10. Quasi-gas dynamic equations

    CERN Document Server

    Elizarova, Tatiana G

    2009-01-01

    This book presents two interconnected mathematical models generalizing the Navier-Stokes system. The models, called the quasi-gas-dynamic and quasi-hydrodynamic equations, are then used as the basis of numerical methods solving gas- and fluid-dynamic problems.

  11. Slave equations for spin models

    International Nuclear Information System (INIS)

    Catterall, S.M.; Drummond, I.T.; Horgan, R.R.

    1992-01-01

    We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)

  12. Solutions of equations in languages

    NARCIS (Netherlands)

    Hesselink, Wim H.

    A context-free grammar corresponds to a system of equations in languages. The language generated by the grammar is the smallest solution of the system. We give a necessary and sufficient condition for an arbitrary solution to be the smallest one. We revive an old criterion to decide that a grammar

  13. A Versatile Technique for Solving Quintic Equations

    Science.gov (United States)

    Kulkarni, Raghavendra G.

    2006-01-01

    In this paper we present a versatile technique to solve several types of solvable quintic equations. In the technique described here, the given quintic is first converted to a sextic equation by adding a root, and the resulting sextic equation is decomposed into two cubic polynomials as factors in a novel fashion. The resultant cubic equations are…

  14. Functional equations in matrix normed spaces

    Indian Academy of Sciences (India)

    Cauchy additive functional equation and the quadratic functional equation in matrix normed spaces. Keywords. Operator space; fixed point; Hyers–Ulam stability; Cauchy additive functional equation; quadratic functional equation. 2000 Mathematics Subject Classification. 47L25, 47H10, 39B82, 46L07, 39B52. 1.

  15. Analytical solution of population balance equation involving ...

    Indian Academy of Sciences (India)

    This paper presents an effective analytical simulation to solve population balance equation (PBE), involving particulate aggregation and breakage, by making use of appropriate solution(s) of associated complementary equation via auxiliary equation method (AEM). Travelling wave solutions of the complementary equation ...

  16. An analytical solution of fractional burgers equation

    Directory of Open Access Journals (Sweden)

    Pang Jing

    2017-01-01

    Full Text Available Using the fractional complex transform, the fractional partial differential equations can be reduced to ordinary differential equations which can be solved by the auxiliary equation method. Non-linear superposition formulation of Riccati equation is applied, and a complex infinite sequence solution is obtained.

  17. The Complexity of One-Step Equations

    Science.gov (United States)

    Ngu, Bing

    2014-01-01

    An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…

  18. Algebraic entropy for differential-delay equations

    OpenAIRE

    Viallet, Claude M.

    2014-01-01

    We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.

  19. Interplays between Harper and Mathieu equations.

    Science.gov (United States)

    Papp, E; Micu, C

    2001-11-01

    This paper deals with the application of relationships between Harper and Mathieu equations to the derivation of energy formulas. Establishing suitable matching conditions, one proceeds by inserting a concrete solution to the Mathieu equation into the Harper equation. For this purpose, one resorts to the nonlinear oscillations characterizing the Mathieu equation. This leads to the derivation of two kinds of energy formulas working in terms of cubic and quadratic algebraic equations, respectively. Combining such results yields quadratic equations to the energy description of the Harper equation, incorporating all parameters needed.

  20. Thermoviscous Model Equations in Nonlinear Acoustics

    DEFF Research Database (Denmark)

    Rasmussen, Anders Rønne

    Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

  1. Maxwell's equations of electrodynamics an explanation

    CERN Document Server

    Ball, David W

    2012-01-01

    Maxwell's Equations of Electrodynamics: An Explanation is a concise discussion of Maxwell's four equations of electrodynamics - the fundamental theory of electricity, magnetism, and light. It guides readers step-by-step through the vector calculus and development of each equation. Pictures and diagrams illustrate what the equations mean in basic terms. The book not only provides a fundamental description of our universe but also explains how these equations predict the fact that light is better described as "electromagnetic radiation."

  2. An Alternative Stability Equation For Rock Armoured Rubble Mound Breakwaters

    DEFF Research Database (Denmark)

    Hald, Tue; Burcharth, H. F.

    2000-01-01

    Rubble mound breakwaters are by far the most common type of breakwater, the importance of which is clearly reflected in the vast amount of published research. Especially, the hydraulic stability of the main armour layer has been studied in order to obtain reliable design equations. It should...... be straight forward to assume, that a relation between the exerted wave loads and the stability of the armour layer would be of major interest, but the normal approach to the problem has simply been to relate easy accessible wave parameters, e.g. wave height and period, directly to the single unit weight...... equations and model test results still exists. When turning toward prototype the situation is even worse. With the objective to reduce some of the variability an alternative approach based on force considerations is presented. The paper will describe a new stability equation for rock armoured slopes derived...

