Directory of Open Access Journals (Sweden)
Wei Li
2014-01-01
Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.
Abdel-Salam, Emad A-B; Hassan, Gmal F
2015-01-01
In this paper, the fractional projective Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Burgers equation, the space-time fractional mKdV equation and time fractional biological population model. The solutions are expressed in terms of fractional hyperbolic functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The fractal index for the obtained results is equal to one. Counter examples to compute the fractal index are introduced in appendix.
On a continued fraction expansion for Euler's constant
Pilehrood, Khodabakhsh Hessami
2010-01-01
Recently, A.~I.~Aptekarev and his collaborators found a sequence of rational approximations to Euler's constant $\\gamma$ defined by a third-order homogeneous linear recurrence. In this paper, we give a new interpretation of Aptekarev's approximations to $\\gamma$ in terms of Meijer $G$-functions and hypergeometric-type series. This approach allows us to describe a very general construction giving linear forms in $1$ and $\\gamma$ with rational coefficients. Using this construction we find new rational approximations to $\\gamma$ generated by a second-order inhomogeneous linear recurrence with polynomial coefficients. This leads to a continued fraction (though not a simple continued fraction) for Euler's constant. It seems to be the first non-trivial continued fraction expansion convergent to Euler's constant sub-exponentially, the elements of which can be expressed as a general pattern. It is interesting to note that the same homogeneous recurrence generates a continued fraction for the Euler-Gompertz constant f...
Directory of Open Access Journals (Sweden)
Emad A.-B. Abdel-Salam
2013-01-01
Full Text Available The fractional Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, space-time fractional Korteweg-de Vries equation, regularized long-wave equation, Boussinesq equation, and Klein-Gordon equation are considered. As a result, abundant types of exact analytical solutions are obtained. These solutions include generalized trigonometric and hyperbolic functions solutions which may be useful for further understanding of the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The periodic and kink solutions are founded as special case.
Unpacking Referent Units in Fraction Operations
Philipp, Randolph A.; Hawthorne, Casey
2015-01-01
Although fraction operations are procedurally straightforward, they are complex, because they require learners to conceptualize different units and view quantities in multiple ways. Prospective secondary school teachers sometimes provide an algebraic explanation for inverting and multiplying when dividing fractions. That authors of this article…
Directory of Open Access Journals (Sweden)
Emad A-B. Abdel-Salam
2015-06-01
Full Text Available In this paper, the improved fractional Riccati expansion method is proposed to solve fractional differential equations. The method is applied to solve space–time fractional modified Korteweg–de Vries equation, space–time fractional modified regularized long-wave equation, time fractional biological population model, and space–time fractional Klein–Gordon equation. The obtained solutions include generalized trigonometric and hyperbolic functions solutions. Among these solutions, some are found for the first time.
Order reduction of z-transfer functions via multipoint Jordan continued-fraction expansion
Lee, Ying-Chin; Hwang, Chyi; Shieh, Leang S.
1992-01-01
The order reduction problem of z-transfer functions is solved by using the multipoint Jordan continued-fraction expansion (MJCFE) technique. An efficient algorithm that does not require the use of complex algebra is presented for obtaining an MJCFE from a stable z-transfer function with expansion points selected from the unit circle and/or the positive real axis of the z-plane. The reduced-order models are exactly the multipoint Pade approximants of the original system and, therefore, they match the (weighted) time-moments of the impulse response and preserve the frequency responses of the system at some characteristic frequencies, such as gain crossover frequency, phase crossover frequency, bandwidth, etc.
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Yan Sheng-Ping
2015-01-01
Full Text Available In this article, we first propose the local fractional Laplace series expansion method, which is a coupling method of series expansion method and Laplace transform via local fractional differential operator. An illustrative example for handling the diffusion equation arising in fractal heat transfer is given.
The (G'/G)-expansion method for the nonlinear time fractional differential equations
Unsal, Omer; Guner, Ozkan; Bekir, Ahmet; Cevikel, Adem C.
2017-01-01
In this paper, we obtain exact solutions of two time fractional differential equations using Jumarie's modified Riemann-Liouville derivative which is encountered in mathematical physics and applied mathematics; namely (3 + 1)-dimensional time fractional KdV-ZK equation and time fractional ADR equation by using fractional complex transform and (G/'G )-expansion method. It is shown that the considered transform and method are very useful in solving nonlinear fractional differential equations.
Asymptotic expansions for Riesz fractional derivatives of Airy functions and applications
N.M. Temme (Nico); V. Varlamov
2009-01-01
textabstractRiesz fractional derivatives of a function, $D_{x}^{\\alpha}f(x)$ (also called Riesz potentials), are defined as fractional powers of the Laplacian. Asymptotic expansions for large $x$ are computed for the Riesz fractional derivatives of the Airy function of the first kind, $Ai(x)$, and
Asymptotic Expansion of the Solutions to Time-Space Fractional Kuramoto-Sivashinsky Equations
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Weishi Yin
2016-01-01
Full Text Available This paper is devoted to finding the asymptotic expansion of solutions to fractional partial differential equations with initial conditions. A new method, the residual power series method, is proposed for time-space fractional partial differential equations, where the fractional integral and derivative are described in the sense of Riemann-Liouville integral and Caputo derivative. We apply the method to the linear and nonlinear time-space fractional Kuramoto-Sivashinsky equation with initial value and obtain asymptotic expansion of the solutions, which demonstrates the accuracy and efficiency of the method.
Sharma, Kamalesh Kumar; Joshi, Shiv Dutt
2007-10-01
We present a generalized convolution theorem in the fractional Fourier domains that preserves the convolution theorem of the conventional Fourier transform. The Papoulis-like generalized sampling expansions in the fractional Fourier domains using this generalized convolution theorem are also derived and it is shown that the classical generalized Papoulis sampling expansion is a special case of it. Its application in the context of the image superresolution is also discussed.
Exact solutions of some fractional differential equations by various expansion methods
Topsakal, Muammer; Guner, Ozkan; Bekir, Ahmet; Unsal, Omer
2016-10-01
In this paper, we construct the exact solutions of some nonlinear spacetime fractional differential equations involving modified Riemann-Liouville derivative in mathematical physics and applied mathematics; namely the fractional modified Benjamin-Bona- Mahony (mBBM) and Kawahara equations by using G'/G and (G'/G, 1/G)-expansion methods.
Iteration: Unit Fraction Knowledge and the French Fry Tasks
Tzur, Ron; Hunt, Jessica
2015-01-01
Often, students who solve fraction tasks respond in ways that indicate inadequate conceptual grounding of unit fractions. Many elementary school curricula use folding, partitioning, shading, and naming parts of various wholes to develop children's understanding of unit and then nonunit fractions (e.g., coloring three of four parts of a pizza and…
Huang, Qing; Wang, Li-Zhen; Zuo, Su-Li
2016-02-01
In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann-Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada-Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed. Supported by the National Natural Science Foundation of China under Grant Nos. 11101332, 11201371, 11371293 and the Natural Science Foundation of Shaanxi Province under Grant No. 2015JM1037
Fujisaka, H; Eckhardt, B; Fujisaka, Hirokazu; Shigematsu, Hideto; Eckhardt, Bruno
1993-01-01
Abstract: A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator) $H_{q}$ relevant to the fluctuation spectrum and poles of the order-$q$ power spectrum is proposed. The ``partition function'' is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A solvable example is presented and the approximate and exact results are compared; good agreement is found.
Observation of a class of disturbance in time series expansion for fractional order systems
Yiheng Wei; Hamid Reza Karimi; Jinwen Pan; Qing Gao; Yong Wang
2014-01-01
This paper is concerned with the problem of designing disturbance observer for fractional order systems, of which the disturbance is in time series expansion. The stability of a special observer with the selected nonlinear weighted function and transient dynamics function is rigorously analyzed for slowly varying disturbance. In addition, the result is also extended to estimate slope forms disturbance and higher order disturbance of fractional order systems. The efficacy of the proposed metho...
Dai, Hongzhe; Zheng, Zhibao; Wang, Wei
2017-08-01
In this paper, a novel fractional equivalent linearization (EL) approach is developed by incorporating a fractional derivative term into the classical linearization equation. Due to the introduction of the fractional derivative term, the accuracy of the new linearization is improved, illustrated by a Duffing oscillator that is subjected to a harmonic excitation. Furthermore, a new method for solving stochastic response of nonlinear SDOF system is developed by combining Karhunen-Loève (K-L) expansion and fractional EL. The method firstly decomposes the stochastic excitation in terms of a set of random variables and deterministic sub-excitations using K-L expansion, and then construct sub-fractional equivalent linear system according to each sub-excitation by fractional EL, the response of the original nonlinear system is finally approximated as the weighed summation of the deterministic response of each sub-system multiplied by the corresponding random variable. The random nature of the final response comes from the set of random variables that is obtained in K-L expansion. In this way, the stochastic response computation is converted to a set of deterministic response analysis problems. The effectiveness of the developed method is demonstrated by a Duffing oscillator that is subjected to stochastic excitation modeled by Winner process. The results are compared with the numerical method and Monte Carlo simulation (MCS).
Verification of somatic CAG repeat expansion by pre-PCR fractionation.
Hunter, Jesse M; Crouse, Andrew B; Lesort, Mathieu; Johnson, Gail V W; Detloff, Peter J
2005-05-15
The inheritance of a long CAG repeat causes several late onset neurological disorders including Huntington's disease (HD). Longer CAG repeats correlate with earlier onset of HD suggesting an increased toxicity for the products of long repeat alleles. PCR based data has been used to show that HD CAG repeat expansion beyond the inherited length occurs in affected tissues indicating a possible role for somatic instability in the disease process. PCR, however, is prone to artifacts resulting from expansion of repeat sequences during amplification. We describe a method to distinguish between CAG repeat expansions that exist in vivo and those that potentially occur during PCR. The method involves size fractionation of genomic restriction fragments containing the expanded repeats followed by PCR amplification. The application of this method confirms the presence of somatic expansions in the brains of a knock-in mouse model of HD.
Mode Conversion Losses in Expansion Units for ITER ECH Transmission Lines
Schaub, S. C.; Shapiro, M. A.; Temkin, R. J.; Hanson, G. R.
2016-01-01
The ITER electron cyclotron heating transmission lines will consist of 63.5-mm-diameter corrugated waveguides, each carrying 1 MW of 170 GHz microwaves. These transmission lines must include expansion units to accommodate expansion and contraction along the path from the gyrotron microwave sources to the tokamak. A numerical mode matching code has been developed to calculate power losses due to mode conversion of the operating mode, HE11, to higher order modes as a result of the radial discontinuities in a sliding joint. Two expansion unit designs were evaluated, a simple gap expansion unit and a more complex tapered expansion unit. The gap expansion unit demonstrated loss that oscillated rapidly with expansion length, due to trapped modes within the unit. The tapered expansion unit has been shown to effectively suppress these trapped modes at the expense of increased fabrication complexity. In a gap expansion unit, for a waveguide step size of 2.5 mm, loss can be kept below 0.1 % to a maximum expansion length of 17 mm. Expansion units without corrugation on interior walls were also evaluated. Expansion units that lack corrugations are found to increase mode trapping within the units, though not beyond useful application. The mode matching code developed in this paper was also used to estimate mode conversion loss in vacuum pumpouts for the ECH lines; the estimated loss was found to be negligibly small.
Periodicity of β-expansions for certain Pisot units*
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Rodrigues Pedro Martins
2012-08-01
Full Text Available Given β > 1, let Tβ egin{eqnarray} T_{eta}:[0,1[ & ightarrow& [0,1[ onumber\\ hspace*{0.5 cm} x & ightarrow & eta x -lfloor eta x floor. onumber end{eqnarray} T β : [ 0 , 1 [ → [ 0 , 1 [ x → βx − ⌊ βx ⌋ . The iteration of this transformation gives rise to the greedy β-expansion. There has been extensive research on the properties of this expansion and its dependence on the parameter β. In [17], K. Schmidt analyzed the set of periodic points of Tβ, where β is a Pisot number. In an attempt to generalize some of his results, we study, for certain Pisot units, a different expansion that we call linear expansion egin{eqnarray} x=sum_{i geq 0} e_i eta^{-i},onumber end{eqnarray} x = ∑ i ≥ 0 e i β − i , where each ei can be superior to ⌊ β ⌋, its properties and the relation with Per (β. Soit β > 1, considérons Tβ egin{eqnarray} T_{eta}:[0,1[ & ightarrow& [0,1[ onumber\\ hspace*{0.5 cm} x & ightarrow & eta x -lfloor eta x floor.onumber end{eqnarray} T β : [ 0 , 1 [ → [ 0 , 1 [ x → βx − ⌊ βx ⌋ . L’itération de cette transformation donne lieu à un développement en série en β. Il y a eu un grand nombre de recherches sur les propriétés de ce développement et de sa dépendance par rapport au paramètre β. Dans [17], K. Schmidt a analysé l’ensemble des points périodiques de Tβ, où β est un nombre de Pisot. Afin de généraliser certains de ces résultats, nous étudions, pour certains nombres de Pisot, un développement différent que nous appelons développement linéaire egin{eqnarray} x=sum_{i geq 0} e_i eta^{-i},onumber end{eqnarray} x = ∑ i ≥ 0 e i β − i , où chaque ei peut être supérieur à ⌊β⌋; nous étudions également ses propriétés et la relation avec Per (β.
Terminal Liquid Mass Fractions and Terminal Mean Droplet Sizes in He Free-Jet Expansions
Knuth, E. L.; Kornilov, O.; Toennies, J. P.
2011-05-01
The terminal liquid mass fraction in He free-jet expansions is deduced from time-of-flight measurements using conservation of energy. Both the present results and results from prior measurements are correlated using a scaling parameter which was used previously for correlating droplet size as a function of source conditions. Deduced values of the mass fraction range from 0.047 to 0.42. The terminal mean droplet size is determined using a novel technique based on a size-dependent attenuation of the beam droplets when impacted by electrons. The determined sizes are in agreement with sizes obtained previously by crossing the droplet beam with an atomic beam, confirming the suitability of the present technique, which is relatively simple in comparison with crossing the droplet beam with an atomic beam. Measured values of the terminal velocity of the droplets are compared with values calculated for a model in which real-fluid properties are used for the enthalpy in the source but conversion of heat of condensation into energy of directed motion is neglected. The deviations from perfect-gas behavior in free-jet expansions are shown to be due to real-fluid properties and condensation.
Bursik, J. W.; Hall, R. M.
1980-01-01
The saturated equilibrium expansion approximation for two phase flow often involves ideal-gas and latent-heat assumptions to simplify the solution procedure. This approach is well documented by Wegener and Mack and works best at low pressures where deviations from ideal-gas behavior are small. A thermodynamic expression for liquid mass fraction that is decoupled from the equations of fluid mechanics is used to compare the effects of the various assumptions on nitrogen-gas saturated equilibrium expansion flow starting at 8.81 atm, 2.99 atm, and 0.45 atm, which are conditions representative of transonic cryogenic wind tunnels. For the highest pressure case, the entire set of ideal-gas and latent-heat assumptions are shown to be in error by 62 percent for the values of heat capacity and latent heat. An approximation of the exact, real-gas expression is also developed using a constant, two phase isentropic expansion coefficient which results in an error of only 2 percent for the high pressure case.
Institute of Scientific and Technical Information of China (English)
ZHENG Bin
2012-01-01
In this paper, the ( G'/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.
Defining chemical expansion: the choice of units for the stoichiometric expansion coefficient
DEFF Research Database (Denmark)
Marrocchelli, Dario; Chatzichristodoulou, Christodoulos; Bishop, Sean R.
2014-01-01
Chemical expansion refers to the spatial dilation of a material that occurs upon changes in its composition. When this dilation is caused by a gradual, iso-structural increase in the lattice parameter with composition, it is related to the composition change by the stoichiometric expansion coeffi...... are provided for changes in oxygen content in fluorite, perovskite, and Ruddlesden-Popper (K2NiF4) phase materials used in solid oxide fuel cells....
Engel连分数展式与Huasdorff维数%Engel Continued Fraction Expansion and Hausdorff Dimension
Institute of Scientific and Technical Information of China (English)
张振亮
2011-01-01
In this paper,we study a exceptional set determined by partial quotients in its Engel continued fraction expansion and the set consisting of the points whose speed of convergence is faster than the "typical" points. By using the principle of mass distribution, we prove that the Hausdorff dimension of these sets are both one.%本文研究了Engel连分数中部分商以某种速度增长的集合,以及Engel连分数展式收敛速度较快的点组成的集合,利用质量分布原理,证明了这些集合的Haus-dorff维数为1.
Efficient Recursive Methods for Partial Fraction Expansion of General Rational Functions
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Youneng Ma
2014-01-01
Full Text Available Partial fraction expansion (pfe is a classic technique used in many fields of pure or applied mathematics. The paper focuses on the pfe of general rational functions in both factorized and expanded form. Novel, simple, and recursive formulas for the computation of residues and residual polynomial coefficients are derived. The proposed pfe methods require only simple pure-algebraic operations in the whole computation process. They do not involve derivatives when tackling proper functions and require no polynomial division when dealing with improper functions. The methods are efficient and very easy to apply for both computer and manual calculation. Various numerical experiments confirm that the proposed methods can achieve quite desirable accuracy even for pfe of rational functions with multiple high-order poles or some tricky ill-conditioned poles.
Indian Academy of Sciences (India)
EMRULLAH YA¸SAR; ILKER BURAK GIRESUNLU
2016-08-01
In this work, we present ($G' /G, 1/G$)-expansion method for solving fractional differential equations based on a fractional complex transform. We apply this method for solving space–time fractional Cahn--Allen equation and space--time fractional Klein–Gordon equation. The fractional derivatives are described in the sense of modified Riemann--Lioville. As a result of some exact solution in the form of hyperbolic, trigonometric and rational solutions are deduced. The obtained solutions may be used for explaining of some physical problems.The($G' /G, 1/G$)-expansion method has a wider applicability for nonlinear equations. We have verified all the obtained solutions with the aid of Maple.
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Ahmet Bekir
2014-09-01
Full Text Available In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear nonfractional ordinary differential equations. Then G′G-expansion method is applied to obtain exact solutions of the space-time fractional Burgers equation, the space-time fractional KdV-Burgers equation and the space-time fractional coupled Burgers’ equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation.
Numerical distribution functions of fractional unit root and cointegration tests
DEFF Research Database (Denmark)
MacKinnon, James G.; Nielsen, Morten Ørregaard
We calculate numerically the asymptotic distribution functions of likelihood ratio tests for fractional unit roots and cointegration rank. Because these distributions depend on a real-valued parameter, b, which must be estimated, simple tabulation is not feasible. Partly due to the presence...... of this parameter, the choice of model specification for the response surface regressions used to obtain the numerical distribution functions is more involved than is usually the case. We deal with model uncertainty by model averaging rather than by model selection. We make available a computer program which, given...
Memory Function Approach to Chaos and Turbulence and the Continued Fraction Expansion
Mori, H.; Kuroki, S.; Tominaga, H.; Ishizaki, R.
2004-05-01
The chaotic orbits of dynamical systems are deterministic and predictable on short timescales τr, but they become stochastic and random on long timescales τM(≫ τr) due to the orbital instability of chaos. This randomization of chaotic orbits has been formulated recently by deriving a non-Markovian stochastic equation for macrovariables in terms of a fluctuating force and a memory function. In order to develop this memory function approach to chaos and turbulence, we explore the following problems by studying the Duffing oscillator and the Navier-Stokes equation for an incompressible fluid: 1) the physical meaning of the projection of macrovariables A(t) onto A(0); 2) the method of calculating the short-lived motion with short timescale τr, which determines the memory functions and the macroscopic transport coefficients due to chaos and turbulence; 3) the continued fraction expansion of the memory function, and the order estimation of short timescales τr and long timescales τM; 4) the relation between the memory function and the time correlation function of a nonlinear force, which gives computable theoretical expressions for the macroscopic transport coefficients.
Hwang, Chyi; Guo, Tong-Yi; Shieh, Leang-San
1991-01-01
A canonical state-space realization based on the multipoint Jordan continued-fraction expansion (CFE) is presented for single-input-single-output (SISO) systems. The similarity transformation matrix which relates the new canonical form to the phase-variable canonical form is also derived. The presented canonical state-space representation is particularly attractive for the application of SISO system theory in which a reduced-dimensional time-domain model is necessary.
Commercial Application of UFR to VRDS Unit Expansion at Qilu Petrochemical Company
Institute of Scientific and Technical Information of China (English)
Sun Lili
2007-01-01
Technology and commercial application of UFR to VRDS unit expansion at Qilu Petrochemical Comply,for which engineering work was done by SINOPEC Engineering Incorporation(the former Beijing Design Institute),were introduced.Successful experience for the first commercial application of up-flow reactor technology and debottlenecking of the unit were summarized.The findings revealed a new route for inferior residue hydrotreating and revamping the existing units of the like.
An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order
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Ricardo Almeida
2013-01-01
Full Text Available We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type.
Sri Ranga, A.
1984-01-01
Just as the denominator polynomials of a J-fraction are orthogonal polynomials with respect to some moment functional, the denominator polynomials of an M-fraction are shown to satisfy a skew orthogonality relation with respect to a stronger moment functional. Many of the properties of the numerators and denominators of an M- fraction are also studied using this pseudo orthogonality relation of the denominator polynomials. Properties of the zeros of the denominator polyno...
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Bučanović Ljubiša J.
2014-01-01
Full Text Available This paper deals with the design of a new algorithm of PID control based on fractional calculus (FC in production of technical gases, i.e. in a cryogenic air separation process. Production of low pressure liquid air was first introduced by P. L. Kapica and involved expansion in a gas turbine. For application in the synthesis of the control law, for the input temperature and flow of air to the expansion turbine, it is necessary to determine the appropriate differential equations of the cryogenic process of mixing of two gaseous airflows at different temperatures before entrance to the expansion turbine. Thereafter, the model is linearized and decoupled and consequently classical PID and fractional order controllers are taken to assess the quality of the proposed technique. A set of optimal parameters of these controllers are achieved through the genetic algorithm optimization procedure by minimizing a cost function. Our design method focuses on minimizing performance criterion which involves IAE, overshoot, as well as settling time. A time-domain simulation was used to identify the performance of controller with respect to a traditional optimized PID controller. [Projekat Ministarstva nauke Republike Srbije, br. 35006
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Dale Bruce E
2009-11-01
Full Text Available Abstract Background Corn stover composition changes considerably throughout the growing season and also varies between the various fractions of the plant. These differences can impact optimal pretreatment conditions, enzymatic digestibility and maximum achievable sugar yields in the process of converting lignocellulosics to ethanol. The goal of this project was to determine which combination of corn stover fractions provides the most benefit to the biorefinery in terms of sugar yields and to determine the preferential order in which fractions should be harvested. Ammonia fiber expansion (AFEX pretreatment, followed by enzymatic hydrolysis, was performed on early and late harvest corn stover fractions (stem, leaf, husk and cob. Sugar yields were used to optimize scenarios for the selective harvest of corn stover assuming 70% or 30% collection of the total available stover. Results The optimal AFEX conditions for all stover fractions, regardless of harvest period, were: 1.5 (g NH3 g-1 biomass; 60% moisture content (dry-weight basis; dwb, 90°C and 5 min residence time. Enzymatic hydrolysis was conducted using cellulase, β-glucosidase, and xylanase at 31.3, 41.3, and 3.1 mg g-1 glucan, respectively. The optimal harvest order for selectively harvested corn stover (SHCS was husk > leaf > stem > cob. This harvest scenario, combined with optimal AFEX pretreatment conditions, gave a theoretical ethanol yield of 2051 L ha-1 and 912 L ha-1 for 70% and 30% corn stover collection, respectively. Conclusion Changing the proportion of stover fractions collected had a smaller impact on theoretical ethanol yields (29 - 141 L ha-1 compared to the effect of altering pretreatment and enzymatic hydrolysis conditions (150 - 462 L ha-1 or harvesting less stover (852 - 1139 L ha-1. Resources may be more effectively spent on improving sustainable harvesting, thereby increasing potential ethanol yields per hectare harvested, and optimizing biomass processing rather than
Zhang, Qinghui; Song, Yulin; Burman, Chandra
2012-01-01
Purpose: To derive a clinical margin formula between clinical target volume (CTV) and planning target volume (PTV) for single-fraction stereotactic radiosurgery (SRS). Methods: In previous publications on the margin between CTV and PTV, a Gaussian function with zero mean sys-tematic error was assumed for systematic errors and the machine systematic error was ignored; in this work we pre-sumed a Dirac delta function for the machine systematic error for a given machine and nonzero mean systematic error was assumed. Mathematical formulas for calculating the CTV-PTV margin for single-fraction SRS cases was proposed. Results: Margins for single fraction treatment were derived such that the CTV receives the prescribed dose in 95% of SRS patients. The margins defined in this study were machine specific and account for nonzero mean systematic error. The differences between our formulas and a previously published formula were discussed. Conclusion: Clinical margin formulas are proposed for determining the margin betwe...
Pinnola, Francesco Paolo
2016-10-01
The statistical characterization of the oscillator response with non-integer order damping under Gaussian noise represents an important challenge in the modern stochastic mechanics. In fact, this kind of problem appears in several issues of different type (wave propagation in viscoelastic media, Brownian motion, fluid dynamics, RLC circuit, etc.). The aim of this paper is to provide a stochastic characterization of the stationary response of linear fractional oscillator forced by normal white noise. In particular, this paper shows a new method to obtain the correlation function by exact complex spectral moments. These complex quantities contain all the information to describe the random processes but in the considered case their analytical evaluation needs some mathematical manipulations. For this reason such complex spectral moment characterization is used in conjunction with a fractional-order state variable analysis. This kind of analysis permits to find the exact expression of complex spectral moments, and the correlation function by using the Mellin transform. Moreover, the proposed approach provides an analytical expression of the response variance of the fractional oscillator. Capability and efficiency of the present method are shown in the numerical examples in which correlation and variance of fractional oscillator response are found and compared with those obtained by Monte Carlo simulations.
Institute of Scientific and Technical Information of China (English)
Jun Wan; Ze Wang; Hezhong Yuan
2010-01-01
Phosphorous (P) fraction characteristics in sediment resuspension were investigated under adequately hydrodynamic conditions.Four forms of P in overlying water,including dissolved inorganic P,dissolved total P,total P,and particulate P,and six fractions of P in suspended particulate matter (SPM),including loosely sorbed P (NH4Cl-P),redox-sensitive P (BD-P),aluminum-bound P (Al-P),organic P (NaOH-nrP),calcium-bound P (Ca-P) and residual P (Res-P),were quantified,respectively.Different hydrodynamic conditions resulted in different P form changes.Four states could be ascribed:(1) P desorption by sediment and SPM,and P adsorption by overlying water;(2) P desorption by SPM,and P adsorption by overlying water;(3) P adsorption by SPM,and P desorption by overlying water;and (4) P equilibrium between SPM and overlying water.The contents of P in overlying water acquired peak values in the middle position of the vertical P distribution due to the combined actions of SPM and sediment.P fractions in SPM were in the following order:BD-P＞NaOH-nrp＞Ca-P＞Al-P＞Res-P＞NH4CI-P.BD-P in SPM frequently exchanged with P forms in overlying water.Resuspension was favorable to forming Ca-P in SPM.
Synthesis, Structure, and Rigid Unit Mode-like Anisotropic Thermal Expansion of BaIr2In9.
Calta, Nicholas P; Han, Fei; Kanatzidis, Mercouri G
2015-09-08
This Article reports the synthesis of large single crystals of BaIr2In9 using In flux and their characterization by variable-temperature single-crystal and synchrotron powder X-ray diffraction, resistivity, and magnetization measurements. The title compound adopts the BaFe2Al9-type structure in the space group P6/mmm with room temperature unit cell parameters a = 8.8548(6) Å and c = 4.2696(4) Å. BaIr2In9 exhibits anisotropic thermal expansion behavior with linear expansion along the c axis more than 3 times larger than expansion in the ab plane between 90 and 400 K. This anisotropic expansion originates from a rigid unit mode-like mechanism similar to the mechanism of zero and negative thermal expansion observed in many anomalous thermal expansion materials such as ZrW2O8 and ScF3.
Maximizing negative thermal expansion via rigid unit modes: a geometry-based approach.
Grima, J N; Bajada, M; Scerri, S; Attard, D; Dudek, K K; Gatt, R
2015-07-08
Existent rigid unit mode (RUM) models based on rotating squares, which may explain the phenomenon of negative thermal expansion (NTE), are generalized so as to assess the NTE potential for novel systems made from rectangular or rhombic rigid units. Analytical models for the area coefficients of thermal expansion (CTE) of these innovative networks are derived in an attempt to determine the optimal geometrical parameters and connectivity for maximum NTE. It was found that all systems exhibit NTE, the extent of which is determined by the shape and connectivity of the elemental rigid units (side lengths ratio or internal angle). It was also found that some of the networks proposed here should exhibit significantly superior NTE properties when compared with the well-known network of squares, and that for optimal NTE characteristics, pencil-like rigid units should be used rather than square-shaped ones, as these permit larger pore sizes that are more conducive to NTE. All this compliments earlier work on the negative Poisson's ratio (auxetic) potential of such systems and may provide a route for the design of new materials exhibiting superior thermo-mechanical characteristics including specifically tailored CTEs or giant NTE characteristics.
Realization of fractional-order Liu chaotic system by a new circuit unit
Institute of Scientific and Technical Information of China (English)
Xu Zhe; Liu Chong-Xin
2008-01-01
A new circuit unit for the analysis and the synthesis of the chaotic behaviours in a fractional-order Liu system is proposed in this paper.Based on the approximation theory of fractional-order operator,an electronic circuit is designed to describe the dynamic behaviours of the fractional-order Liu system with a=0.9.The results between simulation and experiment are in good agreement with each other,thereby proving that the chaos exists indeed in the fractional-order Liu system.
Geographic Expansion of Lyme Disease in the Southeastern United States, 2000-2014.
Lantos, Paul M; Nigrovic, Lise E; Auwaerter, Paul G; Fowler, Vance G; Ruffin, Felicia; Brinkerhoff, R Jory; Reber, Jodi; Williams, Carl; Broyhill, James; Pan, William K; Gaines, David N
2015-12-01
Background. The majority of Lyme disease cases in the United States are acquired on the east coast between northern Virginia and New England. In recent years the geographic extent of Lyme disease has been expanding, raising the prospect of Lyme disease becoming endemic in the southeast. Methods. We collected confirmed and probable cases of Lyme disease from 2000 through 2014 from the Virginia Department of Health and North Carolina Department of Public Health and entered them in a geographic information system. We performed spatial and spatiotemporal cluster analyses to characterize Lyme disease expansion. Results. There was a marked increase in Lyme disease cases in Virginia, particularly from 2007 onwards. Northern Virginia experienced intensification and geographic expansion of Lyme disease cases. The most notable area of expansion was to the southwest along the Appalachian Mountains with development of a new disease cluster in the southern Virginia mountain region. Conclusions. The geographic distribution of Lyme disease cases significantly expanded in Virginia between 2000 and 2014, particularly southward in the Virginia mountain ranges. If these trends continue, North Carolina can expect autochthonous Lyme disease transmission in its mountain region in the coming years.
Tasbozan, Orkun; Çenesiz, Yücel; Kurt, Ali
2016-07-01
In this paper, the Jacobi elliptic function expansion method is proposed for the first time to construct the exact solutions of the time conformable fractional two-dimensional Boussinesq equation and the combined KdV-mKdV equation. New exact solutions are found. This method is based on Jacobi elliptic functions. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.
DiGiulio, Anne; Haddix, Meredith; Jump, Zach; Babb, Stephen; Schecter, Anna; Williams, Kisha-Ann S; Asman, Kat; Armour, Brian S
2016-12-09
In 2015, 27.8% of adult Medicaid enrollees were current cigarette smokers, compared with 11.1% of adults with private health insurance, placing Medicaid enrollees at increased risk for smoking-related disease and death (1). In addition, smoking-related diseases are a major contributor to Medicaid costs, accounting for about 15% (>$39 billion) of annual Medicaid spending during 2006-2010 (2). Individual, group, and telephone counseling and seven Food and Drug Administration (FDA)-approved medications are effective treatments for helping tobacco users quit (3). Insurance coverage for tobacco cessation treatments is associated with increased quit attempts, use of cessation treatments, and successful smoking cessation (3); this coverage has the potential to reduce Medicaid costs (4). However, barriers such as requiring copayments and prior authorization for treatment can impede access to cessation treatments (3,5). As of July 1, 2016, 32 states (including the District of Columbia) have expanded Medicaid eligibility through the Patient Protection and Affordable Care Act (ACA),*(,†) which has increased access to health care services, including cessation treatments (5). CDC used data from the Centers for Medicare and Medicaid Services (CMS) Medicaid Budget and Expenditure System (MBES) and the Behavioral Risk Factor Surveillance System (BRFSS) to estimate the number of adult smokers enrolled in Medicaid expansion coverage. To assess cessation coverage among Medicaid expansion enrollees, the American Lung Association collected data on coverage of, and barriers to accessing, evidence-based cessation treatments. As of December 2015, approximately 2.3 million adult smokers were newly enrolled in Medicaid because of Medicaid expansion. As of July 1, 2016, all 32 states that have expanded Medicaid eligibility under ACA covered some cessation treatments for all Medicaid expansion enrollees, with nine states covering all nine cessation treatments for all Medicaid expansion
Energy Technology Data Exchange (ETDEWEB)
Aoyama, Hidefumi, E-mail: h-aoyama@med.niigata-u.ac.jp [Department of Radiation Medicine, Hokkaido University Graduate School of Medicine, Sapporo (Japan); Department of Radiology, Division of Radiation Oncology, Niigata University Graduate School of Medical and Dental Sciences, Niigata (Japan); Onodera, Shunsuke [Department of Radiation Medicine, Hokkaido University Graduate School of Medicine, Sapporo (Japan); Takeichi, Norihito [Department of Otolaryngology, Hokkaido University Graduate School of Medicine, Sapporo (Japan); Onimaru, Rikiya [Department of Radiation Medicine, Hokkaido University Graduate School of Medicine, Sapporo (Japan); Terasaka, Shunsuke; Sawamura, Yutaka [Department of Neurosurgery, Hokkaido University Graduate School of Medicine, Sapporo (Japan); Shirato, Hiroki [Department of Radiation Medicine, Hokkaido University Graduate School of Medicine, Sapporo (Japan)
2013-02-01
Purpose: The effect of transient tumor expansion after conventionally fractionated stereotactic radiation therapy (SRT) on the symptomatic outcomes is not well-known. Methods and Materials: This study enrolled 201 consecutive patients who received SRT for vestibular schwannoma. A conventional fractionation schedule was applied in 194 patients (97%), and 142 (71%) received a total dose of 50 Gy. The median follow-up time was 72 months. Results: The maximum diameter was 9 mm or less in 13 patients, 10-19 mm in 79 patients, 20-29 mm in 87 patients, and 30 mm or greater in 22 patients. At presentation, tumor size of 20 mm or greater was significantly associated with loss of serviceable hearing and trigeminal neuropathy. After SRT, tumor expansion was observed in 42 patients (21%). By tumor size, tumor expansion was observed in 0%, 11.4%, 25.6%, and 50% of patients with tumors of 9 mm or less, 10-19 mm, 20-29 mm, and 30 mm or greater, respectively, in diameter. The tumor expansion was significantly associated with an increased risk of hydrocephalus requiring shunt placement (P=.004), loss of serviceable hearing (P=.0064), and worsening of facial (P<.0001) and trigeminal nerve (P<.0001) functions. Spontaneous tumor shrinkage was observed in 29 of those 42 patients, mostly within 2 years after the expansion, and the majority of the worsened symptoms except for hearing resolved once the tumor had shrunk. As a result, salvage surgical resection for symptomatic relief was required in only 5% of patients. Conclusions: Fractionated SRT could be safely applied even for medium- to large-sized ({>=}20 mm) tumors. However, greater knowledge of the risks and consequences, including transient symptomatic worsening, and the time span of expansion will be required for the follow-up of patients after SRT to avoid unnecessary surgical intervention.
Lasjaunias, Alain
2010-01-01
In 1985, Robbins observed by computer the continued fraction expansion of certain algebraic power series over a finite field. Incidentally, he came across a particular equation of degree 4 in characteristic p=13. This equation has an analogue for all primes p>=5. There are two patterns for the continued fraction of the solution of this equation, according to the residue of p modulo 3. We describe this pattern in the first case, considering especially p=7 and p=13. in the second case we only give indications.
Hackenberg, Amy J.
2007-01-01
This article communicates findings from a year-long constructivist teaching experiment about the relationship between four sixth-grade students' multiplicative structures and their construction of improper fractions. Students' multiplicative structures are the units coordinations that they can take as given prior to activity--i.e., the units…
Institute of Scientific and Technical Information of China (English)
Liu Xiaosong; Liu Taishun
2009-01-01
In this article, the authors obtain an inequality of homogeneous expansion for f, where f is a quasi-convex mapping (including quasi-convex mapping of type A and quasi-convex mapping of type B) defined on the open unit polydisk in Cn. Meanwhile, the authors also investigate its application.
