Normality of Composite Analytic Functions and Sharing an Analytic Function
Xiao Bing; Yuan Wenjun; Wu Qifeng
2010-01-01
A result of Hinchliffe (2003) is extended to transcendental entire function, and an alternative proof is given in this paper. Our main result is as follows: let be an analytic function, a family of analytic functions in a domain , and a transcendental entire function. If and share IM for each pair , and one of the following conditions holds: (1) has at least two distinct zeros for any ; (2) is nonconstant, and there exists such that has only one distinct zero , and su...
Banach spaces of analytic functions
Hoffman, Kenneth
2007-01-01
A classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc.The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the f
A Functional Analytic Approach to Group Psychotherapy
Vandenberghe, Luc
2009-01-01
This article provides a particular view on the use of Functional Analytical Psychotherapy (FAP) in a group therapy format. This view is based on the author's experiences as a supervisor of Functional Analytical Psychotherapy Groups, including groups for women with depression and groups for chronic pain patients. The contexts in which this approach…
[Contributions and novelties from Functional Analytic Psychotherapy].
Ferro García, Rafael; Valero Aguayo, Luis; López Bermúdez, Miguel A
2007-08-01
Functional Analytic Psychotherapy is based on the principles of radical behaviourism. It emphasises the impact of events occurring during therapeutic sessions, the therapist-client interaction context, functional equivalence of environments, natural reinforcement, and shaping by the therapist. Functional Analytic Psychotherapy makes use of both the basic principles of behaviour analysis: individual functional assessment and application of in vivo treatment. This paper analyses novelties and new contributions of this therapy. New contributions are classified in various categories: integration with other psychotherapies, improvement of therapeutic skills, methods for evaluation and data recording in therapy, its application to several clinical problems, and studies of its efficacy. PMID:17617985
Analytical Properties of Credibilistic Expectation Functions
Shuming Wang; Bo Wang; Junzo Watada
2014-01-01
The expectation function of fuzzy variable is an important and widely used criterion in fuzzy optimization, and sound properties on the expectation function may help in model analysis and solution algorithm design for the fuzzy optimization problems. The present paper deals with some analytical properties of credibilistic expectation functions of fuzzy variables that lie in three aspects. First, some continuity theorems on the continuity and semicontinuity conditions are proved for the expect...
Promoting Efficacy Research on Functional Analytic Psychotherapy
Maitland, Daniel W. M.; Gaynor, Scott T.
2012-01-01
Functional Analytic Psychotherapy (FAP) is a form of therapy grounded in behavioral principles that utilizes therapist reactions to shape target behavior. Despite a growing literature base, there is a paucity of research to establish the efficacy of FAP. As a general approach to psychotherapy, and how the therapeutic relationship produces change,…
Analytical Properties of Credibilistic Expectation Functions
Wang, Bo; Watada, Junzo
2014-01-01
The expectation function of fuzzy variable is an important and widely used criterion in fuzzy optimization, and sound properties on the expectation function may help in model analysis and solution algorithm design for the fuzzy optimization problems. The present paper deals with some analytical properties of credibilistic expectation functions of fuzzy variables that lie in three aspects. First, some continuity theorems on the continuity and semicontinuity conditions are proved for the expectation functions. Second, a differentiation formula of the expectation function is derived which tells that, under certain conditions, the derivative of the fuzzy expectation function with respect to the parameter equals the expectation of the derivative of the fuzzy function with respect to the parameter. Finally, a law of large numbers for fuzzy variable sequences is obtained leveraging on the Chebyshev Inequality of fuzzy variables. Some examples are provided to verify the results obtained. PMID:24723800
CARATHEODORY INEQUALITY FOR ANALYTIC OPERATOR FUNCTION
无
2001-01-01
Suppose H is a complex Hilbert space, AH(△) denotes the set of all analytic operator functions on △, and the set NH(△)= {f(z)｜f(z) is an analytic operator function on the open uint disk △, f(z)f(ω)=f(ω)f(z),f*(z)f(z)=f(z)f*(z), z,ω∈△}. The note proves that if f(z)∈NH(△),(or AH(△) )‖f(z)‖≤1, z∈△ then ‖f＇(T)‖≤(1-‖T‖2)-1‖I-f*(T)f(T)‖1/2‖I-f(T)f*(T)‖1/2,where T ∈ (H)(orT*T=TT*,respectively),‖T‖＜1,Tf=fT.
Approximation of Analytic Functions by Bessel's Functions of Fractional Order
Soon-Mo Jung
2011-01-01
Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.
Approximation of Analytic Functions by Bessel's Functions of Fractional Order
Soon-Mo Jung
2011-01-01
We will solve the inhomogeneous Bessel's differential equation x2y″(x)+xy′(x)+(x2-ν2)y(x)=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.
ON STEIN-WEISS CONJUGATEHARMONIC FUNCTION ANDOCTONION ANALYTIC FUNCTION
Li Xingmin; Peng Lizhong
2000-01-01
It is shown that the Stein-Weiss conjugate harmonic funciton is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have answered the question proposed in [1].
ANALYTIC SOLUTIONS OF SYSTEMS OF FUNCTIONAL EQUATIONS
LiuXinhe
2003-01-01
Let r be a given positive number.Denote by D=D the closed disc in the complex plane C whose center is the origin and radius is r.For any subset K of C and any integer m ≥1,write A(Dm,K)={f|f:Dm→Kis a continuous map,and f|(Dm)*is analytic).For H∈A(Dm,C)(m≥2),f∈A(D,D)and z∈D,write ψH(f)(z)=H(z,f(z)……fm=1(x)).Suppose F,G∈A(D2n+1,C),and Hk,Kk∈A(Dk,C),k=2,……,n.In this paper,the system of functional equations {F(z,f(z),f2(ψHz(f)(z))…,fn(ψk2(g)(x))… gn(ψKn(g)(z)))=0 G(z,f(z),f2(ψH2(f)(z))…fn(ψHn(f)(z)),g(z),g2(ψk2(g)(x))…,gn(ψkn(g)(z)))=0(z∈D)is studied and some conditions for the system of equations to have a solution or a unique solution in A(D,D)×A（D，D）are given.
Nonlinear Riemann-Hilbert Problems for Generalized Analytic Functions
Efendiev, Messoud A.; Wolfgang L. Wendland
2009-01-01
In this study we deal with the nonlinear Riemann--Hilbert problem (in short (RHP)) for generalized analytic functions in multiply connected domains. Using a similarity principle for multiply connected domains (presented here for the first time), we reduce the nonlinear RHP for generalized analytic functions to a corresponding nonlinear RHP for holomorphic functions with Hölder continuous boundary data. Then the Newton--Kantorovič method combined with a continuation procedure as well as a new ...
Quasi-convolution of analytic functions with applications
Babalola, K O
2010-01-01
In this paper we define a new concept of quasi-convolution for analytic functions normalized by $f(0)=0$ and $f^\\prime(0)=1$ in the unit disk $E=\\{z\\in \\mathbb{C}\\colon |z|<1\\}$. We apply this new approach to study the closure properties of a certain class of analytic and univalent functions under some families of (known and new) integral operators.
Analytical potential energy function for the Br + H2 system
Analytical functions with a many-body expansion for the ground and first-excited-state potential energy surfaces for the Br+H2 system are newly presented in this work. These functions describe the abstraction and exchange reactions qualitatively well, although it has been found that the function for the ground-state potential surface is still quantitatively unsatisfactory. (author)
THE ANALYTICAL PROPERTIES FOR HOMOGENEOUS RANDOM TRANSITION FUNCTIONS
无
2007-01-01
The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.
Green functions of graphene: An analytic approach
In this article we derive the lattice Green Functions (GFs) of graphene using a Tight Binding Hamiltonian incorporating both first and second nearest neighbour hoppings and allowing for a non-orthogonal electron wavefunction overlap. It is shown how the resulting GFs can be simplified from a double to a single integral form to aid computation, and that when considering off-diagonal GFs in the high symmetry directions of the lattice this single integral can be approximated very accurately by an algebraic expression. By comparing our results to the conventional first nearest neighbour model commonly found in the literature, it is apparent that the extended model leads to a sizeable change in the electronic structure away from the linear regime. As such, this article serves as a blueprint for researchers who wish to examine quantities where these considerations are important
Green functions of graphene: An analytic approach
Lawlor, James A., E-mail: jalawlor@tcd.ie [School of Physics, Trinity College Dublin, Dublin 2 (Ireland); Ferreira, Mauro S. [School of Physics, Trinity College Dublin, Dublin 2 (Ireland); CRANN, Trinity College Dublin, Dublin 2 (Ireland)
2015-04-15
In this article we derive the lattice Green Functions (GFs) of graphene using a Tight Binding Hamiltonian incorporating both first and second nearest neighbour hoppings and allowing for a non-orthogonal electron wavefunction overlap. It is shown how the resulting GFs can be simplified from a double to a single integral form to aid computation, and that when considering off-diagonal GFs in the high symmetry directions of the lattice this single integral can be approximated very accurately by an algebraic expression. By comparing our results to the conventional first nearest neighbour model commonly found in the literature, it is apparent that the extended model leads to a sizeable change in the electronic structure away from the linear regime. As such, this article serves as a blueprint for researchers who wish to examine quantities where these considerations are important.
Subclasses of Analytic Functions Associated with Generalised Multiplier Transformations
Rashidah Omar; Suzeini Abdul Halim
2012-01-01
New subclasses of analytic functions in the open unit disc are introduced which are defined using generalised multiplier transformations. Inclusion theorems are investigated for functions to be in the classes. Furthermore, generalised Bernardi-Libera-Livington integral operator is shown to be preserved for these classes.
Executive functioning in adult ADHD: a meta-analytic review.
Boonstra, A.M.; Oosterlaan, J.; Sergeant, J.A.; Buitelaar, J. K.
2005-01-01
textabstractBackground: Several theoretical explanations of ADHD in children have focused on executive functioning as the main explanatory neuropsychological domain for the disorder. In order to establish if these theoretical accounts are supported by research data for adults with ADHD, we compared neuropsychological executive functioning and non-executive functioning between adults with ADHD and normal controls in a meta-analytic design. Method: We compared thirteen studies that 1) included ...
Functional Analytic Psychotherapy for Interpersonal Process Groups: A Behavioral Application
Hoekstra, Renee
2008-01-01
This paper is an adaptation of Kohlenberg and Tsai's work, Functional Analytical Psychotherapy (1991), or FAP, to group psychotherapy. This author applied a behavioral rationale for interpersonal process groups by illustrating key points with a hypothetical client. Suggestions are also provided for starting groups, identifying goals, educating…
Equifinality in Functional Analytic Psychotherapy: Different Strokes for Different Folks
Darrow, Sabrina M.; Dalto, Georgia; Follette, William C.
2012-01-01
Functional Analytic Psychotherapy (FAP) is an interpersonal behavior therapy that relies on a therapist's ability to contingently respond to in-session client behavior. Valued behavior change in clients results from the therapist shaping more effective client interpersonal behaviors by providing effective social reinforcement when these behaviors…
Some properties of two-fold symmetric analytic functions
Ali Muhammad
2014-05-01
Full Text Available In this paper, we introduce a new class of two-fold symmetric functions analytic in the unit disc. We prove such results as subordination and superordination properties, convolution properties, distortion theorems, and inequality properties of this new class.
Treatment of a Disorder of Self through Functional Analytic Psychotherapy
Ferro-Garcia, Rafael; Lopez-Bermudez, Miguel Angel; Valero-Aguayo, Luis
2012-01-01
This paper presents a clinical case study of a depressed female, treated by means of Functional Analytic Psychotherapy (FAP) based on the theory and techniques for treating an "unstable self" (Kohlenberg & Tsai, 1991), instead of the classic treatment for depression. The client was a 20-year-old college student. The trigger for her problems was a…
Linear circuit transfer functions an introduction to fast analytical techniques
Basso, Christophe P
2016-01-01
Linear Circuit Transfer Functions: An introduction to Fast Analytical Techniques teaches readers how to determine transfer functions of linear passive and active circuits by applying Fast Analytical Circuits Techniques. Building on their existing knowledge of classical loop/nodal analysis, the book improves and expands their skills to unveil transfer functions in a swift and efficient manner. Starting with simple examples, the author explains step-by-step how expressing circuits time constants in different configurations leads to writing transfer functions in a compact and insightful way. By learning how to organize numerators and denominators in the fastest possible way, readers will speed-up analysis and predict the frequency resp nse of simple to complex circuits. In some cases, they will be able to derive the final expression by inspection, without writing a line of algebra. Key features: * Emphasizes analysis through employing time constant-based methods discussed in other text books but not widely us...
Hemisphere Partition Function and Analytic Continuation to the Conifold Point
Knapp, Johanna; Scheidegger, Emanuel
2016-01-01
We show that the hemisphere partition function for certain U(1) gauged linear sigma models (GLSMs) with D-branes is related to a particular set of Mellin-Barnes integrals which can be used for analytic continuation to the singular point in the K\\"ahler moduli space of an $h^{1,1}=1$ Calabi-Yau (CY) projective hypersurface. We directly compute the analytic continuation of the full quantum corrected central charge of a basis of geometric D-branes from the large volume to the singular point. In the mirror language this amounts to compute the analytic continuation of a basis of periods on the mirror CY to the conifold point. However, all calculations are done in the GLSM and we do not have to refer to the mirror CY. We apply our methods explicitly to the cubic, quartic and quintic CY hypersurfaces.
Analytical Operations Relate Structural and Functional Connectivity in the Brain
Saggio, Maria Luisa; Ritter, Petra; Jirsa, Viktor K.
2016-01-01
Resting-state large-scale brain models vary in the amount of biological elements they incorporate and in the way they are being tested. One might expect that the more realistic the model is, the closer it should reproduce real functional data. It has been shown, instead, that when linear correlation across long BOLD fMRI time-series is used as a measure for functional connectivity (FC) to compare simulated and real data, a simple model performs just as well, or even better, than more sophisticated ones. The model in question is a simple linear model, which considers the physiological noise that is pervasively present in our brain while it diffuses across the white-matter connections, that is structural connectivity (SC). We deeply investigate this linear model, providing an analytical solution to straightforwardly compute FC from SC without the need of computationally costly simulations of time-series. We provide a few examples how this analytical solution could be used to perform a fast and detailed parameter exploration or to investigate resting-state non-stationarities. Most importantly, by inverting the analytical solution, we propose a method to retrieve information on the anatomical structure directly from functional data. This simple method can be used to complement or guide DTI/DSI and tractography results, especially for a better assessment of inter-hemispheric connections, or to provide an estimate of SC when only functional data are available. PMID:27536987
Analytical correlation functions for motion through diffusivity landscapes.
Roosen-Runge, Felix; Bicout, Dominique J; Barrat, Jean-Louis
2016-05-28
Diffusion of a particle through an energy and diffusivity landscape is a very general phenomenon in numerous systems of soft and condensed matter. On the one hand, theoretical frameworks such as Langevin and Fokker-Planck equations present valuable accounts to understand these motions in great detail, and numerous studies have exploited these approaches. On the other hand, analytical solutions for correlation functions, as, e.g., desired by experimentalists for data fitting, are only available for special cases. We explore the possibility to use different theoretical methods in the specific picture of time-dependent switching between diffusive states to derive analytical functions that allow to link experimental and simulation results to theoretical calculations. In particular, we present a closed formula for diffusion switching between two states, as well as a general recipe of how to generalize the formula to multiple states. PMID:27250281
Analytic solution of certain second-order functional differential equation
Theeradach Kaewong
2006-09-01
Full Text Available We consider the existence of analytic solutions of a certain class of iterative second-order functional differential equation of the form xÃ¢Â€Â³(x[r](z=c0z2+c1(x(z2+(c2x[2](z2+Ã¢Â‹Â¯+cm(x[m](z2, m,rÃ¢Â‰Â¥0.
The Adler Function for Light Quarks in Analytic Perturbation Theory
Milton, K. A.; Solovtsov, I. L.; Solovtsova, O. P.
2001-01-01
The method of analytic perturbation theory, which avoids the problem of ghost-pole type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the "light" Adler function corresponding to the non-strange vector channel of the inclusive decay of the $\\tau$ lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is ...
Error estimates for Gaussian quadratures of analytic functions
Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.
2009-12-01
For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points ±1 and the sum of semi-axes [varrho]>1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod's method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures.
Analytical methods to calculate correlation functions in quantum statistical physics
In the work there is presented a brief but clear and quite reserved account of two analytical methods to calculate correlation functions in quantum statistical physics, proceeding from the first principles, i.e., the most broadly used at present two-time temperature Green's functions method and a new, so-called 'direct algebraic' method (DAM). The aim of this work is to show on the concrete examples of live the most broadly used models of quantum statistical physics, mathematical and technical clarity and simplicity of DAM and hence its practical value
Adler function for light quarks in analytic perturbation theory
The method of analytic perturbation theory, which avoids the problem of ghost-pole-type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the 'light' Adler function corresponding to the nonstrange vector channel of the inclusive decay of the τ lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed leads to good agreement with the 'experimental' Adler function down to the lowest energy scale
Analytical strategies to assess the functional metabolome of vitamin E.
Torquato, Pierangelo; Ripa, Orsola; Giusepponi, Danilo; Galarini, Roberta; Bartolini, Desirée; Wallert, Maria; Pellegrino, Roberto; Cruciani, Gabriele; Lorkowski, Stefan; Birringer, Marc; Mazzini, Francesco; Galli, Francesco
2016-05-30
After more than 90 years from its discovery and thousands of papers published, the physiological roles of vitamin E (tocopherols and tocotrienols) are still not fully clarified. In the last few decades, the enzymatic metabolism of this vitamin has represented a stimulating subject of research. Its elucidation has opened up new horizons to the interpretation of the biological function of that class of molecules. The identification of specific properties for some of the physiological metabolites and the definition of advanced analytical techniques to assess the human metabolome of this vitamin in vivo, have paved the way to a series of hypotheses on the functional implications that this metabolism may have far beyond its catabolic role. The present review collects the available information on the most relevant analytical strategies employed to assess the status and metabolism of vitamin E in humans as well as in other model systems. A particular focus is dedicated to the analytical methods used to measure vitamin E metabolites, and particularly long-chain metabolites, in biological fluids and tissues. Preliminary information on a new LC-APCI-MS/MS method to measure these metabolites in human serum is reported. PMID:26947319
On the analytic proton structure function with heavy quarks
The analytic proton structure function including quark mass is derived in the framework of color glass condensate. To get the massive proton structure function we keep the quark mass in photon wave function in the derivation process although the calculation is much more complicated than the massless case. It shows that the quark mass plays a key role in the description of the experimental data of proton structure function, and the cross-section of γ*p scattering will be divergent without quark mass regulation. To have the right threshold behavior and a smooth transition in the limit Q2 → 0, the quark mass has to include in the cross-section. (orig.)
On the analytic proton structure function with heavy quarks
Hu, Y.; Zeng, J.; Li, Q.; Zhou, F. [Guizhou Normal University, College of Physics and Electronics Science, Guiyang (China); Zhou, D. [Huazhong Normal University, Institute of Particle physics, Wuhan (China); Xiang, W. [Guizhou Normal University, College of Physics and Electronics Science, Guiyang (China); South Dakota School of Mines and Technology, Department of Physics, Rapid City, SD (United States)
2015-12-15
The analytic proton structure function including quark mass is derived in the framework of color glass condensate. To get the massive proton structure function we keep the quark mass in photon wave function in the derivation process although the calculation is much more complicated than the massless case. It shows that the quark mass plays a key role in the description of the experimental data of proton structure function, and the cross-section of γ{sup *}p scattering will be divergent without quark mass regulation. To have the right threshold behavior and a smooth transition in the limit Q{sup 2} → 0, the quark mass has to include in the cross-section. (orig.)
Polymer as a function of monomer: Analytical quantum modeling
Nakhaee, Mohammad
2016-01-01
To identify an analytical relation between the properties of polymers and their's monomer a Metal-Molecule-Metal (MMM) junction has been presented as an interesting and widely used object of research in which the molecule is a polymer which is able to conduct charge. The method used in this study is based on the Green's function approach in the tight-binding approximation using basic properties of matrices. For a polymer base MMM system, transmission, density of states (DOS) and local density of states (LDOS) have been calculated as a function of the hamiltonian of the monomer. After that, we have obtained a frequency for LDOS variations in pass from a subunit to the next one which is a function of energy.