  3. Generalized equation for calculation of fractional recoveries and presentation of data for solvent extraction systems

    International Nuclear Information System (INIS)

    Rawajfeh, M. K.; Al-Matar, A.

    2000-01-01

    A generalized equation relating equilibrium data, phase ratio and fractional recovery is developed. The use of this equation reduces the presentation of these data to a single dimensionless curve independent of the system and the operating conditions. The validity of this equation is tested using experimental data for different liquid - liquid systems at various condition. a reasonable agreement between experimental results and predicated ones was obtained. The use of this equation in investigating the effect of phase ratio on the fractional recovery is illustrated. (authors). 6 refs., 4 figs., 3 tabs

  4. Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations

    Science.gov (United States)

    Novruzov, Emil

    2017-11-01

    This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, ut -uxxt +[ f (u) ] x -[ f (u) ] xxx +[ g (u) + f″/(u) 2 ux2 ] x = 0 that includes the Camassa-Holm equation as well as the hyperelastic-rod wave equation (f (u) = ku2 / 2 and g (u) = (3 - k) u2 / 2) as special cases. We establish some a local-in-space blow-up criterion (i.e., a criterion involving only the properties of the data u0 in a neighborhood of a single point) simplifying and precising earlier blow-up criteria for this equation.

  5. A novel quantum-mechanical interpretation of the Dirac equation

    Science.gov (United States)

    K-H Kiessling, M.; Tahvildar-Zadeh, A. S.

    2016-04-01

    A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr-Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit G\\to 0, where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.

  6. The equations icons of knowledge

    CERN Document Server

    Bais, Sander

    2005-01-01

    For thousands of years mankind has tried to understand nature. Exploring the world on all scales with instruments of ever more ingenuity, we have been able to unravel some of the great mysteries that surround us. While collecting an overwhelming multitude of observational facts, we discovered fundamental laws that govern the structure and evolution of physical reality. We know that nature speaks to us in the language of mathematics. In this language most of our basic understanding of the physical world can be expressed in an unambiguous and concise way. The most artificial language turns out to be the most natural of all. The laws of nature correspond to equations. These equations are the icons of knowledge that mark crucial turning points in our thinking about the world we happen to live in. They form the symbolic representation of most of what we know, and as such constitute an important and robust part of our culture.

  7. Nonlocal higher order evolution equations

    KAUST Repository

    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.

  8. MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE

    Directory of Open Access Journals (Sweden)

    Francisco Frutos Alfaro

    2017-04-01

    Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.

  9. Simple equation method for nonlinear partial differential equations and its applications

    Directory of Open Access Journals (Sweden)

    Taher A. Nofal

    2016-04-01

    Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.

  10. Prediction equations for diffusing capacity (transfer factor) of lung for North Indians.

    Science.gov (United States)

    Chhabra, Sunil Kumar; Kumar, Rajeev; Gupta, Uday A

    2016-01-01

    Prediction equations for diffusing capacity of lung for carbon monoxide (DLCO), alveolar volume (VA), and DLCO/VA using the current standardization guidelines are not available for Indian population. The present study was carried out to develop equations for these parameters for North Indian adults and examine the ethnic diversity in predictions. DLCO was measured by single-breath technique and VA by single-breath helium dilution using standardized methodology in 357 (258 males, 99 females) normal nonsmoker adult North Indians and DLCO/VA was computed. The subjects were randomized into training and test datasets for development of prediction equations by multiple linear regressions and for validation, respectively. For males, the following equations were developed: DLCO, -7.813 + 0.318 × ht -0.624 × age + 0.00552 × age(2); VA, -8.152 + 0.087 × ht -0.019 × wt; DLCO/VA, 7.315 - 0.037 × age. For females, the equations were: DLCO, -44.15 + 0.449 × ht -0.099 × age; VA, -6.893 + 0.068 × ht. A statistically acceptable prediction equation was not obtained for DLCO/VA in females. It was therefore computed from predicted DLCO and predicted VA. All equations were internally valid. Predictions of DLCO by Indian equations were lower than most Caucasian predictions in both males and females and greater than the Chinese predictions for males. This study has developed validated prediction equations for DLCO, VA, and DLCO/VA in North Indians. Substantial ethnic diversity exists in predictions for DLCO and VA with Caucasian equations generally yielding higher values than the Indian or Chinese equations. However, DLCO/VA predicted by the Indian equations is slightly higher than that by other equations.