Cortina, Jose Luis; Visnovska, Jana; Zuniga, Claudia
2014-01-01
We analyze a classroom design experiment, conducted in a fourth grade classroom, that served to explore an instructional path in which the introduction of unit fractions and supporting proportional reasoning coincide. Central to this path is the use of means of support in which the objects that unit fractions quantify are not characterized as…
Lamancusa, Carmen; Parvez, Fatema; Wagstrom, Kristina
2017-02-01
This study uses intake fraction, the fraction of emissions that are inhaled from a given source, to quantify how emissions from different regions proportionally contribute to human exposure to both primary and secondary particulate matter species. The intake fraction for secondary species is defined using the common atomic constituents between precursor species and products, allowing estimates to include both primary and secondary species. The Particulate Matter Source Apportionment Technology (PSAT) in the Comprehensive Air Quality Model with Extensions (CAMx) regional air quality model is used to calculate the intake fraction for twenty-five source regions throughout the contiguous United States over four seasons. The calculations use spatially explicit emissions and population density to more accurately capture the variation in intake fraction between regions. The spatially explicit emissions allow for the calculation of spatial trends and variations within the intake fraction. More specifically it allows for the calculation of the amount of intake that occurs within a given distance of the emissions source or source region. Based on the results sulfate inhalation occurs over larger distances than other particulate matter species. For most regions, a substantial fraction (>75%) of the inhalation occurs within 50 km for all seasons, demonstrating that efforts to reduce emissions will have the largest health impact on the local community. Furthermore the distance over which 75% of the inhalation occurs increases by 20% for all species during the winter and a larger percentage of pollutants emitted during the winter are inhaled relative to pollutants emitted during other seasons. This demonstrates that emission reductions during the winter will have a greater impact on health than reductions during other seasons.
Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G′/G-Expansion Method
Directory of Open Access Journals (Sweden)
Muhammad Shakeel
2014-01-01
Full Text Available The fractional derivatives are used in the sense modified Riemann-Liouville to obtain exact solutions for BBM-Burger equation of fractional order. This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. The performance of the method is reliable, useful, and gives newer general exact solutions with more free parameters than the existing methods. Numerical results coupled with the graphical representation completely reveal the trustworthiness of the method.
Crystal fractionation in the SNC meteorites: Implications for surface units on Mars
Treiman, Allan H.
1987-01-01
Almost all rock types in the SNC meteorites are cumulates, products of magma differentiation by crystal fractionation (addition or removal of crystals). If the SNC meteorites are from the surface of Mars or near sub-surface, then most of the igneous units on Mars are differentiated. Basaltic units probably experienced minor to moderate differentiation, but ultrabasic units probably experienced extreme differentiation. Products of this differentiation may include Fe-rich gabbro, pyroxenite, peridotite (and thus serpentine), and possibly massive sulfides. The SNC meteorites include ten lithologies (three in EETA79001), eight of which are crystal cumulates. The other lithologies, EETA79001 A and B are subophitic basalts. The cumulate lithologies ALHA77005 and EETA79001 C were not fully described or discussed.
On the conversion of tritium units to mass fractions for hydrologic applications.
Stonestrom, David A; Andraski, Brian J; Cooper, Clay A; Mayers, C Justin; Michel, Robert L
2013-06-01
We develop a general equation for converting laboratory-reported tritium levels, expressed either as concentrations (tritium isotope number fractions) or mass-based specific activities, to mass fractions in aqueous systems. Assuming that all tritium is in the form of monotritiated water simplifies the derivation and is shown to be reasonable for most environmental settings encountered in practice. The general equation is nonlinear. For tritium concentrations c less than 4.5 × 10(12) tritium units (TU) - i.e. specific tritium activitiestritium isotopes in the absence of sample-specific data. Variation in the relative abundances of non-tritium isotopes in the terrestrial hydrosphere produces a minimum range for the mantissa of the conversion factor of [2.22287; 2.22300].
Stereotactic radiotherapy of the prostate: fractionation and utilization in the United States
Energy Technology Data Exchange (ETDEWEB)
Weiner, Josph P.; Schwartz, David; Shao, Meng; Osborn, Virginia; Schreiber, David [Dept. of Radiation Oncology, Veterans Affairs New York Harbor Healthcare System, Brooklyn (United States); Choi, Kwang [Dept. of Radiation Oncology, SUNY Downstate Medical Center, Brooklyn (United States)
2017-06-15
To analyze the utilization and fractionation of extreme hypofractionation via stereotactic body radiotherapy (SBRT) in the treatment of prostate cancer. Data was analyzed on men diagnosed with localized prostate cancer between 2004–2012 and treated with definitive-intent radiation therapy, as captured in the National Cancer Database. This database is a hospital-based registry that collects an estimated 70% of all diagnosed malignancies in the United States. There were 299,186 patients identified, of which 4,962 (1.7%) were identified as receiving SBRT as primary treatment. Of those men, 2,082 had low risk disease (42.0%), 2,201 had intermediate risk disease (44.4%), and 679 had high risk disease (13.7%). The relative utilization of SBRT increased from 0.1% in 2004 to 4.0% in 2012. Initially SBRT was more commonly used in academic programs, though as time progressed there was a shift to favor an increased absolute number of men treated in the community setting. Delivery of five separate treatments was the most commonly utilized fractionation pattern, with 4,635 patients (91.3%) receiving this number of treatments. The most common dosing pattern was 725 cGy × 5 fractions (49.6%) followed by 700 cGy × 5 fractions (21.3%). Extreme hypofractionation via SBRT is slowly increasing acceptance. Currently 700-725 cGy × 5 fractions appears to be the most commonly employed scheme. As further long-term data regarding the safety and efficacy emerges, the relative utilization of this modality is expected to continue to increase.
Data on burden of comorbidities in the united states and medicaid expansion status
Directory of Open Access Journals (Sweden)
Tomi Akinyemiju
2016-09-01
Full Text Available The high prevalence of comorbidities among US adults is a major public health problem. However, there is limited data on the geographic distribution of comorbidities. In addition, recent changes to health insurance programs in the US through the Affordable Care Act, and the Medicaid expansion program specifically, has the potential to significantly improve the prevention and management of comorbid conditions in the US. In a recent analysis, we examined disparities in the burden of comorbidities among US adults by state Medicaid expansion status, (Akinyemiju et al., 2016 [1]. Here, we provide additional data showing the state level mean number of comorbidities in all 50 US states for African–Americans and whites, stratified by Medicaid expansion status. In addition, we provide a map of the US states showing the geographic distribution of comorbidities and stratified by race/ethnicity and gender.
On the conversion of tritium units to mass fractions for hydrologic applications
Stonestrom, David A.; Andraski, Brain J.; Cooper, Clay A.; Mayers, Charles J.; Michel, Robert L.
2013-01-01
We develop a general equation for converting laboratory-reported tritium levels, expressed either as concentrations (tritium isotope number fractions) or mass-based specific activities, to mass fractions in aqueous systems. Assuming that all tritium is in the form of monotritiated water simplifies the derivation and is shown to be reasonable for most environmental settings encountered in practice. The general equation is nonlinear. For tritium concentrations c less than 4.5×1012 tritium units (TU) - i.e. specific tritium activities11 Bq kg-1 - the mass fraction w of tritiated water is approximated to within 1 part per million by w ≈ c×2.22293×10-18, i.e. the conversion is linear for all practical purposes. Terrestrial abundances serve as a proxy for non-tritium isotopes in the absence of sample-specific data. Variation in the relative abundances of non-tritium isotopes in the terrestrial hydrosphere produces a minimum range for the mantissa of the conversion factor of [2.22287; 2.22300].
Hunt, Jessica Heather; Tzur, Ron; Westenskow, Arla
2016-01-01
The literature seems limited in what is known about conceptual processes that underlie evolution of students with learning disabilities (SLD) conceptions of fractions. This exploratory study examines how a foundational scheme of unit fractions (1/n) may evolve through the mathematical activity of two fifth grade girls. We analyze data segments…
Directory of Open Access Journals (Sweden)
Kênia Barreiro de Souza
2016-05-01
Full Text Available The service sector expansion has shown to be a multiple trend process, producing distinct sectorial compositions. The present paper aims to make a comparison between two large economies in different stages of development with an extensive service sector (Brazil and United States, by focusing on final and intermediary demand changes and sectorial productivity as well. Input–output matrices for Brazil and United States were used and two applications were carried out: structural decomposition analysis and total factor productivity. Main results are as follows. Firstly, the growth in services was fostered by several factors, among which household consumption assumes an important role for both countries. Second, inter-industrial linkages play a major role only for United States. Thirdly, there is now evidence of cost disease for Brazil. Finally, productivity is lower in Brazil, nonetheless labor productivity increased above the average in some service sectors.
Fossil and Contemporary Fine Carbon Fractions at 12 Rural and Urban Sites in the United States
Energy Technology Data Exchange (ETDEWEB)
Schichtel, B; Malm, W; Bench, G; Fallon, S; McDade, C; Chow, J
2007-03-01
Fine particulate matter collected at two urban, four near-urban, and six remote sites throughout the United States were analyzed for total carbon (TC) and radiocarbon ({sup 14}C). Samples were collected at most sites for both a summer and winter season. The radiocarbon was used to partition the TC into fossil and contemporary fractions. On average, contemporary carbon composed about half of the carbon at the urban, {approx}70-97% at near-urban, and 82-100% at remote sites. At Phoenix, Arizona, and Seattle, Washington, one monitor was located within the urban center and one outside to assess the urban excess over background concentrations. During the summer the urban and rural sites had similar contemporary carbon concentrations. However, during the winter the urban sites had more than twice the contemporary carbon measured at the neighboring sites, indicating anthropogenic contributions to the contemporary carbon. The urban fossil carbon was 4-20 times larger than the neighboring rural sites for both seasons. Organic (OC) and elemental carbon (EC) from TOR analysis were available. These and the radiocarbon data were used to estimate characteristic fossil and contemporary EC/TC ratios for the winter and summer seasons. These ratios were applied to carbon data from the Interagency Monitoring of Protected Visual Environments network to estimate the fraction of contemporary carbon at mostly rural sites throughout the United States. In addition, the ratios were used to develop a semiquantitative, lower bound estimate of secondary organic carbon (SOC) contribution to fossil and contemporary carbon. SOC accounted for more than one-third of the fossil and contemporary carbon.
Institute of Scientific and Technical Information of China (English)
施惠元; 苏成利; 曹江涛; 李平; 宋英莉; 李宁波
2015-01-01
The control of gas fractionation unit (GFU) in petroleum industry is very difficult due to multivariable characteristics and a large time delay. PID controllers are still applied in most industry processes. However, the traditional PID control has been proven not sufficient and capable for this particular petro-chemical process. In this work, an incremental multivariable predictive functional control (IMPFC) algorithm was proposed with less online computation, great precision and fast response. An incremental transfer function matrix model was set up through the step-response data, and predictive outputs were deduced with the theory of single-value optimization. The results show that the method can optimize the incremental control variable and reject the constraint of the incremental control variable with the positional predictive functional control algorithm, and thereby making the control variable smoother. The predictive output error and future set-point were approximated by a polynomial, which can overcome the problem under the model mismatch and make the predictive outputs track the reference trajectory. Then, the design of incremental multivariable predictive functional control was studied. Simulation and application results show that the proposed control strategy is effective and feasible to improve control performance and robustness of process.
Brightwell, R J; Labadie, P E; Silverman, J
2010-10-01
The invasive Argentine ant, Linepithema humile (Mayr) (Hymenoptera: Formicidae) has been evident in the North Carolina Piedmont, United States for 90 yr but has failed to spread further north. We investigated the mechanisms preventing this expansion. The Argentine ant ceases foraging at temperatures below 5°C and we hypothesized that winter soil temperatures at higher latitudes restricted foraging long enough to cause colony starvation. We tested if the Argentine ant could successfully feed at temperatures below 5°C and found that colonies would starve. We subjected Argentine ant nests to a range of sub- and above-freezing temperatures and measured worker mortality at various time intervals. We found that Argentine ant colonies will collapse after 8.5 d at 5°C. Argentine ants can escape ambient cold temperatures by moving nests into the soil column. We tested how deeply into the soil Argentine ant queens and workers need to move to survive winter in North Carolina. Soil temperatures in the North Carolina Piedmont do not fall below 5°C for longer than nine consecutive days; therefore, Argentine ant colonies need only to retreat a few centimeters into the soil column to escape unsuitable temperatures. Winter soil temperature data from four climate stations situated from latitudes 35°, the current Eastern United States latitudinal limit for Argentine ant population expansion, to 39° were searched for periods where soil temperatures would have led to colony extirpation. North of their current distributions, extended periods of soil temperatures below 5°C regularly occur, preventing Argentine ant colonies from persisting.
Study on Expansion of Steam Cracking Unit to 660 kt/a at Yanshan Petrochemical Company
Institute of Scientific and Technical Information of China (English)
Cao Xianghong
2003-01-01
Yanshan Petrochemical Company after having expanded its 300 kt/a steam cracking unit to 450 kt/a in 1994 is still experiencing such problems as low feedstock flexibility, high energy consumption and smaller scale of ethylene unit. In order to fully improve technical capability of steam crackers, reduce energy consumption, improve feedstock flexibility and increase production capacity, a lot of technical revamp cases on steam cracking were studied and compared. Revamp of relevant facilities has expanded the ethylene capacity to the target of 660 kt/a with the actual capacity reaching 710 kt/a. This revamp project has remarkably reduced the energy consumption, which is capable of using naphtha, light diesel fuel, heavy diesel fuel and the hydrocracked tail oil as the steam cracking feedstock. This project is the first to apply refrigeration by means of a mixed cooling agent and has succeeded in using C3 catalytic rectification/hydrogenation technology, which has given an impetus to the progress of steam cracking industry in the world.
Urian, Alyson G; Hatle, John D; Gilg, Matthew R
2011-01-01
Cold temperatures are thought to be among the most important determining factors of geographic distribution for tropical and sub-tropical marine invertebrates. The Asian green mussel, Perna viridis, has been introduced into coastal waters of Florida where its current distribution is hypothesized to be limited by low temperatures during winter. Lethal and sub-lethal effects (heat shock protein/Hsp70 expression) of cold water and air temperatures were analyzed in two size classes of P. viridis from Florida in an effort to determine the effects of current and forecasted temperatures on the potential for range expansion. Mussels were exposed to water temperatures of 14, 10, 7 and 3°C for up to 30 days, or to air temperatures of 14, 7, 0 and -10°C for periods of 2 hr. Mortality was significantly increased at all water and air temperatures ≤14°C. No differences in mortality rates were observed between small (15-45 mm) and large (75-105 mm) size classes except after exposure to 7°C air, in which small mussels had higher mortality. Significant increases in Hsp70 expression were observed after a 2-hour exposure to 10°C water, but Hsp70 expression was not significantly increased at any temperatures in which mortality was not also significant. The temperature threshold for survival in this population appears to be between 10 and 14°C, suggesting that under current conditions P. viridis may already be at the northern edge of its potential range in the United States. If water temperatures increase with global climate change, northerly flowing currents may permit range expansion as temperatures allow. Copyright © 2010 Wiley-Liss, Inc., A Wiley Company.
Directory of Open Access Journals (Sweden)
Seong Yeon Chang
2017-01-01
Full Text Available This paper considers testing procedures for the null hypothesis of a unit root process against the alternative of a fractional process, called a fractional unit root test. We extend the Lagrange Multiplier (LM tests of Robinson (1994 and Tanaka (1999, which are locally best invariant and uniformly most powerful, to allow for a slope change in trend with or without a concurrent level shift under both the null and alternative hypotheses. We show that the limit distribution of the proposed LM tests is standard normal. Finite sample simulation experiments show that the tests have good size and power. As an empirical analysis, we apply the tests to the Consumer Price Indices of the G7 countries.
Directory of Open Access Journals (Sweden)
Chun-Lang Yeh
2016-11-01
Full Text Available Sulfur recovery unit (SRU thermal reactors are negatively affected by high temperature operation. In this paper, the effect of the fuel mass fraction on the combustion and fluid flow in a SRU thermal reactor is investigated numerically. Practical operating conditions for a petrochemical corporation in Taiwan are used as the design conditions for the discussion. The simulation results show that the present design condition is a fuel-rich (or air-lean condition and gives acceptable sulfur recovery, hydrogen sulfide (H2S destruction, sulfur dioxide (SO2 emissions and thermal reactor temperature for an oxygen-normal operation. However, for an oxygen-rich operation, the local maximum temperature exceeds the suggested maximum service temperature, although the average temperature is acceptable. The high temperature region must be inspected very carefully during the annual maintenance period if there are oxygen-rich operations. If the fuel mass fraction to the zone ahead of the choke ring (zone 1 is 0.0625 or 0.125, the average temperature in the zone behind the choke ring (zone 2 is higher than the zone 1 average temperature, which can damage the downstream heat exchanger tubes. If the zone 1 fuel mass fraction is reduced to ensure a lower zone 1 temperature, the temperature in zone 2 and the heat exchanger section must be monitored closely and the zone 2 wall and heat exchanger tubes must be inspected very carefully during the annual maintenance period. To determine a suitable fuel mass fraction for operation, a detailed numerical simulation should be performed first to find the stoichiometric fuel mass fraction which produces the most complete combustion and the highest temperature. This stoichiometric fuel mass fraction should be avoided because the high temperature could damage the zone 1 corner or the choke ring. A higher fuel mass fraction (i.e., fuel-rich or air-lean condition is more suitable because it can avoid deteriorations of both zone 1
Fractional complex transforms for fractional differential equations
National Research Council Canada - National Science Library
Ibrahim, Rabha W
2012-01-01
The fractional complex transform is employed to convert fractional differential equations analytically in the sense of the Srivastava-Owa fractional operator and its generalization in the unit disk...
Institute of Scientific and Technical Information of China (English)
Liu Xiaosong; Liu Taishun
2012-01-01
In this article,first,a sufficient condition for a starlike mapping of order α f(x) defined on the unit ball in a complex Banach space is given. Second,the sharp estimate of the third homogeneous expansion for f is established as well,where f(z) =(f1(z),f2(z),…,fn(z))' is a starlike mapping of order α or a normalized biholomorphic starlike mapping defined on the unit polydisk in Cn,and D2fk(0)(z2)/2 =zk(nΣl=1 aklzl),k =1,2,…,n,here,akl =1/2!(6)2fk(0)/(6)zk(6)zl,k,l==1,2,…,n.Our result states that the Bieberbach conjecture in several complex variables (the case of the third homogeneous expansion for starlike mappings of order α and biholomorphic starlike mappings) is partly proved.
Nutritionally important starch fractions of rice cultivars grown in southern United States.
Patindol, James A; Guraya, Harmeet S; Champagne, Elaine T; McClung, Anna M
2010-06-01
Dietary starches can be classified into 3 major fractions according to in vitro digestibility as rapidly digestible (RDS), slowly digestible (SDS), and resistant starch (RS). Literature indicates that SDS and/or RS have significant implications on human health, particularly glucose metabolism, diabetes management, colon cancer prevention, mental performance, and satiety. In this study, the nutritionally important starch fractions (RDS, SDS, and RS) in cooked rice were assayed in vitro, making use of 16 cultivars grown in 5 southern U.S. rice growing locations (Arkansas, Louisiana, Mississippi, Missouri, and Texas). RDS, SDS, and RS were 52.4% to 69.4%, 10.3% to 26.6%, and 1.2% to 9.0%, respectively, of cooked rice dry weight. Cultivar, location, and cultivar-by-location interaction contributed to the variations in RDS, SDS, and RS contents. Means pooled across locations indicated that SDS was higher for the Louisiana samples than those from Texas, whereas RS was higher for the Texas samples than those from Arkansas, Louisiana, and Mississippi. Some cultivars were identified to possess high levels of RS (for example, Bowman and Rondo) or SDS (for example, Dixiebelle and Tesanai-2) and were also stable across growing locations. Apparent amylose content correlated positively with RS (n = 80, r = 0.54, P 0.05). RS and SDS were not collinear (n = 80, r =or-0.18, P > 0.05); it does not follow that a cultivar high in RS will also be high in SDS, and vice versa. The observed differences in RDS, SDS, and RS among the samples are indicative of wide genetic diversity in rice.
Energy Technology Data Exchange (ETDEWEB)
Rutter, Charles E., E-mail: charles.rutter@yale.edu [Department of Therapeutic Radiology, Yale School of Medicine, New Haven, Connecticut (United States); Yale Cancer Center, New Haven, Connecticut (United States); Yu, James B.; Wilson, Lynn D.; Park, Henry S. [Department of Therapeutic Radiology, Yale School of Medicine, New Haven, Connecticut (United States); Yale Cancer Center, New Haven, Connecticut (United States)
2015-03-01
Purpose: To characterize temporal trends in the application of various bone metastasis fractionations within the United States during the past decade, using the National Cancer Data Base; the primary aim was to determine whether clinical practice in the United States has changed over time to reflect the published randomized evidence and the growing movement for value-based treatment decisions. Patients and Methods: The National Cancer Data Base was used to identify patients treated to osseous metastases from breast, prostate, and lung cancer. Utilization of single-fraction versus multiple-fraction radiation therapy was compared according to demographic, disease-related, and health care system details. Results: We included 24,992 patients treated during the period 2005-2011 for bone metastases. Among patients treated to non-spinal/vertebral sites (n=9011), 4.7% received 8 Gy in 1 fraction, whereas 95.3% received multiple-fraction treatment. Over time the proportion of patients receiving a single fraction of 8 Gy increased (from 3.4% in 2005 to 7.5% in 2011). Numerous independent predictors of single-fraction treatment were identified, including older age, farther travel distance for treatment, academic treatment facility, and non-private health insurance (P<.05). Conclusions: Single-fraction palliative radiation therapy regimens are significantly underutilized in current practice in the United States. Further efforts are needed to address this issue, such that evidence-based and cost-conscious care becomes more commonplace.
-Dimensional Fractional Lagrange's Inversion Theorem
Directory of Open Access Journals (Sweden)
F. A. Abd El-Salam
2013-01-01
Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.
Energy Technology Data Exchange (ETDEWEB)
Gilmour, M.I.; McGee, J.; Duvall, R.M.; Dailey, L.; Daniels, M.; Boykin, E.; Cho, S.H.; Doerfler, D.; Gordon, T.; Devlin, R.B. [US EPA, Research Triangle Park, NC (United States)
2007-07-01
Hundreds of epidemiological studies have shown that exposure to ambient particulate matter (PM) is associated with dose-dependent increases in morbidity and mortality. While early reports focused on PM less than 10 {mu}m (PM10), numerous studies have since shown that the effects can occur with PM stratified into ultrafine (UF), fine (FI), and coarse (CO) size modes despite the fact that these materials differ significantly in both evolution and chemistry. Furthermore the chemical makeup of these different size fractions can vary tremendously depending on location, meteorology, and source profile. For this reason, high-volume three-stage particle impactors with the capacity to collect UF, FI, and CO particles were deployed to four different locations in the United States (Seattle, WA; Salt Lake City, UT; Sterling Forest and South Bronx, NY), and weekly samples were collected for 1 mo in each place. The particles were extracted, assayed for a standardized battery of chemical components, and instilled into mouse lungs (female BALB/c) at doses of 25 and 100 {mu}g. Eighteen hours later animals were euthanized and parameters of injury and inflammation were monitored in the bronchoalveolar lavage fluid and plasma. Of the four locations, the South Bronx coarse fraction was the most potent sample in both pulmonary and systemic biomarkers. Receptor source modeling on the PM2.5 samples showed that the South Bronx sample was heavily influenced by emissions from coal fired power plants (31%) and mobile sources (22%). Further studies will assess how source profiles correlate with the observed effects for all locations and size fractions.
On Expressing Two as Sums of Distinct Odd Unit Fractions%关于2表为不同奇单位分数的和
Institute of Scientific and Technical Information of China (English)
边欣; 李忠民
2012-01-01
Abstract： By denoting m = 3^3 x5 x7 x 11 x 13 x 17 x 19 x23 x29 x31 x37, an expression of two as a sum of distinct odd unit fractions： 2=1/3＋1/5＋1/7＋1/9＋1/（11）＋1/（13）＋1/（15）＋1/（17）＋1/（19）＋1/（21）＋1/（27）＋1/（29）＋…＋1/（954 094 903 047） is obtained. There are 4074 odd unit fractions in the expansion. The denominators of unit 954 094 903 047 fractions are all divisors ofm except for 22 divisors 1,23,3×11×29,3×11×23×29×37,3×13×17×19×23×29×37,m/（51）,m/（33）,m/（31）,m/（29）,m/（27）,m/（23）,m/（21）,m/（19）,m/（17）,m/（15）,m/（13）,m/（11）,m/9,m/7,m/5,m/3,m and the max denominator is m/35.%记m=3^3×5×7×11×13×17×19×23×29×31×37,本文得到2的不同奇单位分数之和的分解式：2=1/3＋1/5＋1/7＋1/9＋1/（11）＋1/（13）＋1/（15）＋1/（17）＋1/（19）＋1/（21）＋1/（27）＋1/（29）＋…＋1/（954 094 903 047）。式中共有4 074个奇单位分数,单位分数的分母分别为m的除了1,23,3×11×29,3×11×23×29×37,3×13×17×19×23×29×37,m/（51）,m/（33）,m/（31）,m/（29）,m/（27）,m/（23）,m/（21）,m/（19）,m/（17）,m/（15）,m/（13）,m/（11）,m/9,m/7,m/5,m/3,m共22个因数之外的其余全部因数,最大分母为m/35。
Guerrero, Julien; Oliveira, Hugo; Catros, Sylvain; Siadous, Robin; Derkaoui, Sidi-Mohammed; Bareille, Reine; Letourneur, Didier; Amédée, Joëlle
2015-03-01
Current approaches in bone tissue engineering have shown limited success, mostly owing to insufficient vascularization of the construct. A common approach consists of co-culture of endothelial cells and osteoblastic cells. This strategy uses cells from different sources and differentiation states, thus increasing the complexity upstream of a clinical application. The source of reparative cells is paramount for the success of bone tissue engineering applications. In this context, stem cells obtained from human bone marrow hold much promise. Here, we analyzed the potential of human whole bone marrow cells directly expanded in a three-dimensional (3D) polymer matrix and focused on the further characterization of this heterogeneous population and on their ability to promote angiogenesis and osteogenesis, both in vitro and in vivo, in a subcutaneous model. Cellular aggregates were formed within 24 h and over the 12-day culture period expressed endothelial and bone-specific markers and a specific junctional protein. Ectopic implantation of the tissue-engineered constructs revealed osteoid tissue and vessel formation both at the periphery and within the implant. This work sheds light on the potential clinical use of human whole bone marrow for bone regeneration strategies, focusing on a simplified approach to develop a direct 3D culture without two-dimensional isolation or expansion.
Thermal expansion of glassy polymers.
Davy, K W; Braden, M
1992-01-01
The thermal expansion of a number of glassy polymers of interest in dentistry has been studied using a quartz dilatometer. In some cases, the expansion was linear and therefore the coefficient of thermal expansion readily determined. Other polymers exhibited non-linear behaviour and values appropriate to different temperature ranges are quoted. The linear coefficient of thermal expansion was, to a first approximation, a function of both the molar volume and van der Waal's volume of the repeating unit.
Furukawa, Hiroyasu; Go, Yong Bok; Ko, Nakeun; Park, Young Kwan; Uribe-Romo, Fernando J; Kim, Jaheon; O'Keeffe, Michael; Yaghi, Omar M
2011-09-19
The concept and occurrence of isoreticular (same topology) series of metal-organic frameworks (MOFs) is reviewed. We describe the preparation, characterization, and crystal structures of three new MOFs that are isoreticular expansions of known materials with the tbo (Cu(3)(4,4',4''-(benzene-1,3,5-triyl-tris(benzene-4,1-diyl))tribenzoate)(2), MOF-399) and pto topologies (Cu(3)(4,4',4''-(benzene-1,3,5-triyl-tribenzoate)(2), MOF-143; Cu(3)(4,4',4''-(triazine-2,4,6-triyl-tris(benzene-4,1-diyl))tribenzoate)(2), MOF-388). One of these materials (MOF-399) has a unit cell volume 17 times larger than that of the first reported material isoreticular to it, and has the highest porosity (94%) and lowest density (0.126 g cm(-3)) of any MOFs reported to date.
Energy Technology Data Exchange (ETDEWEB)
Li, Xiaoma; Zhou, Yuyu; Asrar, Ghassem R.; Imhoff, Marc; Li, Xuecao
2017-12-01
Abstract: Urban heat island (UHI), a major concern worldwide, affects human health and energy use. With current and anticipated rapid urbanization, improved understanding of the response of UHI to urbanization is important for impact analysis and developing effective adaptation measures and mitigation strategies. Current studies mainly focus on a single or a few big cities and knowledge on the response of UHI to urbanization for large areas is very limited. Modelling UHI caused by urbanization for large areas that encompass multiple metropolitans remains a major scientific challenge/opportunity. As a major indicator of urbanization, urban area size lends itself well for representation in prognostic models to investigate the impacts of urbanization on UHI and the related socioeconomic and environmental effects. However, we have little knowledge on how UHI responds to the increase of urban area size, namely urban expansion, and its spatial and temporal variation over large areas. In this study, we investigated the relationship between surface UHI (SUHI) and urban area size in the climate and ecological context, and its spatial and temporal variations, based on a panel analysis of about 5000 urban areas of 10 km2 or larger, in the conterminous U.S. We found statistically significant positive relationship between SUHI and urban area size, and doubling the urban area size led to a SUHI increase of higher than 0.7 °C. The response of SUHI to the increase of urban area size shows spatial and temporal variations, with stronger SUHI increase in the Northern region of U.S., and during daytime and summer. Urban area size alone can explain as much as 87% of the variance of SUHI among cities studied, but with large spatial and temporal variations. Urban area size shows higher association with SUHI in regions where the thermal characteristics of land cover surrounding the urban are more homogeneous, such as in Eastern U.S., and in the summer months. This study provides a
Balaban, Victor; Marks, Suzanne M; Etkind, Sue C; Katz, Dolly J; Higashi, Julie; Flood, Jennifer; Cronin, Ann; Ho, Christine S; Khan, Awal; Chorba, Terence
2015-01-01
The Patient Protection and Affordable Care Act can enhance ongoing efforts to control tuberculosis (TB) in the United States by bringing millions of currently uninsured Americans into the health-care system. However, much of the legislative and financial framework that provides essential public health services necessary for effective TB control is outside the scope of the law. We identified three key issues that will still need to be addressed after full implementation of the Affordable Care Act: (1) essential TB-related public health functions will still be needed and will remain the responsibility of federal, state, and local health departments; (2) testing and treatment for latent TB infection (LTBI) is not covered explicitly as a recommended preventive service without cost sharing or copayment; and (3) remaining uninsured populations will disproportionately include groups at high risk for TB. To improve and continue TB control efforts, it is important that all populations at risk be tested and treated for LTBI and TB; that testing and treatment services be accessible and affordable; that essential federal, state, and local public health functions be maintained; that private-sector medical/public health linkages for diagnosis and treatment be developed; and that health-care providers be trained in conducting appropriate LTBI and TB clinical care.
2010-07-01
... concentration throughout the aeration unit by quickly dispersing the recycled biomass and the wastewater... the concentration measurement test that can be used for units with multiple mixing zones. Procedure 2... sludge unit of interest to a concentration such that the biodegradation test will last long enough to...
Expansion of protein domain repeats.
Directory of Open Access Journals (Sweden)
Asa K Björklund
2006-08-01
Full Text Available Many proteins, especially in eukaryotes, contain tandem repeats of several domains from the same family. These repeats have a variety of binding properties and are involved in protein-protein interactions as well as binding to other ligands such as DNA and RNA. The rapid expansion of protein domain repeats is assumed to have evolved through internal tandem duplications. However, the exact mechanisms behind these tandem duplications are not well-understood. Here, we have studied the evolution, function, protein structure, gene structure, and phylogenetic distribution of domain repeats. For this purpose we have assigned Pfam-A domain families to 24 proteomes with more sensitive domain assignments in the repeat regions. These assignments confirmed previous findings that eukaryotes, and in particular vertebrates, contain a much higher fraction of proteins with repeats compared with prokaryotes. The internal sequence similarity in each protein revealed that the domain repeats are often expanded through duplications of several domains at a time, while the duplication of one domain is less common. Many of the repeats appear to have been duplicated in the middle of the repeat region. This is in strong contrast to the evolution of other proteins that mainly works through additions of single domains at either terminus. Further, we found that some domain families show distinct duplication patterns, e.g., nebulin domains have mainly been expanded with a unit of seven domains at a time, while duplications of other domain families involve varying numbers of domains. Finally, no common mechanism for the expansion of all repeats could be detected. We found that the duplication patterns show no dependence on the size of the domains. Further, repeat expansion in some families can possibly be explained by shuffling of exons. However, exon shuffling could not have created all repeats.
National Research Council Canada - National Science Library
Pu, Yi-Fei
2016-01-01
Here and in the companion paper (Part I), a novel conceptual framework on the measurement units and physical dimensions of fractance and rules for fractors in series and parallel is mainly discussed...
Directory of Open Access Journals (Sweden)
Antônio Chagas Mota
2002-03-01
Full Text Available Vicilins (7S storage globulins isolated from cowpea (Vigna unguiculata L. seeds which were susceptible (S and resistant (R to the cowpea weevil (Callosobruchus maculatus F., Coleoptera: Bruchidae were denatured by urea and fractionated by ion-exchange chromatography. Isolated fractions were incorporated in artificial seeds for assessment of their toxicity to C. maculatus. The most acidic fractions of both susceptible (CE-31 cultivar and resistant (IT81D-1045 line seeds were shown to affect development and survival of the bruchid. Results indicated that vicilin polypeptides of toxic nature were expressed in both types of storage globulins although at different levels.Vicilinas (globulinas de reserva 7S isoladas de sementes de feijão-de-corda (Vigna unguiculata L., susceptíveis (S e resistentes (R ao caruncho/gorgulho (Callosobruchus maculatus F., Coleoptera: Bruchidae foram desnaturadas por uréia e fracionadas por cromatografia de troca iônica. As frações isoladas foram incorporadas em sementes artificiais para avaliação de sua toxicidade a C. maculatus. As fracões mais ácidas de ambas vicilinas afetaram o desenvolvimento e a sobrevivência do bruquídeo. Sugerimos que polipeptídeos de vicilinas de natureza tóxica são expressos em ambos tipos de globulinas de reserva, embora em níveis diferentes.
1970-10-01
sale: is disributici is unlimited = F’)RIWRD Seior Ignacio Soto, Rrecutive President, Instituto Mexicano del Cementc y Concreto , invited Mr. Bryant... Concreto , a.c., Kwidco, D. F., Mexico. Based on info.mation largely obtained from ACT Committee 223, Expansive ’ement. Concretes, ACI Journal, August 1Q70
Continued Fractions ofFunctions Connected With Real Quadratic Function Fields
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
@@The theory of continued fractions is very useful in studying real quadratic number fields (see ［2-5］).E. Artin in ［1］ introduced continued fractions of functions to study quadratic function fields, using formal Laurent expansions, which isessentially the theory of completion of the function fields at the infinite valuation. Here we first re-developthe theory of continued fractions of functions in a more elementary and manipulable manner mainly using long division of polynomials; and then study properties of the continued fractions, which will have important applications in studying quadratic function fields obtaining remarkable results on unit groups, class groups, and class numbers.
Alberts, James J.; Giesy, John P.; Evans, David W.
1984-06-01
The binding capacities of surface waters for Cd, Cu, and Pb were determined for eight water samples representing four rivers and two swamps from Florida and Georgia in the southeastern United States The binding capacity ranges were CdBC=0 04 to 0 79 μg atm/L, CuBC=1 0 to 5 4 μg atm/L, and PbBC=5 0 to 17 8 μg atm/L Binding capacity values from the southeastern United States are shown to be in good agreement with values reported from the northeastern part of the country and northern Europe The CdBC was due primarily to inorganic ligand binding, while PbBC was predominantly a result of organic matter The CuBC was due to a complex function of both organic and inorganic binding Significant portions of the CuBC and PbBC could be removed from the waters by ultrafiltration of particles between 0·45 μm and 52 Å in diameter Ultrafiltration, even to removing particles > 13 Å diameter, did not affect the CdBC Distributional studies of the dissolved organic carbon in these systems reveal that significant fractions of the DOC are present in the ultrafilterable fraction which contains significant portions of the CuBC and PbBC
Fractional Reserve Banking: Some Quibbles
Bagus, Philipp; Howden, David
2010-01-01
We explore several unaddressed issues in George Selgin’s (1988) claim that the best monetary system to maintain monetary equilibrium is a fractional reserve free banking one. The claim that adverse clearing balances would limit credit expansion in a fractional reserve free banking system is more troublesome than previously reckoned. Both lengthened clearing periods and interbank agreements render credit expansion unrestrained. “The theory of free banking” confuses increases in money held with...