Evaluation of Analytical Modeling Functions for the Phonation Onset Process
Petermann, Simon; Kniesburges, Stefan; Ziethe, Anke; Schützenberger, Anne; Döllinger, Michael
2016-01-01
The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO), called the voice onset time (VOT), is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps) was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW) during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1) reliability of the fit function for a correct approximation of VO; (2) consistency represented by the standard deviation of VOT; and (3) accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW. PMID:27066108
The boundary value problem for discrete analytic functions
Skopenkov, Mikhail
2013-06-01
This paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete analytic, if for each face the difference quotients along the two diagonals are equal.We prove that the Dirichlet boundary value problem for the real part of a discrete analytic function has a unique solution. In the case when each face has orthogonal diagonals we prove that this solution uniformly converges to a harmonic function in the scaling limit. This solves a problem of S.Smirnov from 2010. This was proved earlier by R.Courant-K.Friedrichs-H.Lewy and L.Lusternik for square lattices, by D.Chelkak-S.Smirnov and implicitly by P.G.Ciarlet-P.-A.Raviart for rhombic lattices.In particular, our result implies uniform convergence of the finite element method on Delaunay triangulations. This solves a problem of A.Bobenko from 2011. The methodology is based on energy estimates inspired by alternating-current network theory. © 2013 Elsevier Ltd.
Functional Analytic Multisensory Environmental Therapy for People with Dementia
Jason A. Staal
2012-01-01
Full Text Available This paper introduces Functional Analytic Multisensory Environmental Therapy (FAMSET for use with elders with dementia while using a multisensory environment/snoezelen room. The model introduces behavioral theory and practice to the multisensory environment treatment, addressing assessment, and, within session techniques, integrating behavioral interventions with emotion-oriented care. A modular approach is emphasized to delineate different treatment phases for multisensory environment therapy. The aim of the treatment is to provide a safe and effective framework for reducing the behavioral disturbance of the disease process, increasing elder well-being, and to promote transfer of positive effects to other environments outside of the multisensory treatment room.
Elements of a function analytic approach to probability.
Ghanem, Roger Georges (University of Southern California, Los Angeles, CA); Red-Horse, John Robert
2008-02-01
We first provide a detailed motivation for using probability theory as a mathematical context in which to analyze engineering and scientific systems that possess uncertainties. We then present introductory notes on the function analytic approach to probabilistic analysis, emphasizing the connections to various classical deterministic mathematical analysis elements. Lastly, we describe how to use the approach as a means to augment deterministic analysis methods in a particular Hilbert space context, and thus enable a rigorous framework for commingling deterministic and probabilistic analysis tools in an application setting.
Functional analytic multisensory environmental therapy for people with dementia.
Staal, Jason A
2012-01-01
This paper introduces Functional Analytic Multisensory Environmental Therapy (FAMSET) for use with elders with dementia while using a multisensory environment/snoezelen room. The model introduces behavioral theory and practice to the multisensory environment treatment, addressing assessment, and, within session techniques, integrating behavioral interventions with emotion-oriented care. A modular approach is emphasized to delineate different treatment phases for multisensory environment therapy. The aim of the treatment is to provide a safe and effective framework for reducing the behavioral disturbance of the disease process, increasing elder well-being, and to promote transfer of positive effects to other environments outside of the multisensory treatment room. PMID:22347667
Usage of analytical diagnostics when evaluating functional surface material defects
R. Frischer
2015-10-01
Full Text Available There are occurring defects due to defects mechanisms on parts of production devices surfaces. Outer defects pronouncement is changing throw the time with unequal speed. This variability of defect’s mechanism development cause that is impossible to evaluate technical state of the device in any moment, without the necessary underlying information. Proposed model is based on analytical diagnostics basis. Stochastic model with usage of Weibull probability distribution can assign probability of function surface defect occurrence on the operational information in any moment basis. The knowledge of defect range limiting moment, then enable when and in what range will be necessary to make renewal.
The Navier-Stokes equations an elementary functional analytic approach
Sohr, Hermann
2001-01-01
The primary objective of this monograph is to develop an elementary and self contained approach to the mathematical theory of a viscous incompressible fluid in a domain 0 of the Euclidean space ]Rn, described by the equations of Navier Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the first two chapters we collect without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain O. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n = 2,3 that are also most significant from the physical point of view. For mathematical generality, we will develop the lin earized theory for all n 2 2. Although the functional-analytic approach developed here is, in principle, known ...
An analytic function approach to weak mutually unbiased bases
Olupitan, T.; Lei, C.; Vourdas, A.
2016-08-01
Quantum systems with variables in Z(d) are considered, and three different structures are studied. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases is 1 /√{ k } (where k | d) or 0. The second is maximal lines through the origin in the Z(d) × Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. For simplicity, the case where d =p1 ×p2, where p1 ,p2 are odd prime numbers different from each other, is considered.
A nonlinear analytic function expansion nodal method for transient calculations
Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)
The Navier-Stokes equations an elementary functional analytic approach
Sohr, Hermann
2001-01-01
The primary objective of this monograph is to develop an elementary and self-contained approach to the mathematical theory of a viscous, incompressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes. Moreover, the theory is presented for completely general domains, in particular, for arbitrary unbounded, nonsmooth domains. Therefore, restriction was necessary to space dimensions two and three, which are also the most significant from a physical point of view. For mathematical generality, however, the linearized theory is expounded for general dimensions higher than one. Although the functional analytic approach developed here is, in principle, known to specialists, the present book fills a gap in the literature providing a systematic treatment of a subject that has been documented until now only in fragments. The book is mainly directed to students familiar with basic tools in Hilbert and Banach spaces. However, for the readers’ convenience, some fundamental properties...
Explicit transverse leakage treatment using an analytic basis function expansion
An explicit method for calculating the transverse leakage is presented in this paper. The method is based upon the use of analytic basis functions, which represent individual eigenfunctions of the neutron diffusion equation. The intranodal flux solution is expressed as an eigenspace, and can be solved by using the already calculated surface currents and flux moments as boundary conditions. The salient feature of the method, therefore, is that no ad hoc presumptions are made with regard to the leakage shape. The individual eigenfunctions are calculated based upon already calculated parameters from the flux solution and response matrix solution, and therefore no additional parameters are introduced into the problem, which could lead to an unwanted increase in computation time. The new transverse leakage method is implemented in PSU's NEM code and is tested against the OECD/NEA 3D C5G7 rodded MOX benchmark and the C3 benchmark. (author)
New analytical potential energy function for doubly charged diatomic molecules
Wang Fan-Hou; Yang Chuan-Lu; Zhu Zheng-He; Jing Fu-Qian
2005-01-01
A new analytical potential function for doubly charged diatomic ions is proposed as V(R)=(∑k n=0anRn-1)exp(-ak+1R)+C/R,where an, ak+1 and C are parameters, and R is the nuclear distance. This function can be used to describe the potential curves for doubly charged diatomic ions with both potential minimum and maximum, or without any stationary point. As examples, potential functions of this form for ground states of BH2+, He22+ and HF2+ have been derived.The calculations using the theoretical method QCISD with basis set 6-311++G* have shown that the potential minimum of BH2+is at Rmin=0.147nm, the maximum at Rmax=0.185nm, and ΔE = Emax - Emin=0.062 eV; for He22+Rmin=0.0736nm, Rmax=0.105nm, and ΔE = Emax - Emin=0.71 eV. It is found that the potential curve for HF2+ is one with a singly repulsive branch. The force constants and spectroscopic data for BH2+ and He22+ have also been worked out.
Olesov, A. V.
2014-10-01
New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak. Bibliography: 27 titles.
Applying fuzzy analytic network process in quality function deployment model
Mohammad Ali Afsharkazemi
2012-08-01
Full Text Available In this paper, we propose an empirical study of QFD implementation when fuzzy numbers are used to handle the uncertainty associated with different components of the proposed model. We implement fuzzy analytical network to find the relative importance of various criteria and using fuzzy numbers we calculate the relative importance of these factors. The proposed model of this paper uses fuzzy matrix and house of quality to study the products development in QFD and also the second phase i.e. part deployment. In most researches, the primary objective is only on CRs to implement the quality function deployment and some other criteria such as production costs, manufacturing costs etc were disregarded. The results of using fuzzy analysis network process based on the QFD model in Daroupat packaging company to develop PVDC show that the most important indexes are being waterproof, resistant pill packages, and production cost. In addition, the PVDC coating is the most important index in terms of company experts’ point of view.
Boundary-value problems for x-analytical functions with weighted boundary conditions
Kapshivyi, A.A. [Kiev Univ. (Ukraine)
1994-11-10
We consider boundary-value problems for x-analytical functions of a complex variable z = x + iy in a number of domains. Limit values with the weight (ln x){sup {minus}1} are given for the real part of the x-analytical function on the sections of the boundary that follow the imaginary axis, and simple limits are given for the real part of the x-analytical functions on the part of the boundary outside the imaginary axis. The apparatus of integral representations of x-analytical functions is applied to obtain a solution of the problem in quadratures.
Olesov, A V [G.I. Nevelskoi Maritime State University, Vladivostok (Russian Federation)
2014-10-31
New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak. Bibliography: 27 titles.
New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak. Bibliography: 27 titles
Analytic structure of many-body Coulombic wave functions
Fournais, Søren; Hoffmann-Ostenhof, Maria; Hoffmann-Ostenhof, Thomas; Sørensen, Thomas Østergaard
2009-01-01
We investigate the analytic structure of solutions of non-relativistic Schrödinger equations describing Coulombic many-particle systems. We prove the following: Let ψ(x) with denote an N-electron wavefunction of such a system with one nucleus fixed at the origin. Then in a neighbourhood of a...
Algebraic and analyticity properties of the n-point function in quantum field theory
The general theory of quantized fields (axiomatic approach) is investigated. A systematic study of the algebraic properties of all the Green functions of a local field, which generalize the ordinary retarded and advanced functions, is presented. The notion emerges of a primitive analyticity domain of the n-point function, and of the existence of auxiliary analytic functions into which the various Green functions can be decomposed. Certain processes of analytic completion are described, and then applied to enlarging the primitive domain, particularly for the case n = 4; among the results the crossing property for all scattering amplitudes which involve two incoming and two outgoing particles is proved. (author)
On Certain Subclasses of Analytic and Univalent Functions based on an Extension of Salagean Operator
T.V. Sudharsan
2012-09-01
Full Text Available There is many subclasses of analytic and univalent functions. A class T of functions with negative coefficients introduced by Silverman [8] opened up a new and fruitful line of research in the theory of univalent functions. Following the works of Khairnar and Meena More [3], Aghalary and Kulkarni [1], Silverman and Silvia [8] and Owa and Nishiwaki [5] on analytic and univalent functions, in this paper we introduce two new classes for a family of analytic function with negative coefficients. We have attempted to obtain coefficient estimate, distortion theorem and extreme points for the class
Analytic Continuation of Hypergeometric Functions in the Resonant Case
Scheidegger, Emanuel
2016-01-01
We perform the analytic continuation of solutions to the hypergeometric differential equation of order $n$ to the third regular singularity, usually denoted $z=1$, with the help of recurrences of their Mellin--Barnes integral representations. In the resonant case, there are necessarily logarithmic solutions. We apply the result to Picard-Fuchs equations of certain one--parameter families of Calabi--Yau manifolds, known as the mirror quartic and the mirror quintic.
Parametric analyticity of functional variations of Dirichlet-Neumann operators
Fazioli, Carlo; Nicholls, David P.
2008-01-01
One of the important open questions in the theory of free--surface ideal fluid flows is the dynamic stability of traveling wave solutions. In a spectral stability analysis, the first variation of the governing Euler equations is required which raises both theoretical and numerical issues. With Zakharov and Craig and Sulem's formulation of the Euler equations in mind, this paper addresses the question of analyticity properties of first (and higher) variations of the Dirichlet--N...
The QCD analysis of xF_3 structure function based on the analytic approach
Sidorov, A. V.; Solovtsova, O. P.
2013-01-01
We apply analytic perturbation theory to the QCD analysis of the xF_3 structure function data of the CCFR collaboration. We use different approaches for the leading order Q^2 evolution of the xF_3 structure function and compare the extracted values of the parameter Lambda_QCD and the shape of the higher twistcontribution. Our consideration is based on the Jacobi polynomial expansion method of the unpolarized structure function. The analysis shows that the analytic approach provides reasonable...
Gori-Giorgi, Paola; Sacchetti, Francesco; Bachelet, Giovanni B.
1999-01-01
We propose a simple and accurate model for the electron static structure factors (and corresponding pair-correlation functions) of the 3D unpolarized homogeneous electron gas. Our spin-resolved pair-correlation function is built up with a combination of analytic constraints and fitting procedures to quantum Monte Carlo data, and, in comparison to previous attempts (i) fulfills more known integral and differential properties of the exact pair-correlation function, (ii) is analytic both in real...
Critical node treatment in the analytic function expansion method for Pin Power Reconstruction
Gao, Z. [Rice University, MS 318, 6100 Main Street, Houston, TX 77005 (United States); Xu, Y. [Argonne National Laboratory, 9700 South Case Ave., Argonne, IL 60439 (United States); Downar, T. [Department of Nuclear Engineering, University of Michigan, 2355 Bonisteel blvd., Ann Arbor, MI 48109 (United States)
2013-07-01
Pin Power Reconstruction (PPR) was implemented in PARCS using the eight term analytic function expansion method (AFEN). This method has been demonstrated to be both accurate and efficient. However, similar to all the methods involving analytic functions, such as the analytic node method (ANM) and AFEN for nodal solution, the use of AFEN for PPR also has potential numerical issue with critical nodes. The conventional analytic functions are trigonometric or hyperbolic sine or cosine functions with an angular frequency proportional to buckling. For a critic al node the buckling is zero and the sine functions becomes zero, and the cosine function become unity. In this case, the eight terms of the analytic functions are no longer distinguishable from ea ch other which makes their corresponding coefficients can no longer be determined uniquely. The mode flux distribution of critical node can be linear while the conventional analytic functions can only express a uniform distribution. If there is critical or near critical node in a plane, the reconstructed pin power distribution is often be shown negative or very large values using the conventional method. In this paper, we propose a new method to avoid the numerical problem wit h critical nodes which uses modified trigonometric or hyperbolic sine functions which are the ratio of trigonometric or hyperbolic sine and its angular frequency. If there are no critical or near critical nodes present, the new pin power reconstruction method with modified analytic functions are equivalent to the conventional analytic functions. The new method is demonstrated using the L336C5 benchmark problem. (authors)
Critical node treatment in the analytic function expansion method for Pin Power Reconstruction
Pin Power Reconstruction (PPR) was implemented in PARCS using the eight term analytic function expansion method (AFEN). This method has been demonstrated to be both accurate and efficient. However, similar to all the methods involving analytic functions, such as the analytic node method (ANM) and AFEN for nodal solution, the use of AFEN for PPR also has potential numerical issue with critical nodes. The conventional analytic functions are trigonometric or hyperbolic sine or cosine functions with an angular frequency proportional to buckling. For a critic al node the buckling is zero and the sine functions becomes zero, and the cosine function become unity. In this case, the eight terms of the analytic functions are no longer distinguishable from ea ch other which makes their corresponding coefficients can no longer be determined uniquely. The mode flux distribution of critical node can be linear while the conventional analytic functions can only express a uniform distribution. If there is critical or near critical node in a plane, the reconstructed pin power distribution is often be shown negative or very large values using the conventional method. In this paper, we propose a new method to avoid the numerical problem wit h critical nodes which uses modified trigonometric or hyperbolic sine functions which are the ratio of trigonometric or hyperbolic sine and its angular frequency. If there are no critical or near critical nodes present, the new pin power reconstruction method with modified analytic functions are equivalent to the conventional analytic functions. The new method is demonstrated using the L336C5 benchmark problem. (authors)
Computing the hadronic vacuum polarization function by analytic continuation
Feng, Xu; Hotzel, Grit; Jansen, Karl; Petschlies, Marcus; Renner, Dru B
2013-01-01
We propose a method to compute the hadronic vacuum polarization function on the lattice at continuous values of photon momenta bridging between the space-like and time-like regions. We provide two independent derivations of this method showing that it leads to the desired hadronic vacuum polarization function in Minkowski space-time. We show with the example of the leading- order QCD correction to the muon anomalous magnetic moment that this approach can provide a valuable alternative method for calculations of physical quantities where the hadronic vacuum polarization function enters.
Computing the hadronic vacuum polarization function by analytic continuation
Feng, Xu [KEK National High Energy Physics, Tsukuba (Japan); Hashimoto, Shoji [KEK National High Energy Physics, Tsukuba (Japan); The Graduate Univ. for Advanced Studies, Tsukuba (Japan). School of High Energy Accelerator Science; Hotzel, Grit [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Petschlies, Marcus [The Cyprus Institute, Nicosia (Cyprus); Renner, Dru B. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
2013-07-15
We propose a method to compute the hadronic vacuum polarization function on the lattice at continuous values of photon momenta bridging between the space-like and time-like regions. We provide two independent derivations of this method showing that it leads to the desired hadronic vacuum polarization function in Minkowski space-time. We show with the example of the leading- order QCD correction to the muon anomalous magnetic moment that this approach can provide a valuable alternative method for calculations of physical quantities where the hadronic vacuum polarization function enters.
Analytic flux formulas and tables of shielding functions
Hand calculations of radiation flux and dose rates are often useful in evaluating radiation shielding and in determining the scope of a problem. The flux formulas appropriate to such calculations are almost always based on the point kernel and allow for at most the consideration of laminar slab shields. These formulas often require access to tables of values of integral functions for effective use. Flux formulas and function tables appropriate to calculations involving homogeneous source regions with the shapes of lines, disks, slabs, truncated cones, cylinders, and spheres are presented. Slab shields may be included in most of these calculations, and the effect of a cylindrical shield surrounding a cylindrical source may be estimated. Detector points may be located axially, laterally, or interior to a cylindrical source. Line sources may be tilted with respect to a slab shield. All function tables are given for a wide range of arguments
Analytic flux formulas and tables of shielding functions
Wallace, O.J.
1981-06-01
Hand calculations of radiation flux and dose rates are often useful in evaluating radiation shielding and in determining the scope of a problem. The flux formulas appropriate to such calculations are almost always based on the point kernel and allow for at most the consideration of laminar slab shields. These formulas often require access to tables of values of integral functions for effective use. Flux formulas and function tables appropriate to calculations involving homogeneous source regions with the shapes of lines, disks, slabs, truncated cones, cylinders, and spheres are presented. Slab shields may be included in most of these calculations, and the effect of a cylindrical shield surrounding a cylindrical source may be estimated. Detector points may be located axially, laterally, or interior to a cylindrical source. Line sources may be tilted with respect to a slab shield. All function tables are given for a wide range of arguments.
Variational characterizations for eigenfunctions of analytic self-adjoint operator functions
Georgios Katsouleas; John Maroulas
2013-01-01
In this paper we consider Rellich's diagonalization theorem for analytic self-adjoint operator functions and investigate variational principles for their eigenfunctions and interlacing statements. As an application, we present a characterization for the eigenvalues of hyperbolic operator polynomials.
ORBITALES. A program for the calculation of wave functions with an analytical central potential
In this paper is described the objective, basis, carrying out in FORTRAN language and use of the program ORBITALES. This program calculate atomic wave function in the case of ths analytical central potential (Author) 8 refs
On Eneström–Kakeya Theorem and Related Analytic Functions
W M Shah; A Liman
2007-08-01
We prove some extensions of the classical results concerning the Eneström–Kakeya theorem and related analytic functions. Besides several consequences, our results considerably improve the bounds by relaxing and weakening the hypothesis in some cases.
Analytic height correlation function of rough surfaces derived from light scattering
Zamani, M; Fazeli, S M; Downer, M C; Jafari, G R
2015-01-01
We obtain an analytic expression for the height correlation function of a rough surface based on the inverse wave scattering method of Kirchhoff theory. The expression directly relates the height correlation function to diffuse scattered intensity. We test the solution by measuring the angular distribution of light scattered from rough silicon surfaces, solving for the height correlation functions, and comparing them to functions derived from AFM measurements. The results show good agreement. The advantages of this method are its accurate analytical equation for the height correlation function and the simplicity of the experimental setup required to measure it.