  11. Numerical simulation of single bubble boiling behavior

    Directory of Open Access Journals (Sweden)

    Junjie Liu

    2017-06-01

    Full Text Available The phenomena of a single bubble boiling process are studied with numerical modeling. The mass, momentum, energy and level set equations are solved using COMSOL multi-physics software. The bubble boiling dynamics, the transient pressure field, velocity field and temperature field in time are analyzed, and reasonable results are obtained. The numeral model is validated by the empirical equation of Fritz and could be used for various applications.

  12. Equation of State Project Overview

    Energy Technology Data Exchange (ETDEWEB)

    Crockett, Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-09-11

    A general overview of the Equation of State (EOS) Project will be presented. The goal is to provide the audience with an introduction of what our more advanced methods entail (DFT, QMD, etc.. ) and how these models are being utilized to better constrain the thermodynamic models. These models substantially reduce our regions of interpolation between the various thermodynamic limits. I will also present a variety example of recent EOS work.

  13. A generalized advection dispersion equation

    Indian Academy of Sciences (India)

    Multiplication. If ux, f (x) and g(x) are differentiable in the opened interval D, then: D ux [f(x) · g(x)]=g(x)f (x) + f(x)g (x). + (gf + fg )(x)ux + u x. (f(x)g(x)). (2.5) ..... for solution of various nonlinear problems without usual restrictive assumptions. To solve equation. (4.2) by means of variational iteration method, we put (4.2) as ...

  14. BERNULLI DIFFERENTIAL EQUATION AND CHAOS

    Directory of Open Access Journals (Sweden)

    V. Ye. Belozerov

    2013-03-01

    Full Text Available Existence conditions of homoclinic orbits for some systems of ordinary quadratic dif­ferential equations with singular linear part are founded. A realization of these conditions guarantees the existence of chaotic attractors at 3-D autonomous quadratic systems. In addition, a chaotic behavior of the solutions of these systems is determined by one-dimensional discrete map at some values of parameters. Examples are given.

  15. Handbook of structural equation modeling

    CERN Document Server

    Hoyle, Rick H

    2012-01-01

    The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu

  16. Integration of Chandrasekhar's integral equation

    International Nuclear Information System (INIS)

    Tanaka, Tasuku

    2003-01-01

    We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA 'explicitly' in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness

  17. Deriving the bond pricing equation

    Directory of Open Access Journals (Sweden)

    Kožul Nataša

    2014-01-01

    Full Text Available Given the recent focus on Eurozone debt crisis and the credit rating downgrade not only of US debt, but that of other countries and many UK major banking institutions, this paper aims to explain the concept of bond yield, its different measures and bond pricing equation. Yields on capital market instruments are rarely quoted on the same basis, which makes direct comparison between different as investment choices impossible. Some debt instruments are quoted on discount basis, whilst coupon-bearing ones accrue interest differently, offer different compounding opportunities, have different coupon payment frequencies, and manage non-business day maturity dates differently. Moreover, rules governing debt vary across countries, markets and currencies, making yield calculation and comparison a rather complex issue. Thus, some fundamental concepts applicable to debt instrument yield measurement, with focus on bond equation, are presented here. In addition, bond equation expressed in annuity form and used to apply Newton-Raphson algorithm to derive true bond yield is also shown.

  18. Wave equations in higher dimensions

    CERN Document Server

    Dong, Shi-Hai

    2011-01-01

    Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...

  19. Effective Schroedinger equations on submanifolds

    Energy Technology Data Exchange (ETDEWEB)

    Wachsmuth, Jakob

    2010-02-11

    In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.

  20. Performance equations of proton exchange membrane fuel cells with feeds of varying degrees of humidification

    International Nuclear Information System (INIS)

    Hsuen, Hsiao-Kuo; Yin, Ken-Ming

    2012-01-01

    Performance equations that describe the dependence of cell potential on current density for proton exchange membrane fuel cells (PEMFCs) with feeds of varying degrees of humidification have been formulated in algebraic form. The equations are developed by the reduction of a one-dimensional multi-domain model that takes into account, in details, the transport limitations of gas species, proton migration and electron conduction, electrochemical kinetics, as well as liquid water flow within the cathode, anode, and membrane. The model equations for the anode and membrane were integrated with those of the cathode developed in the previous studies to form a complete set of equations for one-dimensional single cell model. Because the transport equations for the anode diffuser can be solved analytically, calculations of integrals are only needed in the membrane and the two-phase region of cathode diffuser. The proposed approach greatly reduces the complexity of the model equations, and only iterations of a single algebraic equation are required to obtain final solutions. Since the performance equations are originated from a mechanistic one-dimensional model, all the parameters appearing in the equations are endowed with a precise physical significance.