Lu, Sheng-Yong; Du, Yingzhe; Yan, Jian-Hua; Li, Xiao-Dong; Ni, Ming-Jiang; Cen, Ke-Fa
2012-06-01
The distribution of polychlorinated dibenzo-p-dioxins/dibenzofurans (PCDD/Fs), in brief dioxins, has seldom been addressed systematically in fly ash from municipal solid waste incinerators (MSWIs). This study shows the amount and fingerprint of PCDD/Fs in fly ash from four different Chinese MSWIs, that is, three mechanical grate units and one circulating fluidized bed unit. In these fly ash samples, dioxins-related parameters (international toxic equivalent quantity, total amount of PCDD/Fs, individual isomer classes, and 17 toxic 2,3,7,8-substituted congeners) all tend to increase with decreasing particle size for mechanical grate incinerators, yet only for the finest fraction for fluidized bed units. Moreover, the fluidized bed incinerator seems superior to grate incineration in controlling dioxins, yet a comparison is hampered by internal differences in the sample, for example, the fluidized bed fly ash has much lower carbon and chlorine contents. In addition, the presence of sulfur from mixing coal as supplemental fuel to the MSW may poison the catalytic steps in dioxins formation and thus suppress the formation of dioxins. With more residual carbon and chlorine in the fly ash, it is easier to form dioxins during cooling. Nevertheless, there is no apparent relation between Fe, Cu, and Zn contents and that of dioxins in fly ash.
'The mother of all continued fractions'
Dajani, K.; Kraaikamp, C.
2001-01-01
In this paper we give the relationship between the regular continued fraction and the Lehner fractions using a procedure known as insertion Starting from the regular continued fraction expansion of any real irrational x when the maximal number of insertions is applied one obtains the Lehner fraction
Rational Exponentials and Continued Fractions
Denny, J. K.
2012-01-01
Using continued fraction expansions, we can approximate constants, such as pi and e, using an appropriate integer n raised to the power x[superscript 1/x], x a suitable rational. We review continued fractions and give an algorithm for producing these approximations.
Fuel Thermal Expansion (FTHEXP). [BWR; PWR
Energy Technology Data Exchange (ETDEWEB)
Reymann, G. A.
1978-07-01
A model is presented which deals with dimensional changes in LWR fuel pellets caused by changes in temperature. It is capable of dealing with any combination of UO/sub 2/ and PuO/sub 2/ in solid, liquid or mixed phase states, and includes expansion due to the solid-liquid phase change. The function FTHEXP models fuel thermal expansion as a function of temperature, fraction of PuO/sub 2/, and the fraction of fuel which is molten.
Isotropic Negative Thermal Expansion Metamaterials.
Wu, Lingling; Li, Bo; Zhou, Ji
2016-07-13
Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the three-dimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale.
基于过程模拟的气体分馏装置HAZOP分析%HAZOP analysis of gas fractionation unit based on process simulation
Institute of Scientific and Technical Information of China (English)
康建新; 郭丽杰; 高发明
2014-01-01
气体分馏装置属于火灾、爆炸高危场所，目前常采用危险与可操作性（HAZOP）分析这种系统化、结构化危险辨识和评价方法，来识别现有和潜在的危险。而 HAZOP 分析本质上是一种定性方法，缺乏偏差定量化分析的依据。为了克服这个固有缺点，在传统 HAZOP 方法基础上，建立了基于工艺过程模拟的 HAZOP 方法。采用Unisim软件分别模拟了一个和多个工艺参数波动对装置特性的影响，获取实际装置操作极限状态，得到安全分析数据，实现 HAZOP 分析的定量化。以气体分馏装置脱丙烷塔为例，进行塔顶压力、进料量与进料温度变化的工艺过程模拟，完成了偏差和偏差后果量化分析。研究结果表明，应用该方法可提高 HAZOP 分析的准确性、有效性和可靠性，从而为装置安全生产管理提供依据。%Because of potential fire disaster and explosion hazard, the gas fractionation unit is highly dangerous. The existing and potential hazards are identified by hazard and operability (HAZOP) study, which is a systematic and structured approach of the hazard identification and assessment. However, HAZOP is essentially a qualitative analysis approach, which results in lack of quantitative analysis foundation of the deviation. To overcome the inherent drawbacks, the HAZOP analysis approach based on process simulation is proposed through the improvement of conventional HAZOP. The effect of one and several process parameters on unit characteristic is simulated and studied by Unisim software. As a result, the limitation operation state of the real unit is obtained and the data for safety analysis could be achieved. Therefore, the quantitative HAZOP analysis could be implemented. The process simulation-based HAZOP analysis for depropanizer of gas fractionation unit is carried out as a case study, in which the process parameters, such as overhead pressure, feed flow rate and
Nonlinear fractional relaxation
Indian Academy of Sciences (India)
A Tofighi
2012-04-01
We deﬁne a nonlinear model for fractional relaxation phenomena. We use -expansion method to analyse this model. By studying the fundamental solutions of this model we ﬁnd that when → 0 the model exhibits a fast decay rate and when → ∞ the model exhibits a power-law decay. By analysing the frequency response we ﬁnd a logarithmic enhancement for the relative ratio of susceptibility.
Karras, G; Billard, F; Lavorel, B; Siour, G; Hartmann, J -M; Faucher, O; Gershnabel, Erez; Prior, Yehiam; Averbukh, Ilya Sh
2016-01-01
We report the observation of fractional echoes in a double-pulse excited nonlinear system. Unlike standard echoes which appear periodically at delays which are integer multiple of the delay between the two exciting pulses, the fractional echoes appear at rational fractions of this delay. We discuss the mechanism leading to this phenomenon, and provide the first experimental demonstration of fractional echoes by measuring third harmonic generation in a thermal gas of CO2 molecules excited by a pair of femtosecond laser pulses.
Maria Klimikova
2010-01-01
Understanding the reasons of the present financial problems lies In understanding the substance of fractional reserve banking. The substance of fractional banking is in lending more money than the bankers have. Banking of partial reserves is an alternative form which links deposit banking and credit banking. Fractional banking is causing many unfavorable economic impacts in the worldwide system, specifically an inflation.
Maria Klimikova
2010-01-01
Understanding the reasons of the present financial problems lies In understanding the substance of fractional reserve banking. The substance of fractional banking is in lending more money than the bankers have. Banking of partial reserves is an alternative form which links deposit banking and credit banking. Fractional banking is causing many unfavorable economic impacts in the worldwide system, specifically an inflation.
Tapiero, Charles S.; Vallois, Pierre
2016-11-01
The premise of this paper is that a fractional probability distribution is based on fractional operators and the fractional (Hurst) index used that alters the classical setting of random variables. For example, a random variable defined by its density function might not have a fractional density function defined in its conventional sense. Practically, it implies that a distribution's granularity defined by a fractional kernel may have properties that differ due to the fractional index used and the fractional calculus applied to define it. The purpose of this paper is to consider an application of fractional calculus to define the fractional density function of a random variable. In addition, we provide and prove a number of results, defining the functional forms of these distributions as well as their existence. In particular, we define fractional probability distributions for increasing and decreasing functions that are right continuous. Examples are used to motivate the usefulness of a statistical approach to fractional calculus and its application to economic and financial problems. In conclusion, this paper is a preliminary attempt to construct statistical fractional models. Due to the breadth and the extent of such problems, this paper may be considered as an initial attempt to do so.
Determination of effective thermal expansion coefficients of unidirectional fibrous nanocomposites
Dai, Ming; Schiavone, Peter; Gao, Cun-Fa
2016-10-01
We present an efficient numerical scheme (based on complex variable techniques) to calculate the effective thermal expansion coefficients of a composite containing unidirectional periodic fibers. Moreover, the mechanical behavior of the fibers incorporates interface effects allowing the ensuing analytical model of the composite to accommodate deformations at the nanoscale. The resulting `nanocomposite' is subjected to a uniform temperature variation which leads to periodic deformations within the plane perpendicular to the fibers and uniform deformations along the direction of the fibers. These deformation fields are determined by analyzing a representative unit cell of the composite subsequently leading to the corresponding effective thermal expansion coefficients. Numerical results are illustrated via several physical examples. We find that the influence of interface effects on the effective thermal expansion coefficients (in particular that corresponding to the transverse direction in the plane perpendicular to the fibers) decays rapidly as the fibers become harder. In addition, by comparing the results obtained here with those from effective medium theories, we show that the latter may induce significant errors in the determination of the effective transverse thermal expansion coefficient when the fibers are much softer than the matrix and the fiber volume fraction is relatively high.
Povstenko, Yuriy
2015-01-01
This book is devoted to fractional thermoelasticity, i.e. thermoelasticity based on the heat conduction equation with differential operators of fractional order. Readers will discover how time-fractional differential operators describe memory effects and space-fractional differential operators deal with the long-range interaction. Fractional calculus, generalized Fourier law, axisymmetric and central symmetric problems and many relevant equations are featured in the book. The latest developments in the field are included and the reader is brought up to date with current research. The book contains a large number of figures, to show the characteristic features of temperature and stress distributions and to represent the whole spectrum of order of fractional operators. This work presents a picture of the state-of-the-art of fractional thermoelasticity and is suitable for specialists in applied mathematics, physics, geophysics, elasticity, thermoelasticity and engineering sciences. Corresponding sections of ...
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo I., E-mail: eliazar@post.tau.ac.il [Holon Institute of Technology, P.O. Box 305, Holon 58102 (Israel); Shlesinger, Michael F., E-mail: mike.shlesinger@navy.mil [Office of Naval Research, Code 30, 875 N. Randolph St., Arlington, VA 22203 (United States)
2013-06-10
Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.
Energy Technology Data Exchange (ETDEWEB)
Li, Zheng [Institute of Air Conditioning, China Academy of Building Research, Beijing 100013 (China); Deng, Shiming [Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR (China)
2007-01-15
For residential buildings located in the subtropics, direct expansion (DX) air conditioning (A/C) units are commonly used. Most DX A/C units are currently equipped with single-speed compressors and supply fans, relying on on-off cycling compressors as a low-cost approach to maintain only indoor air dry-bulb temperature, resulting in either space overcooling or an uncontrolled equilibrium indoor relative humidity (RH) level. With the rapid development of A/C industry, the use of variable-speed compressor and supply fan has become more and more prevalent and practical. This paper, the first part of a two-part series, reports on the development of a novel direct digital control (DDC)-based capacity controller for a DX A/C unit having variable-speed compressor and supply fan to simultaneously control indoor air temperature and RH in a conditioned space served by the DX A/C unit. The controller is the first of its kind as a composite parameter, sensible heat ratio (SHR), is used as a controlled parameter. The core element of the capacity controller, a numerical calculation algorithm (NCA) is firstly presented. This is followed by reporting the results of preliminary controllability tests of the DDC-based capacity controller, which suggested that the controller developed could achieve a reasonable control accuracy, but with room for improvement with respect to control sensitivity. Part II of the two-part series reports on the further development of the controller to improve its control sensitivity, and the results of associated controllability tests. (author)
Energy Technology Data Exchange (ETDEWEB)
Hadermann, A. F.
1985-04-09
Soluble polymers are fractionated according to molecular weight by cryogenically comminuting the polymer and introducing the polymer particles, while still in the active state induced by cryogenic grinding, into a liquid having a solvent power selected to produce a coacervate fraction containing high molecular weight polymer species and a dilute polymer solution containing lower molecular weight polymer species. The coacervate may be physically separated from the solution and finds use in the production of antimisting jet fuels and the like.
Testing Fractional Action Cosmology
Shchigolev, V K
2015-01-01
The present work deals with a combined test of the so-called Fractional Action Cosmology (FAC) on the example of a specific model obtained by the author earlier. In this model, the effective cosmological term is proportional to the Hubble parameter squared through the so-called kinematic induction. The reason of studying this cosmological model could be explained by its ability to describe two periods of accelerated expansion, that is in agreement with the recent observations and the cosmological inflation paradigm. First of all, we put our model through the theoretical tests that gives a general conception of the influence of the model parameters on its behavior. Then, we obtain some restrictions on the principal parameters of the model, including the fractional index, by means of the observational data. Finally, the cosmography parameters and the observational data compared to the theoretical predictions are presented both analytically and graphically.
Testing fractional action cosmology
Shchigolev, V. K.
2016-08-01
The present work deals with a combined test of the so-called Fractional Action Cosmology (FAC) on the example of a specific model obtained by the author earlier. In this model, the effective cosmological term is proportional to the Hubble parameter squared through the so-called kinematic induction. The reason of studying this cosmological model could be explained by its ability to describe two periods of accelerated expansion, that is in agreement with the recent observations and the cosmological inflation paradigm. First of all, we put our model through the theoretical tests, which gives a general conception of the influence of the model parameters on its behavior. Then, we obtain some restrictions on the principal parameters of the model, including the fractional index, by means of the observational data. Finally, the cosmography parameters and the observational data compared to the theoretical predictions are presented both analytically and graphically.
Understanding Multiplication of Fractions.
Sweetland, Robert D.
1984-01-01
Discussed the use of Cuisenaire rods in teaching the multiplication of fractions. Considers whole number times proper fraction, proper fraction multiplied by proper fraction, mixed number times proper fraction, and mixed fraction multiplied by mixed fractions. (JN)
An Alternative Starting Point for Fraction Instruction
Cortina, José Luis; Višnovská, Jana; Zúñiga, Claudia
2015-01-01
We analyze the results of a study conducted for the purpose of assessing the viability of an alternative starting point for teaching fractions. The alternative is based on Freudenthal's insights about fraction as comparison. It involves portraying the entities that unit fractions quantify as always being apart from the reference unit, instead of…
Improving Children's Knowledge of Fraction Magnitudes
Fazio, Lisa K.; Kennedy, Casey A.; Siegler, Robert S.
2016-01-01
We examined whether playing a computerized fraction game, based on the integrated theory of numerical development and on the Common Core State Standards' suggestions for teaching fractions, would improve children's fraction magnitude understanding. Fourth and fifth-graders were given brief instruction about unit fractions and played "Catch…
Effects of forest expansion on mountain grassland
DEFF Research Database (Denmark)
Guidi, Claudia; Magid, Jakob; Rodeghiero, Mirco
2014-01-01
Background and aims. Grassland abandonment followed by forest succession is the dominant land-use change in the European Alps. We studied the impact of current forest expansion on mountain grassland on changes in physical soil organic carbon (SOC) fractions along a land-use and management gradient...
Energy efficient perlite expansion process
Energy Technology Data Exchange (ETDEWEB)
Jenkins, K.L.
1982-08-31
A thermally efficient process for the expansion of perlite ore is described. The inlet port and burner of a perlite expansion chamber (Preferably a vertical expander) are enclosed such that no ambient air can enter the chamber. Air and fuel are metered to the burner with the amount of air being controlled such that the fuel/air premix contains at least enough air to start and maintain minimum combustion, but not enough to provide stoichiometric combustion. At a point immediately above the burner, additional air is metered into an insulated enclosure surrounding the expansion chamber where it is preheated by the heat passing through the chamber walls. This preheated additional air is then circulated back to the burner where it provides the remainder of the air needed for combustion, normally full combustion. Flow of the burner fuel/air premix and the preheated additional air is controlled so as to maintain a long luminous flame throughout a substantial portion of the expansion chamber and also to form a moving laminar layer of air on the inner surface of the expansion chamber. Preferably the burner is a delayed mixing gas burner which materially aids in the generation of the long luminous flame. The long luminous flame and the laminar layer of air at the chamber wall eliminate hot spots in the expansion chamber, result in relatively low and uniform temperature gradients across the chamber, significantly reduce the amount of fuel consumed per unit of perlite expanded, increase the yield of expanded perlite and prevent the formation of a layer of perlite sinter on the walls of the chamber.
Number line representations of fractions
Behr, Merlyn J.; Bright, George W.; Wachsmuth, Ipke; Wagner, Sigrid
1982-01-01
The study explored students' interpretations of representations of fractions on number lines and the effect of instruction on those interpretations. Subjects were five fourth-graders, and instruction was a four-day unit on the use of number lines. A 16-item, multiple-choice pre- and posttest was used along with videotaped interviews. Performance improved except when students had to associate a reduced fraction symbol with an equivalent, unreduced fraction representation on a number line. The ...
Pamplona, Djenane C; Velloso, Raquel Q; Radwanski, Henrique N
2014-01-01
This article discusses skin expansion without considering cellular growth of the skin. An in vivo analysis was carried out that involved expansion at three different sites on one patient, allowing for the observation of the relaxation process. Those measurements were used to characterize the human skin of the thorax during the surgical process of skin expansion. A comparison between the in vivo results and the numerical finite elements model of the expansion was used to identify the material elastic parameters of the skin of the thorax of that patient. Delfino's constitutive equation was chosen to model the in vivo results. The skin is considered to be an isotropic, homogeneous, hyperelastic, and incompressible membrane. When the skin is extended, such as with expanders, the collagen fibers are also extended and cause stiffening in the skin, which results in increasing resistance to expansion or further stretching. We observed this phenomenon as an increase in the parameters as subsequent expansions continued. The number and shape of the skin expanders used in expansions were also studied, both mathematically and experimentally. The choice of the site where the expansion should be performed is discussed to enlighten problems that can lead to frustrated skin expansions. These results are very encouraging and provide insight into our understanding of the behavior of stretched skin by expansion. To our knowledge, this study has provided results that considerably improve our understanding of the behavior of human skin under expansion.
Grimm, C. A.
This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…
Bhattacharyya, Sonalee; Namakshi, Nama; Zunker, Christina; Warshauer, Hiroko K.; Warshauer, Max
2016-01-01
Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…
Bhattacharyya, Sonalee; Namakshi, Nama; Zunker, Christina; Warshauer, Hiroko K.; Warshauer, Max
2016-01-01
Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…
Fraction Reduction through Continued Fractions
Carley, Holly
2011-01-01
This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.
Expansion techniques for collisionless stellar dynamical simulations
Energy Technology Data Exchange (ETDEWEB)
Meiron, Yohai [Kavli Institute for Astronomy and Astrophysics at Peking University, Beijing 100871 (China); Li, Baile; Holley-Bockelmann, Kelly [Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 (United States); Spurzem, Rainer, E-mail: ymeiron@pku.edu.cn [National Astronomical Observatories of China, Chinese Academy of Sciences, Beijing 100012 (China)
2014-09-10
We present graphics processing unit (GPU) implementations of two fast force calculation methods based on series expansions of the Poisson equation. One method is the self-consistent field (SCF) method, which is a Fourier-like expansion of the density field in some basis set; the other method is the multipole expansion (MEX) method, which is a Taylor-like expansion of the Green's function. MEX, which has been advocated in the past, has not gained as much popularity as SCF. Both are particle-field methods and optimized for collisionless galactic dynamics, but while SCF is a 'pure' expansion, MEX is an expansion in just the angular part; thus, MEX is capable of capturing radial structure easily, while SCF needs a large number of radial terms. We show that despite the expansion bias, these methods are more accurate than direct techniques for the same number of particles. The performance of our GPU code, which we call ETICS, is profiled and compared to a CPU implementation. On the tested GPU hardware, a full force calculation for one million particles took ∼0.1 s (depending on expansion cutoff), making simulations with as many as 10{sup 8} particles fast for a comparatively small number of nodes.
Exact solutions for nonlinear partial fractional differential equations
Institute of Scientific and Technical Information of China (English)
Khaled A.Gepreel; Saleh Omran
2012-01-01
In this article,we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations.We use the improved (G’/G)-expansion function method to calculate the exact solutions to the time-and space-fractional derivative foam drainage equation and the time-and space-fractional derivative nonlinear KdV equation.This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations.
Expansion of magnetic clouds in the outer heliosphere
Gulisano, A. M.; Démoulin, P.; Dasso, S.; Rodriguez, L.
2012-07-01
Context. A large amount of magnetized plasma is frequently ejected from the Sun as coronal mass ejections (CMEs). Some of these ejections are detected in the solar wind as magnetic clouds (MCs) that have flux rope signatures. Aims: Magnetic clouds are structures that typically expand in the inner heliosphere. We derive the expansion properties of MCs in the outer heliosphere from one to five astronomical units to compare them with those in the inner heliosphere. Methods: We analyze MCs observed by the Ulysses spacecraft using in situ magnetic field and plasma measurements. The MC boundaries are defined in the MC frame after defining the MC axis with a minimum variance method applied only to the flux rope structure. As in the inner heliosphere, a large fraction of the velocity profile within MCs is close to a linear function of time. This is indicative of a self-similar expansion and a MC size that locally follows a power-law of the solar distance with an exponent called ζ. We derive the value of ζ from the in situ velocity data. Results: We analyze separately the non-perturbed MCs (cases showing a linear velocity profile almost for the full event), and perturbed MCs (cases showing a strongly distorted velocity profile). We find that non-perturbed MCs expand with a similar non-dimensional expansion rate (ζ = 1.05 ± 0.34), i.e. slightly faster than at the solar distance and in the inner heliosphere (ζ = 0.91 ± 0.23). The subset of perturbed MCs expands, as in the inner heliosphere, at a significantly lower rate and with a larger dispersion (ζ = 0.28 ± 0.52) as expected from the temporal evolution found in numerical simulations. This local measure of the expansion also agrees with the distribution with distance of MC size, mean magnetic field, and plasma parameters. The MCs interacting with a strong field region, e.g. another MC, have the most variable expansion rate (ranging from compression to over-expansion).
Tenreiro Machado, J. A.; Galhano, Alexandra M.; Oliveira, Anabela M.; Tar, József K.
2010-03-01
This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.
Al-Omran, Layla Salih; Harrad, Stuart
2016-08-01
This study investigates the particle size distribution of eight polybrominated diphenyl ethers (PBDEs) and five "novel" brominated flame retardants (NBFRs) in settled house dust. Elevated surface dust (ESD) and floor dust (FD) were collected from 5 homes in Birmingham, UK, yielding a total of 10 samples. Each sample was fractionated into three different particle sizes: 125-250 μm (P1), 63-125 μm (P2) and 25-63 μm (P3). Non-fractionated bulk dust samples (BD) were also analysed. BDE-209 predominated, comprising an average 74.3%, 77.3%, 69.2%, and 62.7% ΣBFRs of BD, P1, P2 and P3 respectively. Σ5NBFRs contributed 24.2%, 21.5%, 29.0% and 35.3% ΣBFRs, while Σ7tri-hepta-BDEs represented 1.5%, 1.2%, 1.7%, and 2.0% ΣBFRs. BEH-TEBP was the predominant NBFR contributing 76.9%, 75.1%, 83.1%, and 83.9% ΣNBFRs in BD, P1, P2 and P3 respectively; followed by DBDPE which contributed 20.1%, 21.9%, 14.1% and 13.9% ΣNBFRs. EH-TBB, BTBPE and PBEB were the least abundant NBFRs. Concentrations of Σ7tri-hepta-BDEs and BEH-TEBP in P3 exceeded significantly (P surface area to volume ratio, rather than by variations in organic carbon content. Copyright © 2016. Published by Elsevier Ltd.
Fractional order differentiation by integration: An application to fractional linear systems
Liu, Dayan
2013-02-04
In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.
On Continued Fraction Expansion of Real Roots of Polynomial Systems
DEFF Research Database (Denmark)
Mantzaflaris, Angelos; Mourrain, Bernard; Tsigaridas, Elias
2011-01-01
We elaborate on a correspondence between the coefficients of a multivariate polynomial represented in the Bernstein basis and in a tensor-monomial basis, which leads to homography representations of polynomial functions that use only integer arithmetic (in contrast to the Bernstein basis) and are...
An Efficient Method for Performing Partial Fraction Expansion.
1980-02-01
Residues and Coefficients of High Order Poles," IRE Trans. Auto. Cont., AC-4, (1959). [2] Henrici , P., Applied and Computational Complex Analysis , Volume 1, John Wiley aind Sons, (1974). ... Henrici . A numerical example is provided. DD I Fhim3 1473 EDITIONO 01NOVSS1 OBSOLETE Unclassified /)’/, , SECURITY CLASSIFICATION OF THIS PAGE (*?Ion Data...the method of Henrici . A numerical example is provided. MAS (MOS) subject classificatiom (1970). Primary 65F99. Vi I A Introduction. At times it is
Collisional and collisionless expansion of Yukawa balls.
Piel, Alexander; Goree, John A
2013-12-01
The expansion of Yukawa balls is studied by means of molecular dynamics simulations of collisionless and collisional situations. High computation speed was achieved by using the parallel computing power of graphics processing units. When the radius of the Yukawa ball is large compared to the shielding length, the expansion process starts with the blow-off of the outermost layer. A rarefactive wave subsequently propagates radially inward at the speed of longitudinal phonons. This mechanism is fundamentally different from Coulomb explosions, which employ a self-similar expansion of the entire system. In the collisionless limit, the outer layers carry away most of the available energy. The simulations are compared with analytical estimates. In the collisional case, the expansion process can be described by a nonlinear diffusion equation that is a special case of the porous medium equation.
Expansion of magnetic clouds in the outer heliosphere
Gulisano, Adriana Maria; Dasso, Sergio; Rodriguez, Luciano
2012-01-01
A large amount of magnetized plasma is frequently ejected from the Sun as coronal mass ejections (CMEs). Some of these ejections are detected in the solar wind as magnetic clouds (MCs) that have flux rope signatures. Magnetic clouds are structures that typically expand in the inner heliosphere. We derive the expansion properties of MCs in the outer heliosphere from one to five astronomical units to compare them with those in the inner heliosphere. We analyze MCs observed by the Ulysses spacecraft using insitu magnetic field and plasma measurements. The MC boundaries are defined in the MC frame after defining the MC axis with a minimum variance method applied only to the flux rope structure. As in the inner heliosphere, a large fraction of the velocity profile within MCs is close to a linear function of time. This is indicative of} a self-similar expansion and a MC size that locally follows a power-law of the solar distance with an exponent called zeta. We derive the value of zeta from the insitu velocity data...
Energy Technology Data Exchange (ETDEWEB)
Barrera, G D [Departamento de QuImica, Universidad Nacional de la Patagonia SJB, Ciudad Universitaria, 9000 Comodoro Rivadavia (Argentina); Bruno, J A O [Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de QuImica Inorganica, AnalItica y QuImica FIsica, Pabellon 2, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Barron, T H K [School of Chemistry, University of Bristol, Cantock' s Close, Bristol BS8 1TS (United Kingdom); Allan, N L [School of Chemistry, University of Bristol, Cantock' s Close, Bristol BS8 1TS (United Kingdom)
2005-02-02
There has been substantial renewed interest in negative thermal expansion following the discovery that cubic ZrW{sub 2}O{sub 8} contracts over a temperature range in excess of 1000 K. Substances of many different kinds show negative thermal expansion, especially at low temperatures. In this article we review the underlying thermodynamics, emphasizing the roles of thermal stress and elasticity. We also discuss vibrational and non-vibrational mechanisms operating on the atomic scale that are responsible for negative expansion, both isotropic and anisotropic, in a wide range of materials. (topical review)
Engaging Students with Multiple Models of Fractions
Zhang, Xiaofen; Clements, M. A.; Ellerton, Nerida F.
2015-01-01
An understanding of unit fractions, and especially of one-half, one-third, and one-fourth, is crucially important for elementary school children's development of number sense (CCSSI 2010). We describe multimodal activities designed to assist elementary school students in gaining a rich understanding of unit fractions. Research has shown (Zhang,…
Fakhruddin, Hasan
1993-01-01
Describes a paradox in the equation for thermal expansion. If the calculations for heating a rod and subsequently cooling a rod are determined, the new length of the cool rod is shorter than expected. (PR)
Fractional complex transform for fractional differential equations
National Research Council Canada - National Science Library
Lİ, Zheng Biao; HE, Ji Huan
2010-01-01
Fractional complex transform is proposed to convert fractional differential equations into ordinary differential equations, so that all analytical methods devoted to advanced calculus can be easily...
Unanswered Quibbles with Fractional Reserve Free Banking
Philipp Bagus; David Howden
2011-01-01
In this article we reply to George Selgin’s counterarguments to our article “Fractional Reserve Free Banking: Some Quibbles”. Selgin regards holding cash as saving while we focus on the real savings necessary to maintain investment projects. Real savings are unconsumed real income. Variations in real savings are not necessarily equal to variations in cash holdings. We show that a coordinated credit expansion in a fractional reserve free banking (FRFB) system is possible and that precautionary...
Unanswered Quibbles with Fractional Reserve Free Banking
Philipp Bagus; David Howden
2011-01-01
In this article we reply to George Selgin’s counterarguments to our article “Fractional Reserve Free Banking: Some Quibbles”. Selgin regards holding cash as saving while we focus on the real savings necessary to maintain investment projects. Real savings are unconsumed real income. Variations in real savings are not necessarily equal to variations in cash holdings. We show that a coordinated credit expansion in a fractional reserve free banking (FRFB) system is possible and that precautionary...
Thermal expansion behavior of fluor-chlorapatite crystalline solutions
Hovis, G.; Harlov, D.; Gottschalk, M.; Hudacek, W.; Wildermuth, S.
2009-04-01
Apatite Ca5(PO4)3(F,Cl,OH,CO3) occurs widely as an accessory mineral in many igneous and metamorphic rocks and in nature displays a wide range of F-Cl-OH-CO3 mixtures (e.g., O'Reilly and Griffin, 2000) that have been used to interpret the role of fluids, e.g. Cl, F, and OH activities, during metamorphic and igneous processes (e.g., Harlov and Förster, 2002). It is important, therefore, to understand the thermodynamic behavior of these solid solutions, including their thermal expansion properties. Fluorapatite - chlorapatite samples were synthesized at the GFZ-Potsdam (Hovis, Harlov, Hahn and Steigert, 2007) using an adaptation of the molten flux method of Cherniak (2000). Dry CaF2 and CaCl2 (0.1 mole total) were mixed with Ca3(PO4)2 (0.03 moles), placed in a Pt crucible, equilibrated for 15 hours at 1375 °C, cooled to 1220 °C at 3 °C/hour, removed from the oven and cooled in air. Crystals were separated from the flux by boiling the quenched product in water. F:Cl fractions for each sample were determined via Rietveld refinement of X-ray powder diffraction data. Chemical homogeneity was confirmed by Rietveld refinement and high-contrast back-scattered electron imaging. Room-temperature unit-cell volumes were determined at the GFZ-Potsdam through Rietveld analysis of X-ray powder diffraction data and also at Lafayette College by standard unit-cell refinement techniques (Holland and Redfern, 1997) using NBS/NIST 640a Si as an internal standard. High-temperature unit-cell dimensions were calculated from X-ray powder diffraction data collected at Cambridge University from room temperature to 1000 °C on a Bruker D8 X-ray diffractometer. NBS Si again was utilized as an internal standard; high-temperature Si peak positions were taken from Parrish (1953). Results indicate that despite the considerable size difference between fluorine and chlorine ions, reflected by substantially different unit-cell sizes at room temperature, the coefficient of thermal expansion across
Dynamics with Low-Level Fractionality
Tarasov, V E; Tarasov, Vasily E.; Zaslavsky, George M.
2005-01-01
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and field theory. For the fractional linear oscillator the physical meaning of the derivative of order $\\alpha<2$ is dissipation. In systems with many spacially coupled elements (oscillators) the fractional derivative, along the space coordinate, corresponds to a long range interaction. We discuss a method of constructing a solution using an expansion in $\\epsilon=n-\\alpha$ with small $\\epsilon$ and positive integer $n$. The method is applied to the fractional linear and nonlinear oscillators and to fractional Ginzburg-Landau or parabolic equations.
Composite asymptotic expansions
Fruchard, Augustin
2013-01-01
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance pro...
Fractional statistical potential in graphene
Ardenghi, J. S.
2017-03-01
In this work the fractional statistics is applied to an anyon gas in graphene to obtain the special features that the arbitrary phase interchange of the particle coordinates introduce in the thermodynamic properties. The electron gas is constituted by N anyons in the long wavelength approximation obeying fractional exclusion statistics and the partition function is analyzed in terms of a perturbation expansion up to first order in the dimensionless constant λ / L being L the length of the graphene sheet and λ = βℏvF the thermal wavelength. By considering the correct permutation expansion of the many-anyons wavefunction, taking into account that the phase changes with the number of inversions in each permutation, the statistical fermionic/bosonic potential is obtained and the intermediate statistical behavior is found. It is shown that "extra" fermonic and bosonic particles states appears and this "statistical particle" distribution depends on N. Entropy and specific heat is obtained up to first order in λ / L showing that the results obtained differs from those obtained in different approximation to the fractional exclusion statistics.
Explicit Formulae for the Continued Fraction Convergents of "Square Root of D"
Braza, Peter A.
2010-01-01
The formulae for the convergents of continued fractions are always given recursively rather than in explicit form. This article derives explicit formulae for the convergents of the continued fraction expansions for square roots.
Bergstra, Jan A.
2015-01-01
In the context of an involutive meadow a precise definition of fractions is formulated and on that basis formal definitions of various classes of fractions are given. The definitions follow the fractions as terms paradigm. That paradigm is compared with two competing paradigms for storytelling on fractions: fractions as values and fractions as pairs.
Novel Foraminal Expansion Technique
Senturk, Salim; Ciplak, Mert; Oktenoglu, Tunc; Sasani, Mehdi; Egemen, Emrah; Yaman, Onur; Suzer, Tuncer
2016-01-01
The technique we describe was developed for cervical foraminal stenosis for cases in which a keyhole foraminotomy would not be effective. Many cervical stenosis cases are so severe that keyhole foraminotomy is not successful. However, the technique outlined in this study provides adequate enlargement of an entire cervical foraminal diameter. This study reports on a novel foraminal expansion technique. Linear drilling was performed in the middle of the facet joint. A small bone graft was placed between the divided lateral masses after distraction. A lateral mass stabilization was performed with screws and rods following the expansion procedure. A cervical foramen was linearly drilled medially to laterally, then expanded with small bone grafts, and a lateral mass instrumentation was added with surgery. The patient was well after the surgery. The novel foraminal expansion is an effective surgical method for severe foraminal stenosis. PMID:27559460
Soil Organic Carbon Responses to Forest Expansion on Mountain Grasslands
DEFF Research Database (Denmark)
Guidi, Claudia
Grassland abandonment followed by progressive forest expansion is the dominant land-use change in the European Alps. Contrasting trends in soil organic carbon (SOC) stocks have been reported for mountainous regions following forest expansion on grasslands. Moreover, its effects on SOC properties...... involved into long-term stability are largely unknown. The aim of this PhD thesis was to explore changes in: (i) SOC stocks; (ii) physical SOC fractions; and (iii) labile soil carbon components following forest expansion on mountain grasslands. A land-use gradient located in the Southern Alps (Italy....... Changes in labile soil C were assessed by carbohydrate and thermal analyses of soil samples and fractions. Forest expansion on mountain grasslands caused a decrease in SOC stocks within the mineral soil. The SOC accumulation within the organic layers following forest establishment could not fully...
Strategic Expansion Models in Academic Radiology.
Natesan, Rajni; Yang, Wei T; Tannir, Habib; Parikh, Jay
2016-03-01
In response to economic pressures, academic institutions in the United States and their radiology practices, are expanding into the community to build a larger network, thereby driving growth and achieving economies of scale. These economies of scale are being achieved variously via brick-and-mortar construction, community practice acquisition, and partnership-based network expansion. We describe and compare these three expansion models within a 4-part framework of: (1) upfront investment; (2) profitability impact; (3) brand impact; and (4) risk of execution.
Steppe expansion in Patagonia?
Veblen, Thomas T.; Markgraf, Vera
1988-11-01
Westward expansion of the Patagonian steppe and retrocession of Andean forests due to increasing aridity over the past one or two millennia has been a persistent theme in the ecological and paleoecological literature for at least half a century. New evidence from pollen profiles, tree-ring analysis, vegetation structure, and photographic and documentary historical sources does not show the expansion of the steppe. Instead, over the past century trees have invaded the steppe as a consequence mainly of human-induced changes in the fire regime, and trees have regenerated in forest areas that were heavily burnt at the onset of European colonization.
Directory of Open Access Journals (Sweden)
Massimo Giovannini
2015-06-01
Full Text Available Cosmological singularities are often discussed by means of a gradient expansion that can also describe, during a quasi-de Sitter phase, the progressive suppression of curvature inhomogeneities. While the inflationary event horizon is being formed the two mentioned regimes coexist and a uniform expansion can be conceived and applied to the evolution of spatial gradients across the protoinflationary boundary. It is argued that conventional arguments addressing the preinflationary initial conditions are necessary but generally not sufficient to guarantee a homogeneous onset of the conventional inflationary stage.
Energy Technology Data Exchange (ETDEWEB)
Giovannini, Massimo, E-mail: massimo.giovannini@cern.ch [Department of Physics, Theory Division, CERN, 1211 Geneva 23 (Switzerland); INFN, Section of Milan-Bicocca, 20126 Milan (Italy)
2015-06-30
Cosmological singularities are often discussed by means of a gradient expansion that can also describe, during a quasi-de Sitter phase, the progressive suppression of curvature inhomogeneities. While the inflationary event horizon is being formed the two mentioned regimes coexist and a uniform expansion can be conceived and applied to the evolution of spatial gradients across the protoinflationary boundary. It is argued that conventional arguments addressing the preinflationary initial conditions are necessary but generally not sufficient to guarantee a homogeneous onset of the conventional inflationary stage.
For the Long Island, New Jersey, and southern New England region, one facet of marsh drowning as a result of accelerated sea level rise is the expansion of salt marsh ponds and pannes. Over the past century, marsh ponds and pannes have formed and expanded in areas of poor drainag...
Kowalski, Emmanuel
2010-01-01
This is a survey report for the Bourbaki Seminar (Exp. no. 1028, November 2010) concerning sieve and expanders, in particular the recent works of Bourgain, Gamburd and Sarnak introducing "sieve in orbits", and the related developments concerning expansion properties of Cayley graphs of finite linear groups.