Functional calculus for generators of analytic semigroups of operators
Lopushansky O.V.; Sharyn S.V.
2012-01-01
We construct a functional calculus for generators of one-parameter boundedanalytic semigroups of operators on a Banach space. The calculus symbol classconsist of the Laplace image of the convolution algebra $cal S'_+$ of tempereddistributions with supports in $[0, infty)$. Domain of constructed calculus isdense in the Banach space.
Functional calculus for generators of analytic semigroups of operators
Lopushansky O.V.
2012-06-01
Full Text Available We construct a functional calculus for generators of one-parameter boundedanalytic semigroups of operators on a Banach space. The calculus symbol classconsist of the Laplace image of the convolution algebra $cal S'_+$ of tempereddistributions with supports in $[0, infty$. Domain of constructed calculus isdense in the Banach space.
Constructing and Deriving Reciprocal Trigonometric Relations: A Functional Analytic Approach
Ninness, Chris; Dixon, Mark; Barnes-Holmes, Dermot; Rehfeldt, Ruth Anne; Rumph, Robin; McCuller, Glen; Holland, James; Smith, Ronald; Ninness, Sharon K.; McGinty, Jennifer
2009-01-01
Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed…
Newton Algorithms for Analytic Rotation: An Implicit Function Approach
Boik, Robert J.
2008-01-01
In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to "m" factors and "p" variables. The speed of the new algorithms is compared to that of existing algorithms and to…
Function of nuclear analytical techniques in Interuniverinteruniversity research cooperation
The interuniversity institute was established in 1957 with the instruction to use its major research tool - the nuclear research reactor - in cooperation with and for the benefit of all universities in the Netherlands. Developments in the institute have resulted in two forms of neutron activation analysis currently applied on routine basis. A highly sophisticated automated instrumental multi-element analysis is mostly applied to samples containing elements in the ppm-range and in which no strongly dominating activity is formed. These conditions are fulfilled in general for silicous materials as encountered in geological and archeological samples and in soils and sediments. An automated destructive multi-element analysis involving chemical separations is used for samples with element concentrations in the ppb-range containing some type of dominating activities. This occurs in biological and environmental samples where Na, Fe and Br are mostly available in high concentrations. The institute has been asked many times to help in setting up radio-tracer experiments in various fields including analytical chemistry (isotope dilution, radio immuno assay), physical chemistry (adsorption, diffusion and exchange reactions between solids and liquids during crystallization, corrosion), chemical engineering (determination of contact times and their distribution), biomedical engineering (diffusion processes in membranes for artificial kidneys), biology (uptake of chemical by fish, measurement of displacement habits of animals) etc. Special attention is being paid to the behaviour of trace-elements in metabolic processes, which has been initiated by the medical interest in pathological deviations of copper metabolism in Wilson's and Menkes' diseases. (T.G.)
Analytical theory of the probability distribution function of structure formation
Anderson, Johan; Kim, Eun-Jin
2009-01-01
The probability distribution function (PDF) tails of the zonal flow structure formation and the PDF tails of momentum flux by incorporating effect of a shear flow in ion-temperature-gradient (ITG) turbulence are computed in the present paper. The bipolar vortex soliton (modon) is assumed to be the coherent structure responsible for bursty and intermittent events driving the PDF tails. It is found that stronger zonal flows are generated in ITG turbulence than Hasegawa-Mima (HM) turbulence as w...
Windisch, Andreas; Haase, Gundolf; Liebmann, Manfred
2012-01-01
Graphics Processing Units (GPUs) are employed for a numerical determination of the analytic structure of two-point correlation functions of Quantum Field Theories. These functions are represented through integrals in d-dimensional Euclidean momentum space. Such integrals can in general not be solved analytically, and therefore one has to rely on numerical procedures to extract their analytic structures if needed. After describing the general outline of the corresponding algorithm we demonstrate the procedure by providing a completely worked-out example in four dimensions for which an exact solution exists. We resolve the analytic structure by highly parallel evaluation of the correlation functions momentum space integral in the complex plane. The (logarithmically) divergent integral is regularized by applying a BPHZ-like Taylor subtraction to the integrand. We find perfect agreement with the exact solution. The fact that each point in the complex plane does not need any information from other points makes thi...
Bagci, A
2016-01-01
The author in his previous works were presented a numerical integration method, namely, global-adaptive with the Gauss-Kronrod numerical integration extension in order to accurate calculation of molecular auxiliary functions integrals involve power functions with non-integer exponents. They are constitute elements of molecular integrals arising in Dirac equation when Slater-type orbitals with non-integer principal quantum numbers are used. Binomial series representation of power functions method, so far, is used for analytical evaluation of the molecular auxiliary function integrals however, intervals of integration cover areas beyond the condition of convergence. In the present study, analytical evaluation of these integrals is re-examined. They are expressed via prolate spheroidal coordinates. An alternative analytical approximation are derived. Slowly convergent binomial series representation formulae for power functions is investigated through nonlinear sequence transformations for the acceleration of con...
Search for analytic extensions of combinations of thermal two-point functions at one loop
Full text: In this paper, we study the analytic properties of two and three-point amplitudes at Finite Temperature in the Closed Time Path formalism at one loop. In [Phys. Rev. D 71, 036002 (2005)], Weldon has shown the impossibility of analytic continuation for the 2n different n-points functions that appear in the Real Time Formalism in Quantum Field Theory at Finite Temperature, due to the presence of branch cuts at various energy values. Even though none of these functions alone can be extended to complex regions he has found the particular combination of these n-point functions which admit analytic extension to complex energies. In his work, he has considered general properties of thermal average of field operators to analyse the results. On the other hand, at one loop in the perturbation theory more analytic structures appear inside the loop integrals and it is not clear how these results will appear. Here, we consider the λφ3 and the Schwinger Models and study how these analytic properties manifest specifically inside a loop integral. We explicitly extract the branch cuts of the various amplitudes for the self-energies and vertex corrections and show which combinations of them admit analytic continuation for complex energy values. We will extend this paper of n-point functions. (author)
Analytical approach to the current correlation function in dissipative two-state systems
Qin WANG; Cheng JIANG; Hang ZHENG
2008-01-01
Using the spin-boson model with coupling to Ohmic bath, an analytical approach is developed to study the dynamics of the current correlation function in dissipa-tive two-state systems with the view of understanding the ef-fects of environment and tunneling on the coherent oscillation and the long-time decay of the current correlation function in these systems. An analytic expression of current correlation function is obtained and the results agree very well with that of numerical simulations.
Optimization of Quantum Monte Carlo Wave Functions Using Analytical Energy Derivatives
Lin, X; Rappe, A M; Lin, Xi; Zhang, Hongkai; Rappe, Andrew M.
1999-01-01
An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on New ton's method and analytical computation of the first and second derivatives of the variati onal energy. This direct application of the variational principle yields significantly low er energy than variance minimization methods when applied to the same trial wave function. Quadratic convergence to the local minimum of the variational parameters is achieved. A g eneral theorem is presented, which substantially simplifies the analytic expressions of de rivatives in the case of wave function optimization. To demonstrate the method, the ground state energies of the first-row elements are calculated.
The Challenge of Developing a Universal Case Conceptualization for Functional Analytic Psychotherapy
Bonow, Jordan T.; Maragakis, Alexandros; Follette, William C.
2012-01-01
Functional Analytic Psychotherapy (FAP) targets a client's interpersonal behavior for change with the goal of improving his or her quality of life. One question guiding FAP case conceptualization is, "What interpersonal behavioral repertoires will allow a specific client to function optimally?" Previous FAP writings have suggested that a therapist…
Simple analytical expression for work function in the 'nearest neighbour' approximation
Chrzanowski, J. [Institute of Physics, Maritime University of Szczecin, 1-2 Waly Chrobrego, Szczecin 70-500 (Poland); Kravtsov, Yu.A., E-mail: y.kravtsov@am.szczecin.p [Institute of Physics, Maritime University of Szczecin, 1-2 Waly Chrobrego, Szczecin 70-500 (Poland); Space Research Institute, Profsoyuznaya St. 82/34, Moscow 117997 (Russian Federation)
2011-01-17
Nonlocal operator of potential is suggested, based on the 'nearest neighbour' approximation (NNA) for single electron wave function in metals. It is shown that Schroedinger equation with nonlocal potential leads to quite simple analytical expression for work function, which surprisingly well fits to experimental data.
Simple analytical expression for work function in the “nearest neighbour” approximation
Chrzanowski, J.; Kravtsov, Yu. A.
2011-01-01
Nonlocal operator of potential is suggested, based on the “nearest neighbour” approximation (NNA) for single electron wave function in metals. It is shown that Schrödinger equation with nonlocal potential leads to quite simple analytical expression for work function, which surprisingly well fits to experimental data.
Fukushima, Kimichika
2015-01-01
This paper presents analytical eigenenergies for a pair of confined fundamental fermion and antifermion under a linear potential derived from the Wilson loop for the non-Abelian Yang-Mills field. We use basis functions localized in spacetime, and the Hamiltonian matrix of the Dirac equation is analytically diagonalized. The squared system eigenenergies are proportional to the string tension and the absolute value of the Dirac's relativistic quantum number related to the total angular momentum, consistent with the expectation.
Petrenko, Taras; Kossmann, Simone; Neese, Frank
2011-02-01
In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ˜26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ˜27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ˜24 on 30 processors. The
Analytic Solutions of a Second-Order Iterative Functional Differential Equations
Liu, Lingxia
In this paper, the existence of analytic solutions of an iterative functional differential equation is studied. We reduce this problem to finding analytic solutions of a functional differential equation without iteration of the unknown function. For technical reasons, in previous work the constant α given in Schröder transformation is required to fulfill that α is off the unit circle or lies on the circle with the Diophantine condition. In this paper, we break the restraint of the Diophantine condition and obtain results of analytic solutions in the case of α at resonance, i.e., at a root of the unity and the case of α near resonance under the Brjuno condition.
Analytic integration of a common set of microwave beam intensity functions
Potter, S.D. [New York Univ., New York, NY (United States)
1994-12-31
When designing a wireless power transmission system, a virtually limitless number of aperture illumination functions are available. However, a commonly-used set of beam tapers results in received intensities that involve Bessel functions. This family of intensities is convenient to study and compare systematically. A cosntraint on the calculation of reception efficiency is the need to write numerical routines to integrate such functions. It is shown that these functions can be integrated analytically, resulting in a concise formula for reception efficiency as a function of rectifying antenna (rectenna) diameter.
Differential Sandwich Theorems for some Subclasses of Analytic Functions Involving a Linear Operator
S. Sivasubramanian
2007-10-01
Full Text Available By making use of the familiar Carlson-Shaffer operator,the authors derive derive some subordination and superordination results for certain normalized analytic functions in the open unit disk. Relevant connections ofthe results, which are presented in this paper, with various other known results are also pointed out.
On the analyticity of periodic gravity water waves with integrable vorticity function
Escher, Joachim; Matioc, Bogdan-Vasile
2013-01-01
We prove that the streamlines and the profile of periodic gravity water waves traveling over a flat bed with wavespeed which exceeds the horizontal velocity of all fluid particles are real-analytic graphs if the vorticity function is merely integrable.
An Example of a Hakomi Technique Adapted for Functional Analytic Psychotherapy
Collis, Peter
2012-01-01
Functional Analytic Psychotherapy (FAP) is a model of therapy that lends itself to integration with other therapy models. This paper aims to provide an example to assist others in assimilating techniques from other forms of therapy into FAP. A technique from the Hakomi Method is outlined and modified for FAP. As, on the whole, psychotherapy…
LI Zong-tao; GUO Dong
2014-01-01
In this paper, we introduce certain new subclasses of analytic functions defined by generalized multiplier transformation. By using the differential subordination, we study and investigate various inclusion properties of these classes. Also inclusion properties of these classes involving the integral operator are considered.
Functional analytic background for a theory of infinite-dimensional reductive Lie groups
Beltita, Daniel
2007-01-01
Motivated by the interesting and yet scattered developments in representation theory of Banach-Lie groups, we discuss several functional analytic issues which should underlie the notion of infinite-dimensional reductive Lie group: norm ideals, triangular integrals, operator factorizations, and amenability.
Bowen, Sarah; Haworth, Kevin; Grow, Joel; Tsai, Mavis; Kohlenberg, Robert
2012-01-01
Functional Analytic Psychotherapy (FAP; Kohlenberg & Tsai, 1991) aims to improve interpersonal relationships through skills intended to increase closeness and connection. The current trial assessed a brief mindfulness-based intervention informed by FAP, in which an interpersonal element was added to a traditional intrapersonal mindfulness…
Munoz-Martinez, Amanda; Novoa-Gomez, Monica; Gutierrez, Rochy Vargas
2012-01-01
Functional Analytic Psychotherapy (FAP) has been making an important rise in Ibero-America in recent years. This paper presents a review of different contributions, problems and some proposals. Three principal topics are reviewed: (a) general characteristics and theoretical bases of FAP, (b) the uses of FAP and its relationship with other…
Functional Analytic Psychotherapy (FAP): A Review of Publications from 1990 to 2010
Mangabeira, Victor; Kanter, Jonathan; Del Prette, Giovana
2012-01-01
Functional Analytic Psychotherapy (FAP), a therapy based on radical behaviorism, establishes the priority of the therapeutic interaction as a mechanism of change in psychotherapy. Since the first book on FAP appeared in 1991, it has been the focus of many papers and has been incorporated by the community of behavior therapists. This paper is a…
Closed analytical expressions for some useful sums and integrals involving Legendre function
Simple closed analytical expressions are obtained for some integrals and infinite sums involving Legendre functions. They are lacking in the mathematical literature. The limiting values of these expressions pass into the known ones. The obtained expressions for the above sums and integrals may be useful for the calculation of the magnetic fields with configurations close to the toroidal ones (tokamak devices)
A UNIFIED CLASS OF ANALYTIC FUNCTIONS WITH FIXED ARGUMENT OF COEFFICIENTS
J.Dziok
2011-01-01
In this paper we introduce new classes of analytic functions with fixed argument of coefficients defined by subordination.Coefficient estimates,distortion theorems,integral means inequalities,and the radii of convexity and starlikeness are investigated.Convolution properties are also pointed out.
Structure and analytical potential energy function for the ground state of the BCx (x=0, -1)
Geng Zhen-Duo; Zhang Yan-Song; Fan Xiao-Wei; Lu Zhan-Sheng; Luo Gai-Xia
2006-01-01
In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data (αe, ωe and ωeXe) of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.
Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas
Izacard, Olivier
2016-08-01
In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it
On the analytical evaluation of the partition function for unit hypercubes in four dimensions
The group integrations required for the analytic evaluation of the partition function for unit hypercubes in four dimensions are carried out. Modifications of the graphical rules for SU2 group integrations cited in the literature are developed for this purpose. A complete classification of all surfaces that can be embedded in the unit hypercube is given and their individual contribution to the partition function worked out. Applications are discussed briefly. (orig.)
The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps
Lehner, Sabrina
2016-01-01
The well-known Riemann Mapping Theorem states the existence of a conformal map of a simply connected proper domain of the complex plane onto the upper half plane. One of the main topics in geometric function theory is to investigate the behaviour of the mapping functions at the boundary of such domains. In this work, we always assume that a piecewise analytic boundary is given. Hereby, we have to distinguish regular and singular boundary points. While the asymptotic behaviour for regular boun...
Certain Subclasses of Analytic and Bi-Univalent Functions Involving Double Zeta Functions
Saibah Siregar
2012-01-01
Full Text Available In the present paper, we introduce two new subclasses of the functions class Σ of bi-univalent functions involving double zeta functions in the open unit disc U={z:zEC, |z|<1}. The estimates on the coefficients |a2| and |a3| for functions in these new subclasses of the function class Σ are obtained in our investigation.
Robinson, Jennifer L.; Laird, Angela R.; Glahn, David C.; Blangero, John; Sanghera, Manjit K.; Pessoa, Luiz; Fox, P. Mickle; Uecker, Angela; Friehs, Gerhard; Young, Keith A.; Griffin, Jennifer L.; LOVALLO, WILLIAM R.; Fox, Peter T
2011-01-01
Meta-analysis based techniques are emerging as powerful, robust tools for developing models of connectivity in functional neuroimaging. Here, we apply meta-analytic connectivity modeling to the human caudate to 1) develop a model of functional connectivity, 2) determine if meta-analytic methods are sufficiently sensitive to detect behavioral domain specificity within region-specific functional connectivity networks, and 3) compare meta-analytic driven segmentation to structural connectivity p...
A UNIVERSAL ANALYTIC POTENTIAL-ENERGY FUNCTION BASED ON A PHASE FACTOR
C.F. Yu; K. Yan; D.Z. Liu
2006-01-01
Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of fuce-centered cubic (fcc) metals - Al, Cu, Ag, etc. Are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.
Analytic Structure of the SCFT Energy Functional of Multicomponent Block Copolymers
Jiang, Kai; Zhang, Pingwen
2013-01-01
This paper concerns the analytic structure of the self-consistent field theory (SCFT) energy functional of multicomponent block copolymer systems which contain more than two chemically distinct blocks. The SCFT has enjoyed considered success and wide usage in investigation of the complex phase behavior of block copolymers. It is well-known that the physical solutions of the SCFT equations are saddle points, however, the analytic structure of the SCFT energy functional has received little attention over the years. A recent work by Fredrickson and collaborators [see the monograph by Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers, (2006), pp. 203-209] has analysed the mathematical structure of the field energy functional for polymeric systems, and clarified the index-1 saddle point nature of the problem produced by the incompressibility constraint. In this paper, our goals are to draw further attention to multicomponent block copolymers utilizing the Hubbard-Stratonovich transformation used by Fre...
An analytical wall-function for recirculating and impinging turbulent heat transfer
Highlights: ► Improvement of the analytical wall-function is proposed. ► Strain parameter dependency is introduced to the prescribed eddy viscosity profile of the analytical wall-function. ► The model performance is evaluated in turbulent pipe, channel, back-step, abrupt expansion pipe and plane impinging flows. ► Generally improved heat transfer is obtained in all the test cases with the standard k-e model. -- Abstract: The performance of the analytical wall-function (AWF) of Craft et al. [Craft, T.J., Gerasimov, A.V., Iacovides, H., Launder, B.E., 2002, Progress in the generalisation of wall-function treatments. Int. J. Heat Fluid Flow 23, 148–160.] is improved for predicting turbulent heat transfer in recirculating and impinging flows. Since constant parameters of the eddy viscosity formula were used to derive the AWF, the prediction accuracy of the original AWF tends to deteriorate in complex flows where those parameters need changing according to the local turbulence. To overcome such shortcomings, the present study introduces a functional behaviour on the strain parameter into the coefficient of the eddy viscosity of the AWF. The presently modified version of the AWF is validated in turbulent heat transfer of pipe flows, channel flows, back-step flows, pipe flows with abrupt expansion and plane impinging slot jets. The results confirm that the present modification successfully improves the performance of the original AWF for all the flows and heat transfer tested
Analyticity properties of three-point functions in QCD beyond leading order
The removal of unphysical singularities in the perturbatively calculable part of the pion form factor - a classical example of a three-point function in QCD - is discussed. Different 'analytization' procedures in the sense of Shirkov and Solovtsov are examined in comparison with standard QCD perturbation theory. We show that demanding the analyticity of the partonic amplitude as a whole, as proposed before by Karanikas and Stefanis, one can make infrared finite not only the strong running coupling and its powers, but also cure potentially large logarithms (that first appear in the next-to-leading order) containing the factorization scale and modifying the discontinuity across the cut along the negative real axis. The scheme used here generalizes the Analytic Perturbation Theory of Shirkov and Solovtsov to non-integer powers of the strong coupling and diminishes the dependence of QCD hadronic quantities on all perturbative scheme and scale-setting parameters, including the factorization scale
The Voigt function H(a,v) is defined as the convolution of the Gaussian and Lorentzian functions. Recent papers puplished in different areas of physics emphasize the importance of the fast and accurate calculation of the Voigt function for different orders of magnitude of variables a and v. An alternative analytical formulation for the Voigt function is proposed in this paper. This formulation is based on the solution of the non-homogeneous ordinary differential equation, satisfied by the Voigt function, using the Frobenius and parameter variation methods. The functional form of the Voigt function, as proposed, proved simple and precise. Systematic tests are accomplished demonstrating some advantages with other existent methods in the literature and with the numeric method of reference.