Physics suggests that the interplay of momentum, continuity, and geometry in outward radial flow must produce density and concomitant pressure reductions. In other words, this flow is intrinsically auto-expansive. It has been proposed that this process is the key to understanding...
Cardiorenal-endocrine dynamics during and following volume expansion
Energy Technology Data Exchange (ETDEWEB)
Zimmerman, R.S.; Edwards, B.S.; Schwab, T.R.; Heublein, D.M.; Burnett, J.C. Jr.
1987-02-01
The relationship between atrial pressure, atrial natriuretic peptide (ANP), the renin-angiotensin-aldosterone system, and renal hemodynamic and excretory function was examined during and following acute 10% body weight saline volume expansion and measurements were made at 3.3, 6.6, and 10% body weight volume expansion in pentobarbital anesthetized dogs. Right atrial pressure (RAP), pulmonary capillary wedge pressure (PCWP), fractional excretion of Na (FE/sub Na/), and ANP all increased in parallel during volume expansion. Plasma renin activity (PRA) and aldosterone decreased in parallel during 10% volume expansion. ANP, PRA and aldosterone were measured by radioimmunoassay. Following 10% volume expansion, saline was infused at the peak urine flow rate to maintain peak volume expansion. Despite continued saline infusion, RAP, PCWP, and ANP decreased in parallel. In contrast, FE/sub Na/ remained increased, and aldosterone and PRA remained depressed. These studies demonstrate that atrial pressures, ANP, and FE/sub Na/ increase in parallel during volume expansion; this suggests a role for ANP in modulating acute atrial volume overload. During stable volume expansion periods, however, despite a decrease in ANP levels, Na excretion remains elevated, suggesting that non-ANP mechanisms may be important in maintaining natriuresis during stable volume expansion.
Developing Understanding of Fractions through Pattern: Blocks and Fair Trade
Roddick, Cheryl; Silvas-Centeno, Christina
2007-01-01
This article describes the process of design and implementation of a hands-on unit on fractions in the sixth grade. The fraction unit, taught by a classroom teacher with the aid of a university professor, uses pattern blocks to help students develop conceptual understanding of fractions. Student misunderstandings and outcomes are presented, as…
Institute of Scientific and Technical Information of China (English)
杨晨; 朱懿
2012-01-01
N600-24.2/566/566 supercritical steam turbine which is made by Shanghai Steam Turbine Plant, for example, importance and variation of differential expansion controlling of steam turbine, mutual relations of the rotor and stator expansion, and the most effective technical measures of controlling differential expansion in the start-up process of Phase I 2 x 600 MW supercritical steam turbine of Huangjinbu Power Generation Co.,Ltd. of State Power Grid in Jiangxi were analyzed, and had some reference values for other turbines.%以上海汽轮机厂生产的N600．24．2／566／566型超临界汽轮机为例，分析了江西国电黄金埠发电有限公司1期2台600MW超临界汽轮机启动过程中，汽轮机胀差控制的重要性、变化规律、转子和静子膨胀的相互关系以及采取的最有效的控制胀差的技术措施，对于其它汽轮机具有一定的参考价值。
Energy Technology Data Exchange (ETDEWEB)
Lim, Sang Gyu; Jung, Sung Yeop; Kim, Sang Nyung [Kyunghee University, Youngin (Korea, Republic of)
2008-04-15
Four of safety injection (SI) nozzles in a 1000 MWe-class Optimized Power Reactor (OPR-1000) are fitted with thermal sleeves (T/S) to alleviate thermal fatigue. Thermal sleeves in no3 and no4 of Younggwang (YGN) and Ulchin (UCN) nuclear power plant are manufactured out of Inconel-600 and fitted solidly without any problem, whereas YGN and UCN in no5 and no6, also fitted with thermal sleeves made of Inconel-690 for increased corrosion resistance, experienced a loosening of thermal sleeves except T/S of YGN no5-1A. To identify the root cause of T/S loosening, three suspected causes were analyzed: (1) the shear force of flow on the T/S when the safety SI nozzle was in operation, (2) the differences between Inconel-600 and Inconel-690 in terms of physical and chemical properties (notably the thermal expansion coefficient), and (3) the positioning error in explosive expansion of the T/S as well as the asymmetric expansion of T/S. It was confirmed that none of the three suspected causes could be considered as the root cause. However, after reviewing the design change history from the Palo Verde nuclear power plant to YGN and UCN no3,4 and no5,6, it was realized that the two stage design modifications (in terms of groove depth and material) made an additional explosive energy required by 172% in aggregate, but the amount of gunpowder and the explosive expansion method were the same as before, resulting in insufficient explosive force that led to poor thermal sleeve expansion. T/S measurement data and rubbing copies also support this conclusion. And the T/S loosening was also attributable to lenient quality control before and after fitting the T/S that resulted in significant uncertainty. In addition, it is our judgment that the acceptance criterion applicable to T/S fitting was not strict enough, failing to single out thermal sleeves that were not expanded sufficiently. Lastly, the acceptance criterion was scientifically revised to incorporate the thinning effect and
A Gauss-Kusmin theorem for optimal continued fractions
Dajani, K.; Kraaikamp, C.
2001-01-01
One of the first and still one of the most important results in the metrical theory of continued fractions is the so-called Gauss-Kusmin theorem. Let and let be the regular continued fraction (RCF) expansion of then it was observed by Gauss in 1800 that -
Bigravity from gradient expansion
Energy Technology Data Exchange (ETDEWEB)
Yamashita, Yasuho [Yukawa Institute for Theoretical Physics, Kyoto University,606-8502, Kyoto (Japan); Tanaka, Takahiro [Yukawa Institute for Theoretical Physics, Kyoto University,606-8502, Kyoto (Japan); Department of Physics, Kyoto University,606-8502, Kyoto (Japan)
2016-05-04
We discuss how the ghost-free bigravity coupled with a single scalar field can be derived from a braneworld setup. We consider DGP two-brane model without radion stabilization. The bulk configuration is solved for given boundary metrics, and it is substituted back into the action to obtain the effective four-dimensional action. In order to obtain the ghost-free bigravity, we consider the gradient expansion in which the brane separation is supposed to be sufficiently small so that two boundary metrics are almost identical. The obtained effective theory is shown to be ghost free as expected, however, the interaction between two gravitons takes the Fierz-Pauli form at the leading order of the gradient expansion, even though we do not use the approximation of linear perturbation. We also find that the radion remains as a scalar field in the four-dimensional effective theory, but its coupling to the metrics is non-trivial.
Operator product expansion algebra
Energy Technology Data Exchange (ETDEWEB)
Holland, Jan [CPHT, Ecole Polytechnique, Paris-Palaiseau (France)
2014-07-01
The Operator Product Expansion (OPE) is a theoretical tool for studying the short distance behaviour of products of local quantum fields. Over the past 40 years, the OPE has not only found widespread computational application in high-energy physics, but, on a more conceptual level, it also encodes fundamental information on algebraic structures underlying quantum field theories. I review new insights into the status and properties of the OPE within Euclidean perturbation theory, addressing in particular the topics of convergence and ''factorisation'' of the expansion. Further, I present a formula for the ''deformation'' of the OPE algebra caused by a quartic interaction. This formula can be used to set up a novel iterative scheme for the perturbative computation of OPE coefficients, based solely on the zeroth order coefficients (and renormalisation conditions) as initial input.
Continued fractions and heavy sequences
Boshernitzan, Michael
2009-01-01
We initiate the study of the sets $H(c)$, $0=x-[x]$ stands for the fractional part of $x\\in \\mathbb R$. We prove that, for rational $c$, the sets $H(c)$ are of positive Hausdorff dimension and, in particular, are uncountable. For integers $m\\geq1$, we obtain a surprising characterization of the numbers $\\alpha\\in H_m= H(\\frac1m)$ in terms of their continued fraction expansions: The odd entries (partial quotients) of these expansions are divisible by $m$. The characterization implies that $x\\in H_m$ if and only if $\\frac 1{mx} \\in H_m$, for $x>0$. We are unaware of a direct proof of this equivalence, without making a use of the mentioned characterization of the sets $H_m$. We also introduce the dual sets $\\hat H_m$ of reals $y$ for which the sequence of integers $\\big([ky]\\big)_{k\\geq1}$ consistently hits the set $m\\mathbb Z$ with the at least expected frequency $\\frac1m$ and establish the connection with the sets $H_m$: {2mm} If $xy=m$ for $x,y>0$, then $x\\in H_m$ if and only if $y\\in \\hat H_m$. The motivatio...
Tenreiro Machado, J. A.
2015-08-01
This paper addresses the matrix representation of dynamical systems in the perspective of fractional calculus. Fractional elements and fractional systems are interpreted under the light of the classical Cole-Cole, Davidson-Cole, and Havriliak-Negami heuristic models. Numerical simulations for an electrical circuit enlighten the results for matrix based models and high fractional orders. The conclusions clarify the distinction between fractional elements and fractional systems.
Fractional Charge Definitions and Conditions
Energy Technology Data Exchange (ETDEWEB)
Goldhaber, A.S.
2004-06-04
Fractional charge is known through theoretical and experimental discoveries of isolable objects carrying fractions of familiar charge units--electric charge Q, spin S, and the difference of baryon and lepton numbers B-L. With a few simple assumptions all these effects may be described using a generalized version of charge renormalization for locally conserved charges, in which medium correlations yield familiar adiabatic, continuous renormalization, or sometimes nonadiabatic, discrete renormalization. Fractional charges may be carried by fundamental particles or fundamental solitons. Either picture works for the simplest fractional-quantum-Hall-effect quasiholes, though the particle description is far more general. The only known fundamental solitons in three or fewer space dimensions d are the kink (d = 1), the vortex (d = 2), and the magnetic monopole (d = 3). Further, for a charge not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional values of B-L for electrically charged elementary particles.
Operator product expansion algebra
Energy Technology Data Exchange (ETDEWEB)
Holland, Jan [School of Mathematics, Cardiff University, Senghennydd Rd, Cardiff CF24 4AG (United Kingdom); Hollands, Stefan [School of Mathematics, Cardiff University, Senghennydd Rd, Cardiff CF24 4AG (United Kingdom); Institut für Theoretische Physik, Universität Leipzig, Brüderstr. 16, Leipzig, D-04103 (Germany)
2013-07-15
We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE,
Testing Machine for Expansive Mortar
Silva, Romulo Augusto Ventura
2011-01-01
The correct evaluation of a material property is fundamental to, on their application; they met all expectations that were designed for. In development of an expansive cement for ornamental rocks purpose, was denoted the absence of methodologies and equipments to evaluate the expansive pressure and temperature of expansive cement during their expansive process, having that data collected in a static state of the specimen. In that paper, is described equipment designed for evaluation of pressure and temperature of expansive cements applied to ornamental rocks.
Engineering Properties of Expansive Soil
Institute of Scientific and Technical Information of China (English)
DAI Shaobin; SONG Minghai; HUANG Jun
2005-01-01
The components of expansive soil were analyzed with EDAX, and it is shown that the main contents of expansive soil in the northern Hubei have some significant effects on engineering properties of expansive soil. Furthermore, the soil modified by lime has an obvious increase of Ca2+ and an improvement of connections between granules so as to reduce the expansibility and contractility of soil. And it also has a better effect on the modified expansive soil than the one modified by pulverized fuel ash.
Initialized Fractional Calculus
Lorenzo, Carl F.; Hartley, Tom T.
2000-01-01
This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.
Exact solution to fractional logistic equation
West, Bruce J.
2015-07-01
The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.
Fraction Sense: Foundational Understandings.
Fennell, Francis Skip; Karp, Karen
2016-08-09
The intent of this commentary is to identify elements of fraction sense and note how the research studies provided in this special issue, in related but somewhat different ways, validate the importance of such understandings. Proficiency with fractions serves as a prerequisite for student success in higher level mathematics, as well as serving as a gateway to many occupations and varied contexts beyond the mathematics classroom. Fraction sense is developed through instructional opportunities involving fraction equivalence and magnitude, comparing and ordering fractions, using fraction benchmarks, and computational estimation. Such foundations are then extended to operations involving fractions and decimals and applications involving proportional reasoning. These components of fraction sense are all addressed in the studies provided in this issue, with particular consideration devoted to the significant importance of the use of the number line as a central representational tool for conceptually understanding fraction magnitude.
Frequency dependent thermal expansion in binary viscoelasticcomposites
Energy Technology Data Exchange (ETDEWEB)
Berryman, James G.
2007-12-01
The effective thermal expansion coefficient beta* of abinary viscoelastic composite is shown to be frequency dependent even ifthe thermal expansion coefficients beta A and beta B of both constituentsare themselves frequency independent. Exact calculations for binaryviscoelastic systems show that beta* is related to constituent valuesbeta A, beta B, volume fractions, and bulk moduli KA, KB, as well as tothe overall bulk modulus K* of the composite system. Then, beta* isdetermined for isotropic systems by first bounding (or measuring) K* andtherefore beta*. For anisotropic systems with hexagonal symmetry, theprincipal values of the thermal expansion beta*perp and beta*para can bedetermined exactly when the constituents form a layered system. In allthe examples studied, it is shown explicitly that the eigenvectors of thethermoviscoelastic system possess non-negative dissipation -- despite thecomplicated analytical behavior of the frequency dependent thermalexpansivities themselves. Methods presented have a variety ofapplications from fluid-fluid mixtures to fluid-solid suspensions, andfrom fluid-saturated porous media to viscoelastic solid-solidcomposites.
Continued Fraction Algorithm for Matrix Exponentials
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A recursive rational algorithm for matrix exponentials was obtained by making use of the generalized inverse of a matrix in this paper. On the basis of the n-th convergence of Thiele-type continued fraction expansion, a new type of the generalized inverse matrix-valued Padé approximant (GMPA) for matrix exponentials was defined and its remainder formula was proved. The results of this paper were illustrated by some examples.
Conformal expansions and renormalons
Gardi, E; Gardi, Einan; Grunberg, Georges
2001-01-01
The large-order behaviour of QCD is dominated by renormalons. On the other hand renormalons do not occur in conformal theories, such as the one describing the infrared fixed-point of QCD at small beta_0 (the Banks--Zaks limit). Since the fixed-point has a perturbative realization, all-order perturbative relations exist between the conformal coefficients, which are renormalon-free, and the standard perturbative coefficients, which contain renormalons. Therefore, an explicit cancellation of renormalons should occur in these relations. The absence of renormalons in the conformal limit can thus be seen as a constraint on the structure of the QCD perturbative expansion. We show that the conformal constraint is non-trivial: a generic model for the large-order behaviour violates it. We also analyse a specific example, based on a renormalon-type integral over the two-loop running-coupling, where the required cancellation does occur.
Optical imaging. Expansion microscopy.
Chen, Fei; Tillberg, Paul W; Boyden, Edward S
2015-01-30
In optical microscopy, fine structural details are resolved by using refraction to magnify images of a specimen. We discovered that by synthesizing a swellable polymer network within a specimen, it can be physically expanded, resulting in physical magnification. By covalently anchoring specific labels located within the specimen directly to the polymer network, labels spaced closer than the optical diffraction limit can be isotropically separated and optically resolved, a process we call expansion microscopy (ExM). Thus, this process can be used to perform scalable superresolution microscopy with diffraction-limited microscopes. We demonstrate ExM with apparent ~70-nanometer lateral resolution in both cultured cells and brain tissue, performing three-color superresolution imaging of ~10(7) cubic micrometers of the mouse hippocampus with a conventional confocal microscope.
Use of Expansion Turbines in Natural Gas Pressure Reduction Stations
Directory of Open Access Journals (Sweden)
Poivil Jaroslav
2004-09-01
Full Text Available Through the use of expansion turbines in natural gas pressure reduction stations it is possible to produce clean, green electricity.Such energy recovery unit utilize the potential energy of natural gas being delivered under high pressure. Expansion turbines are not onlyefficient and profitable but meet the environmental criteria no emissions of sulfur dioxide, nitrogen oxides or carbon dioxide.
Modelling autogenous expansion for magnesia concrete in arch dams
Institute of Scientific and Technical Information of China (English)
Feng JIN; Guoxin ZHANG; Xiaoqing LUO; Chuhan ZHANG
2008-01-01
Magnesia Concrete is a kind of expansive con-crete used in Chinese hydraulic engineering more and more widely. To evaluate the effects of autogenous expan-sion on the stresses of arch dams, a simple model of auto-genous expansion for Magnesia Concrete in dam engineering is presented. This model is based on three assumptions: 1) the total amount of autogenous expan-sion of Magnesia Concrete is related only to the properties of materials and mixing of concrete; 2) the autogenous expansion of Magnesia Concrete is irreversible due to the irreversibility of hydration reaction of Magnesia in the concrete; 3) the autogenous expansion strain rates of Magnesia Concrete bear a relation between temperature and residual Magnesia per unit volume of concrete. The model is verified by some experimental data of autogen-ous expansion of Magnesia Concrete and field-measured data of an arch dam in China. Embedded into finite ele-ment arch dam simulation software, this model is employed to simulate the effects of autogenous expansion of Magnesia Concrete in hydraulic engineering.
Burial Ground Expansion Hydrogeologic Characterization
Energy Technology Data Exchange (ETDEWEB)
Gaughan , T.F.
1999-02-26
Sirrine Environmental Consultants provided technical oversight of the installation of eighteen groundwater monitoring wells and six exploratory borings around the location of the Burial Ground Expansion.
Dewi, D. A. K.; Suryadi, D.; Suratno, T.; Mulyana, E.; Kurniawan, H.
2017-02-01
Introducing fractions is identical to divide an object. Suppose we divide the apple into two parts. One divided into two parts, the question arises whether one part can be called a half or not. Based on this activity, how can students give meaning to fractions. This study aims at designing a different fractions lesson by applying Didactical Design Research. In doing so, we undertook several research phases: 1) thinking what is fractions and why students should learn this concept; 2) designing didactical situation based on identified learning obstacles; and 3) reflecting retrospectively on the lesson design and its implementation as to redesign the fractions lesson. Our analysis revealed that most students held epistemological obstacles in giving meaning of fractions because they only know fractions as numbers that have numerator and denominator. By positioning ourselves as students, we discuss the ideal design to help students in constructing the meaning of fractions.
Edelman, Mark
2014-01-01
In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential equations describing systems experiencing periodic kicks. Their properties depend on the value of two parameters: the non-linearity parameter, which arises from the corresponding regular dynamical systems; and the memory parameter which is the order of the fractional derivative in the corresponding non-linear fractional differential equations. The examples of the fractional Standard and Logistic maps demonstrate that phase space of non-linear fractional dynamical systems may contain periodic sinks, attracting slow diverging trajectories, attracting accelerator mode trajectories, chaotic attractors, and cascade of bifurcations type trajectories whose properties are different from properties of attractors in regular dynamical systems. The author argues that discovered properties s...
On continued fraction algorithms
Smeets, Ionica
2010-01-01
Is there a good continued fraction approximation between every two bad ones? What is the entropy of the natural extension for alpha-Rosen fractions? How do you find multi-dimensional continued fractions with a guaranteed quality in polynomial time? These, and many more, questions are answered in thi
Graham, Alan; Graham, Louise
2003-01-01
Describes a very successful attempt to teach fractions to year 5 pupils based on pupils making their own fraction pack. Children decided for themselves how to make the fractional slices used in the activity using colored cardboard sheets and templates of a paper circle consisting of 24 equal slices. (Author/NB)
On continued fraction algorithms
Smeets, Ionica
2010-01-01
Is there a good continued fraction approximation between every two bad ones? What is the entropy of the natural extension for alpha-Rosen fractions? How do you find multi-dimensional continued fractions with a guaranteed quality in polynomial time? These, and many more, questions are answered in thi
Learning to Use Fractions: Examining Middle School Students Emerging Fraction Literacy
Johanning, Debra I.
2008-01-01
This article describes one prevalent practice that a group of 6th- and 7th-grade students engaged in when they used fractions in the context of area and perimeter, decimal operations, similarity, and ratios and proportions. The study's results revealed that students did not simply take the concepts and skills learned in formal fractions units and…
An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Moh’d Khier Al-Srihin
2017-01-01
Full Text Available In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to multiterm fractional differential equations, where we overcome the difficulty of computing iterated fractional derivatives, which are difficult to be computed in general. The terms of the series are obtained sequentially using a closed formula, where only integer derivatives have to be computed. Several examples are presented to illustrate the efficiency of the new approach and comparison with the Adomian decomposition method is performed.
Ackerman, Margareta; Lopez-Ortiz, Alejandro
2011-01-01
Over the last fifteen years, web searching has seen tremendous improvements. Starting from a nearly random collection of matching pages in 1995, today, search engines tend to satisfy the user's informational need on well-formulated queries. One of the main remaining challenges is to satisfy the users' needs when they provide a poorly formulated query. When the pages matching the user's original keywords are judged to be unsatisfactory, query expansion techniques are used to alter the result set. These techniques find keywords that are similar to the keywords given by the user, which are then appended to the original query leading to a perturbation of the result set. However, when the original query is sufficiently ill-posed, the user's informational need is best met using entirely different keywords, and a small perturbation of the original result set is bound to fail. We propose a novel approach that is not based on the keywords of the original query. We intentionally seek out orthogonal queries, which are r...
Lattice harmonics expansion revisited
Kontrym-Sznajd, G.; Holas, A.
2017-04-01
The main subject of the work is to provide the most effective way of determining the expansion of some quantities into orthogonal polynomials, when these quantities are known only along some limited number of sampling directions. By comparing the commonly used Houston method with the method based on the orthogonality relation, some relationships, which define the applicability and correctness of these methods, are demonstrated. They are verified for various sets of sampling directions applicable for expanding quantities having the full symmetry of the Brillouin zone of cubic and non-cubic lattices. All results clearly show that the Houston method is always better than the orthogonality-relation one. For the cubic symmetry we present a few sets of special directions (SDs) showing how their construction and, next, a proper application depend on the choice of various sets of lattice harmonics. SDs are important mainly for experimentalists who want to reconstruct anisotropic quantities from their measurements, performed at a limited number of sampling directions.
Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Jianping Zhao
2012-01-01
Full Text Available An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.
Shamim, Atif
2011-03-01
For the first time, a generalized Smith chart is introduced here to represent fractional order circuit elements. It is shown that the standard Smith chart is a special case of the generalized fractional order Smith chart. With illustrations drawn for both the conventional integer based lumped elements and the fractional elements, a graphical technique supported by the analytical method is presented to plot impedances on the fractional Smith chart. The concept is then applied towards impedance matching networks, where the fractional approach proves to be much more versatile and results in a single element matching network for a complex load as compared to the two elements in the conventional approach. © 2010 IEEE.
A Comparison of Textbooks' Presentation of Fractions
Cady, Jo A.; Hodges, Thomas E.; Collins, R. Lee
2015-01-01
In the United States, fractions are an important part of the middle school curriculum, yet many middle school students struggle with fraction concepts. Teachers also have difficulty with the conceptual understanding needed to teach fractions and rely on textbooks when making instructional decisions. This reliance on textbooks, the idea that…
Fractional Dynamics and Control
Machado, José; Luo, Albert
2012-01-01
Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science. Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics Develops new methods for control and synchronization of...
Dey, Aloke
2009-01-01
A one-stop reference to fractional factorials and related orthogonal arrays.Presenting one of the most dynamic areas of statistical research, this book offers a systematic, rigorous, and up-to-date treatment of fractional factorial designs and related combinatorial mathematics. Leading statisticians Aloke Dey and Rahul Mukerjee consolidate vast amounts of material from the professional literature--expertly weaving fractional replication, orthogonal arrays, and optimality aspects. They develop the basic theory of fractional factorials using the calculus of factorial arrangements, thereby providing a unified approach to the study of fractional factorial plans. An indispensable guide for statisticians in research and industry as well as for graduate students, Fractional Factorial Plans features: * Construction procedures of symmetric and asymmetric orthogonal arrays. * Many up-to-date research results on nonexistence. * A chapter on optimal fractional factorials not based on orthogonal arrays. * Trend-free plans...
On genus expansion of superpolynomials
Mironov, A; Sleptsov, A; Smirnov, A
2013-01-01
Recently it was shown that the (Ooguri-Vafa) generating function of HOMFLY polynomials is the Hurwitz partition function, i.e. that the dependence of the HOMFLY polynomials on representation is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and expansion through Vassiliev invariants explicitly demonstrate this phenomenon. In the present letter we claim that the superpolynomials are not functions of such a type: symmetric group characters do not provide an adequate linear basis for their expansions. Deformation to superpolynomials is, however, straightforward in the multiplicative basis:the Casimir operators are beta-deformed to Hamiltonians of the Calogero-Moser-Sutherland system. Applying this trick to the genus and Vassiliev expansions, we observe that the deformation is rather straightforward only for the thin knots. Beyond this family additional algebraically independent terms appear in the Vassiliev and genus expansions. This can suggest that the superpol...
Capacity Expansion Modeling for Storage Technologies
Energy Technology Data Exchange (ETDEWEB)
Hale, Elaine; Stoll, Brady; Mai, Trieu
2017-04-03
The Resource Planning Model (RPM) is a capacity expansion model designed for regional power systems and high levels of renewable generation. Recent extensions capture value-stacking for storage technologies, including batteries and concentrating solar power with storage. After estimating per-unit capacity value and curtailment reduction potential, RPM co-optimizes investment decisions and reduced-form dispatch, accounting for planning reserves; energy value, including arbitrage and curtailment reduction; and three types of operating reserves. Multiple technology cost scenarios are analyzed to determine level of deployment in the Western Interconnection under various conditions.
Preservice Teachers’ Conceptual and Procedural Knowledge of Fraction
Lin, Cheng-Yao; Becker, Jerry; Byun, Mi-Ran; Yang, Der-Ching; Huang, Tsai-Wei
2013-01-01
This study examined (a) the differences in preservice teachers’ procedural knowledge in four areas of fraction operations in Taiwan and the United States, (b) the differences in preservice teachers’ conceptual knowledge in four areas of fraction operations in Taiwan and the United States, and (c) correlation in preservice teachers’ conceptual…
Preservice Teachers’ Conceptual and Procedural Knowledge of Fraction
Lin, Cheng-Yao; Becker, Jerry; Byun, Mi-Ran; Yang, Der-Ching; Huang, Tsai-Wei
2013-01-01
This study examined (a) the differences in preservice teachers’ procedural knowledge in four areas of fraction operations in Taiwan and the United States, (b) the differences in preservice teachers’ conceptual knowledge in four areas of fraction operations in Taiwan and the United States, and (c) correlation in preservice teachers’ conceptual…
Institute of Scientific and Technical Information of China (English)
陈海华; 张菊芳; 李金晟; 贾明; 郭晓波; 王宇燕; 沈海燕
2015-01-01
Objective To investigate the therapeutic effect of soft tissue expansion combined with follicular unit extraction(FUE) for burn cicatricial bald.Methods 48 patients with burn cicatricial bald (＞ 25 cm2) were treated in three stages.The expanders were implanted on the first stage.After expansion for 8 weeks,the expanders were taken out and local flaps were transferred.One year later,follicular unit extraction(FUE) was applied on the bald area.Results 48 cases were followed up for 5 years with satisfactory cosmetic results.The VAS assessment of satisfaction on hair appearance after three-staged surgery was 8.2 ± 2.1.Conclusions Soft tissue expansion combined with FUE has a reliable effect for burn cicatricial bald.%目的 探讨并分析皮肤软组织扩张术联合毛囊单位提取技术治疗烧伤后瘢痕性秃发的效果.方法 2007年3月至2013年6月共收治48例患者,秃发面积均大于25 cm2.一期手术行扩张器置入,注入额定容量的200％～ 300％;二期手术在注水完成后8周,行局部皮瓣转移修复术;三期手术在皮瓣修复后1年,行瘢痕区单体式毛发移植.结果 经扩张器联合毛发移植后,48例患者瘢痕区毛发生长自然,随访5年,效果满意.三期手术后的毛发形态满意度的VAS评分为(8.2±2.1)分.结论 皮肤软组织扩张术联合毛囊单位提取技术对头部烧伤后瘢痕性秃发修复效果确切.
Strong anisotropic thermal expansion in cristobalite-type BPO 4
Achary, S. N.; Tyagi, A. K.
2004-11-01
In this communication, the thermal expansion behavior of cristobalite-type BPO 4, determined from high-temperature X-ray diffraction studies, is being reported. BPO 4 crystallizes in tetragonal lattice, with space group I-4 (No. 82) at room temperature, with unit cell parameters: a=4.3447(2), c=6.6415(5) Å and V=125.37(1) Å 3. The tetragonal unit cell parameters at 900 °C are: a=4.3939(2), c=6.6539(6) Å and V=128.46(1) Å 3. The results show a very strong anisotropic expansion in the lattice, with the typical thermal expansion coefficients along a- and c-axis 12.9×10 -6 and 2.1×10 -6/°C, respectively. The volume thermal expansion coefficient of the lattice is 28.2×10 -6/°C in the temperature range of 25-900 °C. The variation of the crystal structure with temperature and the thermal expansion behavior are explained in this manuscript. The role of inter-polyhedral angle on the thermal expansion behavior has also been established.
Dividing Fractions: A Pedagogical Technique
Lewis, Robert
2016-01-01
When dividing one fraction by a second fraction, invert, that is, flip the second fraction, then multiply it by the first fraction. To multiply fractions, simply multiply across the denominators, and multiply across the numerators to get the resultant fraction. So by inverting the division of fractions it is turned into an easy multiplication of…
Colossal negative thermal expansion in reduced layered ruthenate
Takenaka, Koshi; Okamoto, Yoshihiko; Shinoda, Tsubasa; Katayama, Naoyuki; Sakai, Yuki
2017-01-01
Large negative thermal expansion (NTE) has been discovered during the last decade in materials of various kinds, particularly materials associated with a magnetic, ferroelectric or charge-transfer phase transition. Such NTE materials have attracted considerable attention for use as thermal-expansion compensators. Here, we report the discovery of giant NTE for reduced layered ruthenate. The total volume change related to NTE reaches 6.7% in dilatometry, a value twice as large as the largest volume change reported to date. We observed a giant negative coefficient of linear thermal expansion α=-115 × 10-6 K-1 over 200 K interval below 345 K. This dilatometric NTE is too large to be attributable to the crystallographic unit-cell volume variation with temperature. The highly anisotropic thermal expansion of the crystal grains might underlie giant bulk NTE via microstructural effects consuming open spaces in the sintered body on heating.
Fractional Pure Birth Processes
Orsingher, Enzo; 10.3150/09-BEJ235
2010-01-01
We consider a fractional version of the classical non-linear birth process of which the Yule-Furry model is a particular case. Fractionality is obtained by replacing the first-order time derivative in the difference-differential equations which govern the probability law of the process, with the Dzherbashyan-Caputo fractional derivative. We derive the probability distribution of the number $ \\mathcal{N}_\
Fractional vortex Hilbert's Hotel
Gbur, Greg
2015-01-01
We demonstrate how the unusual mathematics of transfinite numbers, in particular a nearly perfect realization of Hilbert's famous hotel paradox, manifests in the propagation of light through fractional vortex plates. It is shown how a fractional vortex plate can be used, in principle, to create any number of "open rooms," i.e. topological charges, simultaneously. Fractional vortex plates are therefore demonstrated to create a singularity of topological charge, in which the vortex state is completely undefined and in fact arbitrary.
Fractional Electromagnetic Waves
Gómez, J F; Bernal, J J; Tkach, V I; Guía, M
2011-01-01
In the present work we consider the electromagnetic wave equation in terms of the fractional derivative of the Caputo type. The order of the derivative being considered is 0 <\\gamma<1. A new parameter \\sigma, is introduced which characterizes the existence of the fractional components in the system. We analyze the fractional derivative with respect to time and space, for \\gamma = 1 and \\gamma = 1/2 cases.
Thermal Expansion of Polyurethane Foam
Lerch, Bradley A.; Sullivan, Roy M.
2006-01-01
Closed cell foams are often used for thermal insulation. In the case of the Space Shuttle, the External Tank uses several thermal protection systems to maintain the temperature of the cryogenic fuels. A few of these systems are polyurethane, closed cell foams. In an attempt to better understand the foam behavior on the tank, we are in the process of developing and improving thermal-mechanical models for the foams. These models will start at the microstructural level and progress to the overall structural behavior of the foams on the tank. One of the key properties for model characterization and verification is thermal expansion. Since the foam is not a material, but a structure, the modeling of the expansion is complex. It is also exacerbated by the anisoptropy of the material. During the spraying and foaming process, the cells become elongated in the rise direction and this imparts different properties in the rise direction than in the transverse directions. Our approach is to treat the foam as a two part structure consisting of the polymeric cell structure and the gas inside the cells. The polymeric skeleton has a thermal expansion of its own which is derived from the basic polymer chemistry. However, a major contributor to the thermal expansion is the volume change associated with the gas inside of the closed cells. As this gas expands it exerts pressure on the cell walls and changes the shape and size of the cells. The amount that this occurs depends on the elastic and viscoplastic properties of the polymer skeleton. The more compliant the polymeric skeleton, the more influence the gas pressure has on the expansion. An additional influence on the expansion process is that the polymeric skeleton begins to breakdown at elevated temperatures and releases additional gas species into the cell interiors, adding to the gas pressure. The fact that this is such a complex process makes thermal expansion ideal for testing the models. This report focuses on the thermal
Directory of Open Access Journals (Sweden)
Luiz Fabio Mesquiati
2014-05-01
Full Text Available This paper is devoted to a reflection on the dynamics of higher education in the UK and its relation with the modernization of higher education systems in the world. From evaluative parameters used by the main evaluation and resource allocation programs for research and scientific development, we seek to establish guidelines for the development of a system of quality higher education, based on the expansion of the education system focused on criteria of international competitiveness. Presented as a key issue in the higher education policies of the UK, the internationalization builds partnerships, cooperation and exchanges that foster construction of differentiated knowledge. As a quality indicator, it points to the formation of professors able to create new strategies for teaching and learning and to act as facilitators of the development of skills, competencies and knowledge, mediated by technology and qualified to promote social and economic development in the building of competitive nations that strengthen their leading position in the world scenario. Based on the set criteria, the position adopted by countries with emphasized economic development is indicated as a need to rethink the framework of funding for the education sector, aiming at setting up a more dynamic system of better quality with reduced state presence and intense market share. O presente texto dedica-se a uma reflexão sobre a dinâmica da educação superior no Reino Unido e sua relação com a modernização dos sistemas de educação superior no mundo. A partir de parâmetros avaliativos empregados pelos principais programas de avaliação e distribuição de recursos para pesquisa e desenvolvimento científico, busca-se o estabelecimento de diretrizes para o desenvolvimento de um sistema de educação superior de qualidade, com base na expansão do sistema de ensino focada em critérios de competitividade internacional. Apresentada como tema-chave nas políticas de educa
Medicaid enrollment after liver transplantation: Effects of medicaid expansion.
Tumin, Dmitry; Hayes, Don; Washburn, W Kenneth; Tobias, Joseph D; Black, Sylvester M
2016-08-01
Liver transplantation (LT) recipients in the United States have low rates of paid employment, making some eligible for Medicaid public health insurance after transplant. We test whether recent expansions of Medicaid eligibility increased Medicaid enrollment and insurance coverage in this population. Patients of ages 18-59 years receiving first-time LTs in 2009-2013 were identified in the United Network for Organ Sharing registry and stratified according to insurance at transplantation (private versus Medicaid/Medicare). Posttransplant insurance status was assessed through June 2015. Difference-in-difference multivariate competing-risks models stratified on state of residence estimated effects of Medicaid expansion on Medicaid enrollment or use of uninsured care after LT. Of 12,837 patients meeting inclusion criteria, 6554 (51%) lived in a state that expanded Medicaid eligibility. Medicaid participation after LT was more common in Medicaid-expansion states (25%) compared to nonexpansion states (19%; P expansion (January 1, 2014), the hazard of posttransplant Medicaid enrollment increased in states participating in Medicaid expansion (hazard ratio [HR] = 1.5; 95% confidence interval [CI] = 1.1-2.0; P = 0.01), but not in states opting out of Medicaid expansion (HR = 0.8; 95% CI = 0.5-1.3; P = 0.37), controlling for individual characteristics and time-invariant state-level factors. No effects of Medicaid expansion on the use of posttransplant uninsured care were found, regardless of private or government insurance status at transplantation. Medicaid expansion increased posttransplant Medicaid enrollment among patients who had private insurance at transplantation, but it did not improve overall access to health insurance among LT recipients. Liver Transplantation 22 1075-1084 2016 AASLD.
Solving Operator Equation Based on Expansion Approach
Directory of Open Access Journals (Sweden)
A. Aminataei
2014-01-01
Full Text Available To date, researchers usually use spectral and pseudospectral methods for only numerical approximation of ordinary and partial differential equations and also based on polynomial basis. But the principal importance of this paper is to develop the expansion approach based on general basis functions (in particular case polynomial basis for solving general operator equations, wherein the particular cases of our development are integral equations, ordinary differential equations, difference equations, partial differential equations, and fractional differential equations. In other words, this paper presents the expansion approach for solving general operator equations in the form Lu+Nu=g(x,x∈Γ, with respect to boundary condition Bu=λ, where L, N and B are linear, nonlinear, and boundary operators, respectively, related to a suitable Hilbert space, Γ is the domain of approximation, λ is an arbitrary constant, and g(x∈L2(Γ is an arbitrary function. Also the other importance of this paper is to introduce the general version of pseudospectral method based on general interpolation problem. Finally some experiments show the accuracy of our development and the error analysis is presented in L2(Γ norm.