Palma, Daniel A.P., E-mail: dpalmaster@gmail.com [CNEN-Comissao Nacional de Energia Nuclear, 22290-901, Rio de Janeiro (Brazil); Goncalves, Alessandro da C; Martinez, Aquilino S. [COPPE/UFRJ-Programa de Engenharia Nuclear, 21941-972, Rio de Janeiro (Brazil)
2011-10-21
The Voigt function H(a,v) is defined as the convolution of the Gaussian and Lorentzian functions. Recent papers puplished in different areas of physics emphasize the importance of the fast and accurate calculation of the Voigt function for different orders of magnitude of variables a and v. An alternative analytical formulation for the Voigt function is proposed in this paper. This formulation is based on the solution of the non-homogeneous ordinary differential equation, satisfied by the Voigt function, using the Frobenius and parameter variation methods. The functional form of the Voigt function, as proposed, proved simple and precise. Systematic tests are accomplished demonstrating some advantages with other existent methods in the literature and with the numeric method of reference.
Palma, Daniel A. P.; Gonçalves, Alessandro da C.; Martinez, Aquilino S.
2011-10-01
The Voigt function H( a, v) is defined as the convolution of the Gaussian and Lorentzian functions. Recent papers puplished in different areas of physics emphasize the importance of the fast and accurate calculation of the Voigt function for different orders of magnitude of variables a and v. An alternative analytical formulation for the Voigt function is proposed in this paper. This formulation is based on the solution of the non-homogeneous ordinary differential equation, satisfied by the Voigt function, using the Frobenius and parameter variation methods. The functional form of the Voigt function, as proposed, proved simple and precise. Systematic tests are accomplished demonstrating some advantages with other existent methods in the literature and with the numeric method of reference.
Lundengård, Karl; Javor, Vesna; Silvestrov, Sergei
2016-01-01
A multi-peaked form of the analytically extended function (AEF) is used for approximation of lightning current waveforms in this paper. The AEF function's parameters are estimated using the Marquardt least-squares method (MLSM), and the general procedure for fitting the $p$-peaked AEF function to a waveform with an arbitrary (finite) number of peaks is briefly described. This framework is used for obtaining parameters of 2-peaked waveforms typically present when measuring first negative stroke currents. Advantages, disadvantages and possible improvements of the approach are also discussed.
VECTOR-VALUED HOLOMORPHIC FUNCTIONS ON THE COMPLEX BALL AND THE ANALYTIC RADON-NIKODYM PROPERTY
无
2000-01-01
The complex Banach spaces X with values in which every bounded holomorphic function in the unit ball B of Cd(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property.The proof is based on inner Hardy martingales introduced here.The inner Hardy martingales are constructed in terms of inner functions in B and are reasonable discrete approximations for the image processes of the holomorphic Brownian motion under X-valued holomorphic functions in B.
Plane strain analytical solutions for a functionally graded elastic-plastic pressurized tube
Plane strain analytical solutions to functionally graded elastic and elastic-plastic pressurized tube problems are obtained in the framework of small deformation theory. The modulus of elasticity and the uniaxial yield limit of the tube material are assumed to vary radially according to two parametric parabolic forms. The analytical plastic model is based on Tresca's yield criterion, its associated flow rule and ideally plastic material behaviour. Elastic, partially plastic and fully plastic stress states are investigated. It is shown that the elastoplastic response of the functionally graded pressurized tube is affected significantly by the material nonhomogeneity. Different modes of plasticization may take place unlike the homogeneous case. It is also shown mathematically that the nonhomogeneous elastoplastic solution presented here reduces to that of a homogeneous one by appropriate choice of the material parameters
Analytic number theory, approximation theory, and special functions in honor of Hari M. Srivastava
Rassias, Michael
2014-01-01
This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality, and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics, and other computational and applied sciences.
We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields, reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities
On the analytical development of the lunar and solar disturbing functions
Celletti, Alessandra; Pucacco, Giuseppe; Rosengren, Aaron J
2015-01-01
We provide a detailed derivation of the analytical expansion of the lunar and solar disturbing functions. We start with Kaula's expansion of the disturbing function in terms of the equatorial elements of both the perturbed and perturbing bodies. Then we provide a detailed proof of Lane's expansion, in which the elements of the Moon are referred to the ecliptic plane. Using this approach the inclination of the Moon becomes nearly constant, while the argument of perihelion, the longitude of the ascending node, and the mean anomaly vary linearly with time. We make a comparison between the different expansions and we profit from such discussion to point out some mistakes in the existing literature, which might compromise the correctness of the results. As an application, we analyze the long-term motion of the highly elliptical and critically inclined Molniya orbits subject to quadrupolar gravitational interactions. The analytical expansions presented herein are very powerful with respect to dynamical studies base...
Aptamer functionalized lipid multilayer gratings for label free detection of specific analytes
Prommapan, Plengchart; Lowry, Troy W.; van Winkle, David; Lenhert, Steven
2015-03-01
Lipid multilayer gratings have been formed on surfaces with a period of 700 nm. When illuminated with white light incident at about 50°, these gratings diffract green light perpendicular to their surface. We demonstrate the potential of these gratings as sensors for analytes by monitoring changes in the diffracted light due to the changes in the size and shape of the grating in response to analyte binding. To demonstrate this potential application, a lipid multilayer grating was functionalized with a thrombin binding aptamer. The selectivity of our aptamer functionalized lipid gratings was confirmed both by monitoring the diffracted light intensity and by fluorescence microscopy. Furthermore, the results show that the binding activity between the aptamer and thrombin depends on the relative composition of a zwitterionic lipid (DOPC) and a cationic lipid (DOTAP). This work shows that nanostructured lipid multilayers on surfaces are a promising nanomaterial for label-free bio-sensing applications.
李建平; 唐远炎; 严中洪; 张万萍
2001-01-01
Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When/N = 2k- 1 and N = 2k , the unified analytic constructions of orthogonal wavelet filters are put forward,respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.
Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model
Houyu Zhao
2012-01-01
Full Text Available We study the existence of analytic solutions of a functional differential equation (z(s+α2z'(s=β(z(s+z(s-z(s which comes from traffic flow model. By reducing the equation with the Schröder transformation to an auxiliary equation, the author discusses not only that the constant λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition.
Edwards, J B; Guilandoust, M
1980-01-01
Partial differential equations and boundary conditions are derived for the large-and-small-signal behaviour of compositions in an ideal, symmetrical spatially-continuous (packed) distillation column separating a binary mixture. A precise paramemtric transfer-function matrix (T.F.M.) for the system is derived completely analytically so allowing the calculation of parameters of the T.F.M. directly from those of the plant. It is shown that the correct choice of input and output vectors yields a ...
Shun-Hsing Chen; Fei-Yun Chen; Tsu-Ming Yeh
2015-01-01
Customer needs regarding product and service quality are rising. Because of the economic recession, the food and beverage industry faces strong competition. Customer needs can be satisfied only by understanding their needs. Therefore, this study uses Quality Function Deployment (QFD) and the Analytic Hierarchy Process (AHP) to clarify customer needs and to explore the most effective options to improve service quality in the vegetarian foods industry. This study primary objective included: (1)...
Analytic cubic and quartic force fields using density-functional theory
Ringholm, Magnus; Jonsson, Dan; Bast, Radovan; Gao, Bin; Thorvaldsen, Andreas J; Ekström, Ulf; Helgaker, Trygve; Ruud, Kenneth
2014-01-01
We present the first analytic implementation of cubic and quartic force constants at the level of Kohn-Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange-correlation kern...
Proof of Analytic Extension Theorem for Zeta Function Using Abel Transformation and Euler Product
Mbaitiga Zacharie
2010-01-01
Full Text Available Problem statement: In the prime number the Riemann zeta function is unquestionable and undisputable one of the most important questions in mathematics whose many researchers are still trying to find answer to some unsolved problems such as Riemann Hypothesis. In this study we proposed a new method that proves the analytic extension theorem for zeta function. Approach: Abel transformation was used to prove that the extension theorem is true for the real part of the complex variable that is strictly greater than one and consequently provides the required analytic extension of the zeta function to the real part greater than zero and Euler product was used to prove the real part of the complex that are less than zero and greater or equal to one. Results: From this proposed study we noted that the real values of the complex variable are lying between zero and one which may help to understand the relation between zeta function and its properties and consequently can pay the way to solve some complex arithmetic problems including the Riemann Hypothesis. Conclusion: The combination of Abel transformation and Euler product is a powerful tool for proving theorems and functions related to Zeta function including other subjects such as radio atmospheric occultation.
Recent axiomatic results on the (non holonomic) analytic structure of the multiparticle S matrix and Green functions are reviewed and related general conjectures are described: (i) formal expansions of Green functions in terms of (holonomic) Feynman-type integrals in which each vertex represents an irreducible kernel, and (ii) ''graph by graph unitarity'' and other discontinuity formulae of the latter. These conjectures are closely linked with unitarity or asymptotic completeness equations, which they yield in a formal sense. In constructive field theory, a direct proof of the first conjecture (together with an independent proof of the second) would thus imply, as a first step, asymptotic completeness in that sense
Eskandari Jam Jafar
2014-12-01
Full Text Available In this paper, by using a semi-analytical solution based on multi-layered approach, the authors present the solutions of temperature, displacements, and transient thermal stresses in functionally graded circular hollow cylinders subjected to transient thermal boundary conditions. The cylinder has finite length and is subjected to axisymmetric thermal loads. It is assumed that the functionally graded circular hollow cylinder is composed of N fictitious layers and the properties of each layer are assumed to be homogeneous and isotropic. Time variations of the temperature, displacements, and stresses are obtained by employing series solving method for ordinary differential equation, Laplace transform techniques and a numerical Laplace inversion.
Mathematic Model and Analytic Solution for a Cylinder Subject to Exponential Function
LIU Wen; SHAN Rui
2009-01-01
Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lamè solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.
Constraints on the nuclear energy density functional and new possible analytical forms
The theoretical tool of choice for the microscopic description of all medium- and heavy-mass nuclei is the Energy Density Functional (EDF) method. Such a method relies on the concept of spontaneous symmetry breaking and restoration. In that sense, it is intrinsically a two-step approach. However, the symmetry restoration procedure is only well-defined in the particular case where the energy functional derives from a pseudo-potential. Thereby and as it has been recently shown, existing parameterizations of the energy functional provides unphysical results. Such a problem as well as the lack of predictive power call for developing new families of functionals. The first part of the present work is devoted to a study of the symmetry restoration problem and to the identification of properties that could constrain the analytic form of energy functionals that do not derive from a pseudo-potential. The second part deals with the construction of an energy functional that derives from a pseudo potential. The difficulties of such work are: 1) the identification of the minimal complexity of the pseudo-potential necessary to obtain an energy functional that is flexible enough to provide high-quality EDF parameterizations, 2) the tedious analytical derivation of the functional and of the associated one-body fields, 3) the implementation of the latter in existing codes, and 4) the development of an efficient fitting procedure. Eventually, it seems possible to generate a parameterization that strictly derives from a pseudo-potential and that provides as good results as the state-of-the-art (quasi) bilinear functionals. (author)
Federalism. Theory and Neo-Functionalism: Elements for an analytical framework
Dosenrode, Søren
2010-01-01
The purpose of this article is to propose a draft for an analytical frame for analyzing regional integration consisting of federalism theory and neo-functionalism. It starts out discussing the concept of regional integration setting up a stagiest model for categorizing it.Then follows an analysis...... of federalism theory and neo-functionalism. One argument of this article is to understand federalism theory as a regional integration theory. Another is to look at federalism theory as complementary to neo-functionalism when trying to explain regional integration. Federalism theory, in an extended...... Riker-McKayian way, is able to explain the cases of ‘big bang’ integration (USA, Australia, Canada), but not an ‘organic’ integration process. Neo-functionalism, on the other hand, is not able to explain this relatively fast form of integration, but it is – in its new version - able to analyze and...
Complete text of publication follows. Nanoscale materials find use in a variety of different areas such as electronic, biomedical, sensing sciences, pharmaceutical, cosmetic, energy, environmental, catalytic and material applications. The environmental nanoparticles (NPs) can be classified in two groups: Natural NPs and Engineered or Anthropogenic NPs. Today the development of analytical methods for physical and chemical characterization of nanoparticles is still in its infancy .The natural and the engineered NPs can be investigated with an integrated analytical methodology by using several complementary techniques . We will show our experimental results on new analytical methodology to investigate the rol of the elements Cd, Cr, Cu, Hg, Ni, Pb, Zn, As, Co, Mo, Al, B, Fe, Mn, Sb, Sn, Ti, V in Organic and Inorganic Nanoparticles, by using specially hyphenated techniques like as: AsFIFFF-ICP-MS, AsFIFFF-UV.VIS, HPLC-SEC-UV.VIS-ICP-MS, PAGE-ICP-MS, PAGE-LA-ICP-MS, and Solid NPs Voltametry . The application of mathematical deconvolution to the fractograms to refine analytical signals provides a high resolution and the determination of polydispersity of particles as a very interesting information. The obtained results give a useful information about the Bioavailability, Mobility and Toxicity of the elements associated to nanoparticles. We will show also the experimental results and conclusions about the use of these hyphenated techniques to develop analytical methodology from three important point of view: Particle Size-Particle Kind and Chemical Composition, to establish a model of Functional Speciation of engineered nanoparticles like colloidal silver, and several nano-biocolloids from aquatic pseudo-multiphases. The work has been supported by Spanish Department of Science (Project CTQ 2006-00894 BQU).
Mussard, Bastien; Ángyán, János G
2015-01-01
Analytical forces have been derived in the Lagrangian framework for several random phase approximation (RPA) correlated total energy methods based on the range separated hybrid (RSH) approach, which combines a short-range density functional approximation for the short-range exchange-correlation energy with a Hartree-Fock-type long-range exchange and RPA long-range correlation. The RPA correlation energy has been expressed as a ring coupled cluster doubles (rCCD) theory. The resulting analytical gradients have been implemented and tested for geometry optimization of simple molecules and intermolecular charge transfer complexes, where intermolecular interactions are expected to have a non-negligible effect even on geometrical parameters of the monomers.
Kántor, Tibor; Bartha, András
2015-11-01
The self-absorption of spectral lines was studied with up to date multi-element inductively coupled plasma atomic emission spectrometry (ICP-AES) instrumentation using radial and axial viewing of the plasma, as well, performing line peak height and line peak area measurements. Two resonance atomic and ionic lines of Cd and Mg were studied, the concentration range was extended up to 2000 mg/L. At the varying analyte concentration, constant matrix concentration of 10,000 mg/L Ca was ensured in the pneumatically nebulized solutions. The physical and the phenomenological formulation of the emission analytical function is overviewed and as the continuity of the earlier results the following equation is offered:
Towards an Analytical Age-Dependent Model of Contrast Sensitivity Functions for an Ageing Society
Joulan, Karine; Brémond, Roland
2015-01-01
The Contrast Sensitivity Function (CSF) describes how the visibility of a grating depends on the stimulus spatial frequency. Many published CSF data have demonstrated that contrast sensitivity declines with age. However, an age-dependent analytical model of the CSF is not available to date. In this paper, we propose such an analytical CSF model based on visual mechanisms, taking into account the age factor. To this end, we have extended an existing model from Barten (1999), taking into account the dependencies of this model's optical and physiological parameters on age. Age-dependent models of the cones and ganglion cells densities, the optical and neural MTF, and optical and neural noise are proposed, based on published data. The proposed age-dependent CSF is finally tested against available experimental data, with fair results. Such an age-dependent model may be beneficial when designing real-time age-dependent image coding and display applications. PMID:26078994
Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Herve
1992-01-01
It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.
An analytic distribution function for a massless cored stellar system in a cuspy dark matter halo
Breddels, Maarten A
2013-01-01
We demonstrate the existence of distribution functions that can be used to represent spherical massless cored stellar systems embedded in cuspy dark matter halos with constant mildly tangential velocity anisotropy. In particular, we derive analytically the functional form of the distribution function for a Plummer stellar sphere in a Hernquist dark halo, for \\beta_0 = -0.5 and for different degrees of embedding. This particular example satisfies the condition that the central logarithmic slope of the light profile \\gamma_0 > 2 \\beta_0. Our models have velocity dispersion profiles similar to those observed in nearby dwarf spheroidal galaxies. Hence they can be used to generate initial conditions for a variety of problems, including N-body simulations that may represent dwarf galaxies in the Local Group.
Analytic function theory of several variables elements of Oka’s coherence
Noguchi, Junjiro
2016-01-01
The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert's two volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a lowering of the level for novice graduate students (here, Grauert's direct image theorem is limited to the case of finite maps). The core of the theory is "Oka's Coherence", found and proved by Kiyoshi Oka. It is indispensable, not only in the study of complex analysis and complex geometry, but also in a large area of modern mathematics. In this book, just after an introductory chapter on holomorphic functions (Chap. 1), we prove Oka's First Coherence Theorem for holomorphic functions in Chap. 2. This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appear...
Shen, Shuang
2015-06-01
We construct exact dimensional measures whose support is the whole interval and whose Olsen's multifractal functions and are real analytic and agree at two points only. These measures satisfy an extended multifractal formalism in the sense that, for in some interval, the Hausdorff dimension of the level sets of the local Hölder exponent of is the Legendre transform of whereas their packing dimension is the Legendre transform of . We first construct such measures on a symbolic space. Then we obtain the measures by projecting on after composition with a Gray code.
Comprehensive analytic formulae for stellar evolution as a function of mass and metallicity
Hurley, J. R.; Pols, O. R.; Tout, C. A.
2000-01-01
We present analytic formulae that approximate the evolution of stars for a wide range of mass and metallicity. Stellar luminosity, radius and core mass are given as a function of age, M and Z, for all phases from the zero-age main-sequence up to, and including, the remnant stages. For the most part we find continuous formulae accurate to within 5% of detailed models. These formulae are useful for purposes such as population synthesis that require very rapid but accurate evaluation of stellar ...
Jan, Chyan-Deng
2014-01-01
Gradually-varied flow (GVF) is a steady non-uniform flow in an open channel with gradual changes in its water surface elevation. The evaluation of GVF profiles under a specific flow discharge is very important in hydraulic engineering. This book proposes a novel approach to analytically solve the GVF profiles by using the direct integration and Gaussian hypergeometric function. Both normal-depth- and critical-depth-based dimensionless GVF profiles are presented. The novel approach has laid the foundation to compute at one sweep the GVF profiles in a series of sustaining and adverse channels, w
In a previous paper, one of the authors suggested an analytical method for calculation of the response function of an alpha spectrometer for the case of large solid angles. This paper describes the experimental verification of the method. Spectra of a well-known natural uranium sample were measured with a 450 mm2 Si detector and compared to the theoretical predictions. The measurements were carried out with two different geometrical configurations. In both cases a good agreement was observed between experimental and theoretical results
Moawad, S. M., E-mail: smmoawad@hotmail.com [Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef (Egypt)
2015-02-15
In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.
Moawad, S. M.
2015-02-01
In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.
In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics
Integrasi Taguchi Loss Function dengan Fuzzy Analytical Hierarchy Process dalam Pemilih Pemasok
Ahmad S. Indrapriyatna
2011-01-01
Full Text Available One important issue in the line production is the selection of the company's best supplier. Various criteria should be considered for determining the best supplier. Answering to that challenge, we apply Taguchi loss function- Analytical Hierarchy Process Fuzzy-Linear Programming (Taguchi loss function-Fuzzy AHP to find out the best supplier. Moreover, we also consider multiple criteria, i.e., goods’ completeness, quality, delivery, and quality loss in that analysis. By maximizing the suppliers’ performances based on each criterion and aggregated the suppliers’ performances based on the overall criteria, we selected the best one. Applying this method for selecting the best pressure gauge’s supplier in PT. Coca Cola Bottling Indonesia Central Sumatera (PT. CCBICS, we found out that among three suppliers, the second supplier is the best one.