Electronic realization of the fractional-order systems
Directory of Open Access Journals (Sweden)
Františka Dorčáková
2007-10-01
Full Text Available This article is devoted to the electronic (analogue realization of the fractional-order systems – controllers or controlled objects whose we earlier used, identified, and analyzed as a mathematical models only ��� namely a fractional-order differential equation, and solved numerically using a method based on the truncated version of the Grunwald - Letnikov formula for fractional derivative. The electronic realization of the fractional derivative is based on the continued fraction expansion of the rational approximation of the fractional differentiator from which we obtained the values of the resistors and capacitors of the electronic circuit. Along with the mathematical description are presented also simulation and measurement results.
Gradient expansion for anisotropic hydrodynamics
Florkowski, Wojciech; Ryblewski, Radoslaw; Spaliński, Michał
2016-12-01
We compute the gradient expansion for anisotropic hydrodynamics. The results are compared with the corresponding expansion of the underlying kinetic-theory model with the collision term treated in the relaxation time approximation. We find that a recent formulation of anisotropic hydrodynamics based on an anisotropic matching principle yields the first three terms of the gradient expansion in agreement with those obtained for the kinetic theory. This gives further support for this particular hydrodynamic model as a good approximation of the kinetic-theory approach. We further find that the gradient expansion of anisotropic hydrodynamics is an asymptotic series, and the singularities of the analytic continuation of its Borel transform indicate the presence of nonhydrodynamic modes.
Gradient expansion for anisotropic hydrodynamics
Florkowski, Wojciech; Spaliński, Michał
2016-01-01
We compute the gradient expansion for anisotropic hydrodynamics. The results are compared with the corresponding expansion of the underlying kinetic-theory model with the collision term treated in the relaxation time approximation. We find that a recent formulation of anisotropic hydrodynamics based on an anisotropic matching principle yields the first three terms of the gradient expansion in agreement with those obtained for the kinetic theory. This gives further support for this particular hydrodynamic model as a good approximation of the kinetic-theory approach. We further find that the gradient expansion of anisotropic hydrodynamics is an asymptotic series, and the singularities of the analytic continuation of its Borel transform indicate the presence of non-hydrodynamic modes.
Strategic Complexity and Global Expansion
DEFF Research Database (Denmark)
Oladottir, Asta Dis; Hobdari, Bersant; Papanastassiou, Marina
2012-01-01
The purpose of this paper is to analyse the determinants of global expansion strategies of newcomer Multinational Corporations (MNCs) by focusing on Iceland, Israel and Ireland. We argue that newcomer MNCs from small open economies pursue complex global expansion strategies (CGES). We distinguish....... The empirical evidence suggests that newcomer MNCs move away from simplistic dualities in the formulation of their strategic choices towards more complex options as a means of maintaining and enhancing their global competitiveness....
Fractional and noncommutative spacetimes
Arzano, M.; Calcagni, M.; Oriti, D.; Scalisi, M.
2011-01-01
We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale determi
Can Kindergartners Do Fractions?
Cwikla, Julie
2014-01-01
Mathematics professor Julie Cwikla decided that she needed to investigate young children's understandings and see what precurricular partitioning notions young minds bring to the fraction table. Cwikla realized that only a handful of studies have examined how preschool-age and early elementary school-age students solve fraction problems (Empson…
Can Kindergartners Do Fractions?
Cwikla, Julie
2014-01-01
Mathematics professor Julie Cwikla decided that she needed to investigate young children's understandings and see what precurricular partitioning notions young minds bring to the fraction table. Cwikla realized that only a handful of studies have examined how preschool-age and early elementary school-age students solve fraction problems (Empson…
Wilkerson, Trena L.; Bryan, Tommy; Curry, Jane
2012-01-01
This article describes how using candy bars as models gives sixth-grade students a taste for learning to represent fractions whose denominators are factors of twelve. Using paper models of the candy bars, students explored and compared fractions. They noticed fewer different representations for one-third than for one-half. The authors conclude…
Categories of Fractions Revisited
Fritz, Tobias
2008-01-01
The theory of categories of fractions as originally developed by Gabriel and Zisman is reviewed in a pedagogical manner giving detailed proofs of all statements. A weakening of the category of fractions axioms used by Higson is discussed and shown to be equivalent to the original axioms.
Energy Technology Data Exchange (ETDEWEB)
Bajona-Xandri, C.; Martinez-Legaz, J.E.
1994-12-31
This paper studies the minimax fractional programming problem, assuming quasiconvexity of the objective function, under the lower subdifferentiability viewpoint. Necessary and sufficient optimality conditions and dual properties are found. We present applications of this theory to find the Pareto efficient solutions of a multiobjective fractional problem and to solve several economic models.
Teaching American Diplomacy Using Primary Sources. The Expansion of NATO.
Miles, Michael; Schuster, Heidi
In this high school U.S. government and U.S. history curriculum unit, students examine in depth the expansion of the North Atlantic Treaty Organization (NATO). Detailed activities are provided to teach students about the origins of NATO, its impact on U.S. foreign policy, and its future directions, particularly the enlargement of NATO in the…
On k-Fibonacci Numbers with Applications to Continued Fractions
Rabago, Julius Fergy T.
2016-02-01
Let be the sequence of k-Fibonacci numbers recursively defined by and m be a fixed positive integer. In this work we prove that, for almost every x ɛ (0,1), the pattern k, k,..., k (comprising of m-digits) appears in the continued fraction expansion x = [0; a1,a2,. ..] with frequency where where
Decomposition of fractional quantum Hall states: New symmetries and approximations
Thomale, R.; Estienne, B.; Regnault, N.; Bernevig, B.A.
2010-01-01
Abstract: We provide a detailed description of a new symmetry structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall states first obtained in Ref. 1, which we now extend to spin-singlet states. We show that the Haldane-Rezayi spin-singlet state can
Soil Organic Carbon Responses to Forest Expansion on Mountain Grasslands
DEFF Research Database (Denmark)
Guidi, Claudia
Grassland abandonment followed by progressive forest expansion is the dominant land-use change in the European Alps. Contrasting trends in soil organic carbon (SOC) stocks have been reported for mountainous regions following forest expansion on grasslands. Moreover, its effects on SOC properties ...... grasslands, which can be explained by lower accumulation of binding agents of microbial origin. This can have implications for the accumulation of atmospheric CO2 in soil and for the susceptibility of SOC to external disturbances such as management and environmental changes.......Grassland abandonment followed by progressive forest expansion is the dominant land-use change in the European Alps. Contrasting trends in soil organic carbon (SOC) stocks have been reported for mountainous regions following forest expansion on grasslands. Moreover, its effects on SOC properties...... involved into long-term stability are largely unknown. The aim of this PhD thesis was to explore changes in: (i) SOC stocks; (ii) physical SOC fractions; and (iii) labile soil carbon components following forest expansion on mountain grasslands. A land-use gradient located in the Southern Alps (Italy...
Fractional calculus in bioengineering.
Magin, Richard L
2004-01-01
Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub
Generation Expansion Planning with High Penetration of Wind Power
Sharan, Ishan; Balasubramanian, R.
2016-08-01
Worldwide thrust is being provided in generation of electricity from wind. Planning for the developmental needs of wind based power has to be consistent with the objective and basic framework of overall resource planning. The operational issues associated with the integration of wind power must be addressed at the planning stage. Lack of co-ordinated planning of wind turbine generators, conventional generating units and expansion of the transmission system may lead to curtailment of wind power due to transmission inadequacy or operational constraints. This paper presents a generation expansion planning model taking into account fuel transportation and power transmission constraints, while addressing the operational issues associated with the high penetration of wind power. For analyzing the operational issues, security constrained unit commitment algorithm is embedded in the integrated generation and transmission expansion planning model. The integrated generation and transmission expansion planning problem has been formulated as a mixed integer linear problem involving both binary and continuous variables in GAMS. The model has been applied to the expansion planning of a real system to illustrate the proposed approach.
Social Trust and Fractionalization:
DEFF Research Database (Denmark)
Bjørnskov, Christian
2008-01-01
This paper takes a closer look at the importance of fractionalization for the creation of social trust. It first argues that the determinants of trust can be divided into two categories: those affecting individuals' trust radii and those affecting social polarization. A series of estimates using...... a much larger country sample than in previous literature confirms that fractionalization in the form of income inequality and political diversity adversely affects social trust while ethnic diversity does not. However, these effects differ systematically across countries, questioning standard...... interpretations of the influence of fractionalization on trust....
Expansion Nets and Expansion Processes of Elementary Net Systems
Institute of Scientific and Technical Information of China (English)
曹存根
1995-01-01
Occurrence nets are insufficient to precisely describe executions of elementary net systems with contacts.Traditionally,S-complementation is used for removal of contacts from the systems.Although the main behavior and properties of the original elementary net systems are preserved during S-complementation,their topologies may be changed greatly.This paper introduces a new kind of nets-expansion nets-for representing behavior of elementary net systems.As shown in the paper,expansion nets are natural as well as sufficient for describing the precise behavior of elementary net systems with or without contactks.
Reed's Conjecture on hole expansions
Fouquet, Jean-Luc
2012-01-01
In 1998, Reed conjectured that for any graph $G$, $\\chi(G) \\leq \\lceil \\frac{\\omega(G) + \\Delta(G)+1}{2}\\rceil$, where $\\chi(G)$, $\\omega(G)$, and $\\Delta(G)$ respectively denote the chromatic number, the clique number and the maximum degree of $G$. In this paper, we study this conjecture for some {\\em expansions} of graphs, that is graphs obtained with the well known operation {\\em composition} of graphs. We prove that Reed's Conjecture holds for expansions of bipartite graphs, for expansions of odd holes where the minimum chromatic number of the components is even, when some component of the expansion has chromatic number 1 or when a component induces a bipartite graph. Moreover, Reed's Conjecture holds if all components have the same chromatic number, if the components have chromatic number at most 4 and when the odd hole has length 5. Finally, when $G$ is an odd hole expansion, we prove $\\chi(G)\\leq\\lceil\\frac{\\omega(G)+\\Delta(G)+1}{2}\\rceil+1$.
Directory of Open Access Journals (Sweden)
Waleed M. Abd-Elhameed
2016-09-01
Full Text Available Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fibonacci expansion were carefully investigated. Some numerical examples with comparisons are presented to ensure the efficiency, applicability and high accuracy of the proposed algorithms. Two accurate semi-analytic polynomial solutions for linear and nonlinear fractional differential equations are the result.
Void fraction instrument acceptance test procedure
Energy Technology Data Exchange (ETDEWEB)
Pearce, K.L.
1994-09-15
This acceptance test procedure (ATP) was written to test the void fraction instrument (VFI) and verify that the unit is ready for field service. The procedure verifies that the mechanical and electrical features (not specifically addressed in the software ATP) and software alarms are operating as designed.
Void fraction instrument acceptance test procedure
Energy Technology Data Exchange (ETDEWEB)
Pearce, K.L.
1994-09-15
This acceptance test procedure (ATP) was written to test the void fraction instrument (VFI) and verify that the unit is ready for field service. The procedure verifies that the mechanical and electrical features (not specifically addressed in the software ATP) and software alarms are operating as designed.
Goodrich, Christopher
2015-01-01
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...
Fractional Derivative Cosmology
Roberts, Mark D
2009-01-01
The degree by which a function can be differentiated need not be restricted to integer values. Usually most of the field equations of physics are taken to be second order, curiosity asks what happens if this is only approximately the case and the field equations are nearly second order. For Robertson-Walker cosmology there is a simple fractional modification of the Friedman and conservation equations. In general fractional gravitational equations similar to Einstein's are hard to define as this requires fractional derivative geometry. What fractional derivative geometry might entail is briefly looked at and it turns out that even asking very simple questions in two dimensions leads to ambiguous or intractable results. A two dimensional line element which depends on the Gamma-function is looked at.
Thermal Expansion of Hafnium Carbide
Grisaffe, Salvatore J.
1960-01-01
Since hafnium carbide (HfC) has a melting point of 7029 deg. F, it may have many high-temperature applications. A literature search uncovered very little information about the properties of HfC, and so a program was initiated at the Lewis Research Center to determine some of the physical properties of this material. This note presents the results of the thermal expansion investigation. The thermal-expansion measurements were made with a Gaertner dilatation interferometer calibrated to an accuracy of +/- 1 deg. F. This device indicates expansion by the movement of fringes produced by the cancellation and reinforcement of fixed wave-length light rays which are reflected from the surfaces of two parallel quartz glass disks. The test specimens which separate these disks are three small cones, each approximately 0.20 in. high.
Low thermal expansion glass ceramics
1995-01-01
This book is one of a series reporting on international research and development activities conducted by the Schott group of companies With the series, Schott aims to provide an overview of its activities for scientists, engineers, and managers from all branches of industry worldwide where glasses and glass ceramics are of interest Each volume begins with a chapter providing a general idea of the current problems, results, and trends relating to the subjects treated This volume describes the fundamental principles, the manufacturing process, and applications of low thermal expansion glass ceramics The composition, structure, and stability of polycrystalline materials having a low thermal expansion are described, and it is shown how low thermal expansion glass ceramics can be manufactured from appropriately chosen glass compositions Examples illustrate the formation of this type of glass ceramic by utilizing normal production processes together with controlled crystallization Thus glass ceramics with thermal c...
Low Thermal Expansion Glass Ceramics
Bach, Hans
2005-01-01
This book appears in the authoritative series reporting the international research and development activities conducted by the Schott group of companies. This series provides an overview of Schott's activities for scientists, engineers, and managers from all branches of industry worldwide in which glasses and glass ceramics are of interest. Each volume begins with a chapter providing a general idea of the current problems, results, and trends relating to the subjects treated. This new extended edition describes the fundamental principles, the manufacturing process, and applications of low thermal expansion glass ceramics. The composition, structure, and stability of polycrystalline materials having a low thermal expansion are described, and it is shown how low thermal expansion glass ceramics can be manufactured from appropriately chosen glass compositions. Examples illustrate the formation of this type of glass ceramic by utilizing normal production processes together with controlled crystallization. Thus g...
Intracellular Cadmium Isotope Fractionation
Horner, T. J.; Lee, R. B.; Henderson, G. M.; Rickaby, R. E.
2011-12-01
Recent stable isotope studies into the biological utilization of transition metals (e.g. Cu, Fe, Zn, Cd) suggest several stepwise cellular processes can fractionate isotopes in both culture and nature. However, the determination of fractionation factors is often unsatisfactory, as significant variability can exist - even between different organisms with the same cellular functions. Thus, it has not been possible to adequately understand the source and mechanisms of metal isotopic fractionation. In order to address this problem, we investigated the biological fractionation of Cd isotopes within genetically-modified bacteria (E. coli). There is currently only one known biological use or requirement of Cd, a Cd/Zn carbonic anhydrase (CdCA, from the marine diatom T. weissfloggii), which we introduce into the E. coli genome. We have also developed a cleaning procedure that allows for the treating of bacteria so as to study the isotopic composition of different cellular components. We find that whole cells always exhibit a preference for uptake of the lighter isotopes of Cd. Notably, whole cells appear to have a similar Cd isotopic composition regardless of the expression of CdCA within the E. coli. However, isotopic fractionation can occur within the genetically modified E. coli during Cd use, such that Cd bound in CdCA can display a distinct isotopic composition compared to the cell as a whole. Thus, the externally observed fractionation is independent of the internal uses of Cd, with the largest Cd isotope fractionation occurring during cross-membrane transport. A general implication of these experiments is that trace metal isotopic fractionation most likely reflects metal transport into biological cells (either actively or passively), rather than relating to expression of specific physiological function and genetic expression of different metalloenzymes.
Courtemanche, Charles; Marton, James; Ukert, Benjamin; Yelowitz, Aaron; Zapata, Daniela
2017-01-01
The Affordable Care Act (ACA) aimed to achieve nearly universal health insurance coverage in the United States through a combination of insurance market reforms, mandates, subsidies, health insurance exchanges, and Medicaid expansions, most of which took effect in 2014. This paper estimates the causal effects of the ACA on health insurance coverage in 2014 using data from the American Community Survey. We utilize difference-in-difference-in-differences models that exploit cross-sectional variation in the intensity of treatment arising from state participation in the Medicaid expansion and local area pre-ACA uninsured rates. This strategy allows us to identify the effects of the ACA in both Medicaid expansion and non-expansion states. Our preferred specification suggests that, at the average pre-treatment uninsured rate, the full ACA increased the proportion of residents with insurance by 5.9 percentage points compared to 2.8 percentage points in states that did not expand Medicaid. Private insurance expansions from the ACA were due to increases in both employer-provided and non-group coverage. The coverage gains from the full ACA were largest for those without a college degree, non-whites, young adults, unmarried individuals, and those without children in the home. We find no evidence that the Medicaid expansion crowded out private coverage.
Directory of Open Access Journals (Sweden)
Agnès Bouvier
2009-01-01
Full Text Available Salammbô, c’est nous. Nous comme héritiers du christianisme mais aussi, nous comme êtres humains, comme appartenant à ce genre humain dont Voltaire disait qu’on ne pouvait en lire l’histoire sans concevoir pour lui de l’horreur. Car c’est l’humanité historique dans son ensemble qui se trouve prise dans l’accusation de molochisme et que Flaubert réunit pêle-mêle dans Carthage, toutes « races » confondues et se « barbarisant » les unes les autres, toutes religions mêlées et se dissolvant au contact les unes des autres. L’humanité est toute entière attachée à Moloch, ici et ailleurs, hier et aujourd’hui. Le molochisme envahit d’abord la Grèce, c’est-à-dire « nous » au sens où Flaubert l’entendait quand il reprochait à Sainte-Beuve de regretter dans Salammbô « que je n’aie point introduit parmi les Grecs un philosophe, un raisonneur chargé de nous faire un cours de morale, ou commettant de bonnes actions, un monsieur enfin “sentant comme nous” ». Le chemin sanglant de Moloch traverse toute l’Europe et c’est ainsi qu’il touche à une autre partie de nous-mêmes : la Gaule. La présence des Gaulois en arrière-plan de la description de Moloch ne relève pas davantage du remplissage que celle des Grecs dans la procession qui précède le sacrifice des enfants au chapitre XIII. Elle est motivée par le même souci d’envisager « Moloch » dans son épaisseur historique, théologique et anthropologique, dans ce que celui-ci a d’effroyablement totalisant. Les strates de textes qui s’accumulent sous lui construisent d’insondables fondations à la statue remise en service dans le chapitre de Salammbô qui porte son nom. Ce qui était épars est à nouveau rassemblé, ce qui était caché ressort : « Tous les temples à la fois » s’ouvrent pour faire escorte au « Baal suprême », et même ce qu’on ne comprend plus et dont on a perdu le sens resurgit pour l
Compressibility and thermal expansion of cubic silicon nitride
DEFF Research Database (Denmark)
Jiang, Jianzhong; Lindelov, H.; Gerward, Leif
2002-01-01
The compressibility and thermal expansion of the cubic silicon nitride (c-Si3N4) phase have been investigated by performing in situ x-ray powder-diffraction measurements using synchrotron radiation, complemented with computer simulations by means of first-principles calculations. The bulk...... compressibility of the c-Si3N4 phase originates from the average of both Si-N tetrahedral and octahedral compressibilities where the octahedral polyhedra are less compressible than the tetrahedral ones. The origin of the unit cell expansion is revealed to be due to the increase of the octahedral Si-N and N-N bond...
Bearing-Mounting Concept Accommodates Thermal Expansion
Nespodzany, Robert; Davis, Toren S.
1995-01-01
Pins or splines allow radial expansion without slippage. Design concept for mounting rotary bearing accommodates differential thermal expansion between bearing and any structure(s) to which bearing connected. Prevents buildup of thermal stresses by allowing thermal expansion to occur freely but accommodating expansion in such way not to introduce looseness. Pin-in-slot configuration also maintains concentricity.
Properties of Ettringite Type Expansive Agent
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
By employing different forms and amounts of materials,many kinds of ettringite type expansive agents had been prepared.The relationship between the compositions and properties of expansive agents was analyzed.The design methods of expansive agent have been put forward according to the property requirement of expansive concrete.
18 CFR 154.309 - Incremental expansions.
2010-04-01
... 18 Conservation of Power and Water Resources 1 2010-04-01 2010-04-01 false Incremental expansions... Changes § 154.309 Incremental expansions. (a) For every expansion for which incremental rates are charged... incremental facilities to be rolled-in to the pipeline's rates. For every expansion that has an at-risk...
Caloric Curves and Nuclear Expansion
Natowitz, J B; Ma, Y; Murray, M; Qin, L; Shlomo, S; Wada, R; Wang, J
2002-01-01
Nuclear caloric curves have been analyzed using an expanding Fermi gas hypothesis to extract average nuclear densities. In this approach the observed flattening of the caloric curves reflects progressively increasing expansion with increasing excitation energy. This expansion results in a corresponding decrease in the density and Fermi energy of the excited system. For nuclei of medium to heavy mass apparent densities $~0.3\\rho_0$ are reached at the higher excitation energies. The average densities derived in this manner are in good agreement with those derived using other, more complicated, techniques.
Multipole Expansion in Generalized Electrodynamics
Bonin, C A; Ortega, P H
2016-01-01
In this article we study some classical aspects of Podolsky Electrodynamics in the static regime. We develop the multipole expansion for the theory in both the electrostatic and the magnetostatic cases. We also address the problem of consistently truncating the infinite series associated with the several kinds of multipoles, yielding approximations for the static Podolskian electromagnetic field to any degree of precision required. Moreover, we apply the general theory of multipole expansion to some specific physical problems. In those problems we identify the first terms of the series with the monopole, dipole and quadrupole terms in the generalized theory. We also propose a situation in which Podolsky theory can be experimentally tested.
Thermal Expansion of Irradiated Polytetrafluoroethylene
Subrahmanyam, HN; Subramanyam, SV
1987-01-01
The thermal expansion coefficient of gamma-irradiated Polytetrafluoroethylene (PTFE) has been measured in the temperature range 80-340 K by using a three-terminal capacitance technique. The samples are irradiated in air at room temperature with gamma rays from a $Co^{60}$ source at a dose rate of 0.26 Mrad/h. The change in crystallinity is measured by an x-ray technique. The expansion coefficient is found to increase with radiation dose below 140 K owing to the predominant effect of degradati...
Removable Type Expansion Bolt Innovative Design
Wang, Feng-Lan; Zhang, Bo; Gao, Bo; Liu, Yan-Xin; Gao, Bo
2016-05-01
Expansion bolt is a kind of the most common things in our daily life. Currently, there are many kinds of expansion bolts in the market. However, they have some shortcomings that mainly contain underuse and unremovement but our innovation of design makes up for these shortcomings very well. Principle of working follows this: expansion tube is fixed outside of bolt, steel balls and expansion covers are fixed inside. Meanwhile, the steel balls have 120° with each other. When using it ,expansion cover is moved in the direction of its internal part. So the front part of expansion bolt cover is increasingly becoming big and steel halls is moved outside. Only in this way can it be fixed that steel balls make expansion tube expand. When removing them, expansion bolt is moved outside. So the front part of expansion bolt cover is gradually becoming small and steel balls moves inside, after expansion tube shrinks, we can detach them.
The Thermal Expansion Of Feldspars
Hovis, G. L.; Medford, A.; Conlon, M.
2009-12-01
Hovis and others (1) investigated the thermal expansion of natural and synthetic AlSi3 feldspars and demonstrated that the coefficient of thermal expansion (α) decreases significantly, and linearly, with increasing room-temperature volume (VRT). In all such feldspars, therefore, chemical expansion limits thermal expansion. The scope of this work now has been broadened to include plagioclase and Ba-K feldspar crystalline solutions. X-ray powder diffraction data have been collected between room temperature and 925 °C on six plagioclase specimens ranging in composition from anorthite to oligoclase. When combined with thermal expansion data for albite (2,3,4) a steep linear trend of α as a function of VRT emerges, reflecting how small changes in composition dramatically affect expansion behavior. The thermal expansion data for five synthetic Ba-K feldspars ranging in composition from 20 to 100 mole percent celsian, combined with data for pure K-feldspar (3,4), show α-VRT relationships similar in nature to the plagioclase series, but with a slope and intercept different from the latter. Taken as a group all Al2Si2 feldspars, including anorthite and celsian from the present study along with Sr- (5) and Pb-feldspar (6) from other workers, show very limited thermal expansion that, unlike AlSi3 feldspars, has little dependence on the divalent-ion (or M-) site occupant. This apparently is due to the necessitated alternation of Al and Si in the tetrahedral sites of these minerals (7), which in turn locks the tetrahedral framework and makes the M-site occupant nearly irrelevant to expansion behavior. Indeed, in feldspar series with coupled chemical substitution it is the change away from a 1:1 Al:Si ratio that gives feldspars greater freedom to expand. Overall, the relationships among α, chemical composition, and room-temperature volume provide useful predictive tools for estimating feldspar thermal expansion and give insight into the controls of expansion behavior in
New Fractional Complex Transform for Conformable Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
Çenesiz Y.
2016-12-01
Full Text Available Conformable fractional complex transform is introduced in this paper for converting fractional partial differential equations to ordinary differential equations. Hence analytical methods in advanced calculus can be used to solve these equations. Conformable fractional complex transform is implemented to fractional partial differential equations such as space fractional advection diffusion equation and space fractional telegraph equation to obtain the exact solutions of these equations.
Histone deacetylase complexes promote trinucleotide repeat expansions.
Directory of Open Access Journals (Sweden)
Kim Debacker
2012-02-01
Full Text Available Expansions of DNA trinucleotide repeats cause at least 17 inherited neurodegenerative diseases, such as Huntington's disease. Expansions can occur at frequencies approaching 100% in affected families and in transgenic mice, suggesting that specific cellular proteins actively promote (favor expansions. The inference is that expansions arise due to the presence of these promoting proteins, not their absence, and that interfering with these proteins can suppress expansions. The goal of this study was to identify novel factors that promote expansions. We discovered that specific histone deacetylase complexes (HDACs promote CTG•CAG repeat expansions in budding yeast and human cells. Mutation or inhibition of yeast Rpd3L or Hda1 suppressed up to 90% of expansions. In cultured human astrocytes, expansions were suppressed by 75% upon inhibition or knockdown of HDAC3, whereas siRNA against the histone acetyltransferases CBP/p300 stimulated expansions. Genetic and molecular analysis both indicated that HDACs act at a distance from the triplet repeat to promote expansions. Expansion assays with nuclease mutants indicated that Sae2 is one of the relevant factors regulated by Rpd3L and Hda1. The causal relationship between HDACs and expansions indicates that HDACs can promote mutagenesis at some DNA sequences. This relationship further implies that HDAC3 inhibitors being tested for relief of expansion-associated gene silencing may also suppress somatic expansions that contribute to disease progression.
Regulation of gas infrastructure expansion
De Joode, J.
2012-01-01
The topic of this dissertation is the regulation of gas infrastructure expansion in the European Union (EU). While the gas market has been liberalised, the gas infrastructure has largely remained in the regulated domain. However, not necessarily all gas infrastructure facilities – such as gas storag
On persistently positively expansive maps
Directory of Open Access Journals (Sweden)
Alexander Arbieto
2010-06-01
Full Text Available In this paper, we prove that any C¹-persistently positively expansive map is expanding. This improves a result due to Sakai (Sakai 2004.Neste artigo, mostramos que todo mapa C¹-persistentemente positivamente expansivo e expansor. Isto melhora um resultado devido a Sakai (Sakai 2004.
Liflyand, E.
2012-01-01
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.
Large N Expansion. Vector Models
Nissimov, E; Nissimov, Emil; Pacheva, Svetlana
2006-01-01
Preliminary version of a contribution to the "Quantum Field Theory. Non-Perturbative QFT" topical area of "Modern Encyclopedia of Mathematical Physics" (SELECTA), eds. Aref'eva I, and Sternheimer D, Springer (2007). Consists of two parts - "main article" (Large N Expansion. Vector Models) and a "brief article" (BPHZL Renormalization).
The Laplace series solution for local fractional Korteweg-de Vries equation
Directory of Open Access Journals (Sweden)
Ye Shan-Shan
2016-01-01
Full Text Available In this paper, we consider a new application of the local fractional Laplace series expansion method to handle the local fractional Korteweg-de Vries equation. The obtained solution with non-differentiable type shows that the technology is accurate and efficient.
Effective Expansion: Balance between Shrinkage and Hygroscopic Expansion.
Suiter, E A; Watson, L E; Tantbirojn, D; Lou, J S B; Versluis, A
2016-05-01
The purpose of this study was to investigate the relationship between hygroscopic expansion and polymerization shrinkage for compensation of polymerization shrinkage stresses in a restored tooth. One resin-modified glass-ionomer (RMGI) (Ketac Nano, 3M ESPE), 2 compomers (Dyract, Dentsply; Compoglass, Ivoclar), and a universal resin-based composite (Esthet•X HD, Dentsply) were tested. Volumetric change after polymerization ("total shrinkage") and during 4 wk of water storage at 37°C was measured using an optical method (n= 10). Post-gel shrinkage was measured during polymerization using a strain gauge method (n= 10). Extracted human molars with large mesio-occluso-distal slot preparations were restored with the tested restorative materials. Tooth surfaces at baseline (preparation), after restoration, and during 4 wk of 37°C water storage were scanned with an optical scanner to determine cuspal flexure (n= 8). Occlusal interface integrity was measured using dye penetration. Data were analyzed using analysis of variance and post hoc tests (significance level 0.05). All tested materials shrunk after polymerization. RMGI had the highest total shrinkage (4.65%) but lowest post-gel shrinkage (0.35%). Shrinkage values dropped significantly during storage in water but had not completely compensated polymerization shrinkage after 4 wk. All restored teeth initially exhibited inward (negative) cuspal flexure due to polymerization shrinkage. Cuspal flexure with the RMGI restoration was significantly less (-6.4 µm) than with the other materials (-12.1 to -14.1 µm). After 1 d, cuspal flexure reversed to +5.0 µm cuspal expansion with the RMGI and increased to +9.3 µm at 4 wk. After 4 wk, hygroscopic expansion compensated cuspal flexure in a compomer (Compoglass) and reduced flexure with Dyract and resin-based composite. Marginal integrity (93.7% intact restoration wall) was best for the Compoglass restorations and lowest (73.1%) for the RMGI restorations. Hygroscopic
Energy Technology Data Exchange (ETDEWEB)
Jumarie, Guy E-mail: jumarie.guy@uqam.ca
2004-11-01
There are presently two different models of fractional Brownian motions available in the literature: the Riemann-Liouville fractional derivative of white noise on the one hand, and the complex-valued Brownian motion of order n defined by using a random walk in the complex plane, on the other hand. The paper provides a comparison between these two approaches, and in addition, takes this opportunity to contribute some complements. These two models are more or less equivalent on the theoretical standpoint for fractional order between 0 and 1/2, but their practical significances are quite different. Otherwise, for order larger than 1/2, the fractional derivative model has no counterpart in the complex plane. These differences are illustrated by an example drawn from mathematical finance. Taylor expansion of fractional order provides the expression of fractional difference in terms of finite difference, and this allows us to improve the derivation of Fokker-Planck equation and Kramers-Moyal expansion, and to get more insight in their relation with stochastic differential equations of fractional order. In the case of multi-fractal systems, the Fokker-Planck equation can be solved by using path integrals, and the fractional dynamic equations of the state moments of the stochastic system can be easily obtained. By combining fractional derivative and complex white noise of order n, one obtains a family of complex-valued fractional Brownian motions which exhibits long-range dependence. The conclusion outlines suggestions for further research, mainly regarding Lorentz transformation of fractional noises.
Thermal Expansion Behavior of La1-xSrxMn1-yCoyO3-δ Perovskites
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The thermal expansion behavior of La1-xSrxMn1-yCoyO3-δ (x=0.2～0.4, y=0.1～0.3) perovskites in air has been investigated. The average linear thermal expansion coefficients increased with increasing Sr content up to 40 mole fraction or Co content up to 30 mole fraction. The expansion is generally attributed to an increase in the average cation radius as some of the cations in the perovskite are reduced in valence when oxygen ions are removed from the structure.
Multi-Agent simulation of generation capacity expansion decisions.
Energy Technology Data Exchange (ETDEWEB)
Botterud, A.; Mahalik, M.; Conzelmann, G.; Silva, R.; Vilela, S.; Pereira, R. (Decision and Information Sciences); (Energias de Portugal); (Rede Electrica Nacional)
2008-01-01
In this paper, we use a multi-agent simulation model, EMCAS, to analyze generation expansion in the Iberian electricity market. The expansion model simulates generation investment decisions of decentralized generating companies (GenCos) interacting in a complex, multidimensional environment. A probabilistic dispatch algorithm calculates prices and profits for new candidate units in different future states of the system. Uncertainties in future load, hydropower conditions, and competitorspsila actions are represented in a scenario tree, and decision analysis is used to identify the optimal expansion decision for each individual GenCo. We run the model using detailed data for the Iberian market. In a scenario analysis, we look at the impact of market design variables, such as the energy price cap and carbon emission prices. We also analyze how market concentration and GenCospsila risk preferences influence the timing and choice of new generating capacity.
Chemical and Thermal Expansion of Calcium-Doped Lanthanum Chromite
Williford, R. E.; Armstrong, T. R.; Gale, J. D.
2000-02-01
Atomistic free-energy minimization techniques were used to simulate three simultaneous volumetric shrinkage/expansion phenomena in calcium-doped lanthanum chromite solid oxide fuel cell (SOFC) interconnect materials. Four sets of interatomic potentials were developed and tested over the temperature range 0-1273 K. The predicted unit-cell volumes, elastic properties, volumetric shrinkage due to A-site doping of the ABO3 perovskite (La1-xCax)CrO3, defect-induced volumetric expansion due to reducing atmospheres, and thermal expansion were in reasonable agreement with experiment, though not all concurrently with a single set of potentials. Potentials based either on simple oxides or on partial charge models appeared to give the best overall predictions. Additional experimental data are needed to improve the potentials.
Homogenizing atomic dynamics by fractional differential equations
Tang, Shaoqiang; Ying, Yuping
2017-10-01
In this paper, we propose two ways to construct fractional differential equations (FDE) for approximating atomic chain dynamics. Taking harmonic chain as an example, we add a power function of fractional order to Taylor expansion of the dispersion relation, and determine the parameters by matching two selected wave numbers. This approximate function leads to an FDE after considering both directions for wave propagation. As an alternative, we consider the symbol of the force term, and approximate it by a similar function. It also induces an FDE. Both approaches produce excellent agreement with the harmonic chain dynamics. The accuracy may be improved by optimizing the selected wave numbers, or starting with higher order Taylor expansions. When resolved in the lattice constant, the resulting FDE's faithfully reproduce the lattice dynamics. When resolved in a coarse grid instead, they systematically generate homogenized algorithms. Numerical tests are performed to verify the proposed approaches. Moreover, FDE's are also constructed for diatomic chain and anharmonic lattice, to illustrate the generality of the proposed approaches.
DEFF Research Database (Denmark)
Haack-Sørensen, Mandana; Follin, Bjarke; Juhl, Morten
2016-01-01
) over two passages in the automated and functionally closed Quantum Cell Expansion System (Quantum system) is compared with traditional manual cultivation. Methods: Stromal vascular fraction was isolated from abdominal fat, suspended in α-MEM supplemented with 10% Fetal Bovine Serum and seeded......Background: Adipose derived stromal cells (ASCs) are a rich and convenient source of cells for clinical regenerative therapeutic approaches. However, applications of ASCs often require cell expansion to reach the needed dose. In this study, cultivation of ASCs from stromal vascular fraction (SVF...... enhances ASC expansion rate and yield significantly relative to manual processing in T-flasks, while maintaining the purity and quality essential to safe and robust cell production. Notably, the use of the Quantum system entails significantly reduced working hours and thereby costs....
Eto, Minoru; Gudnason, Sven Bjarke; Konishi, Kenichi; Nagashima, Takayuki; Nitta, Muneto; Ohashi, Keisuke; Vinci, Walter
2009-01-01
We study what might be called fractional vortices, vortex configurations with the minimum winding from the viewpoint of their topological stability, but which are characterized by various notable substructures in the transverse energy distribution. The fractional vortices occur in diverse Abelian or non-Abelian generalizations of the Higgs model. The global and local features characterizing these are studied, and we identify the two crucial ingredients for their occurrence - the vacuum degeneracy leading to non-trivial vacuum moduli M, and the BPS nature of the vortices. Fractional vortices are further classified into two kinds. The first type of such vortices appear when M has orbifold Z_n singularities; the second type occurs in systems in which the vacuum moduli space M possesses either a deformed geometry or some singularity. These general features are illustrated with several concrete models.
Biswas, Karabi; Caponetto, Riccardo; Mendes Lopes, António; Tenreiro Machado, José António
2017-01-01
This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new types of integrated circuits. The majority of the book addresses FOEs. The interest in these topics is related to the need to produce “analogue” electronic devices characterized by non-integer order impedance, and to the characterization of natural phenomena, which are systems with memory or aftereffects and for which the fractional-order calculus tool is the ideal choice for analysis. FOEs represent the building blocks for designing and realizing analogue integrated electronic circuits, which the authors believe hold the potential for a wealth of mass-market applications. The freedom to choose either an integer- or non-integer-order analogue integrator...
Fractional and noncommutative spacetimes
Arzano, Michele; Calcagni, Gianluca; Oriti, Daniele; Scalisi, Marco
2011-12-01
We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale determining the log-period coincides with the nonrotation-invariant but cyclicity-preserving measure of κ-Minkowski spacetime. At scales larger than the log-period, the fractional measure is averaged and becomes a power law with real exponent. This can be also regarded as the cyclicity-inducing measure in a noncommutative spacetime defined by a certain nonlinear algebra of the coordinates, which interpolates between κ-Minkowski and canonical spacetime. These results are based upon a braiding formula valid for any nonlinear algebra which can be mapped onto the Heisenberg algebra.
Fractional and noncommutative spacetimes
Arzano, Michele; Oriti, Daniele; Scalisi, Marco
2011-01-01
We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale determining the log-period coincides with the non-rotation-invariant but cyclicity-preserving measure of \\kappa-Minkowski. At scales larger than the log-period, the fractional measure is averaged and becomes a power-law with real exponent. This can be also regarded as the cyclicity-inducing measure in a noncommutative spacetime defined by a certain nonlinear algebra of the coordinates, which interpolates between \\kappa-Minkowski and canonical spacetime. These results are based upon a braiding formula valid for any nonlinear algebra which can be mapped onto the Heisenberg algebra.
Energy Technology Data Exchange (ETDEWEB)
Edelman, Mark, E-mail: edelman@cims.nyu.ed [Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States)] [Department of Physics, Stern College at Yeshiva University, 245 Lexington Avenue, New York, NY 10016 (United States); Tarasov, Vasily E. [Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States)] [Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119991 (Russian Federation)
2009-12-28
Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the map parameter and the fractional order of the derivative in the original differential equation, this nonlinear dynamical system demonstrates attractors (fixed points, stable periodic trajectories, slow converging and slow diverging trajectories, ballistic trajectories, and fractal-like structures) and/or chaotic trajectories. At least one type of fractal-like sticky attractors in the chaotic sea was observed.
Superconducting wires and fractional flux
Sá de Melo, C. A. R.
1996-05-01
The quantization of flux quanta in superconductors is revisited and analyzed in a new geometry. The system analyzed is a superconducting wire. The geometry is such that the superconducting wire winds N times around an insulating cylinder and that the wire has its end connected back to its beginning, thus producing an N-loop short circuited solenoid. The winding number N acts as a topological index that controls flux quantization. In this case, fractional flux quanta can be measured through the center of the insulating cylinder, provided that the cylinder radius is small enough. The Little-Parks experiment for an identical geometry is discussed. The period of oscillation of the transition temperature of the wire is found to vary as 1/N in units of flux Φ relative to the flux quantum Φ0. When a SQUID is made in such a geometry the maximal current through the SQUID varies with period Φ0/N.
Dean flow fractionation of chromosomes
Hockin, Matt; Sant, Himanshu J.; Capecchi, Mario; Gale, Bruce K.
2016-03-01
Efforts to transfer intact mammalian chromosomes between cells have been attempted for more than 50 years with the consistent result being transfer of sub unit length pieces regardless of method. Inertial microfluidics is a new field that has shown much promise in addressing the fractionation of particles in the 2-20 μm size range (with unknown limits) and separations are based upon particles being carried by curving confined flows (within a spiral shaped, often rectangular flow chamber) and migrating to stable "equilibrium" positions of varying distance from a chamber wall depending on the balance of dean and lift forces. We fabricated spiral channels for inertial microfluidic separations using a standard soft lithography process. The concentration of chromosomes, small contaminant DNA and large cell debris in each outlets were evaluated using microscope (60X) and a flow cytometer. Using Dean Flow Fractionation, we were able to focus 4.5 times more chromosomes in outlet 2 compared to outlet 4 where most of the large debris is found. We recover 16% of the chromosomes in outlet #1- 50% in 2, 23% in 3 and 11% in 4. It should be noted that these estimates of recovery do not capture one piece of information- it actually may be that the chromosomes at each outlet are physically different and work needs to be done to verify this potential.
Coulomb blockade in fractional topological superconductors
Kim, Younghyun; Clarke, David J.; Lutchyn, Roman M.
2017-07-01
We study charge transport through a floating mesoscopic superconductor coupled to counterpropagating fractional quantum Hall edges at filling fraction ν =2 /3 . We consider a superconducting island with finite charging energy and investigate its effect on transport through the device. We calculate conductance through such a system as a function of temperature and gate voltage applied to the superconducting island. We show that transport is strongly affected by the presence of parafermionic zero modes, leading at zero temperature to a zero-bias conductance quantized in units of ν e2/h independent of the applied gate voltage.
Fractions: The New Frontier for Theories of Numerical Development
Siegler, Robert S.; Fazio, Lisa K.; Bailey, Drew H.; Zhou, Xinlin
2013-01-01
Recent research on fractions has broadened and deepened theories of numerical development. Learning about fractions requires children to recognize that many properties of whole numbers are not true of numbers in general and also to recognize that the one property that unites all real numbers is that they possess magnitudes that can be ordered on…
Effects of emergency department expansion on emergency department patient flow.
Mumma, Bryn E; McCue, James Y; Li, Chin-Shang; Holmes, James F
2014-05-01
Emergency department (ED) crowding is an increasing problem associated with adverse patient outcomes. ED expansion is one method advocated to reduce ED crowding. The objective of this analysis was to determine the effect of ED expansion on measures of ED crowding. This was a retrospective study using administrative data from two 11-month periods before and after the expansion of an ED from 33 to 53 adult beds in an academic medical center. ED volume, staffing, and hospital admission and occupancy data were obtained either from the electronic health record (EHR) or from administrative records. The primary outcome was the rate of patients who left without being treated (LWBT), and the secondary outcome was total ED boarding time for admitted patients. A multivariable robust linear regression model was used to determine whether ED expansion was associated with the outcome measures. The mean (±SD) daily adult volume was 128 (±14) patients before expansion and 145 (±17) patients after. The percentage of patients who LWBT was unchanged: 9.0% before expansion versus 8.3% after expansion (difference = 0.6%, 95% confidence interval [CI] = -0.16% to 1.4%). Total ED boarding time increased from 160 to 180 hours/day (difference = 20 hours, 95% CI = 8 to 32 hours). After daily ED volume, low-acuity area volume, daily wait time, daily boarding hours, and nurse staffing were adjusted for, the percentage of patients who LWBT was not independently associated with ED expansion (p = 0.053). After ED admissions, ED intensive care unit (ICU) admissions, elective surgical admissions, hospital occupancy rate, ICU occupancy rate, and number of operational ICU beds were adjusted for, the increase in ED boarding hours was independently associated with the ED expansion (p = 0.005). An increase in ED bed capacity was associated with no significant change in the percentage of patients who LWBT, but had an unintended consequence of an increase in ED boarding hours. ED expansion alone does
Isotopic fractionation of tritium in biological systems.
Le Goff, Pierre; Fromm, Michel; Vichot, Laurent; Badot, Pierre-Marie; Guétat, Philippe
2014-04-01
Isotopic fractionation of tritium is a highly relevant issue in radiation protection and requires certain radioecological considerations. Sound evaluation of this factor is indeed necessary to determine whether environmental compartments are enriched/depleted in tritium or if tritium is, on the contrary, isotopically well-distributed in a given system. The ubiquity of tritium and the standard analytical methods used to assay it may induce biases in both the measurement and the signification that is accorded to the so-called fractionation: based on an exhaustive review of the literature, we show how, sometimes large deviations may appear. It is shown that when comparing the non-exchangeable fraction of organically bound tritium (neOBT) to another fraction of tritium (e.g. tritiated water) the preparation of samples and the measurement of neOBT reported frequently led to underestimation of the ratio of tritium to hydrogen (T/H) in the non-exchangeable compartment by a factor of 5% to 50%. In the present study, corrections are proposed for most of the biological matrices studied so far. Nevertheless, the values of isotopic fractionation reported in the literature remain difficult to compare with each other, especially since the physical quantities and units often vary between authors. Some improvements are proposed to better define what should encompass the concepts of exchangeable and non-exchangeable fractions. Copyright © 2014 Elsevier Ltd. All rights reserved.
From Complex Fractional Fourier Transform to Complex Fractional Radon Transform
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; JIANG Nian-Quan
2004-01-01
We show that for n-dimensional complex fractional Fourier transform the corresponding complex fractional Radon transform can also be derived, however, it is different from the direct product of two n-dimensional real fractional Radon transforms. The complex fractional Radon transform of two-mode Wigner operator is calculated.
ON THE BOTTLENECK CAPACITY EXPANSION PROBLEMS ON NETWORKS
Institute of Scientific and Technical Information of China (English)
Yang Chao; Zhang Jianzhong
2006-01-01
This article considers a class of bottleneck capacity expansion problems. Such problems aim to enhance bottleneck capacity to a certain level with minimum cost. Given a network G(V, A,(-C)) consisting of a set of nodes V = {v1, v2,………, vn}, a set of arcs A(∪-){(vi, vj) | i = 1, 2,………, n; j = 1, 2,………, n} and a capacity vector (-C). The component (-C)ij of (-C) is the capacity of arc (vi, vj). Define the capacity of a subset A' of A as the minimum capacity of the arcs in A, the capacity of a family F of subsets of A is the maximum capacity of its members. There axe two types of expanding models. In the arc-expanding model, the unit cost to increase the capacity of arc (vi, vj) is wij. In the node-expanding model, it is assumed that the capacities of all arcs (vi, vi) which start at the same node vi should be increased by the same amount and that the unit cost to make such expansion is wi. This article considers three kinds of bottleneck capacity expansion problems (path,spanning arborescence and maximum flow) in both expanding models. For each kind of expansion problems, this article discusses the characteristics of the problems and presents several results on the complexity of the problems.
Hart, Kathleen; Kerslake, Daphne
The Concepts in Secondary Mathematics and Science (CSMS) and Strategies and Errors in Secondary Mathematics (SESM) research projects based at Chelsa College, England, have shown the marked reluctance of secondary school students to use fractions when solving mathematical problems, even though they have been taught the topic for a number of years.…
Brewing with fractionated barley
Donkelaar, van L.H.G.
2016-01-01
Brewing with fractionated barley Beer is a globally consumed beverage, which is produced from malted barley, water, hops and yeast. In recent years, the use of unmalted barley and exogenous enzymes have become more popular because they enable simpler processing and reduced environmental impact. Raw
Stephens, Ana C.; Bottge, Brian A.; Rueda, Enrique
2009-01-01
This article describes a technology-based and hands-on instructional intervention designed to advance middle school students' understandings of fractions. This problem-solving experience is based on the principles of Enhanced Anchored Instruction (EAI) and proved instructionally worthwhile and motivating to teachers and students in both inclusive …
Vinogradova, Natalya; Blaine, Larry
2013-01-01
Almost everyone loves chocolate. However, the same cannot be said about fractions, which are loved by markedly fewer. Middle school students tend to view them with wary respect, but little affection. The authors attempt to sweeten the subject by describing a type of game involving division of chocolate bars. The activity they describe provides a…
Momentum fractionation on superstrata
Bena, Iosif; Martinec, Emil; Turton, David; Warner, Nicholas P.
2016-05-01
Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in high-degree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifold singularities. Upon taking the AdS3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions.
Fractional statistics and confinement
Gaete, P; Gaete, Patricio; Wotzasek, Clovis
2004-01-01
It is shown that a pointlike composite having charge and magnetic moment displays a confining potential for the static interaction while simultaneously obeying fractional statistics in a pure gauge theory in three dimensions, without a Chern-Simons term. This result is distinct from the Maxwell-Chern-Simons theory that shows a screening nature for the potential.
Brewing with fractionated barley
Donkelaar, van L.H.G.
2016-01-01
Brewing with fractionated barley Beer is a globally consumed beverage, which is produced from malted barley, water, hops and yeast. In recent years, the use of unmalted barley and exogenous enzymes have become more popular because they enable simpler processing and reduced environmental impact. Raw
Fractional Differential Equation
Directory of Open Access Journals (Sweden)
Moustafa El-Shahed
2007-01-01
where 2<α<3 is a real number and D0+α is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.
Solution of Moving Boundary Space-Time Fractional Burger’s Equation
Directory of Open Access Journals (Sweden)
E. A.-B. Abdel-Salam
2014-01-01
Full Text Available The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger’s equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time. The linear and periodic moving boundaries for the kink solution of the Burger’s equation are presented graphically and discussed.
Exponential Expansion in Evolutionary Economics
DEFF Research Database (Denmark)
Frederiksen, Peter; Jagtfelt, Tue
2013-01-01
concepts are described in detail. Taken together it provides the rudimentary aspects of an economic system within an analytical perspective. It is argued that the main dynamic processes of the evolutionary perspective can be reduced to these four concepts. The model and concepts are evaluated in the light...... of Thomas Kuhn’s notion of scientific paradigms and criteria for a good theory (1977, 1996). The paper thus aims to augment and assimilate the fragmented and scattered body of concepts presently residing within the field of evolutionary economics, by presenting an intuitive framework, applicable within...... to this problem is proposed in the form of a model of exponential expansion. The model outlines the overall structure and function of the economy as exponential expansion. The pictographic model describes four axiomatic concepts and their exponential nature. The interactive, directional, emerging and expanding...
Fractions but not negative numbers are represented on the mental number line.
Ganor-Stern, Dana
2012-02-01
The present study is the first to directly compare numerical representations of positive numbers, negative numbers and unit fractions. The results show that negative numbers and unit fractions were not represented in the same way. Distance effects were found when positive numbers were compared with fractions but not when they were compared with negative numbers, thus suggesting that unit fractions but not negative numbers were represented on the number line with positive numbers. As indicated by the semantic congruity effect, negative numbers were perceived to be small, positive numbers were perceived as large, while unit fractions were perceived neither as large nor small. Comparisons between negative numbers were faster than between unit fractions, possibly due to the smaller differences between the holistic magnitudes of the unit fractions. Finally, comparing unit fractions to 1 was faster than comparing them to 0, consistent with the idea that unit fractions are perceived as entities smaller than 1 (Kallai & Tzelgov, 2009). The results are consistent with the idea of a mental division between numbers that represent a quantity (positive numbers and unit fractions) and those that do not (negative numbers).
Multiscale expansions in discrete world
Indian Academy of Sciences (India)
Ömer Ünsal; Filiz Taşcan; Mehmet Naci Özer
2014-07-01
In this paper, we show the attainability of KdV equation from some types of nonlinear Schrödinger equation by using multiscale expansions discretely. The power of this manageable method is confirmed by applying it to two selected nonlinear Schrödinger evolution equations. This approach can also be applied to other nonlinear discrete evolution equations. All the computations have been made with Maple computer packet program.
College Expansion and Curriculum Choice
Kaganovich, Michael; Su, Xuejuan
2012-01-01
This paper analyzes the impact of college enrollment expansion on student academic achievements and labor market outcomes in the context of competition among colleges. When public policies promote “access” to college education, colleges adjust their curricula: Less selective public colleges adopt a less demanding curriculum in order to accommodate the influx of less able students. As we argue in the paper, this adjustment benefits low-ability college students at the expense of those of medium...
RELIABILITY OF LENTICULAR EXPANSION COMPENSATORS
Directory of Open Access Journals (Sweden)
Gabriel BURLACU,
2011-11-01
Full Text Available Axial lenticular compensators are made to take over the longitudinal heat expansion, shock , vibration and noise, made elastic connections for piping systems. In order to have a long life for installations it is necessary that all elements, including lenticular compensators, have a good reliability. This desire can be did by technology of manufactoring and assembly of compensators, the material for lenses and by maintenance.of compensator
Topological expansion and boundary conditions
Eynard, Bertrand
2008-01-01
In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with all possible given boundary conditions. The method is recursive, and amounts to recursively cutting surfaces along interfaces. The result is best represented in a diagrammatic way, and is thus rather simple to use.
Multiple scattering expansion with distortion
Tandy, P. C.; Thaler, R. M.
1980-12-01
A multiple scattering description of elastic scattering is formulated in terms of impulsive scatterings from single target nucleons and pairs of target nucleons. In this description, distortion effects on the projectile from the residual medium are also described by multiple scattering in terms of the same single and pair amplitudes. At the level of single scattering, this procedure yields the first order optical potential result of Kerman, McManus, and Thaler. When scattering from both single nucleons and pairs of nucleons is included, the method leads to a one-body integral equation which requires the physical projectile-nucleon and projectile-pair transition amplitudes as input. This input is similar, but not exactly equivalent to that required by the spectator expansion for the optical potential truncated at second order. A principal advantage of the present formulation is that there need be no explicit dependence upon the projection operator Q which projects off the target ground state. This feature introduces a scaling which appears to be a direct extension of the first order Kerman, McManus, and Thaler type of scaling. We follow up suggestions arising in the foregoing to show that the exact optical potential to second order in the spectator expansion can also be cast into a form having no explicit dependence upon Q, and requiring physical projectile-nucleon and projectile-pair transition amplitudes as input. NUCLEAR REACTIONS Multiple scattering from single nucleons, pairs of nucleons in nucleus. Distortion from residual medium. Optical potential. spectator expansion.
Urban underground network expansion planning
Energy Technology Data Exchange (ETDEWEB)
Bozic, Z. [Sinclair Knight Merz Pty Ltd., Perth (Australia); Hobson, E. [HI Consulting Services Pty Ltd., Adelaide (Australia)
1997-03-01
The authors describe a three step approach to expansion planning of high voltage (HV) urban underground distribution networks. Although the techniques are specifically oriented to underground systems, they are equally applicable to overhead system design. The fundamental engineering problem is how to connect individual high voltage to low voltage substations (HV/LV SS) and zone HV SS into a future urban underground network. The problem is to rearrange the HV network to minimise the cost of expansion subject to provision of an alternative supply, specified load transfer among the neighbouring zone SS, and other general planning constraints such as feeder capacity, voltage regulation, operational requirements and losses. A review of the current state of the art of distribution expansion planning is provided. The normal manual approach is discussed together with more recent research into computer methods. Three lines of computer research are identified and classified as radially constrained, security constrained and utilisation of travelling salesman/vehicle routing problem algorithms (TSP/VRP). The TSP/VRP line of research has been extended here to produce practical techniques for the assistance of network planners. (Author)
Rational numbers with purely periodic $\\beta$-expansion
Adamczewski, Boris; Siegel, Anne; Steiner, Wolfgang
2009-01-01
We study real numbers $\\beta$ with the curious property that the $\\beta$-expansion of all sufficiently small positive rational numbers is purely periodic. It is known that such real numbers have to be Pisot numbers which are units of the number field they generate. We complete known results due to Akiyama to characterize algebraic numbers of degree 3 that enjoy this property. This extends results previously obtained in the case of degree 2 by K. Schmidt, Hama and Imahashi. Let $\\gamma(\\beta)$ denote the supremum of the real numbers $c$ in $(0,1)$ such that all positive rational numbers less than $c$ have a purely periodic $\\beta$-expansion. We prove that $\\gamma(\\beta)$ is irrational for a class of cubic Pisot units that contains the smallest Pisot number $\\eta$. This result is motivated by the observation of Akiyama and Scheicher that $\\gamma(\\eta)=0.666 666 666 086 ...$ is surprisingly close to 2/3.
Proposal for a material with negative thermal expansion
Abdullah, Mikrajuddin
2016-09-01
I propose a model of a material that exhibits negative thermal expansion (NTE) properties and criteria for the occurrence of linear and volumetric NTE. I derived the criteria for an arbitrary force between rigid units in the material. These criteria are also discussed specifically for the Lennard-Jones (6-12) potential and in more detail for metal-organic framework (MOF) materials comprising rigid units connected by organic linkers. Qualitatively, the model predictions can explain some observed results. Surprisingly, the model can produce equations for the transition temperature from NTE to positive thermal expansion (PTE), Tc ≈ T0 - 50 K, which is exactly the same as the temperature at which the glass transition begins to occur in most polymers, i.e., Tc ≈ Tg - 50 K.
2013-06-17
... Federal Register (77 FR 43047, 07/23/12) and the application has been processed pursuant to the FTZ Act... Foreign-Trade Zones Board Reorganization/Expansion of Foreign-Trade Zone 104; (Expansion of Service Area and Expansion of Zone); Under Alternative Site Framework, Savannah, Georgia Pursuant to its...
Lack of anion effect on volume expansion natriuresis in the developing canine kidney.
Lorenz, J M; Kleinman, L I; Disney, T A
1986-10-01
The renal response to volume expansion with sodium chloride or sodium bicarbonate was studied in 15 newborn and 13 adult dogs. Proximal and distal nephron function were estimated using the technique of distal nephron blockade. Fractional sodium reabsorption was 99.0 +/- 0.3% in newborn and 96.6 +/- 0.06% in adult during the NaCl expansion (P less than 0.01) and 98.1 +/- 0.7% in the newborn and 93.2 +/- 0.7% in the adult during NaHCO3 expansion (P less than 0.001). With either anion the higher fractional sodium reabsorption in the newborn was due to reabsorption of a greater fraction of the load presented to the distal nephron segment. The percent of the distal sodium load that was reabsorbed was 98.0 +/- 0.6% in the newborn and 92.2 +/- 1.0% in the adult during NaCl expansion, and 96.1 +/- 1.3% in the newborn and 81.5 +/- 2.4% in the adult during NaHCO3 expansion. Differences in distal nephron chloride, potassium and bicarbonate reabsorption among the groups support the hypothesis that the enhanced distal sodium reabsorption in the newborn occurred largely in the ascending loop of Henle with NaCl expansion, while it occurred in the late distal and cortical collecting tubules with NaHCO3 expansion. There was no difference between the natriuretic responses to NaCl or NaHCO3 in the newborn (P greater than 0.20); however, the natriuretic response to NaCl was less than that to NaHCO3 in the adult (P less than 0.001). This suggests that the bulk of the sodium that escaped reabsorption in Henle's loop during NaHCO3 expansion was reabsorbed in the late distal tubule in the newborn, but not in the adult.
Perturbative expansions for area-preserving maps
Energy Technology Data Exchange (ETDEWEB)
Servizi, G.; Turchetti, G.
1986-10-11
The structure of perturbation series for area-preserving maps is investigated. A basically different behaviour is found between the Birkhoff series, which formally conjugate with circles all the orbits in a neighbourhood of the origin, and the series which map into circles the individual invariant curves with fixed diophantine winding number. The former series exhibit an asymptotic character, the latter a convergent one, as one should expect from the KAM theorem. The source of this difference is found to be the different way in which the contributions of the relevant resonances propagate. In the first case, if epsilon is the size of the divisor associated to a resonance M/N, then at each order n>N an epsilon/sup -1/ contribution occurs, in the second case subtle cancellations provide a new epsilon/sup -1/ only when a harmonic (that is n=pN) is reached. This precise asymptotic statement and the properties of the relevant resonances obtained from the continued fraction expansion allow us, in the case of quadratic irrationals, to understand the limit process which leads to divergence or convergence. In the divergent case the asymptotic properties of the series are exhaustively described.
Creating, Naming, and Justifying Fractions
Siebert, Daniel; Gaskin, Nicole
2006-01-01
For students to develop meaningful conceptions of fractions and fraction operations, they need to think of fractions in terms other than as just whole-number combinations. In this article, we suggest two powerful images for thinking about fractions that move beyond whole-number reasoning. (Contains 5 figures.)
Statistical Inference with Data Augmentation and Parameter Expansion
Yatracos, Yannis G.
2015-01-01
Statistical pragmatism embraces all efficient methods in statistical inference. Augmentation of the collected data is used herein to obtain representative population information from a large class of non-representative population's units. Parameter expansion of a probability model is shown to reduce the upper bound on the sum of error probabilities for a test of simple hypotheses, and a measure, R, is proposed for the effect of activating additional component(s) in the sufficient statistic.
Fractional and multivariable calculus model building and optimization problems
Mathai, A M
2017-01-01
This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...
Institute of Scientific and Technical Information of China (English)
丁晓斌; 耿康; 刘洪均; 熊爱兵
2015-01-01
Objective To observe the clinical ef ect of extraction technology for the treatment of Burn Scar Baldness after soft tissue expansion application of skin and hair fol icle unit. Methods In our hospital from 2012 March~2014 year in May 98 cases receiving the burn scar alopecia patients, randomly divided into observation group and control group, each 49 cases, observation group of patients with Burn Scar Baldness after application of skin soft tissue expansion operation combined with treatment of fol icular unit extraction technology. The control group of patients with Burn Scar Baldness after application of conventional composite skin graft. Observation of two groups of patients before and after treatment in two groups were recorded respectively, needed for cure time and whether adverse reactions were observed during the treatment. Results The time of cicatricial alopecia patients with skin healing in two groups after burn, the observation group was significantly shorter than the control group, there was significant dif erence, with statistical significance ( <0.05). The total ef iciency of the observation group 95.9%, control group total ef ective rate 77.5%, total ef ective rate of observation group is higher than that of the control group, there was significant dif erence, with statistical significance ( <0.05). The incidence of adverse reactions in 6.1%, the control group adverse reaction rate was 22.4%, the adverse reaction rate of observation group was lower than that of control group were significantly dif erent, with statistical significance ( < 0.05). Conclusion Skin soft tissue expansion operation combined with fol icular unit extraction of significant technique in treating burn scar baldness, significantly improve the healing rate of burn patients, promote the recovery and reconstruction of damaged hair, its clinical advantages of higher, no serious adverse reactions, it is worthy of clinical popularization and application.%目的观察探讨应用皮肤
Lascu, Dan
2014-01-01
We consider a family {τ m : m ≥ 2} of interval maps which are generalizations of the Gauss transformation. For the continued fraction expansion arising from τ m , we solve a Gauss-Kuzmin-type problem.
Thermal expansion of ceramics around room temperature
橋本, 忍; 安達, 信泰; 太田, 敏孝; 宮崎, 英敏; ハシモト, シノブ; アダチ, ノブヤス; オオタ, トシタカ; Hashimoto, Shinobu; Adachi, Nobuyasu; Ota, Toshitaka
2010-01-01
Thermal expansion of some ceramics, polymers and metals was measured by dilatometer around room temperature (from -140℃to +200℃), and compared with thermal expansion in the high temperature region. The CTE (coefficient of thermal expansion)of almost ceramics changed drastically between room temperature and high temperature region. On the other hand, the CTE ofmetals did not change between room temperature and high temperature region. The difference on thermal expansion betweenceramics and met...
Fractional lattice charge transport
Flach, Sergej; Khomeriki, Ramaz
2017-01-01
We consider the dynamics of noninteracting quantum particles on a square lattice in the presence of a magnetic flux α and a dc electric field E oriented along the lattice diagonal. In general, the adiabatic dynamics will be characterized by Bloch oscillations in the electrical field direction and dispersive ballistic transport in the perpendicular direction. For rational values of α and a corresponding discrete set of values of E(α) vanishing gaps in the spectrum induce a fractionalization of the charge in the perpendicular direction - while left movers are still performing dispersive ballistic transport, the complementary fraction of right movers is propagating in a dispersionless relativistic manner in the opposite direction. Generalizations and the possible probing of the effect with atomic Bose-Einstein condensates and photonic networks are discussed. Zak phase of respective band associated with gap closing regime has been computed and it is found converging to π/2 value. PMID:28102302
Fractions in elementary education
Quinn, Frank
2013-01-01
This paper is one of a series in which elementary-education practice is analyzed by comparison with the history of mathematics, mathematical structure, modern practice, and (occasionally) cognitive neuroscience. The primary concerns are: Why do so many children find elementary mathematics difficult? And, why are the ones who succeed still so poorly prepared for college material needed for technical careers? The answer provided by conventional wisdom is essentially that mathematics is difficult. Third-graders are not developmentally ready for the subtlety of fractions, for instance, and even high-performing students cannot be expected to develop the skills of experienced users. However we will see that this is far from the whole story and is probably wrong: elementary-education fractions are genuinely harder and less effective than the version employed by experienced users. Experts discard at least 90% of what is taught in schools. Our educational system is actually counterproductive for skill development, and...
Unanswered Quibbles with Fractional Reserve Free Banking
Directory of Open Access Journals (Sweden)
Philipp Bagus
2011-07-01
Full Text Available In this article we reply to George Selgin’s counterarguments to our article “Fractional Reserve Free Banking: Some Quibbles”. Selgin regards holding cash as saving while we focus on the real savings necessary to maintain investment projects. Real savings are unconsumed real income. Variations in real savings are not necessarily equal to variations in cash holdings. We show that a coordinated credit expansion in a fractional reserve free banking (FRFB system is possible and that precautionary reserves consequently do not pose a necessary limit. We discuss various instances in which a FRFB system may expand credit without a prior increase in real savings. These facets all demonstrate why a fractional reserve banking system – even a free banking one – is inherently unstable, and incentivized to impose a stabilizing central bank. We find that at the root of our disagreements with Selgin lies a different approach to monetary theory. Selgin subscribes to the aggregative equation of exchange, which impedes him from seeing the microeconomic problems that the stabilization of “MV” by a FRFB system causes.
Brewing with fractionated barley
Donkelaar, van, CC René
2016-01-01
Brewing with fractionated barley Beer is a globally consumed beverage, which is produced from malted barley, water, hops and yeast. In recent years, the use of unmalted barley and exogenous enzymes have become more popular because they enable simpler processing and reduced environmental impact. Raw barley, however, contains less endogenous enzymes and more undesired components for the use of beer brewing, compared to malted barley. The overall aim of this thesis is to investigate how ba...
Microscopic calculations and energy expansions for neutron-rich matter
Energy Technology Data Exchange (ETDEWEB)
Drischler, Christian; Soma, Vittorio [Institut fuer Kernphysik, Technische Universitaet Darmstadt (Germany); ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum fuer Schwerionenforschung GmbH (Germany); Schwenk, Achim [ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum fuer Schwerionenforschung GmbH (Germany); Institut fuer Kernphysik, Technische Universitaet Darmstadt (Germany)
2014-07-01
We investigate the properties of asymmetric nuclear matter with two- and three-nucleon interactions based on chiral effective field theory. Focusing on neutron-rich matter, we calculate the energy for different proton fractions and include estimates of the theoretical uncertainty. We use our ab-initio results to test the quadratic expansion around symmetric matter with the symmetry energy term, and confirm its validity for highly asymmetric systems. Our calculated energy densities are in remarkable agreement with an empirical parameterization, developed to interpolate between pure neutron and symmetric nuclear matter. These findings are very useful for astrophysical applications and for developing new equations of state.
Bobev, Svilen; Williams, Darrick J.; Thompson, J.D.; Sarrao, J L
2004-01-01
Thermal expansion and magnetic susceptibility measurements as a function of temperature are reported for YbGaGe. Despite the fact that this material has been claimed to show zero thermal expansion over a wide temperature range, we observe thermal expansion typical of metals and Pauli paramagnetic behavior, which perhaps indicates strong sample dependence in this system.
Multiplier theorems for special Hermite expansions on
Institute of Scientific and Technical Information of China (English)
张震球; 郑维行
2000-01-01
The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calderon-Zygmund decomposition. Then the multiplier theorem in Lp(1 < p < ω ) is obtained. The special Hermite expansions in twisted Hardy space are also considered. As an application, the multipli-ers for a certain kind of Laguerre expansions are given in Lp space.
An All-Orders Derivative Expansion
Dunne, Gerald(Department of Physics, University of Connecticut, Storrs, CT, 06269, U.S.A.)
1996-01-01
We evaluate the exact $QED_{2+1}$ effective action for fermions in the presence of a family of static but spatially inhomogeneous magnetic field profiles. This exact result yields an all-orders derivative expansion of the effective action, and indicates that the derivative expansion is an asymptotic, rather than a convergent, expansion.
Quantum fields and "Big Rip" expansion singularities
Calderon, H; Calderon, Hector; Hiscock, William A.
2005-01-01
The effects of quantized conformally invariant massless fields on the evolution of cosmological models containing a ``Big Rip'' future expansion singularity are examined. Quantized scalar, spinor, and vector fields are found to strengthen the accelerating expansion of such models as they approach the expansion singularity.
Momentum Fractionation on Superstrata
Bena, Iosif; Turton, David; Warner, Nicholas P
2016-01-01
Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in high-degree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifold singularities. Upon taking the AdS3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Our construction establishes the very nontrivial fact that large classes of CFT states with mom...
A note on the fundamental unit in some types of the real quadratic number fields
Özer, Ö.
2016-10-01
Let k =Q (√{d }) be a real quadratic numbefield where d > 0 is a positive square-free integer. The map d →Q (√{d }) is a bijection from the set off all square-free integers d ≠ 0, 1 to the set of all quadratic fields Q (√{d })={ x +y √{d }|x ,y ∈Q } . Furthermore, integral basis element of algebraic integer's ring in real quadratic fields is determined by either wd=√{d }=[ a0;a1,a2,⋯,aℓ (d)-1,2 a0 ¯ ] in the case of d ≡ 2,3(mod 4) or wd=1/+√{d } 2 =[ a0;a1,a2,⋯,aℓ (d)-1,2 a0-1 ¯ ] in the case of d ≡ 1(mod 4) where ℓ (d ) is the period length of continued fraction expansion. The purpose of this paper is to obtain classification of some types of real quadratic fields Q (√{d }) , which include the specific form of continued fraction expansion of integral basis element wd, for which has all partial quotient elements are equal to each other and written as ξs (except the last digit of the period) for ξ positive even integer where period length is ℓ =ℓ (d ) and d ≡ 2,3(mod 4) is a square free positive integer. Moreover, the present paper deals with determining new certain parametric formula of fundamental unit ɛd=t/d+ud√{d } 2 >1 with norm N (ɛd)=(-1) ℓ (d ) for such types of real quadratic fields. Besides, Yokoi's d-invariants nd and md in the relation to continued fraction expansion of wd are calculated by using coefficients of fundamental unit. All supported results are given in numerical tables. These new results and tables are not known in the literature of real quadratic fields.
Probabilistic Forecast of Global Urban Expansion for 2030
Guneralp, B.; Seto, K. C.
2011-12-01
Future urbanization trends will have far-reaching consequences for sustainability and human well-being. Specifically, the location, rate, and magnitude of global urban expansion will affect wide-ranging phenomena from biogeochemical cycles to the vulnerability of millions of urban dwellers to disaster risk. In this study, we ask the following questions: 1) What will be the rates and magnitudes of urban expansion worldwide over the next twenty years and how will these patterns distribute geographically? 2) What regions will experience high rates of urban expansion and increased risk to coastal hazards? We develop a probabilistic forecast out to 2030 of the magnitudes and spatial distributions of global urban expansion, broadly based on the United Nations-defined world regions. We combine analytical methods from Monte Carlo techniques with spatially explicit forecasts of urban growth to derive probabilistic maps of urban extent for 2030 by region. The forecasts suggest that the most extensive urban expansion will concentrate in low and middle income countries and they may become even larger megapols than those in the U.S. and Western Europe. Three of the largest of these potential hotspots are in and around the Niger Delta in Africa and across the Indo-Gangetic plain and across eastern and central China in Asia. On average, largest increases in urban expansion will occur in Asia (900,000km2) with the greatest percentage increase (700%) predicted for Africa. China and India will experience similar proportional increases (500%) in their urban extents reaching on average 486,000 km2 and 174,000 km2 of urban land in 2030, respectively. Combined, the average urban extent of these two countries in 2030 is larger than the total land area of Madagascar. We evaluate the vulnerability of future urban expansion to sea-level rise and storm surges by calculating the urban extent that will fall within low elevation coastal zones (LECZ). On average, urban areas in LECZ will
On MEG forward modelling using multipolar expansions
Energy Technology Data Exchange (ETDEWEB)
Jerbi, K. [Signal and Image Processing Institute, University of Southern California, Los Angeles, CA (United States); Cognitive Neuroscience and Brain Imaging Laboratory, Hopital de la Salpetiere, CNRS, Paris (France); Mosher, J.C. [Los Alamos National Laboratory, Los Alamos, NM (United States); Baillet, S. [Cognitive Neuroscience and Brain Imaging Laboratory, Hopital de la Salpetiere, CNRS, Paris (France); Leahy, R.M. [Signal and Image Processing Institute, University of Southern California, Los Angeles, CA (United States)]. E-mail: leahy@sipi.usc.edu
2002-02-21
Magnetoencephalography (MEG) is a non-invasive functional imaging modality based on the measurement of the external magnetic field produced by neural current sources within the brain. The reconstruction of the underlying sources is a severely ill-posed inverse problem typically tackled using either low-dimensional parametric source models, such as an equivalent current dipole (ECD), or high-dimensional minimum-norm imaging techniques. The inability of the ECD to properly represent non-focal sources and the over-smoothed solutions obtained by minimum-norm methods underline the need for an alternative approach. Multipole expansion methods have the advantages of the parametric approach while at the same time adequately describing sources with significant spatial extent and arbitrary activation patterns. In this paper we first present a comparative review of spherical harmonic and Cartesian multipole expansion methods that can be used in MEG. The equations are given for the general case of arbitrary conductors and realistic sensor configurations and also for the special cases of spherically symmetric conductors and radially oriented sensors. We then report the results of computer simulations used to investigate the ability of a first-order multipole model (dipole and quadrupole) to represent spatially extended sources, which are simulated by 2D and 3D clusters of elemental dipoles. The overall field of a cluster is analysed using singular value decomposition and compared to the unit fields of a multipole, centred in the middle of the cluster, using subspace correlation metrics. Our results demonstrate the superior utility of the multipolar source model over ECD models in providing source representations of extended regions of activity. (author)
A Novel Effective Approach for Solving Fractional Nonlinear PDEs.