Bruce, S D; Higinbotham, J; Marshall, I; Beswick, P H
2000-01-01
The approximation of the Voigt line shape by the linear summation of Lorentzian and Gaussian line shapes of equal width is well documented and has proved to be a useful function for modeling in vivo (1)H NMR spectra. We show that the error in determining peak areas is less than 0.72% over a range of simulated Voigt line shapes. Previous work has concentrated on empirical analysis of the Voigt function, yielding accurate expressions for recovering the intrinsic Lorentzian component of simulated line shapes. In this work, an analytical approach to the approximation is presented which is valid for the range of Voigt line shapes in which either the Lorentzian or Gaussian component is dominant. With an empirical analysis of the approximation, the direct recovery of T(2) values from simulated line shapes is also discussed. PMID:10617435
Xie, Wen-Jie; Jiang, Zhi-Qiang; Gu, Gao-Feng; Xiong, Xiong; Zhou, Wei-Xing
2015-10-01
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive analytically several important properties. We apply the method numerically to binomial measures with multifractal cross correlations and bivariate fractional Brownian motions without multifractal cross correlations. For binomial multifractal measures, the explicit expressions of mass function, singularity strength and multifractal spectrum of the cross correlations are derived, which agree excellently with the numerical results. We also apply the method to stock market indexes and unveil intriguing multifractality in the cross correlations of index volatilities.
Bruce, William J; Maxwell, E A; Sneddon, I N
1963-01-01
Analytic Trigonometry details the fundamental concepts and underlying principle of analytic geometry. The title aims to address the shortcomings in the instruction of trigonometry by considering basic theories of learning and pedagogy. The text first covers the essential elements from elementary algebra, plane geometry, and analytic geometry. Next, the selection tackles the trigonometric functions of angles in general, basic identities, and solutions of equations. The text also deals with the trigonometric functions of real numbers. The fifth chapter details the inverse trigonometric functions
Generic smooth connection functions: a new analytic approach to Hermite interpolation
We present a new analytic approach to Hermite's interpolation problem in two dimensions. The interpolating curves are the exact solutions of a variational problem that is invariant under translations and rotations. We study the general case of functionals that are given by the integral of the curvature raised to some power ν along the curve. The parameter ν determines the importance of minimal curvature with respect to minimal length. The boundary conditions are given by the initial and final points of the curve and the tangent vectors at these points. In order to find the family of functions that obtain the minimal weight, we use extensively notions that are well known in classical mechanics. The minimization of the weight functional via the Euler-Lagrange formalism leads to a highly non-trivial differential equation. Using the symmetries of the problem it is possible to find conserved quantities that help to simplify the problem to a level where the solution functions can be written in a closed form for any given ν. (author)
Univalence and Starlikeness of Nonlinear Integral Transform of Certain Class of Analytic Functions
M Obradović; S Ponnusamy; P Vasundhra
2009-11-01
Let $\\mathcal{U}(, )$ denote the class of all normalized analytic functions in the unit disk $|z| < 1$ satisfying the condition \\begin{equation*}\\frac{f(z)}{z}≠ 0\\quad\\text{and}\\quad\\left|f'(z)\\left(\\frac{z}{f(z)}\\right)^{ +1}-1\\right| < ,\\quad |z| < 1.\\end{equation*} For $f\\in\\mathcal{U}(, )$ with ≤ 1 and $0≠_1≤ 1$, and for a positive real-valued integrable function defined on [0,1] satisfying the normalized condition $\\int^1_0\\varphi(t)dt=1$, we consider the transform $G_\\varphi f(z)$ defined by \\begin{equation*}G_\\varphi f(z)=z\\left[\\int^1_0\\varphi(t)\\left(\\frac{zt}{f(tz)}\\right)^ dt\\right]^{-1/ 1},\\quad z\\in.\\end{equation*} In this paper, we find conditions on the range of parameters and so that the transform $G_\\varphi f$ is univalent or star-like. In addition, for a given univalent function of certain form, we provide a method of obtaining functions in the class $\\mathcal{U}(, )$.
Non-linear Dynamics and Mass Function of Cosmic Structures; 1, Analytical Results
Audit, E; Teyssier, R; Audit, Edouard; Teyssier, Romain
1997-01-01
We investigate some modifications to the Press & Schechter (1974) (PS) prescription resulting from shear and tidal effects. These modifications rely on more realistic treatments of the collapse process than the standard approach based on the spherical model. First, we show that the mass function resulting from a new approximate Lagrangian dynamic (Audit & Alimi 96), contains more objects at high mass, than the classical PS mass function and is well fitted by a PS-like function with a threshold density of $\\delta_c \\simeq 1.4$. However, such a Lagrangian description can underestimate the epoch of structure formation since it defines it as the collapse of the first principal axis. We therefore suggest some analytical prescriptions, for computing the collapse time along the second and third principal axes, and we deduce the corresponding mass functions. The collapse along the third axis is delayed by the shear and the number of objects of high mass then decreases. Finally, we show that the shear also str...
Hamid Nasiri
2015-01-01
Full Text Available Functional neurological symptom disorder commonly presents with symptoms and defects of sensory and motor functions. Therefore, it is often mistaken for a medical condition. It is well known that functional neurological symptom disorder more often caused by psychological factors. There are three main approaches namely analytical, cognitive and biological to manage conversion disorder. Any of such approaches can be applied through short-term treatment programs. In this case, study a 12-year-old boy with the diagnosed functional neurological symptom disorder (psychogenic myopia was put under a cognitive-analytical treatment. The outcome of this treatment modality was proved successful.
Comprehensive analytic formulae for stellar evolution as a function of mass and metallicity
Hurley, J R; Tout, C A
2000-01-01
We present analytic formulae that approximate the evolution of stars for a wide range of mass and metallicity. Stellar luminosity, radius and core mass are given as a function of age, M and Z, for all phases from the zero-age main-sequence up to, and including, the remnant stages. For the most part we find continuous formulae accurate to within 5% of detailed models. These formulae are useful for purposes such as population synthesis that require very rapid but accurate evaluation of stellar properties, and in particular for use in combination with N-body codes. We describe a mass loss prescription that can be used with these formulae and investigate the resulting stellar remnant distribution.
Performance Analytical Model of IEEE 802.11 Distributed Coordination Function
无
2006-01-01
IEEE 802.11 distributed coordination function (DCF) is a distributed medium access scheme based on carrier sense multiple access with collision avoidance (CSMA/CA) protocol. Many literatures have analyzed the performance of IEEE 802.11 DCF. However, such literatures either used simulation methods or built the analytical models under the assumption that the saturation condition was satisfied. To overcome such a problem, in this paper, a bi-dimensional Markovian model has been introduced to depict the DCF mechanism. The proposed model introduced an idle stage and a discrete time M/G/1 queue to deduce the channel throughput under finite load traffic. Simulation results proved the accuracy of the proposed model.
BOOMERanG Constraints on Primordial Non-Gaussianity from Analytical Minkowski Functionals
Natoli, P; Hikage, C; Komatsu, E; Migliaccio, M; Ade, P A R; Bock, J J; Bond, J R; Borrill, J; Boscaleri, A; Contaldi, C R; Crill, B P; De Bernardis, P; De Gasperis, G; De Oliveira-Costa, A; Di Stefano, G; Hivon, E; Kisner, T S; Jones, W C; Lange, A E; Masi, S; Mauskopf, P D; MacTavish, C J; Melchiorri, A; Montroy, T E; Netterfield, C B; Pascale, E; Piacentini, F; Polenta, G; Ricciardi, S; Romeo, G; Ruhl, J E; Tegmark, M; Veneziani, M; Vittorio, N
2009-01-01
We use Minkowski Functionals (MF) to constrain a primordial non-Gaussian contribution to the CMB intensity field as observed in the 150 GHz and 145 GHz BOOMERanG maps from the 1998 and 2003 flights, respectively, performing for the first time a joint analysis of the two datasets. A perturbative expansion of the MF formulae in the limit of a weakly non-Gaussian field yields analytical formulae, derived by Hikage et al. (2006), which can be used to constrain the coupling parameter f_NL without the need for non-Gaussian simulations. We find -1020
BOOMERanG constraints on primordial non-Gaussianity from analytical Minkowski functionals
Natoli, P.; de Troia, G.; Hikage, C.; Komatsu, E.; Migliaccio, M.; Ade, P. A. R.; Bock, J. J.; Bond, J. R.; Borrill, J.; Boscaleri, A.; Contaldi, C. R.; Crill, B. P.; de Bernardis, P.; de Gasperis, G.; de Oliveira-Costa, A.; di Stefano, G.; Hivon, E.; Kisner, T. S.; Jones, W. C.; Lange, A. E.; Masi, S.; Mauskopf, P. D.; MacTavish, C. J.; Melchiorri, A.; Montroy, T. E.; Netterfield, C. B.; Pascale, E.; Piacentini, F.; Polenta, G.; Ricciardi, S.; Romeo, G.; Ruhl, J. E.; Tegmark, M.; Veneziani, M.; Vittorio, N.
2010-11-01
We use Minkowski functionals (MFs) to constrain a primordial non-Gaussian contribution to the cosmic microwave background intensity field as observed in the 150- and 145-GHz BOOMERanG maps from the 1998 and 2003 flights, respectively, performing for the first time a joint analysis of the two data sets. A perturbative expansion of the MF formulae in the limit of a weakly non-Gaussian field yields analytical formulae, derived by Hikage et al., which can be used to constrain the coupling parameter fNL without the need for non-Gaussian simulations. We find -770 Troia et al. on the BOOMERanG 2003 data set. These are the best fNL limits to date for suborbital probes.
Analytic cubic and quartic force fields using density-functional theory.
Ringholm, Magnus; Jonsson, Dan; Bast, Radovan; Gao, Bin; Thorvaldsen, Andreas J; Ekström, Ulf; Helgaker, Trygve; Ruud, Kenneth
2014-01-21
We present the first analytic implementation of cubic and quartic force constants at the level of Kohn-Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange-correlation kernels. We use generalized second-order vibrational perturbation theory to calculate the fundamental frequencies of methane, ethane, benzene, and aniline, comparing B3LYP, BLYP, and Hartree-Fock results. The Hartree-Fock anharmonic corrections agree well with the B3LYP corrections when calculated at the B3LYP geometry and from B3LYP normal coordinates, suggesting that the inclusion of electron correlation is not essential for the reliable calculation of cubic and quartic force constants. PMID:25669359
Differences of Composition Operators on the Space of Bounded Analytic Functions in the Polydisc
Ze-Hua Zhou
2009-01-01
Full Text Available This paper gives some estimates of the essential norm for the difference of composition operators induced by ÃÂ† and ÃÂˆ acting on the space, HÃ¢ÂˆÂž(Dn, of bounded analytic functions on the unit polydisc Dn, where ÃÂ† and ÃÂˆ are holomorphic self-maps of Dn. As a consequence, one obtains conditions in terms of the CarathÃƒÂ©odory distance on Dn that characterizes those pairs of holomorphic self-maps of the polydisc for which the difference of two composition operators on HÃ¢ÂˆÂž(Dn is compact.
Many-body Expanded Analytical Potential Energy Function for Ground State PuOH Molecule
LI Yue-Xun; GAO Tao; ZHU Zheng-He
2006-01-01
Using the density functional method B3LYP with relativistic effective core potential (RECP) for Pu atom, the low-lying excited states (4∑+, 6∑+, 8∑+) for three structures of PuOH molecule were optimized. The results show that the ground state is X6∑+of the linear Pu-O-H (C∞v), its corresponding equilibrium geometry and dissociation energy are RPu-O=0.20595 nm, RO-H=0.09581 nm and -8.68 eV, respectively. At the same time, two other metastable structures [PuOH (Cs) and H-Pu-O (C∞v)] were found. The analytical potential energy function has also been derived for whole range using the many-body expansion method. This potential energy function represents the considerable topographical features of PuOH molecule in detail, which is adequately accurate in the whole potential surface and can be used for the molecular reaction dynamics research.
Single fermion Green's function in the quantum ordered Fermi-system: Analytic solution
Mukhin, S. I.; Galimzyanov, T. R.
2012-06-01
An exact self-consistent solution for a finite temperature quantum-ordered state of correlated electron system found previously (Mukhin, 2009, 2011) is used to derive the fermionic single-particle Green's function. The quantum order parameter (QOP) found in the form of a periodic (elliptic Jacoby) function of the Matsubara's imaginary time (Mukhin, 2009), plays the role of effective scattering potential seen by electrons. The analytic solution for the Green's function demonstrates the following new features: (1) the pseudo-gap behavior of the single-electron density of states (DOS) near the (shifted) Fermi-level;(2) the side-bands of decreasing intensity away from the Fermi-level; (3) scaling of the quasi-particle energies with the QOP amplitude; (4) fermionic quasi-particles in the QOP state are combined from two confined “odd” and “even” fermions that separately would be unstable. The false-color plot of single-fermion DOS in the limit of a periodic kink-like Matsubara time-dependence of QOP is presented and could be used as prediction for the ARPES experiments. The plot of the DOS transfer between different energies at the “fermi-surface” momentum for a given kink-like QOP is also presented. Some possibly observable consequences of the found finger-prints are discussed.
Manduchi, Katia; Schoendorff, Benjamin
2012-01-01
Practicing Functional Analytic Psychotherapy (FAP) for the first time can seem daunting to therapists. Establishing a deep and intense therapeutic relationship, identifying FAP's therapeutic targets of clinically relevant behaviors, and using contingent reinforcement to help clients emit more functional behavior in the therapeutic relationship all…
Serap Bulut
2013-01-01
Full Text Available We introduce and investigate two new subclasses and of analytic and bi-univalent functions in the open unit disk For functions belonging to these classes, we obtain estimates on the first two Taylor-Maclaurin coefficients and
Xiang-Rong Fu; Li-Na Ge; Ge Tian; Ming-Wu Yuan
2013-01-01
This paper presents a novel way to formulate the triangular flat shell element. The basic analytical solutions of membrane and bending plate problem for anisotropy material are studied separately. Combining with the conforming displacement along the sides and hybrid element strategy, the triangular flat shell elements based on the analytical trial functions (ATF) for anisotropy material are formulated. By using the explicit integral formulae of the triangular element, the matrices used in pro...
Use of analytic functions and polynomials within the framework of nodal expansion method
A method using one-dimensional flux approximation expressed in terms of polynomials and hyperbolic functions was derived and the accuracy of the method was explored. This method called SANEM(Semi-Analytic Nodal Expansion Method) employs the same transverse leakage approximation used in NEM(Nodal Expansion Method) and flux moment balance equations to find coupling coefficients in current continuity equation. An one-dimensional flux approximation is expressed in the second order/the third order/the fourth order polynomials combined with hyperbolic functions for which several weighting functions are applied and the accuracy of methods were compared. This method has advantages of minimizing memory increase and easy implementation to a nodal code based on the conventional NEM. Benchmark calculations for the code were performed using problems such as IAEA 3D problem, NEACRP-L336 problem and EPRI-9R problem. Results show that both reactivity and assembly power density prediction by the SANEM is better than NEM for NEACRP-L336 problem, which uses MOX fuel, EPRI-9R problem, which shows characteristics of assembly in core periphery. A step function weighting applied to the third order polynomial expansion of a one-dimensional flux approximation produced better results than the polynomial weighting applied to the third order polynomial expansion for IAEA 3D problem. Furthermore, Galerkin weighting applied to the fourth order polynomial expansion shows worse results than polynomial weighting applied to the third order polynomial expansion for IAEA 3D, NEACRP-L336 and EPRI-9R problems
An Analytical Model for the Prediction of a Micro-Dosimeter Response Function
Badavi, Francis F.; Xapsos, Mike
2008-01-01
A rapid analytical procedure for the prediction of a micro-dosimeter response function in low Earth orbit (LEO), correlated with the Space Transportation System (STS, shuttle) Tissue Equivalent Proportional Counter (TEPC) measurements is presented. The analytical model takes into consideration the energy loss straggling and chord length distribution of the detector, and is capable of predicting energy deposition fluctuations in a cylindrical micro-volume of arbitrary aspect ratio (height/diameter) by incoming ions through both direct and indirect (ray) events. At any designated (ray traced) target point within the vehicle, the model accepts the differential flux spectrum of Galactic Cosmic Rays (GCR) and/or trapped protons at LEO as input. On a desktop PC, the response function of TEPC for each ion in the GCR/trapped field is computed at the average rate of 30 seconds/ion. The ionizing radiation environment at LEO is represented by O'Neill fs GCR model (2004), covering charged particles in the 1 less than or equal to Z less than or equal to 28. O'Neill's free space GCR model is coupled with the Langley Research Center (LaRC) angular dependent geomagnetic cutoff model to compute the transmission coefficient in LEO. The trapped proton environment is represented by a LaRC developed time dependent procedure which couples the AP8MIN/AP8MAX, Deep River Neutron Monitor (DRNM) and F10.7 solar radio frequency measurements. The albedo neutron environment is represented by the extrapolation of the Atmospheric Ionizing Radiation (AIR) measurements. The charged particle transport calculations correlated with STS 51 and 114 flights are accomplished by using the most recent version (2005) of the LaRC deterministic High charge (Z) and Energy TRaNsport (HZETRN) code. We present the correlations between the TEPC model predictions (response function) and TEPC measured differential/integral spectra in the lineal energy (y) domain for both GCR and trapped protons, with the conclusion
Analytical theory for the initial mass function: III time dependence and star formation rate
Hennebelle, Patrick
2013-01-01
The present paper extends our previous theory of the stellar initial mass function (IMF) by including the time-dependence, and by including the impact of magnetic field. The predicted mass spectra are similar to the time independent ones with slightly shallower slopes at large masses and peak locations shifted toward smaller masses by a factor of a few. Assuming that star-forming clumps follow Larson type relations, we obtain core mass functions in good agreement with the observationally derived IMF, in particular when taking into account the thermodynamics of the gas. The time-dependent theory directly yields an analytical expression for the star formation rate (SFR) at cloud scales. The SFR values agree well with the observational determinations of various Galactic molecular clouds. Furthermore, we show that the SFR does not simply depend linearly on density, as sometimes claimed in the literature, but depends also strongly on the clump mass/size, which yields the observed scatter. We stress, however, that ...
The molecular structure and the analytical potential energy function of S-2 and S-3
Liu Yu-Fang; Li Jun-Yu; Han Xiao-Qin; Sun Jin-Feng
2007-01-01
In this paper, the equilibrium geometry, harmonic frequency and dissociation energy of S-2 and S-3 have been calculated at QCISD/6-311++G(3d2f) and B3P86/6-311++G(3d2f) level. The S-2 ground state is of 2Ⅱg, the S-3 ground state is of 2B1 and S-3 has a bent (C2V) structure with an angle of 115.65° The results are in good agreement with these reported in other literature. For S-3 ion, the vibration frequencies and the force constants have also been calculated. Base on the general principles of microscopic reversibility, the dissociation limits has been deduced. The Murrell-Sorbie potential energy function for S-2 has been derived according to the ab initio data through the leastsquares fitting. The force constants and spectroscopic data for S-2 have been calculated, then compared with other theoretical data. The analytical potential energy function of S-3 have been obtained based on the many-body expansion theory. The structure and energy can correctly reappear on the potential surface.
Hamid Nasiri; Amrollah Ebrahimi; Arash Zahed; Mostafa Arab; Rahele Samouei
2015-01-01
Functional neurological symptom disorder commonly presents with symptoms and defects of sensory and motor functions. Therefore, it is often mistaken for a medical condition. It is well known that functional neurological symptom disorder more often caused by psychological factors. There are three main approaches namely analytical, cognitive and biological to manage conversion disorder. Any of such approaches can be applied through short-term treatment programs. In this case, study a 12-year-ol...
Sidorov, A. V.; Solovtsova, O. P.
2014-01-01
We apply analytic perturbation theory to the QCD analysis of the xF_3(x,Q^2) structure function considering a combined set of deep inelastic scattering data presented by several collaborations, and extract values of the scale parameter Lambda_{QCD}, the parameters of the form of the xF_3 structure function, and the x-shape of the higher twist contribution. We study the difference between the results obtained within the standard perturbative and analytic approaches in comparison with the exper...
Sidorov, A. V.; Solovtsova, O. P.
2014-01-01
We discuss the application of an analytic approach called the analytic perturbation theory (APT) to the QCD analysis of DIS data. In particular, the results of the QCD analysis of a set of `fake' data on the polarized nonsinglet Delta{q3} and the nonsinglet fragmentation function D^{pi+}_{u_v} by using the Q^2-evolution within the APT are considered. The `fake' data are constructed based on parametrization of the polarized PDF and nonsinglet combination of the pion fragmentation functions. We...
Ya. V. Vasyl’kiv
2011-07-01
Full Text Available The best possible asymptotic estimates for Lebesgue integral means $m_{p}(r,log f, 1 leq p$ of logarithms of analytic functions $f(z$ in the unit disc in terms of their Nevanlinna characteristic $T(r,f$ are obtained. We get sharp relation between the order of $T(r,f$ and the order of $m_{p}(r,log f$ for an analytic function $f(z$ of finite order $alpha(f.$ This generalizes well-known results of L.~R.~Sons and C.~N.~Linden.
Wave-function frozen-density embedding: Approximate analytical nuclear ground-state gradients.
Heuser, Johannes; Höfener, Sebastian
2016-05-01
We report the derivation of approximate analytical nuclear ground-state uncoupled frozen density embedding (FDEu) gradients for the resolution of identity (RI) variant of the second-order approximate coupled cluster singles and doubles (RICC2) as well as density functional theory (DFT), and an efficient implementation thereof in the KOALA program. In order to guarantee a computationally efficient treatment, those gradient terms are neglected which would require the exchange of orbital information. This approach allows for geometry optimizations of single molecules surrounded by numerous molecules with fixed nuclei at RICC2-in-RICC2, RICC2-in-DFT, and DFT-in-DFT FDE level of theory using a dispersion correction, required due to the DFT-based treatment of the interaction in FDE theory. Accuracy and applicability are assessed by the example of two case studies: (a) the Watson-Crick pair adenine-thymine, for which the optimized structures exhibit a maximum error of about 0.08 Å for our best scheme compared to supermolecular reference calculations, (b) carbon monoxide on a magnesium oxide surface model, for which the error amount up to 0.1 Å for our best scheme. Efficiency is demonstrated by successively including environment molecules and comparing to an optimized conventional supermolecular implementation, showing that the method is able to outperform conventional RICC2 schemes already with a rather small number of environment molecules, gaining significant speed up in computation time. © 2016 Wiley Periodicals, Inc. PMID:26804310
Gori-Giorgi, Paola; Perdew, John P.
2002-01-01
We construct analytic formulas that represent the coupling-constant-averaged pair distribution function $\\gxcav(r_s,\\zeta, k_Fu)$ of a uniform electron gas with density parameter $r_s =(9\\pi/4)^{1/3}/k_F$ and relative spin polarization $\\zeta$ over the whole range $0
Weeks, Cristal E.; Kanter, Jonathan W.; Bonow, Jordan T.; Landes, Sara J.; Busch, Andrew M.
2012-01-01
Functional analytic psychotherapy (FAP) provides a behavioral analysis of the psychotherapy relationship that directly applies basic research findings to outpatient psychotherapy settings. Specifically, FAP suggests that a therapist's in vivo (i.e., in-session) contingent responding to targeted client behaviors, particularly positive reinforcement…
Oshiro, Claudia Kami Bastos; Kanter, Jonathan; Meyer, Sonia Beatriz
2012-01-01
Functional Analytic Psychotherapy (FAP) is emerging as an effective psychotherapy for psychiatric clinical cases. However, there is little research demonstrating the process of change of FAP. The present study evaluated the introduction and withdrawal of FAP interventions on therapy-interfering verbal behaviors of two participants who were in…
Grigorenko, Elena L.; Sternberg, Robert J.
2001-01-01
Studied the efficacy of the triarchic theory of intelligence as a basis for predicting adaptive functioning in a rapidly changing society, that of Russia. Results of intelligence measures administered to 452 women and 293 men show that analytical, practical, and creative intelligence all relate in some degree to self-reported everyday adaptive…
General principles of construction of functional-analytical training facility of a NPP, which represents the computation system consisting of the ES-1045 type computer and personal computers, are considered. The KIPR program used for the ES computer describes stationary and dynamic regimes of a power unit real time operation. The personal computers perform service functions of displaying the information required by an operator. The high efficiency of the algorithms used for NPP operator training is proved
On the Riemann-Hilbert problem for analytic functions in circular domains
Efimushkin, A. S.; Ryazanov, V. I.
2015-01-01
It is proved the existence of single-valued analytic solutions in the unit disk and multivalent analytic solutions in domains bounded by a finite collection of circles for the Riemann-Hilbert problem with coefficients of sigma-finite variation and with boundary data that are measurable with respect to logarithmic capacity. It is shown that these spaces of solutions have the infinite dimension.
Xiang-Rong Fu
2013-01-01
Full Text Available This paper presents a novel way to formulate the triangular flat shell element. The basic analytical solutions of membrane and bending plate problem for anisotropy material are studied separately. Combining with the conforming displacement along the sides and hybrid element strategy, the triangular flat shell elements based on the analytical trial functions (ATF for anisotropy material are formulated. By using the explicit integral formulae of the triangular element, the matrices used in proposed shell element are calculated efficiently. The benchmark examples showed the high accuracy and high efficiency.
A next-to-leading order QCD calculation of nonsinglet spin structure function g1NS(x,t) at small x is presented using the analytical methods: Lagrange’s method and method of characteristics. The compatibility of these analytical approaches is tested by comparing the analytical solutions with the available polarized global fits
Considering the results of recent distinguished analytical calculations of the 5-loop single-fermion loop corrections to the QED β-function we emphasize that to our point of view it is important to perform their independent cross-checks. We propose one of the ways of these cross-check. It is based on the application of the original Crewther relation. We derive the new analytical expressions for the CF4αs4-contributions to the Bjorken polarized sum rule. If results of possible direct calculations will agree with the presented expression, then the appearance of ζ3-term in the 5-loop correction to the QED β-function and in the CF4αs4 contribution into the e+e- annihilation Adler function will get independent support and may be analysed within the framework of the recently introduced concept of 'maximal transcendentality'
Loch, Hanna; Janczura, Joanna; Weron, Aleksander
2016-04-01
In this paper we study asymptotic behavior of a dynamical functional for an α -stable autoregressive fractionally integrated moving average (ARFIMA) process. We find an analytical formula for this important statistics and show its usefulness as a diagnostic tool for ergodic properties. The obtained results point to the very fast convergence of the dynamical functional and show that even for short trajectories one may obtain reliable conclusions on the ergodic properties of the ARFIMA process. Moreover we use the obtained theoretical results to illustrate how the dynamical functional statistics can be used in the verification of the proper model for an analysis of some biophysical experimental data.
Analytic solutions of the multigroup discrete ordinates transport equation with linearly anisotropic scattering and fission source for multi-layered slab problems are obtained by using the infinite medium Green's function (IMGF) and Placzek's lemma. In this approach, the infinite medium Green's function is derived analytically by using the spectral analysis for the multigroup discrete ordinates transport equation and its transposed equation, and this infinite medium solution is related to the finite medium solution by Placzek's lemma. In eigenvalue problems having fission source, complex eigenvalues can occur. As such equations involve the k eigenvalue as a non-linear parameter, to obtain criticality Newton's chord method combined with bisection is used. The resulting equation leads to an exact relation that represents the outgoing angular fluxes in terms of the incoming angular fluxes and fission source for each slab. For heterogeneous problems having multi-layered slabs, the slabs are coupled through the interface angular fluxes. Since all derivations are performed analytically, the method gives exact solution with no truncation error. After the interface angular fluxes are calculated by using an iterative method, the continuous spatial distribution of the angular flux (i.e. analytic solution) in each slab is given straightforwardly in terms of the IMGF and the boundary angular fluxes. Therefore, in our method, the number of meshes that is equal to the number of the homogeneous slabs is sufficient
Hari M. Srivastava
2013-01-01
It is indeed a fairly common practice for scientific research journals and scientific research periodicals to publish special issues as well as conference proceedings. Quite frequently, these special issues are devoted exclusively to specific topics and/or are dedicated respectfully to commemorate the celebrated works of renowned research scientists. The following Special Issue: “q-Series and Related Topics in Special Functions and Analytic Number Theory” (see [1–8] below) is an outcome of th...
Wagner, Edward Dishman
2002-01-01
This paper compares two technologies, Public Key Infrastructure (PKI) and Virtual Private Network (VPN). PKI and VPN are two approaches currently in use to resolve the problem of securing data in computer networks. Making this comparison difficult is the lack of available data. Additionally, an organization will make their decision based on circumstances unique to their information security needs. Therefore, this paper will illustrate a method using a utility function and the Analytic Hie...
Two accurate, yet simple, analytic approximations to the integral of the Bessel function J0 are presented. These first and second-order approximations are obtained by improving on the recently developed method known as two-point quasi-rational approximations. The accuracy of the first-order approximant is better than 0.05. The second-order approximant is practically indistinguishable from the true integral, even for very large values of the argument (overall accuracy is better than 0.002 05). Our approximants are, in addition, analytic and therefore replace with significant advantages both the well known power series and the asymptotic formulae of the integral. Approximants to the transmittance function of a plane wave through a circular aperture are derived, a problem which arises in diffraction theory and particle scattering. The second-order approximant to the transmittance is analytic too, and can be evaluated for small and large values of the argument, just with a hand-calculator. Its accuracy is better than 0.0011. As an extension, two first-order approximations to the integrals of the Bessel functions Jν, of fractional order ν, are derived. (author)
The nonlinear finite difference method (FDM) iterative scheme has been widely used as an alternative way to the core-wise response matrix formalism in modern nodal methods. This scheme turned out to be very effective in minimizing memory requirement and computing time associated with higher-order nodal methods. This conventional nonlinear FDM iterative scheme uses the modified FDM current definition with a nonlinear correction factor at an interface between two nodes. Determining the nonlinear correction factor so that the interface current should preserve the value of a higher-order nodal method makes the solution of this finite difference scheme equivalent to that of the higher-order nodal method itself. For the nonlinear FDM iterative scheme with the usual higher-order nodal methods that use the transverse-integration, this is done by solving two-node problems consisting of neighboring nodes periodically after a specified number of outer iterations of the FDM routine. Using the higher-order nodal method, the two-node problem is solved for the interface current of the two nodes with currently available node-average fluxes and transverse-leakage shapes of both nodes as boundary conditions. The nonlinear correction factor at the interface is updated by equating the resultant higher-order interface current with the modified FDM current. Then, the FDM routine is continued utilizing the updated nonlinear correction factor. The entire process is repeated until convergence of the effective multiplication factor and the node average fluxes is achieved. In this study, as an acceleration means and for the convenience of its implementation into existing FDM codes, we develop a nonlinear iterative scheme for the analytic function expansion nodal (AFEN) method. Developing a nonlinear iterative scheme for the AFEN method is not straightforward, because this method needs higher-order accurate interface and corner-point fluxes as well as interface currents in solving the two
Analytical representation of time correlation functions and application to relaxation problems
Two analytical representations of the Laplace transform of the time autocorrelation of a dynamical variable, namely the moment expansion and Mori's continued fraction expansion, are investigated from the point of view of structure and convergence properties, and the relation between them is established. The general theory is applied first to a dynamical model exactly solvable, the isotopic impurity in a linear chain of coupled harmonic oscillators, and then to two stochastic models recently introduced by Gordon for the rotational diffusion of molecules. In the latter case, the continued fraction expansion yields simple analytical expressions for the infrared absorption band shapes, showing that these models contain all the features of observed shapes in compressed gases, liquids and solutions. (author)
EXTREME POINTS AND SUPPORT POINTS OF A CLASS OF ANALYTIC FUNCTIONS
无
2000-01-01
Suppose that {bn} and {cn} are two positive sequences.Let F({bn},{cn})={f(z) :f(z) is analytic in ｜z｜<1,f(z) = z-∑+∞n=2 anzn,an 0,∑+∞n=2 bnan 1 and ∑+∞n=2 cnan ≤1}.This article obtains the extreme points and support points of F({bn},{cn}).
Analytic expression for the proton structure function in deep inelastic scattering
XIANG Wen-Chang; ZHOU Dai-Cui; WAN Ren-Zhuo; YUAN Xian-Bao
2009-01-01
The analytic expression of proton in deep inelastic scattering is studied by using the color glass condensate model and the dipole picture. We get a better description of the HERA DIS data than the CBW model which was inspired by the Glauber model. We find that our model satisfies the unitarity limit and Froissart Bound which refers to an energy dependence of the total cross-section rising no more rapidly than ln2s.
Padhy, Bholanath
2016-01-01
A simple method is outlined for analytic evaluation of the basic 2-electron atomic integral with integrand containing products of atomic s-type Slater orbitals and exponentially correlated function of the form $r_{ij} exp(-\\lambda_{ij}r_{ij})$, by employing the Fourier representation of $exp(-\\lambda_{ij}r_{ij})/r_{ij}$ without the use of either the spherical harmonic addition theorem or the Feynman technique. This method is applied to obtain closed-form expressions, in a simple manner, for certain other 2-,3- and 4-electron atomic integrals with integrands which are products of exponentially correlated functions and atomic s-type Slater orbitals.
Liu, Jie; Liang, WanZhen
2011-07-01
We present the analytical expression and computer implementation for the second-order energy derivatives of the electronic excited state with respect to the nuclear coordinates in the time-dependent density functional theory (TDDFT) with Gaussian atomic orbital basis sets. Here, the Tamm-Dancoff approximation to the full TDDFT is adopted, and therefore the formulation process of TDDFT excited-state Hessian is similar to that of configuration interaction singles (CIS) Hessian. However, due to the replacement of the Hartree-Fock exchange integrals in CIS with the exchange-correlation kernels in TDDFT, many quantitative changes in the derived equations are arisen. The replacement also causes additional technical difficulties associated with the calculation of a large number of multiple-order functional derivatives with respect to the density variables and the nuclear coordinates. Numerical tests on a set of test molecules are performed. The simulated excited-state vibrational frequencies by the analytical Hessian approach are compared with those computed by CIS and the finite-difference method. It is found that the analytical Hessian method is superior to the finite-difference method in terms of the computational accuracy and efficiency. The numerical differentiation can be difficult due to root flipping for excited states that are close in energy. TDDFT yields more exact excited-state vibrational frequencies than CIS, which usually overestimates the values. PMID:21744894
Resonances and analyticity of scattering wave function for square-well-type potentials
In this paper we extend our previous analysis of the scattering of wave packets in one dimension to the case of the square-well potential. The analytic properties of the general scattering solution are emphasized thereby making the analysis useful as introductory material for a more sophisticated S-matrix treatment. The square-well model is particularly interesting because of its application to the deuteron problem. Resonance scattering, barrier penetration, time delay, and line shape are discussed at the level of the first-year graduate student
Functional-analytical capabilities of GIS technology in the study of water use risks
Nevidimova, O. G.; Yankovich, E. P.; Yankovich, K. S.
2015-02-01
Regional security aspects of economic activities are of great importance for legal regulation in environmental management. This has become a critical issue due to climate change, especially in regions where severe climate conditions have a great impact on almost all types of natural resource uses. A detailed analysis of climate and hydrological situation in Tomsk Oblast considering water use risks was carried out. Based on developed author's techniques an informational and analytical database was created using ArcGIS software platform, which combines statistical (quantitative) and spatial characteristics of natural hazards and socio-economic factors. This system was employed to perform areal zoning according to the degree of water use risks involved.
Functions of diffraction correction and analytical solutions in nonlinear acoustic measurement
Alliès, Laurent; Nadi, M
2008-01-01
This paper presents an analytical formulation for correcting the diffraction associated to the second harmonic of an acoustic wave, more compact than that usually used. This new formulation, resulting from an approximation of the correction applied to fundamental, makes it possible to obtain simple solutions for the second harmonic of the average acoustic pressure, but sufficiently precise for measuring the parameter of nonlinearity B/A in a finite amplitude method. Comparison with other expressions requiring numerical integration, show the solutions are precise in the nearfield.
Dobson, John F.; Rubio, Angel
2005-01-01
We highlight the non-universality of the asymptotic behavior of dispersion forces, such that a sum of inverse sixth power contributions is often inadequate. We analytically evaluate the cross-correlation energy Ec between two pi-conjugated layers separated by a large distance D within the electromagnetically non-retarded Random Phase Approximation, via a tight-binding model. For two perfect semimetallic graphene sheets at T=0K we find Ec = C D^{-3}, in contrast to the "insulating" D^{-4} depe...
The desire for improved control over electric discharge phenomena in a wide variety of scientific, technological, manufacturing, and waste processing activities spurs the development of non-equilibrium, non-uniform, and time dependent models. This paper addresses the situation of slightly ionized, spatially uniform gas with a time varying electric field, and in which inelastic collisions occur. The purpose here is to present a reasonably consistent, and reasonably accessible analytical result for the electron kinetics in a gas discharge regime of technological interest. This paper will be structured as follows. First, the analytical result for the time dependent electron distribution function is stated. Second, a summary of the solution procedure with its attendant assumptions is given. Lastly, examples of the solution are given for an idealized nitrogen-like gas where the electric field ramps between static conditions, and then for sinusoidal behavior
The solution to a non-autonomous second order ordinary differential equation is presented. The real function, dependent on the differentiation variable, is a squared hyperbolic tangent function plus a term that involves the quotient of hyperbolic functions. This function varies from one limiting value to another without having any singularities. The solution is remarkably simple and involves only trigonometric and hyperbolic trigonometric functions. The solution is analyzed in the context of wave propagation in an inhomogeneous one-dimensional medium. The profile is shown to act as a perfect anti-reflection interface, providing a possible alternative route to the fabrication of reflectionless surfaces. (paper)
Simplex and duplex event-specific analytical methods for functional biotech maize.
Lee, Seong-Hun; Kim, Su-Jeong; Yi, Bu-Young
2009-08-26
Analytical methods are very important in the control of genetically modified organism (GMO) labeling systems or living modified organism (LMO) management for biotech crops. Event-specific primers and probes were developed for qualitative and quantitative analysis for biotech maize event 3272 and LY 038 on the basis of the 3' flanking regions, respectively. The qualitative primers confirmed the specificity by a single PCR product and sensitivity to 0.05% as a limit of detection (LOD). Simplex and duplex quantitative methods were also developed using TaqMan real-time PCR. One synthetic plasmid was constructed from two taxon-specific DNA sequences of maize and two event-specific 3' flanking DNA sequences of event 3272 and LY 038 as reference molecules. In-house validation of the quantitative methods was performed using six levels of mixing samples, from 0.1 to 10.0%. As a result, the biases from the true value and the relative deviations were all within the range of +/-30%. Limits of quantitation (LOQs) of the quantitative methods were all 0.1% for simplex real-time PCRs of event 3272 and LY 038 and 0.5% for duplex real-time PCR of LY 038. This study reports that event-specific analytical methods were applicable for qualitative and quantitative analysis for biotech maize event 3272 and LY 038. PMID:19650633
Sharma, Pankaj; Parashar, Sandeep Kumar
2016-05-01
The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d15 effect. In piezoelectric actuators, the potential use of d15 effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d31 and d33. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton`s principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.
Analytical method for the evaluation of sulfur functionalities in American coals. Final report
Attar, A.
1983-05-01
This investigation consisted of the following 6 tasks: (1) improve the instrumentation for the sulfur functional groups analysis and make it more reliable. (2) create a set of reference standards of sulfur-containing compounds. (3) examine the sulfur groups distribution in untreated and desulfurized coals. (4) examine the sulfur functionalities in raw and processed coals, i.e., liquefied coals. (5) determine the distribution of sulfur functionalities in modified coals. (6) prepare computer programs for calculations related to the distribution of sulfur functional groups in coal. Each task is discussed and results are presented. Appendix A contains the computer program used to interpret the data. 31 references, 56 figures, 17 tables.
Martin, E. Dale
1989-01-01
The paper introduces a new theory of N-dimensional complex variables and analytic functions which, for N greater than 2, is both a direct generalization and a close analog of the theory of ordinary complex variables. The algebra in the present theory is a commutative ring, not a field. Functions of a three-dimensional variable were defined and the definition of the derivative then led to analytic functions.
Li, W.; Cai, X.
2000-12-01
Starting from the master equation for the hierarchical structure of avalanches of a different kind within the frame of the Bak-Sneppen evolution model, we derive the exact formula of the scaling function describing the probability distribution of avalanches. The scaling function displays features required by the scaling ansatz and verified by simulations. Using the scaling function we investigate the avalanche moment, denoted by Δf¯. It is found that for any non-negative integer k, Δf¯ diverges as Δf¯-k, which gives an infinite group of exact critical exponents. Simulation outcomes of avalanche moments with k=1,2,3, are found to be consistent with the corresponding analytical results.