Aminikhah, Hossein; Malekzadeh, Nasrin; Rezazadeh, Hadi
2014-01-01
The present work introduces an effective modification of homotopy perturbation method for the solution of nonlinear time-fractional biological population model and a system of three nonlinear time-fractional partial differential equations. In this approach, the solution is considered a series expansion that converges to the nonlinear problem. The new approximate analytical procedure depends only on two iteratives. The analytical approximations to the solution are reliable and confirm the ability of the new homotopy perturbation method as an easy device for computing the solution of nonlinear equations.
An efficient technique for higher order fractional differential equation.
Ali, Ayyaz; Iqbal, Muhammad Asad; Ul-Hassan, Qazi Mahmood; Ahmad, Jamshad; Mohyud-Din, Syed Tauseef
2016-01-01
In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems.
Numerical Solution of Stochastic Nonlinear Fractional Differential Equations
El-Beltagy, Mohamed A.
2015-01-07
Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.
Energy Technology Data Exchange (ETDEWEB)
Estrada S, G. J.; Martin del Campo M, C., E-mail: gestradas@yahoo.co [UNAM, Facultad de Ingenieria, Departamento de Sistemas Energeticos, Ciudad Universitaria, 04510 Mexico D. F. (Mexico)
2009-10-15
In this work the results of four studies appear that were realized to analyze plans of long term expansion of Mexican electrical system of generation for the study period 2005-2025. The objective is to identify between the two third generation reactors with greater maturity at present which is it is that it can be integrated better in the expansion of the Mexican electrical system of generation. It was analyzed which of the four cases represents the best expansion plan in terms of two only parameters that are: 1) total cost of generation and, 2) the diversity of generated energy in all the period. In all studies candidates three different units of combined cycle were considered (802, 583 and 291 MW), a turbo gas unit of 267 MW, units of 700 MW with coal base and integrated de sulphur, geo thermo electrical units of 26.95 MW and two different types of nuclear units. In both first studies the Advanced Boiling Water Reactor (A BWR) for the nuclear units is considered, considering that is technology with more maturity of all the third generation reactors. In the following two studies were considered the European Pressurized Reactor (EPR), also of third generation, that uses in essence technology more spread to world-wide level. For this task was used the uni nodal planning model WASP-IV, developed by the IAEA to find the expansion configuration with less generation cost for each study. Considering the present situation of the generation system, the capacity additions begin starting from the year 2012 for the four studies. It is not considered the installation of nuclear plants before 2016 considering that its planning period takes 3 years, and the construction period requires at least of 5 years. In order to evaluate the diversity of each study it was used the Stirling Index or of Shannon-Weiner. In order to classify the studies in cost terms and diversity it was used like decision tool the Savage criterion, called also of minimal repentance. With this data, taking
Gravitational entropy of cosmic expansion
Sussman, Roberto A
2014-01-01
We apply a recent proposal to define "gravitational entropy" to the expansion of cosmic voids within the framework of non-perturbative General Relativity. By considering CDM void configurations compatible with basic observational constraints, we show that this entropy grows from post-inflationary conditions towards a final asymptotic value in a late time fully non-linear regime described by the Lemaitre-Tolman-Bondi (LTB) dust models. A qualitatively analogous behavior occurs if we assume a positive cosmological constant consistent with a $\\Lambda$-CDM background model. However, the $\\Lambda$ term introduces a significant suppression of entropy growth with the terminal equilibrium value reached at a much faster rate.
Contribution of thermal expansion and
Directory of Open Access Journals (Sweden)
O.I.Pursky
2007-01-01
Full Text Available A theoretical model is developed to describe the experimental results obtained for the isobaric thermal conductivity of rare gas solids (RGS. The isobaric thermal conductivity of RGS has been analysed within Debye approximation with regard to the effect of thermal expansion. The suggested model takes into consideration the fact that thermal conductivity is determined by U-processes while above the phonon mobility edge it is determined by "diffusive" modes migrating randomly from site to site. The mobility edge ω0 is determined from the condition that the phonon mean-free path restricted by the U-processes cannot be smaller than half of the phonon wavelength.
Cosmic Growth and Expansion Conjoined
Linder, Eric V
2016-01-01
Cosmological measurements of both the expansion history and growth history have matured, and the two together provide an important test of general relativity. We consider their joint evolutionary track, showing that this has advantages in distinguishing cosmologies relative to considering them individually or at isolated redshifts. In particular, the joint comparison relaxes the shape degeneracy that makes $f\\sigma_8(z)$ curves difficult to separate from the overall growth amplitude. The conjoined method further helps visualization of which combinations of redshift ranges provide the clearest discrimination. We examine standard dark energy cosmologies, modified gravity, and "stuttering" growth, each showing distinct signatures.
Generation expansion planning in a competitive electric power industry
Chuang, Angela Shu-Woan
This work investigates the application of non-cooperative game theory to generation expansion planning (GEP) in a competitive electricity industry. We identify fundamental ways competition changes the nature of GEP, review different models of oligopoly behavior, and argue that assumptions of the Cournot model are compatible with GEP. Applying Cournot theory of oligopoly behavior, we formulate a GEP model that may characterize expansion in the new competitive regime, particularly in pool-dominated generation supply industries. Our formulation incorporates multiple markets and is patterned after the basic design of the California ISO/PX system. Applying the model, we conduct numerical experiments on a test system, and analyze generation investment and market participation decisions of different candidate expansion units that vary in costs and forced outage rates. Simulations are performed under different scenarios of competition. In particular, we observe higher probabilistic measures of reliability from Cournot expansion compared to the expansion plan of a monopoly with an equivalent minimum reserve margin requirement. We prove several results for a subclass of problems encompassed by our formulation. In particular, we prove that under certain conditions Cournot competition leads to greater total capacity expansion than a situation in which generators collude in a cartel. We also show that industry output after introduction of new technology is no less than monopoly output. So a monopoly may lack sufficient incentive to introduce new technologies. Finally, we discuss the association between capacity payments and the issue of pricing reliability. And we derive a formula for computing ideal capacity payment rates by extending the Value of Service Reliability technique.
Development of Fraction Comparison Strategies: A Latent Transition Analysis.
Rinne, Luke F; Ye, Ai; Jordan, Nancy C
2017-02-20
The present study investigated the development of fraction comparison strategies through a longitudinal analysis of children's responses to a fraction comparison task in 4th through 6th grades (N = 394). Participants were asked to choose the larger value for 24 fraction pairs blocked by fraction type. Latent class analysis of performance over item blocks showed that most children initially exhibited a "whole number bias," indicating that larger numbers in numerators and denominators produce larger fraction values. However, some children instead chose fractions with smaller numerators and denominators, demonstrating a partial understanding that smaller numbers can yield larger fractions. Latent transition analysis showed that most children eventually adopted normative comparison strategies. Children who exhibited a partial understanding by choosing fractions with smaller numbers were more likely to adopt normative comparison strategies earlier than those with larger number biases. Controlling for general math achievement and other cognitive abilities, whole number line estimation accuracy predicted the probability of transitioning to normative comparison strategies. Exploratory factor analyses showed that over time, children appeared to increasingly represent fractions as discrete magnitudes when simpler strategies were unavailable. These results support the integrated theory of numerical development, which posits that an understanding of numbers as magnitudes unifies the process of learning whole numbers and fractions. The findings contrast with conceptual change theories, which propose that children must move from a view of numbers as counting units to a new view that accommodates fractions to overcome whole number bias. (PsycINFO Database Record
Fractional random walk lattice dynamics
Michelitsch, Thomas; Riascos, Alejandro Perez; Nowakowski, Andrzeij; Nicolleau, Franck
2016-01-01
We analyze time-discrete and continuous `fractional' random walks on undirected regular networks with special focus on cubic periodic lattices in $n=1,2,3,..$ dimensions.The fractional random walk dynamics is governed by a master equation involving {\\it fractional powers of Laplacian matrices $L^{\\frac{\\alpha}{2}}$}where $\\alpha=2$ recovers the normal walk.First we demonstrate thatthe interval $0\\textless{}\\alpha\\leq 2$ is admissible for the fractional random walk. We derive analytical expressions for fractional transition matrix and closely related the average return probabilities. We further obtain thefundamental matrix $Z^{(\\alpha)}$, and the mean relaxation time (Kemeny constant) for the fractional random walk.The representation for the fundamental matrix $Z^{(\\alpha)}$ relates fractional random walks with normal random walks.We show that the fractional transition matrix elements exihibit for large cubic $n$-dimensional lattices a power law decay of an $n$-dimensional infinite spaceRiesz fractional deriva...
Digital expansions with negative real bases
Steiner, Wolfgang
2011-01-01
Similarly to Parry's characterization of $\\beta$-expansions of real numbers in real bases $\\beta > 1$, Ito and Sadahiro characterized digital expansions in negative bases, by the expansions of the endpoints of the fundamental interval. Parry also described the possible expansions of 1 in base $\\beta > 1$. In the same vein, we characterize the sequences that occur as $(-\\beta)$-expansion of $\\frac{-\\beta}{\\beta+1}$ for some $\\beta > 1$. These sequences also describe the itineraries of 1 by linear mod one transformations with negative slope.
The Grand Strategy of the United States
2014-10-01
United States both militarily and by setting the terms of trade. While cultural and ideological affinities with European democra- cies played...military establishments (Japan, Russia, India, South Korea, Vietnam, Taiwan, Indonesia , Malaysia, Singapore) can check possible military expansion when
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.
Gauge Invariant Fractional Electromagnetic Fields
Lazo, Matheus Jatkoske
2011-01-01
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.
Fractional Langevin equation and Riemann-Liouville fractional derivative.
Sau Fa, Kwok
2007-10-01
In this present work we consider a fractional Langevin equation with Riemann-Liouville fractional time derivative which modifies the classical Newtonian force, nonlocal dissipative force, and long-time correlation. We investigate the first two moments, variances and position and velocity correlation functions of this system. We also compare them with the results obtained from the same fractional Langevin equation which uses the Caputo fractional derivative.
Gyrification from constrained cortical expansion
Tallinen, Tuomas; Biggins, John S; Mahadevan, L
2015-01-01
The exterior of the mammalian brain - the cerebral cortex - has a conserved layered structure whose thickness varies little across species. However, selection pressures over evolutionary time scales have led to cortices that have a large surface area to volume ratio in some organisms, with the result that the brain is strongly convoluted into sulci and gyri. Here we show that the gyrification can arise as a nonlinear consequence of a simple mechanical instability driven by tangential expansion of the gray matter constrained by the white matter. A physical mimic of the process using a layered swelling gel captures the essence of the mechanism, and numerical simulations of the brain treated as a soft solid lead to the formation of cusped sulci and smooth gyri similar to those in the brain. The resulting gyrification patterns are a function of relative cortical expansion and relative thickness (compared with brain size), and are consistent with observations of a wide range of brains, ranging from smooth to highl...
Primordial vorticity and gradient expansion
Giovannini, Massimo; Rezaei, Zahra
2012-02-01
The evolution equations of the vorticities of the electrons, ions and photons in a pre-decoupling plasma are derived, in a fully inhomogeneous geometry, by combining the general relativistic gradient expansion and the drift approximation within the Adler-Misner-Deser decomposition. The vorticity transfer between the different species is discussed in this novel framework and a set of general conservation laws, connecting the vorticities of the three-component plasma with the magnetic field intensity, is derived. After demonstrating that a source of large-scale vorticity resides in the spatial gradients of the geometry and of the electromagnetic sources, the total vorticity is estimated to lowest order in the spatial gradients and by enforcing the validity of the momentum constraint. By acknowledging the current bounds on the tensor to scalar ratio in the (minimal) tensor extension of the ΛCDM paradigm, the maximal comoving magnetic field induced by the total vorticity turns out to be, at most, of the order of 10-37 G over the typical comoving scales ranging between 1 and 10 Mpc. While the obtained results seem to be irrelevant for seeding a reasonable galactic dynamo action, they demonstrate how the proposed fully inhomogeneous treatment can be used for the systematic scrutiny of pre-decoupling plasmas beyond the conventional perturbative expansions.
Imagination as expansion of experience.
Zittoun, Tania; Cerchia, Frédéric
2013-09-01
This paper proposes a developmental view on imagination: from this perspective, imagination can be seen as triggered by some disrupting event, which generates a disjunction from the person's unfolding experience of the "real" world, and as unfolding as a loop, which eventually comes back to the actual experience. Examining recent and classical theorization of imagination in psychology, the paper opposes a deficitary view of imagination to an expansive notion of imagination. The paper explores Piaget, Vygotsky, Harris and Pelaprat & Cole consider: 1) What does provoke a "rupture" or disjunction? 2) What are the psychological processes involved in the imaginary loop? 3) What nourishes such processes? 4) What are the consequences of such imaginary loop, or what does it enable doing? The paper proposes to adopt an expansive view of imagination, as Vygotsky proposed-a perspective that has been under-explored empirically since his seminal work. To stimulate such sociocultural psychology of imagination, two empirical examples are provided, one showing how children make sense of metaphor in an experimental setting, the other showing a young person using a novel met at school as symbolic resource.
Evolutionary expansion of the Monogenea.
Kearn, G C
1994-12-01
The evolutionary expansion of the monogeneans has taken place in parallel with the diversification of the fish-like vertebrates. In this article the main trends in monogenean evolution are traced from a hypothetical skin-parasitic ancestor on early vertebrates. Special consideration is given to the following topics: early divergence between skin feeders and blood feeders; diversification and specialization of the haptor for attachment to skin; transfer from host to host, viviparity and the success of the gyrodactylids; predation on skin parasites and camouflage; colonization of the buccal and branchial cavities; diversification and specialization of the haptor for attachment to the gills; phoresy in gill parasites; the development of endoparasitism and the origin of the cestodes; the success of dactylogyroidean gill parasites; the uniqueness of the polyopisthocotyleans; ovoviviparity and the colonization of the tetrapods. Host specificity has been the guiding force of coevolution between monogeneans and their vertebrate hosts, but the establishment of monogeneans on unrelated hosts sharing the same environment (host-switching) may have been underestimated. Host-switching has provided significant opportunities for evolutionary change of direction and is probably responsible for the establishment of monogeneans on cephalopod molluscs, on the hippopotamus and possibly on chelonians. There are indications that host-switching may be more common in monogeneans that spread by direct transfer of adults/juveniles from host to host. A limitation on the further expansion of monogeneans is the need for water for the dispersal of the infective larva (oncomiracidium).
Preheating with fractional powers
Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-11-01
We consider preheating in models in which the potential for the inflaton is given by a fractional power, as is the case in axion monodromy inflation. We assume a standard coupling between the inflaton field and a scalar matter field. We find that in spite of the fact that the oscillation of the inflaton about the field value which minimizes the potential is anharmonic, there is nevertheless a parametric resonance instability, and we determine the Floquet exponent which describes this instability as a function of the parameters of the inflaton potential.
Fractional cointegration rank estimation
DEFF Research Database (Denmark)
Lasak, Katarzyna; Velasco, Carlos
We consider cointegration rank estimation for a p-dimensional Fractional Vector Error Correction Model. We propose a new two-step procedure which allows testing for further long-run equilibrium relations with possibly different persistence levels. The fi…rst step consists in estimating......-likelihood ratio test of no-cointegration on the estimated p - r common trends that are not cointegrated under the null. The cointegration degree is re-estimated in the second step to allow for new cointegration relationships with different memory. We augment the error correction model in the second step...
Andreasen, Niels; Bjerregaard, Mads; Lund, Jonas; Olsen, Ove Bitsch; Rasmussen, Andreas Dalgas
2012-01-01
Projektet er bygget op omkring kritisk realisme, som er det gennemgående videnskabelige fundament til undersøgelsen af hvilke strukturelle grunde der er til finansiel ustabilitet i Danmark. Projektet går i dybden med Fractional Reserve Banking og incitamentsstrukturen i banksystemet. Vi bevæger os både på det makro- og mikroøkonomiske niveau i analysen. På makro niveau bruger vi den østrigske skole om konjunktur teori (The Positive Theory of the Cycle). På mikro niveau arbejder vi med princip...
Andreasen, Niels; Bjerregaard, Mads; Lund, Jonas; Olsen, Ove Bitsch; Rasmussen, Andreas Dalgas
2012-01-01
Projektet er bygget op omkring kritisk realisme, som er det gennemgående videnskabelige fundament til undersøgelsen af hvilke strukturelle grunde der er til finansiel ustabilitet i Danmark. Projektet går i dybden med Fractional Reserve Banking og incitamentsstrukturen i banksystemet. Vi bevæger os både på det makro- og mikroøkonomiske niveau i analysen. På makro niveau bruger vi den østrigske skole om konjunktur teori (The Positive Theory of the Cycle). På mikro niveau arbejder vi med princip...
Fractional Integral Inequalities via Hadamard’s Fractional Integral
2014-01-01
We establish new fractional integral inequalities, via Hadamard’s fractional integral. Several new integral inequalities are obtained, including a Grüss type Hadamard fractional integral inequality, by using Young and weighted AM-GM inequalities. Many special cases are also discussed.
Body Fractions: A Physical Approach to Fraction Learning
Mills, Judith
2011-01-01
Many students experience great difficulty understanding the meaning of fractions. For many students who have spent their early mathematics lessons focusing on counting (whole) numbers, recognising that there are many numbers between those whole numbers called fractional numbers, is quite revolutionary. The foundation of understanding fractions is…
Cosmological Models with Fractional Derivatives and Fractional Action Functional
Institute of Scientific and Technical Information of China (English)
V.K. Shchigolev
2011-01-01
Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional cosmological models in both eases is given.
Fast algorithms for Quadrature by Expansion I: Globally valid expansions
Rachh, Manas; Klöckner, Andreas; O'Neil, Michael
2017-09-01
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast algorithms for solving the resulting dense linear systems. Classically, these tools were developed separately. In this work, we present a unified numerical scheme based on coupling Quadrature by Expansion, a recent quadrature method, to a customized Fast Multipole Method (FMM) for the Helmholtz equation in two dimensions. The method allows the evaluation of layer potentials in linear-time complexity, anywhere in space, with a uniform, user-chosen level of accuracy as a black-box computational method. Providing this capability requires geometric and algorithmic considerations beyond the needs of standard FMMs as well as careful consideration of the accuracy of multipole translations. We illustrate the speed and accuracy of our method with various numerical examples.
Development and Application of Heat-integrated Aromatics Fractionation Process
Institute of Scientific and Technical Information of China (English)
Yang Weisheng; Kong Dejin; Tan Yongzhong
2009-01-01
The PRO/Ⅱ process simulation software was applied to carry out simulated calculation of the aromatics frac-tionation unit and the heat integrated rectification process was proposed for the aromatics fractionation section of the 1.0 Mt/a toluene disproportionation unit at the Zhenhai Refining and Chemical Company. The optimized operating parameters were obtained through the energy utilization analysis, process simulation, heat exchanger calculations and comparisons of utility consumption. The operation of commercialized unit has revealed that the design parameters of each rectification column were consistent with the operation results, and the utility consumption was about 47% lower than the waditional heat integrated process.
Harding, A K; Gonthier, P L; Harding, Alice K.; Grenier, Isabelle A.; Gonthier, Peter L.
2007-01-01
Radio-quiet gamma-ray pulsars like Geminga may account for a number of the unidentified EGRET sources in the Galaxy. The number of Geminga-like pulsars is very sensitive to the geometry of both the gamma-ray and radio beams. Recent studies of the shape and polarization of pulse profiles of young radio pulsars have provided evidence that their radio emission originates in wide cone beams at altitudes that are a significant fraction (1 -10%) of their light cylinder radius. Such wide radio emission beams will be visible at a much larger range of observer angles than the narrow core components thought to originate at lower altitude. Using 3D geometrical modeling that includes relativistic effects from pulsar rotation, we study the visibility of such radio cone beams as well as that of the gamma-ray beams predicted by slot gap and outer gap models. From the results of this study one can obtain revised predictions for the fraction of Geminga-like, radio quiet pulsars present in the gamma-ray pulsar population.
NESDIS VIIRS Green Vegetation Fraction
National Oceanic and Atmospheric Administration, Department of Commerce — This dataset contains weekly Green Vegetation Fraction (GVF) derived from VIIRS. The Green Vegetation Fraction product is updated daily and is used as an input to...
Advances in robust fractional control
Padula, Fabrizio
2015-01-01
This monograph presents design methodologies for (robust) fractional control systems. It shows the reader how to take advantage of the superior flexibility of fractional control systems compared with integer-order systems in achieving more challenging control requirements. There is a high degree of current interest in fractional systems and fractional control arising from both academia and industry and readers from both milieux are catered to in the text. Different design approaches having in common a trade-off between robustness and performance of the control system are considered explicitly. The text generalizes methodologies, techniques and theoretical results that have been successfully applied in classical (integer) control to the fractional case. The first part of Advances in Robust Fractional Control is the more industrially-oriented. It focuses on the design of fractional controllers for integer processes. In particular, it considers fractional-order proportional-integral-derivative controllers, becau...
Comparison of the methods for discrete approximation of the fractional-order operator
Directory of Open Access Journals (Sweden)
Zborovjan Martin
2003-12-01
Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.
Culture materials affect ex vivo expansion of hematopoietic progenitor cells.
LaIuppa, J A; McAdams, T A; Papoutsakis, E T; Miller, W M
1997-09-01
Ex vivo expansion of hematopoietic cells is important for applications such as cancer treatment, gene therapy, and transfusion medicine. While cell culture systems are widely used to evaluate the biocompatibility of materials for implantation, the ability of materials to support proliferation of primary human cells in cultures for reinfusion into patients has not been addressed. We screened a variety of commercially available polymer (15 types), metal (four types), and glass substrates for their ability to support expansion of hematopoietic cells when cultured under conditions that would be encountered in a clinical setting. Cultures of peripheral blood (PB) CD34+ cells and mononuclear cells (MNC) were evaluated for expansion of total cells and colony-forming unit-granulocyte monocyte (CFU-GM; progenitors committed to the granulocyte and/or monocyte lineage). Human hematopoietic cultures in serum-free medium were found to be extremely sensitive to the substrate material. The only materials tested that supported expansion at or near the levels of polystyrene were tissue culture polystyrene, Teflon perfluoroalkoxy, Teflon fluorinated ethylene propylene, cellulose acetate, titanium, new polycarbonate, and new polymethylpentene. MNC were less sensitive to the substrate materials than the primitive CD34+ progenitors, although similar trends were seen for expansion of the two cell populations on the substrates tested. CFU-GM expansion was more sensitive to substrate materials than was total cell expansion. The detrimental effects of a number of the materials on hematopoietic cultures appear to be caused by protein adsorption and/or leaching of toxins. Factors such as cleaning, sterilization, and reuse significantly affected the performance of some materials as culture substrates. We also used PB CD34+ cell cultures to examine the biocompatibility of gas-permeable cell culture and blood storage bags and several types of tubing commonly used with biomedical equipment
Fractional Reserve in Banking System
Valkonen, Maria
2016-01-01
This thesis is aimed to provide understanding of the role of the fractional reserve in the mod-ern banking system worldwide and particularly in Finland. The fractional reserve banking is used worldwide, but the benefits of this system are very disputable. On the one hand, experts say that the fractional reserve is a necessary instrument for the normal business and profit making. On the other hand, sceptics openly criticize the fractional reserve system and blame it for fiat money (money n...
Fractional Reserve in Banking System
Valkonen, Maria
2016-01-01
This thesis is aimed to provide understanding of the role of the fractional reserve in the mod-ern banking system worldwide and particularly in Finland. The fractional reserve banking is used worldwide, but the benefits of this system are very disputable. On the one hand, experts say that the fractional reserve is a necessary instrument for the normal business and profit making. On the other hand, sceptics openly criticize the fractional reserve system and blame it for fiat money (money n...
Experimental observation of fractional echoes
Karras, G.; Hertz, E.; Billard, F.; Lavorel, B.; Siour, G.; Hartmann, J.-M.; Faucher, O.; Gershnabel, Erez; Prior, Yehiam; Averbukh, Ilya Sh.
2016-09-01
We report the observation of fractional echoes in a double-pulse excited nonlinear system. Unlike standard echoes, which appear periodically at delays which are integer multiples of the delay between the two exciting pulses, the fractional echoes appear at rational fractions of this delay. We discuss the mechanism leading to this phenomenon, and provide experimental demonstration of fractional echoes by measuring third harmonic generation in a thermal gas of CO2 molecules excited by a pair of femtosecond laser pulses.
Leonard, Thomas M.
This paper analyzes the issues regarding current expansion of NATO membership to include Romania and Bulgaria. The perspective given is that of the United States and places the Romanian and Bulgarian cases within the context of those issues. Sections of the paper include: (1) "The Road to Madrid: Expansion of NATO"; (2) "No Easy…
Thermal expansion of an epoxy-glass microsphere composite
Price, H. L.; Burks, H. D.
1977-01-01
The thermal expansion of a composite of epoxy (diglycidyl ether of bisphenol A) and solid glass microspheres was investigated. The microspheres had surfaces which were either untreated or treated with a silicone release agent, an epoxy coupling agent, or a general purpose silane coupling agent. Both room temperature (about 300 K) and elevated temperature (about 475 K) cures were used for the epoxy. Two microsphere size ranges were used, about 50 microns, which is applicable in filled moldings, and about 125 microns, which is applicable as bond line spacers. The thermal expansion of the composites was measured from 300 to 350 K or from 300 to 500 K, depending on the epoxy cure temperature. Measurements were made on composites containing up to .6 volume fraction microspheres. Two predictive models, which required only the values of thermal expansion of the polymer and glass and their specific gravities, were tested against the experimental data. A finite element analysis was made of the thermal strain of a composite cell containing a single microsphere surrounded by a finite-thickness interface.
Space matters: meristem expansion triggers corona formation in Passiflora.
Claßen-Bockhoff, Regine; Meyer, Charlotte
2016-02-01
Flower meristems differ from vegetative meristems in various aspects. One characteristic is the capacity for ongoing meristem expansion providing space for new structures. Here, corona formation in four species of Passiflora is investigated to understand the spatio-temporal conditions of its formation and to clarify homology of the corona elements. One bird-pollinated species with a single-rowed tubular corona (Passiflora tulae) and three insect-pollinated species with three (P. standleyi Killip), four (P. foetida L. 'Sanctae Martae') and six (P. foetida L. var. hispida) ray-shaped corona rows are chosen as representative examples for the study. Flower development is documented by scanning electron microscopy. Meristem expansion is reconstructed by morphometric data and correlated with the sequential corona element formation. In all species, corona formation starts late in ontogeny after all floral organs have been initiated. It is closely correlated with meristem expansion. The rows appear with increasing space in centripetal or convergent sequence. Based on the concept of fractionation, space induces primordia formation which is a self-regulating process filling the space completely. Correspondingly, the corona is interpreted as a structure of its own, originating from the receptacle. Considering the principle capacity of flower meristems to generate novel structures widens the view and allows new interpretations in combination with molecular, phylogenetic and morphogenetic data. © The Author 2015. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Stochastic Neural Field Theory and the System-Size Expansion
Bressloff, Paul C.
2010-01-01
We analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and transition rates are chosen so that in the thermodynamic or deterministic limit (N → ∞) we recover standard activity-based or voltage-based rate models. We derive the lowest order corrections to these rate equations for large but finite N using two different approximation schemes, one based on the Van Kampen system-size expansion and the other based on path integral methods. Both methods yield the same series expansion of the moment equations, which at O(1/N) can be truncated to form a closed system of equations for the first-and second-order moments. Taking a continuum limit of the moment equations while keeping the system size N fixed generates a system of integrodifferential equations for the mean and covariance of the corresponding stochastic neural field model. We also show how the path integral approach can be used to study large deviation or rare event statistics underlying escape from the basin of attraction of a stable fixed point of the mean-field dynamics; such an analysis is not possible using the system-size expansion since the latter cannot accurately determine exponentially small transitions. © by SIAM.
Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.
Pu, Yi-Fei; Yi, Zhang; Zhou, Ji-Liu
2016-07-14
This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks. Therefore, it is naturally makes one ponder how to generalize the first-order Hopfield neural networks to the fractional-order ones, and how to implement FHNN by means of fractional calculus. We propose to introduce a novel mathematical method: fractional calculus to implement FHNN. First, we implement fractor in the form of an analog circuit. Second, we implement FHNN by utilizing fractor and the fractional steepest descent approach, construct its Lyapunov function, and further analyze its attractors. Third, we perform experiments to analyze the stability and convergence of FHNN, and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting. The main contribution of our work is to propose FHNN in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach, construct its Lyapunov function, prove its Lyapunov stability, analyze its attractors, and apply FHNN to the defense against chip cloning attacks for anticounterfeiting. A significant advantage of FHNN is that its attractors essentially relate to the neuron's fractional order. FHNN possesses the fractional-order-stability and fractional-order-sensitivity characteristics.
Nonholonomic constraints with fractional derivatives
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E [Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119992 (Russian Federation); Zaslavsky, George M [Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York, NY 10012 (United States)
2006-08-04
We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle. We prove that fractional constraints can be used to describe the evolution of dynamical systems in which some coordinates and velocities are related to velocities through a power-law memory function.
How Weird Are Weird Fractions?
Stuffelbeam, Ryan
2013-01-01
A positive rational is a weird fraction if its value is unchanged by an illegitimate, digit-based reduction. In this article, we prove that each weird fraction is uniquely weird and initiate a discussion of the prevalence of weird fractions.
On the Equisummability of Hermite and Fourier Expansions
Indian Academy of Sciences (India)
E K Narayanan; S Thangavelu
2001-02-01
We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions. We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions.
Microbial Enzyme Activity and Carbon Cycling in Grassland Soil Fractions
Allison, S. D.; Jastrow, J. D.
2004-12-01
Extracellular enzymes are necessary to degrade complex organic compounds present in soils. Using physical fractionation procedures, we tested whether old soil carbon is spatially isolated from degradative enzymes across a prairie restoration chronosequence in Illinois, USA. We found that carbon-degrading enzymes were abundant in all soil fractions, including macroaggregates, microaggregates, and the clay fraction, which contains carbon with a mean residence time of ~200 years. The activities of two cellulose-degrading enzymes and a chitin-degrading enzyme were 2-10 times greater in organic matter fractions than in bulk soil, consistent with the rapid turnover of these fractions. Polyphenol oxidase activity was 3 times greater in the clay fraction than in the bulk soil, despite very slow carbon turnover in this fraction. Changes in enzyme activity across the restoration chronosequence were small once adjusted for increases in soil carbon concentration, although polyphenol oxidase activity per unit carbon declined by 50% in native prairie versus cultivated soil. These results are consistent with a `two-pool' model of enzyme and carbon turnover in grassland soils. In light organic matter fractions, enzyme production and carbon turnover both occur rapidly. However, in mineral-dominated fractions, both enzymes and their carbon substrates are immobilized on mineral surfaces, leading to slow turnover. Soil carbon accumulation in the clay fraction and across the prairie restoration chronosequence probably reflects increasing physical isolation of enzymes and substrates on the molecular scale, rather than the micron to millimeter scale.
Shrub expansion in SW Greenland
DEFF Research Database (Denmark)
Jørgensen, Rasmus Halfdan
to increasing shrub cover. Despite this, there is only limited experimental evidence that growth of the species responds to warming. Plant populations in fragmented and isolated locations could face problems adapting to a warming climate due to limited genetic variation and restricted migration from southern...... of firewood collection. A delayed reaction to the ending of the little ice age cannot be excluded, but seems rather unlikely considering other studies from Greenland. Effects of global warming in SW Greenland must be studied over even longer time periods than the 120 years of the current study. To answer......Arctic regions have experienced higher temperatures in recent decades, and the warming trend is projected to continue in the coming years. Arctic ecosystems are considered to be particularly vulnerable to climate change. Expansion of shrubs has been observed widely in tundra areas across the Arctic...
Bilinear Expansion For Redistribution Functions
Harutyunian, Haik; Alecian, Georges; Khachatryan, Knarik; Vardanyan, Ani
2016-11-01
We suggest here a method for construction of a bilinear expansion for an angle-averaged redistribution function. This function describes the elementary act of a photon scattering by a model two-level atom with the upper level broadened due to radiation damping. An eigenvalue and eigenvector determination problem is formulated and the relevant matrices are found analytically. Numerical procedures for their computations are elaborated as well. A simple method for the numerical calculations accuracy evaluation is suggested. It is shown that a family of redistribution functions describing the light scattering process within the spectral line frequencies can be constructed if the eigenvalue problem for the considered function is solved. It becomes possible if the eigenvalues and eigenvectors with the appropriate basic functions are used. The Voigt function and its derivatives used as basic functions are studied in detail as well.
Accelerating Expansion of the Universe
Chakraborty, Writambhara
2011-01-01
This thesis concentrates on the accelerated expansion of the Universe recently explored by measurements of redshift and luminosity-distance relations of type Ia Supernovae. We have considered a model of the universe filled with modified Chaplygin gas and barotropic fluid. The role of dynamical cosmological constant has been explored with Modified Chaplygin Gas as the background fluid. Various phenomenological models for \\Lambda have been studied in presence of the gravitational constant G to be constant or time dependent. A new form of the well known Chaplygin gas model has been presented by introducing inhomogeneity in the EOS. This model explains w=-1 crossing. An interaction of this model with the scalar field has also been investigated through a phenomenological coupling function. Tachyonic field has been depicted as dark energy model to represent the present acceleration of the Universe. A mixture of the tachyonic fluid has been considered with Generalized Chaplygin Gas to show the role of the later as a...
Asymptotic expansions in nonlinear rotordynamics
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
Increased pulmonary vascular permeability as a cause of re-expansion edema in rabbits
Energy Technology Data Exchange (ETDEWEB)
Pavlin, D.J.; Nessly, M.L.; Cheney, F.W.
1981-01-01
In order to study the mechanism(s) underlying re-expansion edema, we measured the concentration of labeled albumin (RISA) in the extravascular, extracellular water (EVECW) of the lung as a measure of pulmonary vascular permeability. Re-expansion edema was first induced by rapid re-expansion of rabbit lungs that had been collapsed for 1 wk by pneumothorax. The RISA in EVECW was expressed as a fraction of its plasma concentration: (RISA)L/(RISA)PL. The volume of EVECW (ml/gm dry lung) was measured using a /sup 24/Na indicator. Results in re-expansion edema were compared with normal control lungs and with oleic acid edema as a model of permeability edema. In re-expanded lungs, EVECW (3.41 +/- SD 1.24 ml/g) and (RISA)L/(RISA)PL 0.84 +/- SD 0.15) were significantly increased when compared with normal control lungs (2.25 +/- 0.41 ml/g and 0.51 +/- 0.20, respectively). Results in oleic acid edema (5.66 +/- 2.23 ml/g and 0.84 +/- 0.23) were similar to re-expansion edema. This suggested that re-expansion edema is due to increased pulmonary vascular permeability caused by mechanical stresses applied to the lung during re-expansion.
Rectangle expansion A∗ pathfinding for grid maps
Directory of Open Access Journals (Sweden)
Zhang An
2016-10-01
Full Text Available Search speed, quality of resulting paths and the cost of pre-processing are the principle evaluation metrics of a pathfinding algorithm. In this paper, a new algorithm for grid-based maps, rectangle expansion A∗ (REA∗, is presented that improves the performance of A∗ significantly. REA∗ explores maps in units of unblocked rectangles. All unnecessary points inside the rectangles are pruned and boundaries of the rectangles (instead of individual points within those boundaries are used as search nodes. This makes the algorithm plot fewer points and have a much shorter open list than A∗. REA∗ returns jump and grid-optimal path points, but since the line of sight between jump points is protected by the unblocked rectangles, the resulting path of REA∗ is usually better than grid-optimal. The algorithm is entirely online and requires no offline pre-processing. Experimental results for typical benchmark problem sets show that REA∗ can speed up a highly optimized A∗ by an order of magnitude and more while preserving completeness and optimality. This new algorithm is competitive with other highly successful variants of A∗.
Improving Power System Modeling. A Tool to Link Capacity Expansion and Production Cost Models
Energy Technology Data Exchange (ETDEWEB)
Diakov, Victor [National Renewable Energy Lab. (NREL), Golden, CO (United States); Cole, Wesley [National Renewable Energy Lab. (NREL), Golden, CO (United States); Sullivan, Patrick [National Renewable Energy Lab. (NREL), Golden, CO (United States); Brinkman, Gregory [National Renewable Energy Lab. (NREL), Golden, CO (United States); Margolis, Robert [National Renewable Energy Lab. (NREL), Golden, CO (United States)
2015-11-01
Capacity expansion models (CEM) provide a high-level long-term view at the prospects of the evolving power system. In simulating the possibilities of long-term capacity expansion, it is important to maintain the viability of power system operation in the short-term (daily, hourly and sub-hourly) scales. Production-cost models (PCM) simulate routine power system operation on these shorter time scales using detailed load, transmission and generation fleet data by minimizing production costs and following reliability requirements. When based on CEM 'predictions' about generating unit retirements and buildup, PCM provide more detailed simulation for the short-term system operation and, consequently, may confirm the validity of capacity expansion predictions. Further, production cost model simulations of a system that is based on capacity expansion model solution are 'evolutionary' sound: the generator mix is the result of logical sequence of unit retirement and buildup resulting from policy and incentives. The above has motivated us to bridge CEM with PCM by building a capacity expansion - to - production cost model Linking Tool (CEPCoLT). The Linking Tool is built to onset capacity expansion model prescriptions onto production cost model inputs. NREL's ReEDS and Energy Examplar's PLEXOS are the capacity expansion and the production cost models, respectively. Via the Linking Tool, PLEXOS provides details of operation for the regionally-defined ReEDS scenarios.