Functional-analytical capabilities of GIS technology in the study of water use risks
Regional security aspects of economic activities are of great importance for legal regulation in environmental management. This has become a critical issue due to climate change, especially in regions where severe climate conditions have a great impact on almost all types of natural resource uses. A detailed analysis of climate and hydrological situation in Tomsk Oblast considering water use risks was carried out. Based on developed author's techniques an informational and analytical database was created using ArcGIS software platform, which combines statistical (quantitative) and spatial characteristics of natural hazards and socio-economic factors. This system was employed to perform areal zoning according to the degree of water use risks involved
Analytical Derivation of Three Dimensional Vorticity Function for wave breaking in Surf Zone
Dutta, R
2015-01-01
In this report, Mathematical model for generalized nonlinear three dimensional wave breaking equations was de- veloped analytically using fully nonlinear extended Boussinesq equations to encompass rotational dynamics in wave breaking zone. The three dimensional equations for vorticity distributions are developed from Reynold based stress equations. Vorticity transport equations are also developed for wave breaking zone. This equations are basic model tools for numerical simulation of surf zone to explain wave breaking phenomena. The model reproduces most of the dynamics in the surf zone. Non linearity for wave height predictions is also shown close to the breaking both in shoaling as well as surf zone. Keyword Wave breaking, Boussinesq equation, shallow water, surf zone. PACS : 47.32-y
Accorsi, Roberto
2005-10-01
Near-field coded-aperture data from a single view contain information useful for three-dimensional (3D) reconstruction. A common approach is to reconstruct the 3D image one plane at a time. An analytic expression is derived for the 3D point-spread function of coded-aperture laminography. Comparison with computer simulations and experiments for apertures with different size, pattern, and pattern family shows good agreement in all cases considered. The expression is discussed in the context of the completeness conditions for projection data and is applied to explain an example of nonlinear behavior inherent in 3D laminographic imaging.
Peng Zhigang
2012-01-01
Let ζ=(0,z1,z2,...,zn)with|zj|＜≤ 1for 1≤j ≤n,ω=(1,w1,w2,...,wn),and P(ζ,w) denote the set of functions p(z) that are analytic in D ={z:|z| ＜ 1} and satisfy Rep(z) ≥ 0 (|z| ＜ 1),p(0) =1,p(zj) =wj,j =1,2,…,n.In this article we investigate the extreme points of P(ζ,w).
Lundengård, Karl; Javor, Vesna; Silvestrov, Sergei
2016-01-01
A multi-peaked version of the analytically extended function (AEF) intended for approximation of multi-peaked lightning current wave-forms will be presented along with some of its basic properties. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks as well as a given charge trans-fer and specific energy will also be described. This framework is used to find parameters for some common single-peak wave-forms and some advantages and disadvantages of the approach will be discussed.
Gottlieb, David; Shu, Chi-Wang
1994-01-01
The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.
Kanter, Jonathan W.; Landes, Sara J.; Busch, Andrew M.; Rusch, Laura C.; Brown, Keri R.; Baruch, David E.; Holman, Gareth I.
2006-01-01
The current study investigated a behavior-analytic treatment, functional analytic psychotherapy (FAP), for outpatient depression utilizing two single-subject A/A+B designs. The baseline condition was cognitive behavioral therapy. Results demonstrated treatment success in 1 client after the addition of FAP and treatment failure in the 2nd. This…
Analytical Formulation of the Single-visit Completeness Joint Probability Density Function
Garrett, Daniel; Savransky, Dmitry
2016-09-01
We derive an exact formulation of the multivariate integral representing the single-visit obscurational and photometric completeness joint probability density function for arbitrary distributions for planetary parameters. We present a derivation of the region of nonzero values of this function, which extends previous work, and discuss the time and computational complexity costs and benefits of the method. We present a working implementation and demonstrate excellent agreement between this approach and Monte Carlo simulation results.
Catoni, Francesco; Zampetti, Paolo [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Energia; Cannata, Roberto [ENEA, Centro Ricerche Casaccia, Rome (Italy). Funzione Centrale INFO; Nichelatti, Enrico [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Innovazione
1997-10-01
Systems of two-dimensional hypercomplex numbers are usually studied in their canonical form, i.e. according to the multiplicative rule for the ``imaginary``versor i{sup 2} = {+-} 1, 0. In this report those systems for which i{sup 2} = {alpha} + {beta}i are studied and expressions are derived for functions given by series expansion as well as for some elementary functions. The results obtained for systems which can be decomposed are then extended to all systems.
Analytical formulation of the single-visit completeness joint probability density function
Garrett, Daniel
2016-01-01
We derive an exact formulation of the multivariate integral representing the single-visit obscurational and photometric completeness joint probability density function for arbitrary distributions for planetary parameters. We present a derivation of the region of nonzero values of this function which extends previous work, and discuss time and computational complexity costs and benefits of the method. We present a working implementation, and demonstrate excellent agreement between this approach and Monte Carlo simulation results
System identification method proposed by the authors to estimate the dynamic characteristic of a building itself, under an imaginary fixed base condition in the other words, is studied for buildings with large soil-structure interaction (SSI) effect. The applicability of the method to buildings with embedment is studied in this paper. The assumed system model for the method is slightly different from the actual SSI system. This difference as well as the additional input to the underground wall may produce some system identification error. For these reasons, the proposed method and other spectral analysis procedures as well as the ARX method are applied to the response of an analytical model and results are compared. The benefit of the use of such model response instead of actual measured data is that the causality is very clear. In result, relative merits and demerits of the methods, cause and mechanism of them become clear. Furthermore, the applicability of the proposed method is confirmed. Such a method can be used to check the change of dynamic characteristics of the buildings after large earthquakes or long-term service. (author)
Application of ANFIS for analytical modeling of tensile strength of functionally graded steels
Ali Nazari
2012-06-01
Full Text Available In the present study, the tensile strength of ferritic and austenitic functionally graded steels produced by electroslag remelting has been modeled. To produce functionally graded steels, two slices of plain carbon steel and austenitic stainless steels were spot welded and used as electroslag remelting electrode. Functionally graded steel containing graded layers of ferrite and austenite may be fabricated via diffusion of alloying elements during remelting stage. Vickers microhardness profile of the specimen has been obtained experimentally and modeled with adaptive network-based fuzzy inference systems (ANFIS. To build the model for graded ferritic and austenitic steels, training, testing and validation using respectively 174 and 120 experimental data were conducted. According to the input parameters, in the ANFIS model, the Vickers microhardness of each layer was predicted. A good fit equation which correlates the Vickers microhardness of each layer to its corresponding chemical composition was achieved by the optimized network for both ferritic and austenitic graded steels. Afterwards; the Vickers microhardness of each layer in functionally graded steels was related to the yield stress of the corresponding layer and by assuming Holloman relation for stress-strain curve of each layer, they were acquired. Finally, by applying the rule of mixtures, tensile strength of functionally graded steels configuration was found through a numerical method. The obtained results from the proposed model are in good agreement with those acquired from the experiments.
Highlights: • A new AFEN code, MGANSP3, is developed for simplified P3 (SP3) calculations. • Surface averaged partial currents are used for coupling the nodes. • Coarse group rebalancing method is applied to increase the speed of calculations. • Four benchmark problems are used to examine the accuracy of the MGANSP3 code. - Abstract: In this study, a new analytic function expansion nodal (AFEN) method was developed to solve multi-group and three dimensional neutron simplified P3 equations (SP3) in reactor cores with rectangular fuel assemblies. In this method, the intranodal fluxes are expanded into a set of analytic basis functions for each group and moment. The nodes are coupled through the surface averaged partial currents at each nodal interface. Thus, six boundary conditions at each group and Legendre moments have been considered. Coarse group rebalancing (CGR) method was applied to increase the speed of code calculations. The code takes few-groups cross sections produced by a lattice code such as WIMS and calculates the effective multiplication factor, zeroth and second moments of the flux in multi-group energy, reactivity, and the relative power density at each fuel assembly. The numerical results for different benchmark problems demonstrate that solution of SP3 equations by our AFEN method improves both effective multiplication factor (keff) and power distribution compared to our AFEN diffusion method, especially in heterogeneous geometry and mixed-oxide (MOX) fuel problems
Yunta Carretero; Rodriguez Mayquez, E.
1974-07-01
In this paper is described the objective, basis, carrying out in FORTRAN language and use of the program ORBITALES. This program calculate atomic wave function in the case of ths analytical central potential (Author) 8 refs.
Opoola, T O
2009-01-01
In this paper we give some applications of a lemma of Babalola and Opoola \\cite{BO}, which is a classical extension of an earlier one by Lewandowski, Miller and Zlotkiewicz \\cite{LMZ}. The applications were given via a new generalization of some well-known subclasses of univalent functions, and they unify many known results.
An Analytical Approach to Document Clustering Based on Internal Criterion Function
Ranjan, Alok; Kandpal, Eatesh; Dhar, Joydip
2010-01-01
Fast and high quality document clustering is an important task in organizing information, search engine results obtaining from user query, enhancing web crawling and information retrieval. With the large amount of data available and with a goal of creating good quality clusters, a variety of algorithms have been developed having quality-complexity trade-offs. Among these, some algorithms seek to minimize the computational complexity using certain criterion functions which are defined for the whole set of clustering solution. In this paper, we are proposing a novel document clustering algorithm based on an internal criterion function. Most commonly used partitioning clustering algorithms (e.g. k-means) have some drawbacks as they suffer from local optimum solutions and creation of empty clusters as a clustering solution. The proposed algorithm usually does not suffer from these problems and converge to a global optimum, its performance enhances with the increase in number of clusters. We have checked our algor...
In classical Drude theory the conductivity is determined by the mass of the propagating particles and the mean free path between two scattering events. For a quantum particle this simple picture of diffusive transport loses relevance if strong correlations dominate the particle motion. We study a situation where the propagation of a fermionic particle is possible only through creation and annihilation of local bosonic excitations. This correlated quantum transport process is outside the Drude picture, since one cannot distinguish between free propagation and intermittent scattering. The characterization of transport is possible using the Drude weight obtained from the f-sum rule, although its interpretation in terms of free mass and mean free path breaks down. For the situation studied we calculate the Green's function and Drude weight using a Green's functions expansion technique, and discuss their physical meaning.
Kamikado, Kazuhiko; Uchino, Shun
2016-01-01
Motivated by experiments with cold atoms, we investigate a mobile impurity immersed in a Fermi sea in three dimensions at zero temperature by means of the functional renormalization group. We first perform the derivative expansion of the effective action to calculate the ground state energy and Tan's contact across the polaron-molecule transition for several mass imbalances. Next we study quasiparticle properties of the impurity by using a real-time method recently developed in nuclear physics, which allows one to go beyond the derivative expansion. We obtain the spectral function of the polaron, the effective mass and quasiparticle weight of attractive and repulsive polarons, and clarify how they are affected by mass imbalances.
Fractional Calculus of Analytic Functions Concerned with Möbius Transformations
Nicoleta Breaz
2016-01-01
Full Text Available Let A be the class of functions f(z in the open unit disk U with f(0=0 and f′(0=1. Also, let w(ζ be a Möbius transformation in U for some z∈U. Applying the Möbius transformations, we consider some properties of fractional calculus (fractional derivatives and fractional integrals of f(z∈A. Also, some interesting examples for fractional calculus are given.
A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels
Zahedinejad, P. [Department of Mechanical Engineering, Islamic Azad University, Branch of Shiraz, Shiraz (Iran, Islamic Republic of); Malekzadeh, P., E-mail: malekzadeh@pgu.ac.i [Department of Mechanical Engineering, Persian Gulf University, Persian Gulf University Boulevard, Bushehr 75168 (Iran, Islamic Republic of); Center of Excellence for Computational Mechanics, Shiraz University, Shiraz (Iran, Islamic Republic of); Farid, M. [Department of Mechanical Engineering, Islamic Azad University, Branch of Shiraz, Shiraz (Iran, Islamic Republic of); Karami, G. [Department of Mechanical Engineering and Applied Mechanics, North Dakota State University, Fargo, ND 58105-5285 (United States)
2010-08-15
Based on the three-dimensional elasticity theory, free vibration analysis of functionally graded (FG) curved thick panels under various boundary conditions is studied. Panel with two opposite edges simply supported and arbitrary boundary conditions at the other edges are considered. Two different models of material properties variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential distribution of the material properties through the thickness are considered. Differential quadrature method in conjunction with the trigonometric functions is used to discretize the governing equations. With a continuous material properties variation assumption through the thickness of the curved panel, differential quadrature method is efficiently used to discretize the governing equations and to implement the related boundary conditions at the top and bottom surfaces of the curved panel and in strong form. The convergence of the method is demonstrated and to validate the results, comparisons are made with the solutions for isotropic and FG curved panels. By examining the results of thick FG curved panels for various geometrical and material parameters and subjected to different boundary conditions, the influence of these parameters and in particular, those due to functionally graded material parameters are studied.
Molecular structure and analytical potential energy function of SeCO
The density functional method (B3P86/6-311G) is used for calculating the possible structures of SeC, SeO, and SeCO molecules. The result shows that the ground state of the SeC molecule is 1Σ, the equilibrium nuclear distance is RSeC = 0.1699 nm, and the dissociation energy is De = 8.7246 eV. The ground state of the SeO molecule is 3Σ, with equilibrium nuclear distance RSeO = 0.1707 nm and dissociation energy De = 7.0917 eV. There are two structures for the ground state of the SeCO molecule: Se=C=O and Se=O=C. The linear Se=C=O is 1Σ. Its equilibrium nuclear distances and dissociation energy are RSeC = 0.1715 nm, RCO = 0.1176 nm and 18.8492 eV, respectively. The other structure Se=O=C is 1Σ. Its equilibrium nuclear distances and dissociation energy are RCO = 0.1168 nm, RSeO = 0.1963 nm and 15.5275 eV, respectively. The possible dissociative limit of the SeCO molecule is analyzed. The potential energy function for the SeCO molecule has been obtained from the many-body expansion theory. The contour of the potential energy curve describes the structure characters of the SeCO molecule. Furthermore, contours of the molecular stretching vibration based on this potential energy function are discussed. (atomic and molecular physics)
Gori-Giorgi, Paola; Perdew, John P.
2002-10-01
We construct analytic formulas that represent the coupling-constant-averaged pair distribution function gxc(rs,ζ,kFu) of a three-dimensional nonrelativistic ground-state electron gas constrained to a uniform density with density parameter rs=(9π/4)1/3/kF and relative spin polarization ζ over the whole range 0∞) oscillations averaged out. The pair distribution function gxc at the physical coupling constant is then given by differentiation with respect to rs. Our formulas are constructed using only known theoretical constraints plus the correlation energy ɛc(rs,ζ), and accurately reproduce the gxc of the quantum Monte Carlo method and of the fluctuation-dissipation theorem with the Richardson-Ashcroft dynamical local-field factor. Our gxc is correct even in the high-density (rs-->0) and low-density (rs-->∞) limits. When the spin resolution of ɛc into ↑↑, ↓↓, and ↑↓ contributions is known, as it is in the high- and low-density limits, our formulas also yield the spin resolution of gxc. Because of these features, our formulas may be useful for the construction of density functionals for nonuniform systems. We also analyze the kinetic energy of correlation into contributions from density fluctuations of various wave vectors. The exchange and long-range correlation parts of our gxc(rs,ζ,kFu)-1 are analytically Fourier transformable, so that the static structure factor Sxc(rs,ζ,k/kF) is easily evaluated.
Liu, Jie; Liang, WanZhen
2011-11-01
The paper presents the formalism, implementation, and performance of the analytical approach for the excited-state Hessian in the time-dependent density functional theory (TDDFT) that extends our previous work [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011)] on the analytical Hessian in TDDFT within Tamm-Dancoff approximation (TDA) to full TDDFT. In contrast to TDA-TDDFT, an appreciable advantage of full TDDFT is that it maintains the oscillator strength sum rule, and therefore yields more precise results for the oscillator strength and other related physical quantities. For the excited-state harmonic vibrational frequency calculation, however, full TDDFT does not seem to be advantageous since the numerical tests demonstrate that the accuracy of TDDFT with and without TDA are comparable to each other. As a common practice, the computed harmonic vibrational frequencies are scaled by a suitable scale factor to yield good agreement with the experimental fundamental frequencies. Here we apply both the optimized ground-state and excited-state scale factors to scale the calculated excited-state harmonic frequencies and find that the scaling decreases the root-mean-square errors. The optimized scale factors derived from the excited-state calculations are slightly smaller than those from the ground-state calculations.
Analytical Phase Equilibrium Function for Mixtures Obeying Raoult's and Henry's Laws
Hayes, Robert
When a mixture of two substances exists in both the liquid and gas phase at equilibrium, Raoults and Henry's laws (ideal solution and ideal dilute solution approximations) can be used to estimate the gas and liquid mole fractions at the extremes of either very little solute or solvent. By assuming that a cubic polynomial can reasonably approximate the intermediate values to these extremes as a function of mole fraction, the cubic polynomial is solved and presented. A closed form equation approximating the pressure dependence on mole fraction of the constituents is thereby obtained. As a first approximation, this is a very simple and potentially useful means to estimate gas and liquid mole fractions of equilibrium mixtures. Mixtures with an azeotrope require additional attention if this type of approach is to be utilized. This work supported in part by federal Grant NRC-HQ-84-14-G-0059.
Atai, Ali Asghar [University of Tehran, Tehran (Iran, Islamic Republic of); Lak, Davaod [National Iranian Oil Co., Tehran (Iran, Islamic Republic of)
2016-01-15
In this work, the effect of electric potential on the mechanical (Stresses, strains, displacement) and electrical (electrical displacement and intensity) response of a Functionally graded piezoelectric (FGP) hollow sphere is analytically investigated. The sphere is under the action of internal/external pressure and temperature gradient as well. The inhomogeneity is based on power law in radial direction. The analysis is done in two parts: elastic response and plastic response, using Tresca yield criterion. It is shown by illustrative example that under internal pressure and assumed model parameters, the commencement of plastic region is from outside surface towards inside in the plastic zone is extended with the increase of electric potential. Interestingly, radial stress and displacement have an extreme not on the boundaries, but on the inside.
Minkowski functionals are a powerful tool to constrain the Gaussianity of the Cosmic Microwave Background (CMB). In the limit of a weakly non Gaussian field, a perturbative approach can be derived [Hikage C., Komatsu E., and Matsubara T., 2006, ApJ, 653, 11] that is completely based on analytical formulae without requiring computationally intensive, dedicated Monte Carlo non Gaussian simulations of the CMB anisotropy. We apply this machinery to an intensity map derived from the 1998 and 2003 flights of BOOMERanG, analyzed here together for the first time. We set limits on the non-linear coupling parameter fNL as -1020NL<390 at 95% CL, markedly improving the previous constraints set by [De Troia G. et al., 2007, ApJ, 670, L73] whose analysis was limited to the BOOMERanG 2003 dataset. These limits are the most stringent ever set among suborbital experiments.
Migliaccio, M.; Natoli, P.; De Troia, G. [Dipartimento di Fisica, Universita di Roma ' Tor Vergata' , Via della Ricerca Scientifica, 1 I-00133 Roma (Italy); Hikage, C. [School of Physics and Astronomy, Cardiff University, Cardiff, CF24 3AA (United Kingdom); Komatsu, E. [Texas Cosmology Center, University of Texas at Austin, 1 University Station, C1400, Austin, TX 78712 (United States); Ade, P.A.R. [School of Physics and Astronomy, Cardiff University, Cardiff, CF24 3AA (United Kingdom); Bock, J.J. [Jet Propulsion Laboratory, Pasadena, CA (United States); Bond, J.R. [Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario (Canada); Borrill, J. [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA (United States); Boscaleri, A. [IFAC-CNR, Firenze (Italy); Contaldi, C.R. [Theoretical Physics Group, Imperial College, London (United Kingdom); Crill, B.P. [Jet Propulsion Laboratory, Pasadena, CA (United States); Bernardis, P. de [Dipartimento di Fisica, Universita La Sapienza, Roma (Italy); Gasperis, G. de [Dipartimento di Fisica, Universita di Roma ' Tor Vergata' , Via della Ricerca Scientifica, 1 I-00133 Roma (Italy); Oliveira-Costa, A. de [Department of Physics, MIT, Cambridge, MA 02139 (United States); Di Stefano, G. [Istituto Nazionale di Geofisica e Vulcanologia, 00143 Rome (Italy); Hivon, E. [Institut d' Astrophysique, Paris (France); Kisner, T.S. [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA (United States); Jones, W.C. [Department of Physics, Princeton University, Princeton, NJ 0854 (United States); Lange, A.E. [Observational Cosmology, California Institute of Technology, Pasadena, CA (United States)
2009-10-15
Minkowski functionals are a powerful tool to constrain the Gaussianity of the Cosmic Microwave Background (CMB). In the limit of a weakly non Gaussian field, a perturbative approach can be derived [Hikage C., Komatsu E., and Matsubara T., 2006, ApJ, 653, 11] that is completely based on analytical formulae without requiring computationally intensive, dedicated Monte Carlo non Gaussian simulations of the CMB anisotropy. We apply this machinery to an intensity map derived from the 1998 and 2003 flights of BOOMERanG, analyzed here together for the first time. We set limits on the non-linear coupling parameter f{sub NL} as -1020
Migliaccio, M.; Natoli, P.; De Troia, G.; Hikage, C.; Komatsu, E.; Ade, P. A. R.; Bock, J. J.; Bond, J. R.; Borrill, J.; Boscaleri, A.; Contaldi, C. R.; Crill, B. P.; de Bernardis, P.; de Gasperis, G.; de Oliveira-Costa, A.; Di Stefano, G.; Hivon, E.; Kisner, T. S.; Jones, W. C.; Lange, A. E.; Masi, S.; Mauskopf, P. D.; MacTavish, C. J.; Melchiorri, A.; Montroy, T. E.; Netterfield, C. B.; Pascale, E.; Piacentini, F.; Polenta, G.; Ricciardi, S.; Romeo, G.; Ruhl, J. E.; Tegmark, M.; Veneziani, M.; Vittorio, N.
2009-10-01
Minkowski functionals are a powerful tool to constrain the Gaussianity of the Cosmic Microwave Background (CMB). In the limit of a weakly non Gaussian field, a perturbative approach can be derived [Hikage C., Komatsu E., & Matsubara T., 2006, ApJ, 653, 11] that is completely based on analytical formulae without requiring computationally intensive, dedicated Monte Carlo non Gaussian simulations of the CMB anisotropy. We apply this machinery to an intensity map derived from the 1998 and 2003 flights of BOOMERanG, analyzed here together for the first time. We set limits on the non-linear coupling parameter f as -1020Troia G. et al., 2007, ApJ, 670, L73] whose analysis was limited to the BOOMERanG 2003 dataset. These limits are the most stringent ever set among suborbital experiments.
The experience is reviewed from the development and utilization of a functional-analytic training simulator used in the USSR for training the personnel of nuclear power plants with WWER-1000 reactors. The training facility consists of a central ES 1066 computer where the mathematical model of the power unit is implemented, and of four teaching workplaces with Elektronika-85 personal computers. An Elektronika-60 computer links these computers to the central unit. The training facility enables reactor operators to practise in understanding dynamic power unit characteristics and relations between dynamic parameters, to gain basic skills for unit control with respect to limitations following from nuclear safety requirements, to master non-standard situations and to perform analyses of accidents. The facility is also used to check the professional skills of operators and to provide preliminary training prior to switching over to full-scale training facilities. (Z.M.). 2 refs
Huang, Weidong; Hu, Peng; Chen, Zeshao
2011-01-01
Parabolic solar dish concentrator with sphere receiver is less studied. We present an analytic function to calculate the intercept factor of the system with real sun bright distribution and Gaussian distribution, the results indicate that the intercept factor is related to the rim angle of reflector and the ratio of open angle of receiver at the top of reflector to optical error when the optical error is larger than or equal to 5 mrad, but is related to the rim angle, open angle and optical error in less than 5 mrad optical error. Furthermore we propose a quick process to optimize the system to provide the maximum solar energy to net heat efficiency for different optical error under typical condition. The results indicate that the parabolic solar dish concentrator with sphere receiver has rather high solar energy to net heat efficiency which is 20% more than solar trough and tower system including higher cosine factor and lower heat loss of the receiver.
Functional data analytic approach of modeling ECG T-wave shape to measure cardiovascular behavior
Zhou, Yingchun; 10.1214/09-AOAS273
2010-01-01
The T-wave of an electrocardiogram (ECG) represents the ventricular repolarization that is critical in restoration of the heart muscle to a pre-contractile state prior to the next beat. Alterations in the T-wave reflect various cardiac conditions; and links between abnormal (prolonged) ventricular repolarization and malignant arrhythmias have been documented. Cardiac safety testing prior to approval of any new drug currently relies on two points of the ECG waveform: onset of the Q-wave and termination of the T-wave; and only a few beats are measured. Using functional data analysis, a statistical approach extracts a common shape for each subject (reference curve) from a sequence of beats, and then models the deviation of each curve in the sequence from that reference curve as a four-dimensional vector. The representation can be used to distinguish differences between beats or to model shape changes in a subject's T-wave over time. This model provides physically interpretable parameters characterizing T-wave sh...
Liu, Na; Ma, Zhanfang
2014-01-15
In this work, an Au-ionic liquid functionalized reduced graphene oxide nanocomposite (IL-rGO-Au) was fabricated via the self-assembly of ionic liquid functionalized reduced graphene oxide (IL-rGO) and gold nanoparticles (AuNPs) by electrostatic interaction. The IL-rGO can be synthesized and stabilized by introducing the cations of the amine-terminated ionic liquids (IL-NH2) into the graphene oxide (GO). With the assistance of IL-NH2, AuNPs were uniformly and densely absorbed on the surfaces of the IL-rGO. The proposed IL-rGO-Au nanocomposite can be used as an immunosensing platform because it can not only facilitate the electrons transfer of the electrode surface but also provide a large accessible surface area for the immobilization of abundant antibody. To assess the performance of the IL-rGO-Au nanocomposite, a sandwich-type electrochemical immunosensor was designed for simultaneous multianalyte detection (carcinoembryonic antigen (CEA) and alpha-fetoprotein (AFP) as model analytes). The chitosan (CS) coated prussian blue nanoparticles (PBNPs) or cadmium hexacyanoferrate nanoparticles (CdNPs) and loaded with AuNPs were used as distinguishable signal tags. The resulting immunosensor exhibited high selectivity and sensitivity in simultaneous determination of CEA and AFP in a single run. The linear ranges were from 0.01 to 100 ng mL(-1) for both CEA and AFP. The detection limits reached 0.01 ng mL(-1) for CEA and 0.006 ng mL(-1) for AFP, respectively. No obvious nonspecific adsorption and cross-talk was observed during a series of analyses to detect target analytes. In addition, for the detection of clinical serum samples, it is well consistent with the data determined by the ELISA, indicating that the immunosensor provides a possible application for the simultaneous multianalyte determination of CEA and AFP in clinical diagnostics. PMID:23962704
Fractal analytical approach of urban form based on spatial correlation function
Highlights: ► Many fractal parameter relations of cities can be derived by scaling analysis. ► The area-radius scaling of cities suggests a spatial correlation function. ► Spectral analysis can be used to estimate fractal dimension values of urban form. ► The valid range of fractal dimension of urban form comes between 1.5 and 2. ► The traditional scale concept will be replaced by scaling concept in geography. -- Abstract: Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities are not yet revealed in theory. By mathematical deduction and transform (e.g., Fourier transform), I find that scaling analysis, spectral analysis, and spatial correlation analysis are all associated with fractal concepts and can be integrated into a new approach to fractal analysis of cities. This method can be termed ‘3S analyses’ of urban form. Using the 3S analysis, I derived a set of fractal parameter equations, by which different fractal parameters of cities can be linked up with one another. Each fractal parameter has its own reasonable extent of values. According to the fractal parameter equations, the intersection of the rational ranges of different fractal parameters suggests the proper scale of the fractal dimension of urban patterns, which varies from 1.5 to 2. The fractal dimension equations based on the 3S analysis and the numerical relationships between different fractal parameters are useful for geographers to understand urban evolution and potentially helpful for future city planning
Garrabos, Yves; Lecoutre, Carole; Marre, Samuel; LeNeindre, Bernard
2016-08-01
A non-analytical scaling determination of the Ising-like crossover parameter is proposed considering the critical isochore of a simple fluid at finite distance from its critical temperature. The mean crossover functions, estimated from the bounded results of the massive renormalization scheme in field theory applied to the ( Φ 2) d2( n) model in three dimensions (d=3) and scalar order parameter (n=1), are used to formulate the corresponding scaling equations valid in two well-defined temperature ranges from the critical temperature. The validity range and the Ising-like nature of the corresponding crossover description are discussed in terms of a single Ising-like scale factor characterizing the critical isochore. The asymptotic value of this scale factor can be predicted within the Ising-like preasymptotic domain. Unfortunately, the absence of precise experimental data in such a close vicinity of the critical point leads the direct testing impossible. A contrario, from our scaling equations and the use of precise measurements performed at finite distance from the critical point, its local value can be estimated beyond the Ising-like preasymptotic domain. This non-analytical scaling determination only needs to make reference to the universal features estimated from the mean crossover functions and to introduce a single master dimensionless length common to all the simple fluids. This latter parameter guaranties the uniqueness of the physical length unit used for the theoretical crossover functions and the fluid singular properties when the generalized critical coordinates of the vapor-liquid critical point of each fluid are known. Xenon case along its critical isochore is considered as a typical example to demonstrate the singleness of the Ising-like crossover parameter. With the measurements at finite temperature range of the effective singular behaviors of the isothermal compressibility in the homogeneous domain, and the vapor-liquid coexisting densities in the
.-butyl by O-CH3) was found, which led to a new stable α-oxoketene. The oxoketenes also only differ by one methoxygroup and were generated from their furandiones at about the same reaction conditions: Sublimed together, the α-oxoketenes were formed simultaneously already during FV-pyrolysis, guaranteeing a perfect mixture. By warming up, these oxoketenes dimerize slowly via [2+4] cycloaddition reaction in another unusual way, since one oxoketene adds onto the carbonyl double bond of the other oxoketene to afford a new dimer with ketene-functionality. Its structure was determined by several spectroscopic measurements, including IR, 2D-NMR and a x-ray analysis. Scope and limitations of the chemistry of this novel α -oxoketene is discussed in detail. (author)
Moghtader Dindarlu, M. H.; Kavosh Tehrani, M.; Saghafifar, H.; Maleki, A.
2016-05-01
In this paper, an analytical model is introduced for temperature distribution of an end diode-pumped laser slab by Green’s function method. To solve the heat equation, Robin boundary conditions are considered because four lateral faces of the slab are cooled by water. An analytical model is extracted for single and dual end-pumping configuration. For an example, the 2D and 3D temperature distributions are plotted and our analytical model is validated by numerical solution based on the finite element method (FEM). The results show that our model has very good agreement with numerical solution. Furthermore, dependence of the temperature distribution on absorbed pump power is shown.
Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in SN2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented
Nakata, Hiroya; Fedorov, Dmitri G; Zahariev, Federico; Schmidt, Michael W; Kitaura, Kazuo; Gordon, Mark S; Nakamura, Shinichiro
2015-03-28
Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in SN2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented. PMID:25833559
During the last decade, the analytic function expansion nodal (AFEN) method has been developed and successfully applied to the static and kinetic problems in rectangular geometry and also applied to the static problems in hexagonal geometry. Although the results of two-dimensional hexagonal problems were very accurate, the accuracy becomes poor when the current hexagonal-z method is applied to the three-dimensional hexagonal problems. In this thesis, we develop a new method which improves the accuracy in three-dimensional hexagonal geometry and computerize the method into a new kinetics code. At first we add the edge fluxes in the upper and lower planes as additional nodal unknowns in axial direction to improve the accuracy. These nodal unknowns are updated through leakage balance equations by using a simple expansion of nodal fluxes at the vicinity of the edge fluxes. The relation of delayed neutron precursor densities between time steps is obtained analytically by using the transformed fluxes and assuming linear variations of the fission rates within a time step. The code developed for the steady state is verified in the cases of 2-D VVER-1000, 3-D SNR-300, and 3-D VVER-440 benchmark problems. The results of the static problems show higher accuracy than those of the original formulations in hexagonal geometry. Finally, a kinetics code is developed and tested by introducing step changes of nodal cross sections for the VVER-440 benchmark problem. The results appear to be accurate enough for this code to be useful for analyzing realistic three-dimensional hexagonal reactors
LIU Yu-min; YU Zhong-yuan; YANG Hong-bo; ZHANG Na
2005-01-01
The general analytic expression of the chirped sampled function is derived based on coupled mode theory. This function can be used to describe how to use uniform period fiber Bragg grating to produce the equal chirp at will in the specific reflection channel. As an example,the exact sampled function expression that produces a linear chirped at the +4 channel is given. The simulation results by using the transfer-matrix show that the theory is correct.
Kataev, A. L.
2012-02-01
The generalized Crewther relations in the channels of the non-singlet and vector quark currents are considered. These relations follow from the double application of the operator product expansion approach to the same axial vector-vector-vector triangle amplitude in two regions, adjoining to the angle sides ( x, y) (or p 2, q 2). We assume that the generalized Crewther relations in these two kinematic regimes result in the existence of the same perturbation expression for two products of the coefficient functions of annihilation and deepinelastic scattering processes in the non-singlet and vector channels. This feature explains the conformal symmetry motivated cancellations between the singlet α{/s 3} corrections to the Gross-Llewellyn Smith sum rule S GLS of ν N deep inelastic scattering and the singlet α{/s 3} correction to the e + e --annihilation Adler function D {/A V } in the product of the corresponding perturbative series. Taking into account the Baikov-Chetyrkin-Kuhn fourth order result for S GLS and the perturbative effects of the violation of the conformal symmetry in the generalized Crewther relation, we obtain the analytical contribution to the singlet α{/s 4} correction to the D {/A V } function. Its a-posteriori comparison with the recent result of direct diagram-by-diagram evaluation of the singlet fourth order corrections to D {/A V } function demonstrates the coincidence of the predicted and obtained ζ{3/2}-contributions to the singlet term. They can be obtained in the conformal invariant limit from the original Crewther relation. Therefore, on the contrary to previous belief, the appearance of ζ3-terms in the perturbative series in quantum field theory gauge models does not contradict to the property of the conformal symmetry and can be considered as regular feature. The Banks-Zaks motivated relation between our predicted and the obtained directly fourth order corrections is mentioned. It confirms the expectation, previously made by Baikov
Gottlieb, David; Shu, Chi-Wang
1993-01-01
The investigation of overcoming Gibbs phenomenon was continued, i.e., obtaining exponential accuracy at all points including at the discontinuities themselves, from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. It was shown that if we are given the first N expansion coefficients of an L(sub 2) function f(x) in terms of either the trigonometrical polynomials or the Chebyshev or Legendre polynomials, an exponentially convergent approximation to the point values of f(x) in any sub-interval in which it is analytic can be constructed.
Javier Cubas
2014-06-01
Full Text Available Due to the high dependence of photovoltaic energy efficiency on environmental conditions (temperature, irradiation..., it is quite important to perform some analysis focusing on the characteristics of photovoltaic devices in order to optimize energy production, even for small-scale users. The use of equivalent circuits is the preferred option to analyze solar cells/panels performance. However, the aforementioned small-scale users rarely have the equipment or expertise to perform large testing/calculation campaigns, the only information available for them being the manufacturer datasheet. The solution to this problem is the development of new and simple methods to define equivalent circuits able to reproduce the behavior of the panel for any working condition, from a very small amount of information. In the present work a direct and completely explicit method to extract solar cell parameters from the manufacturer datasheet is presented and tested. This method is based on analytical formulation which includes the use of the Lambert W-function to turn the series resistor equation explicit. The presented method is used to analyze commercial solar panel performance (i.e., the current-voltage–I-V–curve at different levels of irradiation and temperature. The analysis performed is based only on the information included in the manufacturer’s datasheet.
Xiao, R; Wang, C W; Zhu, A N; Long, F
2016-05-15
SERS biosensor has demonstrated remarkable potential to analyze various bio/chemical targets with ultrahigh sensitivity. However, the development of universal SERS biosensing platforms with a uniform and reproducible structure that can quantitatively detect a broad range of trace analytes remains a significant challenge. The production of SERS nanotags with abundant Raman reporters and rational structure to conjugate with detection biomolecules is another key to design SERS-nanobioprobes. Here, we introduce a facile single magnetic-bead biosensing platform, formed by combining the captured antibodies/antigens conjugated magnetic-beads and the Au@Raman-Reporters@Ag sandwich-based nanorod tags labeled nanobioprobes. The advantage of the robust sandwich-structure-based nanotags is attributed not only to the high density Raman reporters contained inside, with high EF value because of enhanced electromagnetic field density, but also to the flexibility for bioconjugation of the detection biomolecules. The 3-D structure of the functional magnetic-bead provides a perfect platform to rapidly capture and enrich biomolecules. Ultrasensitive detection of two small molecules and a protein was achieved in samples, respectively. PMID:26765530
ANALYTIC SOLUTIONS OF SYSTEMS OF FUNCTIONAL EQUATIONS%泛函方程组的解析解
刘新和
2003-01-01
Let r be a given positive numberDenote by D=Dr the closed disc in the complexplane C whose center is the origin and radius is rFor any subset K of C and any integer m≥1,write A(Dm,K)= {f|f: Dm→K is a continuous map, and f| (Dm)° is analytic}For H∈A(Dm,C)(m≥2),f∈A(D,D)and z∈D,write ΨH(f)(z)=H(z,f(z),...,fm-1(z)).Suppose F,G∈A(D2n+1,C),and Hk,Kk∈A(Dk,C),k=2,...,n.In this paper,the system of functional equations F(z,f(z),f2(ΨH2(f)(z)),...,fn(ΨHn(f)(z)),g(z),g2(ΨK2(g)(z)),...,gn(ΨKn(g)(z))=0 G(z,f(z),f2(ΨH2(f)(z)),...,fn(ΨHn(f)(z)),g(z),g2(ΨK2(g)(z)),...,gn(ΨKn(g)(z))=0 (z∈D) is studied and some conditions for the system of equations to have a solution or a uniquesolution in A(D,D)×A(D,D) are given.
Eismin, Ryan J.; Fu, Mingkun; Yem, Sonoeun; Widjaja, Fanny; Kenttämaa, Hilkka I.
2012-01-01
A mass spectrometric method has been delineated for the identification of the epoxide functionalities in unknown monofunctional analytes. This method utilizes gas-phase ion/molecule reactions of protonated analytes with neutral trimethyl borate (TMB) followed by collision-activated dissociation (CAD) in an ion trapping mass spectrometer (tested for a Fourier-transform ion cyclotron resonance and a linear quadrupole ion trap). The ion/molecule reaction involves proton transfer from the protonated analyte to TMB, followed by addition of the analyte to TMB and elimination of methanol. Based on literature, this reaction allows the general identification of oxygen-containing analytes. Vinyl and phenyl epoxides can be differentiated from other oxygen-containing analytes, including other epoxides, based on the loss of a second methanol molecule upon CAD of the addition/methanol elimination product. The only other analytes found to undergo this elimination are some amides but they also lose O = B-R (R = group bound to carbonyl), which allows their identification. On the other hand, other epoxides can be differentiated from vinyl and phenyl epoxides and from other monofunctional analytes based on the loss of (CH3O)2BOH or formation of protonated (CH3O)2BOH upon CAD of the addition/methanol elimination product. For propylene oxide and 2,3-dimethyloxirane, the (CH3O)2BOH fragment is more basic than the hydrocarbon fragment, and the diagnostic ion (CH3O)2BOH{2/+} is formed. These reactions involve opening of the epoxide ring. The only other analytes found to undergo (CH3O)2BOH elimination are carboxylic acids, but they can be differentiated from the rest based on several published ion/molecule reaction methods. Similar results were obtained in the Fourier-transform ion cyclotron resonance and linear quadrupole ion trap mass spectrometer.
We show that the N.N. Bogolubov generating functional method is a very effective tool for studying distribution functions of both equilibrium and non equilibrium states of classical many-particle dynamical systems. In some cases the Bogolubov generating functionals can be represented by means of infinite Ursell-Mayer diagram expansions, whose convergence holds under some additional constraints on statistical system. The classical Bogolubov idea to use the Wigner density operator transformation for studying the non equilibrium distribution functions is developed and new analytic non-stationary solution to the classical N.N. Bogolubov evolution functional equation is constructed. (author)