Nonhomogeneous fractional Poisson processes
Energy Technology Data Exchange (ETDEWEB)
Wang Xiaotian [School of Management, Tianjin University, Tianjin 300072 (China)]. E-mail: swa001@126.com; Zhang Shiying [School of Management, Tianjin University, Tianjin 300072 (China); Fan Shen [Computer and Information School, Zhejiang Wanli University, Ningbo 315100 (China)
2007-01-15
In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes W{sub H}{sup (j)}(t), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes W{sub H}{sup (j)}(t) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function {lambda}(t) strongly influences the existence of the highest finite moment of W{sub H}{sup (j)}(t) and the behaviour of the tail probability of W{sub H}{sup (j)}(t)
Membrane Assisted Enzyme Fractionation
DEFF Research Database (Denmark)
Yuan, Linfeng
. In this thesis, separations using crossflow elecro-membrane filtration (EMF) of amino acids, bovine serum albumin (BSA) and industrial enzymes from Novozymes were performed. The main objective of this study was to investigate the technological feasibility of EMF in the application of industrial enzyme...... fractionation, such as removal of a side activity from the main enzyme activity. As a proof-of-concept, amino acids were used as model solution to test the feasibility of EMF in the application of amphoteric molecule separation. A single amino acid was used to illustrate the effect of an electric field...... on the separation performance were very small in the investigated range. The mass transport of each enzyme can be well explained by the Extended-Nernst-Planck equation. Better separation was observed at lower feed concentration, higher solution pH in the investigated range and with a polysulfone (PS) MF membrane...
Membrane Assisted Enzyme Fractionation
DEFF Research Database (Denmark)
Yuan, Linfeng
. In this thesis, separations using crossflow elecro-membrane filtration (EMF) of amino acids, bovine serum albumin (BSA) and industrial enzymes from Novozymes were performed. The main objective of this study was to investigate the technological feasibility of EMF in the application of industrial enzyme...... fractionation, such as removal of a side activity from the main enzyme activity. As a proof-of-concept, amino acids were used as model solution to test the feasibility of EMF in the application of amphoteric molecule separation. A single amino acid was used to illustrate the effect of an electric field...... on the separation performance were very small in the investigated range. The mass transport of each enzyme can be well explained by the Extended-Nernst-Planck equation. Better separation was observed at lower feed concentration, higher solution pH in the investigated range and with a polysulfone (PS) MF membrane...
Fractional Chemotaxis Diffusion Equations
Langlands, T A M
2010-01-01
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.
Pressurized electrolysis stack with thermal expansion capability
Bourgeois, Richard Scott
2015-07-14
The present techniques provide systems and methods for mounting an electrolyzer stack in an outer shell so as to allow for differential thermal expansion of the electrolyzer stack and shell. Generally, an electrolyzer stack may be formed from a material with a high coefficient of thermal expansion, while the shell may be formed from a material having a lower coefficient of thermal expansion. The differences between the coefficients of thermal expansion may lead to damage to the electrolyzer stack as the shell may restrain the thermal expansion of the electrolyzer stack. To allow for the differences in thermal expansion, the electrolyzer stack may be mounted within the shell leaving a space between the electrolyzer stack and shell. The space between the electrolyzer stack and the shell may be filled with a non-conductive fluid to further equalize pressure inside and outside of the electrolyzer stack.
Novel thermal expansion of lead titanate
Institute of Scientific and Technical Information of China (English)
XING Xianran; DENG Jinxia; CHEN Jun; LIU Guirong
2003-01-01
Lattice parameters of lead titanate were precisely re-determined in the ternperature range of-150-950℃ by high precision XRPD measurements. It was clarified that there was no any evidence for a new phase transition at low temperatures. Tetragonal distortion strain decreases with temperature increasing. A novel thermal expansion was observed, positive thermal expansion from-150℃ to room temperature (RT) and above 490℃, and the negative thermal expansion in the temperature range of RT-490℃. A big jump of thermal expansion coefficient is attributed to the tetragonal-cubic phase transition. A rationalization for the negative thermal expansion of PbTiO3 is due to the decrease of anion-anion repulsion as polyhedra become more regular at heating. The mechanisms of positive and negative thermal expansions were elucidated as the same nature in the homogenous tetragonal phase at present case.
Directory of Open Access Journals (Sweden)
Sherwin Ting
2014-09-01
In conclusion, we have developed a simple robust and scalable platform that integrates both hESC expansion and CM differentiation in one unit process which is capable of meeting the need for large amounts of CMs.
Anomalous thermal expansion in $\\alpha$-titanium
Souvatzis, P.; O. Eriksson; M. I. Katsnelson
2007-01-01
We provide a complete quantitative explanation for the anisotropic thermal expansion of hcp Ti at low temperature. The observed negative thermal expansion along the c-axis is reproduced theoretically by means of a parameter free theory which involves both the electron and phonon contributions to the free energy. The thermal expansion of titanium is calculated and found to be negative along the c-axis for temperatures below $\\sim$ 170 K, in good agreement with observations. We have identified ...
Hydration and Thermal Expansion in Anatase Nanoparticles.
Zhu, He; Li, Qiang; Ren, Yang; Fan, Longlong; Chen, Jun; Deng, Jinxia; Xing, Xianran
2016-08-01
A tunable thermal expansion is reported in nanosized anatase by taking advantage of surface hydration. The coefficient of thermal expansion of 4 nm TiO2 along a-axis is negative with a hydrated surface and is positive without a hydrated surface. High-energy synchrotron X-ray pair distribution function analysis combined with ab initio calculations on the specific hydrated surface are carried out to reveal the local structure distortion that is responsible for the unusual negative thermal expansion.
Hydration and Thermal Expansion in Anatase Nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Zhu, He [Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083 China; Li, Qiang [Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083 China; Ren, Yang [Argonne National Laboratory, X-Ray Science Division, Argonne IL 60439 USA; Fan, Longlong [Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083 China; Chen, Jun [Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083 China; Deng, Jinxia [Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083 China; Xing, Xianran [Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083 China
2016-06-06
A tunable thermal expansion is reported in nanosized anatase by taking advantage of surface hydration. The coefficient of thermal expansion of 4 nm TiO2 along a-axis is negative with a hydrated surface and is positive without a hydrated surface. High-energy synchrotron X-ray pair distribution function analysis combined with ab initio calculations on the specific hydrated surface are carried out to reveal the local structure distortion that is responsible for the unusual negative thermal expansion.
GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION
Institute of Scientific and Technical Information of China (English)
陈泽乾
2002-01-01
A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators (e)t and its dual, creation operators (e)*t.
Multi-agent simulation of generation expansion in electricity markets.
Energy Technology Data Exchange (ETDEWEB)
Botterud, A; Mahalik, M. R.; Veselka, T. D.; Ryu, H.-S.; Sohn, K.-W.; Decision and Information Sciences; Korea Power Exchange
2007-06-01
We present a new multi-agent model of generation expansion in electricity markets. The model simulates generation investment decisions of decentralized generating companies (GenCos) interacting in a complex, multidimensional environment. A probabilistic dispatch algorithm calculates prices and profits for new candidate units in different future states of the system. Uncertainties in future load, hydropower conditions, and competitors actions are represented in a scenario tree, and decision analysis is used to identify the optimal expansion decision for each individual GenCo. We test the model using real data for the Korea power system under different assumptions about market design, market concentration, and GenCo's assumed expectations about their competitors investment decisions.
Martin, Taylor; Petrick Smith, Carmen; Forsgren, Nicole; Aghababyan, Ani; Janisiewicz, Philip; Baker, Stephanie
2015-01-01
The struggle with fraction learning in kindergarten through Grade 12 in the United States is a persistent problem and one of the major stumbling blocks to succeeding in higher mathematics. Research into this problem has identified several areas where students commonly struggle with fractions. While there are many theories of fraction learning,…
DEFF Research Database (Denmark)
Haack-Sørensen, Mandana; Follin, Bjarke; Juhl, Morten
2016-01-01
BACKGROUND: Adipose derived stromal cells (ASCs) are a rich and convenient source of cells for clinical regenerative therapeutic approaches. However, applications of ASCs often require cell expansion to reach the needed dose. In this study, cultivation of ASCs from stromal vascular fraction (SVF......) over two passages in the automated and functionally closed Quantum Cell Expansion System (Quantum system) is compared with traditional manual cultivation. METHODS: Stromal vascular fraction was isolated from abdominal fat, suspended in α-MEM supplemented with 10% Fetal Bovine Serum and seeded......, and endotoxins, in addition to the assessment of cell counts, viability, immunophenotype, and differentiation potential. RESULTS: The viability of ASCs passage 0 (P0) and P1 was above 96%, regardless of cultivation in flasks or Quantum system. Expression of surface markers and differentiation potential...
Structure and thermal expansion of liquid bismuth
Directory of Open Access Journals (Sweden)
Mudry S.
2015-12-01
Full Text Available Experimental structural data for liquid Bi were used for estimation of the main structure parameters as well as the thermal expansion coefficient both in supercooled and superheated temperature ranges. It was shown that the equilibrium melt had a positive thermal expansion coefficient within a temperature range upon melting and a negative one at higher temperatures. The former was related to structure changes upon melting, whereas the latter with topologic disordering upon further heating. It was found that the superheated melt had a negative thermal expansion coefficient. The results obtained from structural data were compared with the thermal expansion coefficient calculated from the data of density for liquid Bi.
TAYLOR EXPANSION METHOD FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
HE Yin-nian
2005-01-01
A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0-th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1-st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example,namely, the two-dimensional Navier-Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.
Anisotropic thermal expansion in a metal-organic framework.
Madsen, Solveig Røgild; Lock, Nina; Overgaard, Jacob; Iversen, Bo Brummerstedt
2014-06-01
Ionothermal reaction between Mn(II)(acetate)2·4H2O and 1,3,5-benzenetricarboxylic acid (H3BTC) in either of the two ionic liquids 1-ethyl-3-methylimidazolium bromide (EMIMBr) and 1-ethyl-3-methylimidazolium tosylate (EMIMOTs) resulted in the formation of the new metal-organic framework (MOF) EMIM[Mn(II)BTC] (BTC = 1,3,5-benzenetricarboxylate). The compound crystallizes in the orthorhombic space group Pbca with unit-cell parameters of a = 14.66658 (12), b = 12.39497 (9), c = 16.63509 (14) Å at 100 K. Multi-temperature single-crystal (15-340 K) and powder X-ray diffraction studies (100-400 K) reveal strongly anisotropic thermal expansion properties. The linear thermal expansion coefficients, αL(l), attain maximum values at 400 K along the a- and b-axis, with αL(a) = 115 × 10(-6) K(-1) and αL(b) = 75 × 10(-6) K(-1). At 400 K a negative thermal expansion coefficient of -40 × 10(-6) K(-1) is observed along the c-axis. The thermal expansion is coupled to a continuous deformation of the framework, which causes the structure to expand in two directions. Due to the rigidity of the linker, the expansion in the ab plane causes the network to contract along the c-axis. Hirshfeld surface analysis has been used to describe the interaction between the framework structure and the EMIM cation that resides within the channel. This reveals a number of rather weak interactions and one governing hydrogen-bonding interactions.
Condensed-Phase Mass Fraction in a Supersonic Molecular Beam Containing Clusters
Knuth, Eldon L.; Toennies, J. Peter
2008-12-01
For a supersonic molecular beam containing clusters, a relatively general and simple conservation-of-energy procedure for deducing from time-of-flight measurements the fraction of the beam in the condensed phase is developed. The procedure is applied to measurements for 4He beams formed by expansions which approach the two-phase region either near the critical point or to the liquid side of the critical point. The deduced values of the mass fraction are correlated using a scaling parameter which was used previously for correlating mean values of cluster sizes formed via fragmentation in free-jet expansions of liquid 4He.
Direct observation of a fractional charge
de-Picciotto, R.; Reznikov, M.; Heiblum, M.; Umansky, V.; Bunin, G.; Mahalu, D.
1997-09-01
Since Millikan's famous oil-drop experiments, it has been well known that electrical charge is quantized in units of the charge of an electron, e. For this reason, the theoretical prediction, by Laughlin of the existence of fractionally charged `quasiparticles'-proposed as an explanation for the fractional quantum Hall (FQH) effect-is very counterintuitive. The FQH effect is a phenomenon observed in the conduction properties of a two-dimensional electron gas subjected to a strong perpendicular magnetic field. This effect results from the strong interaction between electrons, brought about by the magnetic field, giving rise to the aforementioned fractionally charged quasiparticles which carry the current. Here we report the direct observation of these counterintuitive entities by using measurements of quantum shot noise. Quantum shot noise results from the discreteness of the current-carrying charges and so is proportional to both the charge of the quasiparticles and the average current. Our measurements of quantum shot noise show unambiguously that current in a two-dimensional electron gas in the FQH regime is carried by fractional charges-e/3 in the present case-in agreement with Laughlin's prediction.
The bound fraction of young star clusters
Brinkmann, N; Motwani, B; Kroupa, P
2016-01-01
The residual gas within newly formed star clusters is expelled through stellar feedback on timescales ~ 1 Myr. The subsequent expansion of the cluster results in an unbinding of a fraction of stars, before the remaining cluster members can re-virialize and form a surviving cluster. We investigate the bound fraction after gas expulsion as a function of initial cluster mass in stars and gauge the influence of primordial mass segregation, stellar evolution and the tidal field at solar distance. We also assess the impact of the star-formation efficiency and gas expulsion velocity. We perform N-body simulations using Sverre Aarseth's NBODY7 code, starting with compact clusters in their embedded phase and approximate the gas expulsion by means of an exponentially depleting external gravitational field. We follow the process of re-virialization through detailed monitoring of different Lagrange radii over several Myr, examining initial half-mass radii of 0.1 pc, 0.3 pc and 0.5 pc and masses usually ranging from 5x10^...
Void fraction prediction in saturated flow boiling
Energy Technology Data Exchange (ETDEWEB)
Francisco J Collado [Dpto de Ingenieria Mecanica-Motores Termicos, CPS-B, Universidad de Zaragoza, Maria de Luna 50018-Zaragoza (Spain)
2005-07-01
Full text of publication follows: An essential element in thermal-hydraulics is the accurate prediction of the vapor void fraction, or fraction of the flow cross-sectional area occupied by steam. Recently, the author has suggested to calculate void fraction working exclusively with thermodynamic properties. It is well known that the usual 'flow' quality, merely a mass flow rate ratio, is not at all a thermodynamic property because its expression in function of thermodynamic properties includes the slip ratio, which is a parameter of the process not a function of state. By the other hand, in the classic and well known expression of the void fraction - in function of the true mass fraction of vapor (also called 'static' quality), and the vapor and liquid densities - does not appear the slip ratio. Of course, this would suggest a direct procedure for calculating the void fraction, provided we had an accurate value of the true mass fraction of vapor, clearly from the heat balance. However the classic heat balance is usually stated in function of the 'flow' quality, what sounds really contradictory because this parameter, as we have noted above, is not at all a thermodynamic property. Then we should check against real data the actual relationship between the thermodynamic properties and the applied heat. For saturated flow boiling just from the inlet of the heated tube, and not having into account the kinetic and potential terms, the uniform applied heat per unit mass of inlet water and per unit length (in short, specific linear heat) should be closely related to a (constant) slope of the mixture enthalpy. In this work, we have checked the relation between the specific linear heat and the thermodynamic enthalpy of the liquid-vapor mixture using the actual mass fraction. This true mass fraction is calculated using the accurate measurements of the outlet void fraction taken during the Cambridge project by Knights and Thom in the sixties for
The impact of fraction magnitude knowledge on algebra performance and learning.
Booth, Julie L; Newton, Kristie J; Twiss-Garrity, Laura K
2014-02-01
Knowledge of fractions is thought to be crucial for success with algebra, but empirical evidence supporting this conjecture is just beginning to emerge. In the current study, Algebra 1 students completed magnitude estimation tasks on three scales (0-1 [fractions], 0-1,000,000, and 0-62,571) just before beginning their unit on equation solving. Results indicated that fraction magnitude knowledge, and not whole number knowledge, was especially related to students' pretest knowledge of equation solving and encoding of equation features. Pretest fraction knowledge was also predictive of students' improvement in equation solving and equation encoding skills. Students' placement of unit fractions (e.g., those with a numerator of 1) was not especially useful for predicting algebra performance and learning in this population. Placement of non-unit fractions was more predictive, suggesting that proportional reasoning skills might be an important link between fraction knowledge and learning algebra. Copyright © 2013 Elsevier Inc. All rights reserved.
Fractional Calculus: Integral and Differential Equations of Fractional Order
Gorenflo, Rudolf
2008-01-01
We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating these operators in a way accessible to applied scientists, avoiding unproductive generalities and excessive mathematical rigor. By applying this technique we shall derive the analytical solutions of the most simple linear integral and differential equations of fractional order. We show the fundamental role of the Mittag-Leffler function, whose properties are reported in an ad hoc Appendix. The topics discussed here will be: (a) essentials of Riemann-Liouville fractional calculus with basic formulas of Laplace transforms, (b) Abel type integral equations of first and second kind, (c) relaxation and oscillation type differential equations of fractional order.
Elementary Proof of Yu. V. Nesterenko Expansion of the Number Zeta(3 in Continued Fraction
Directory of Open Access Journals (Sweden)
Gutnik Leonid
2010-01-01
Full Text Available Yu. V. Nesterenko has proved that , , , , , , and for ; , , and , for His proof is based on some properties of hypergeometric functions. We give here an elementary direct proof of this result.
An improved fractional divider for fractional-N frequency synthesizers
Zhang, Wei; Liu, Yang; Zhou, Yongqi
2009-07-01
This paper presents an improved fractional divider used in 1.8~2GHz fractional-N frequency synthesizers. A new clock setting for delta-sigma modulator (DSM) is proposed to prevent the potential problems of traditional fractional dividers: the DSM output would be wrongly loaded and the action of DSM circuit may affect the phase-detection of phase-frequency-detector (PFD). Simulation result shows the effectiveness of this improvement.
Magnetic Clouds: Global and local expansion
Gulisano, Adriana; Demoulin, Pascal; Soledad Nakwacki, Ms Maria; Dasso, Sergio; Emilia Ruiz, Maria
Magnetic clouds (MCs) are magnetized objects forming flux ropes, which are expelled from the Sun and travel through the heliosphere, transporting important amounts of energy, mass, magnetic flux, and magnetic helicity from the Sun to the interplanetary medium. To know the detailed dynamical evolution of MCs is very useful to improve the knowledge of solar processes, for instance from linking a transient solar source with its interplanetary manifestation. During its travel, and mainly due to the decrease of the total (magnetic plus thermal) pressure in the surrounding solar wind, MCs are objects in expansion. However, the detailed magnetic structure and the dynamical evolution of MCs is still not fully known. Even the identification of their boundaries is an open question in some cases. In a previous work we have shown that from onepoint observations of the bulk velocity profile, it is possible to infer the 'local' expansion rate for a given MC, i.e., the expansion rate while the MC is observed by the spacecraft. By the another hand, and from the comparison of sizes for different MCs observed at different heliodistances, it is possible to quantify an 'average' expansion law (i.e., a global expansion). In this work, in order to study the variability of the 'local' expansion with respect to the 'average' expansion of MCs during their travel, we present results and a comparison between both approaches. We make a detailed study of one-point observations (magnetic and bulk velocity) using a set of MCs and we get the 'local' expansion rate for each studied event. We compare the obtained 'local' expansion rates with the 'average' expansion law, and also with the expansion rates for the stationary solar wind.
Primordial vorticity and gradient expansion
Giovannini, Massimo
2012-01-01
The evolution equations of the vorticities of the electrons, ions and photons in a pre-decoupling plasma are derived, in a fully inhomogeneous geometry, by combining the general relativistic gradient expansion and the drift approximation within the Adler-Misner-Deser decomposition. The vorticity transfer between the different species is discussed in this novel framework and a set of general conservation laws, connecting the vorticities of the three-component plasma with the magnetic field intensity, is derived. After demonstrating that a source of large-scale vorticity resides in the spatial gradients of the geometry and of the electromagnetic sources, the total vorticity is estimated to lowest order in the spatial gradients and by enforcing the validity of the momentum constraint. By acknowledging the current bounds on the tensor to scalar ratio in the (minimal) tensor extension of the $\\Lambda$CDM paradigm the maximal comoving magnetic field induced by the total vorticity turns out to be, at most, of the or...
Negative thermal expansion materials: technological key for control of thermal expansion
Koshi Takenaka
2012-01-01
Most materials expand upon heating. However, although rare, some materials contract upon heating. Such negative thermal expansion (NTE) materials have enormous industrial merit because they can control the thermal expansion of materials. Recent progress in materials research enables us to obtain materials exhibiting negative coefficients of linear thermal expansion over −30 ppm K−1. Such giant NTE is opening a new phase of control of thermal expansion in composites. Specifically examining pra...
Thermal expansion behavior of KZr2P3O12-SrZr4P6O24 ceramics
Institute of Scientific and Technical Information of China (English)
张彪; 郭景坤; 诸培南
1996-01-01
The relationships between thermal expansion and density,microcracking,stress and phase transition in K1/2Sr1/4Zr2P3O12(K2) and with K2 containing 2 mass fraction of MgO (K2M2) have been studied.The materials showed a little thermal expansion anisotropy,hysteresis,and microcracking Thermal shock-induced cracks resulted in a decrease of the coefficient of thermal expansion.Phase transition caused crack healing resulting in a decrease in specimen size.
On digit patterns in expansions of rational numbers with prime denominator
Shparlinski, Igor E
2012-01-01
We show that, for any fixed $\\varepsilon > 0$ and almost all primes $p$, the $g$-ary expansion of any fraction $m/p$ with $\\gcd(m,p) = 1$ contains almost all $g$-ary strings of length $k < (5/24 - \\varepsilon) \\log_g p$. This complements a result of J. Bourgain, S. V. Konyagin, and I. E. Shparlinski that asserts that, for almost all primes, all $g$-ary strings of length $k < (41/504 -\\varepsilon) \\log_g p$ occur in the $g$-ary expansion of $m/p$.
The Expansion Postponement in Pure Type Systems
Institute of Scientific and Technical Information of China (English)
宋方敏
1997-01-01
The expansion postponement problem in Pure Type Systems is an open problem raised by R.Pollack in 1992.In this paper,the author presents a set of necessary and sufficient conditions for this problem and a set of sufficient conditions for it.The author also gives some properties for pure typ systems without the expansion rule.
Multipole expansion method for supernova neutrino oscillations
Energy Technology Data Exchange (ETDEWEB)
Duan, Huaiyu; Shalgar, Shashank, E-mail: duan@unm.edu, E-mail: shashankshalgar@unm.edu [Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131 (United States)
2014-10-01
We demonstrate a multipole expansion method to calculate collective neutrino oscillations in supernovae using the neutrino bulb model. We show that it is much more efficient to solve multi-angle neutrino oscillations in multipole basis than in angle basis. The multipole expansion method also provides interesting insights into multi-angle calculations that were accomplished previously in angle basis.
Finnish Higher Education Expansion and Regional Policy
Saarivirta, Toni
2010-01-01
This paper concentrates on the expansion of Finnish higher education between the 1960s and 1970s, exposes its background in the light of the policy decisions that were made, compares the unique features of this expansion with those of certain other countries, discusses the impact of the controlled "top down" governance of higher…
Flash Expansion Threshold in Whirligig Swarms.
Directory of Open Access Journals (Sweden)
William L Romey
Full Text Available In the selfish herd hypothesis, prey animals move toward each other to avoid the likelihood of being selected by a predator. However, many grouped animals move away from each other the moment before a predator attacks. Very little is known about this phenomenon, called flash expansion, such as whether it is triggered by one individual or a threshold and how information is transferred between group members. We performed a controlled experiment with whirligig beetles in which the ratio of sighted to unsighted individuals was systematically varied and emergent flash expansion was measured. Specifically, we examined: the percentage of individuals in a group that startled, the resulting group area, and the longevity of the flash expansion. We found that one or two sighted beetles in a group of 24 was not enough to cause a flash expansion after a predator stimulus, but four sighted beetles usually initiated a flash expansion. Also, the more beetles that were sighted the larger the resulting group area and the longer duration of the flash expansion. We conclude that flash expansion is best described as a threshold event whose adaptive value is to prevent energetically costly false alarms while quickly mobilizing an emergent predator avoidance response. This is one of the first controlled experiments of flash expansion, an important emergent property that has applications to understanding collective motion in swarms, schools, flocks, and human crowds. Also, our study is a convincing demonstration of social contagion, how the actions of one individual can pass through a group.
A reduced volumetric expansion factor plot
Hendricks, R. C.
1979-01-01
A reduced volumetric expansion factor plot has been constructed for simple fluids which is suitable for engineering computations in heat transfer. Volumetric expansion factors have been found useful in correlating heat transfer data over a wide range of operating conditions including liquids, gases and the near critical region.
Earnings Returns to the British Education Expansion
Devereux, Paul J.; Fan, Wen
2011-01-01
We study the effects of the large expansion in British educational attainment that took place for cohorts born between 1970 and 1975. Using the Quarterly Labour Force Survey, we find that the expansion caused men to increase education by about a year on average and gain about 8% higher wages; women obtained a slightly greater increase in education…
The heavy quark expansion of QCD
Energy Technology Data Exchange (ETDEWEB)
Falk, A.F. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy
1997-06-01
These lectures contain an elementary introduction to heavy quark symmetry and the heavy quark expansion. Applications such as the expansion of heavy meson decay constants and the treatment of inclusive and exclusive semileptonic B decays are included. Heavy hadron production via nonperturbative fragmentation processes is also discussed. 54 refs., 7 figs.
CONCEPT OF TISSUE EXPANSION IN RECONSTRUCTIVE SURGERY
Directory of Open Access Journals (Sweden)
Sheeja Rajan
2015-01-01
Full Text Available BACKGROUND: Tissue expansion is a unique reconstructive option in the armamentarium of a reconstructive surgeon whereby skin and soft tissues of our body can be stretched to large dimensions for wound coverage. The basis for such stretch ability lies in the inherent viscoelastic properties of skin. AIMS: This paper explores the prospects of using tissue expanders to reconstruct defects arising due to a kaleidoscope of pathological conditions including burns scars, post traumatic scars, congenital anomalies like hairy nevus, involutional scars in haemangioma as well as in post mastectomy breast reconstruction . MATERIALS AND METHODS: Our experience with tissue expansion in 14 patients over 24 months is presented. Tissue expanders made of silicone in sizes from 100 - 250ml, of round, rectangular or croissant (crescent shapes have been used. Areas expanded include scalp, forehead, neck, abdomen and forearm. Multiple expanders have been used when possible. Average expansion time was 8 - 12 weeks and the expanded tissue was transferred as advancement flaps. RESULTS AND CONCLUSIONS: Tissue expansion was successfully completed in 13 patients. Expansion had to be aborted in 1 paediatric patient undergoing neck expansion due to infection. Implant failure occurred in 1 patient during serial expansion. Nevertheless, in our experience tissue expan sion is an invaluable reconstructive tool to give excellent donor tissue with colour and texture match in countless situations demanding aesthetic and functional reconstruction. KEYWORDS: Burns scars, Reconstruction, Tissue expansion .
Virial expansion coefficients in the harmonic approximation
DEFF Research Database (Denmark)
R. Armstrong, J.; Zinner, Nikolaj Thomas; V. Fedorov, D.
2012-01-01
The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated...
Perturbative expansion of Chern-Simons theory
SAWON, Justin
2005-01-01
An overview of the perturbative expansion of the Chern--Simons path integral is given. The main goal is to describe how trivalent graphs appear: as they already occur in the perturbative expansion of an analogous finite-dimensional integral, we discuss this case in detail.
Institute of Scientific and Technical Information of China (English)
Yu Nan
2011-01-01
IT is a well-known saying that whenever the United States sneezes,the world is sure to catch a cold.However,this analogy now seems more appropriate for the economic might of China.This year marks the 10th anniversary of China's accession to the World Trade Organization (WTO).The nation has gone from being relatively isolated from international trade standards and regulations,to meeting requirements for full participation in world trade.
Incompressible Stars and Fractional Derivatives
Bayin, S S
2014-01-01
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum mechanics. In this paper we investigate the fractional versions of the stellar structure equations for non radiating spherical objects. Using incompressible fluids as a comparison, we develop models for constant density Newtonian objects with fractional mass distributions or stress conditions. To better understand the fractional effects, we discuss effective values for the density, gravitational field and equation of state. The fractional ob- jects are smaller and less massive than integer models. The fractional parameters are related to a polytropic index for the models considered.
Proton Fraction in Neutron Stars
Institute of Scientific and Technical Information of China (English)
张丰收; 陈列文
2001-01-01
The proton fraction in β-stable neutron stars is investigated within the framework of the Skyrme-Hartree-Fock theory using the extended Skyrme effective interaction for the first time. The calculated results show that the proton fraction disappears at high density, which implies that the pure neutron matter may exist in the interior of neutron stars. The incompressibility of the nuclear equation-of-state is shown to be more important to determine the proton fraction. Meanwhile, it is indicated that the addition of muons in neutron stars will change the proton fraction. It is also found that the higher-order terms of the nuclear symmetry energy have obvious effects on the proton fraction and the parabolic law of the nuclear symmetry energy is not enough to determine the proton fraction.
Accessible solitons of fractional dimension
Energy Technology Data Exchange (ETDEWEB)
Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Belić, Milivoj [Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Zhang, Yiqi [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)
2016-05-15
We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.
Unit Fractions and Their "Basimal" Representations: Exploring Patterns
Herman, Marlena; Milou, Eric; Schiffman, Jay
2004-01-01
Different representations of rational numbers are considered and students are lead through activities that explore patterns in base ten and other bases. With this students are encouraged to solve problems and investigate situations designed to foster flexible thinking about rational numbers.
Fractional Calculus of Analytic Functions Concerned with Möbius Transformations
Nicoleta Breaz; Daniel Breaz; Shigeyoshi Owa
2016-01-01
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.
Fractional Calculus of Analytic Functions Concerned with Möbius Transformations
Directory of Open Access Journals (Sweden)
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.
Green’s functions and energy eigenvalues for delta-perturbed space-fractional quantum systems
Energy Technology Data Exchange (ETDEWEB)
Nayga, M. M., E-mail: mnayga@nip.upd.edu.ph; Esguerra, J. P. [National Institute of Physics, University of the Philippines-Diliman, Quezon City (Philippines)
2016-02-15
Starting from the propagator, we introduced a time-ordered perturbation expansion and employed Wick rotation to obtain a general energy-dependent Green’s function expressions for space-fractional quantum systems with Dirac delta-function perturbation. We then obtained the Green’s functions and equations for the bound state energies for the space-fractional Schrödinger equation with single and double Dirac delta well potentials and the delta-perturbed infinite well.
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
Development of Soda Residue Concrete Expansion Agent
Institute of Scientific and Technical Information of China (English)
WANG Bao-min; WANG Li-jiu; M F Mohd Zain; F C Lai
2003-01-01
A new type of concrete expansion agent has been successfully developed for the first time in the world by utilizing an industrial waste residue-soda residue and an industrial wasteliquor.Adding 3%-6% of the agent into Portland cement enables a shrinkage-compensating concrete to be prepared.Mortar and concrete containing this expansion agent have better shrinkage-compensating and mechanical properties.The raw materials component,production process,technical properties,micro-analysis of mortar made with this expansion agent,mechanism of expansion and research results are described in this article.The experimental results show that the new type of concrete expansion agent accords with the standard and its main mineral component is xCaO-ySO3-zAl2O3.
Business information query expansion through semantic network
Gong, Zhiguo; Muyeba, Maybin; Guo, Jingzhi
2010-02-01
In this article, we propose a method for business information query expansions. In our approach, hypernym/hyponymy and synonym relations in WordNet are used as the basic expansion rules. Then we use WordNet Lexical Chains and WordNet semantic similarity to assign terms in the same query into different groups with respect to their semantic similarities. For each group, we expand the highest terms in the WordNet hierarchies with hypernym and synonym, the lowest terms with hyponym and synonym and all other terms with only synonym. In this way, the contradictory caused by full expansion can be well controlled. Furthermore, we use collection-related term semantic network to further improve the expansion performance. And our experiment reveals that our solution for query expansion can improve the query performance dramatically.
Maxwell superalgebras and Abelian semigroup expansion
Energy Technology Data Exchange (ETDEWEB)
Concha, P.K.; Rodríguez, E.K. [Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Dipartimento di Scienza Applicata e Tecnologia (DISAT), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Via Pietro Giuria, 1, 10125 Torino (Italy)
2014-09-15
The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2) leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM{sup (N)} recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N). Moreover, we show that new minimal Maxwell superalgebras type sM{sub m+2} and their N-extended generalization can be obtained using the S-expansion procedure.
Maxwell superalgebras and Abelian semigroup expansion
Directory of Open Access Journals (Sweden)
P.K. Concha
2014-09-01
Full Text Available The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2 leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM(N recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N. Moreover, we show that new minimal Maxwell superalgebras type sMm+2 and their N-extended generalization can be obtained using the S-expansion procedure.
Fractional Fourier transform of apertured paraboloid refracting system
Institute of Scientific and Technical Information of China (English)
Jiannong Chen; Jinliang Yan; Defa Wang; Yongjiang Yu
2007-01-01
The limitation of paraxial condition of paraboloid refracting system in performing fractional Fourier transform acts like an aperture, which makes the system different from ideal systems. With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of fractional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented. Complicated and practical fractional Fourier transform systems can be constructed by cascading several apertured paraboloid refracting systems which are the simplest and the most basic units for performing more precise transform.
Simulation and optimization of fractional crystallization processes
DEFF Research Database (Denmark)
Thomsen, Kaj; Rasmussen, Peter; Gani, Rafiqul
1998-01-01
A general method for the calculation of various types of phase diagrams for aqueous electrolyte mixtures is outlined. It is shown how the thermodynamic equilibrium precipitation process can be used to satisfy the operational needs of industrial crystallizer/centrifuge units. Examples of simulation...... and optimization of fractional crystallization processes are shown. In one of these examples, a process with multiple steady states is analyzed. The thermodynamic model applied for describing the highly non-ideal aqueous electrolyte systems is the Extended UNIQUAC model. (C) 1998 Published by Elsevier Science Ltd...
Comment on "Fractional quantum mechanics" and "Fractional Schroedinger equation"
Wei, Yuchuan
2016-01-01
In this comment, we point out some shortcomings in two papers "Fractional quantum mechanics" [Phys. Rev. E 62, 3135 (2000)] and "Fractional Schroedinger equation" [Phys. Rev. E 66, 056108 (2002)]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from one place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to a destination.
Qu, Jingyuan; Kadic, Muamer; Naber, Andreas; Wegener, Martin
2017-01-01
Controlling the thermal expansion of materials is of great technological importance. Uncontrolled thermal expansion can lead to failure or irreversible destruction of structures and devices. In ordinary crystals, thermal expansion is governed by the asymmetry of the microscopic binding potential, which cannot be adjusted easily. In artificial crystals called metamaterials, thermal expansion can be controlled by structure. Here, following previous theoretical work, we fabricate three-dimensional (3D) two-component polymer micro-lattices by using gray-tone laser lithography. We perform cross-correlation analysis of optical microscopy images taken at different sample temperatures. The derived displacement-vector field reveals that the thermal expansion and resulting bending of the bi-material beams leads to a rotation of the 3D chiral crosses arranged onto a 3D checkerboard pattern within one metamaterial unit cell. These rotations can compensate the expansion of the all positive constituents, leading to an effectively near-zero thermal length-expansion coefficient, or over-compensate the expansion, leading to an effectively negative thermal length-expansion coefficient. This evidences a striking level of thermal-expansion control.
42 CFR 412.30 - Exclusion of new rehabilitation units and expansion of units already excluded.
2010-10-01
... number of beds can be added to the hospital's licensure and certification and considered “new” under... the hospital seeks to add the beds. To the extent bed capacity was removed from the hospital's... approval, under State licensure and Medicare certification, for an increase in its hospital bed capacity...
COMMERCIAL SNF ACCIDENT RELEASE FRACTIONS
Energy Technology Data Exchange (ETDEWEB)
S.O. Bader
1999-10-18
The purpose of this design analysis is to specify and document the total and respirable fractions for radioactive materials that are released from an accident event at the Monitored Geologic Repository (MGR) involving commercial spent nuclear fuel (CSNF) in a dry environment. The total and respirable release fractions will be used to support the preclosure licensing basis for the MGR. The total release fraction is defined as the fraction of total CSNF assembly inventory, typically expressed as an activity inventory (e.g., curies), of a given radionuclide that is released to the environment from a waste form. The radionuclides are released from the inside of breached fuel rods (or pins) and from the detachment of radioactive material (crud) from the outside surfaces of fuel rods and other components of fuel assemblies. The total release fraction accounts for several mechanisms that tend to retain, retard, or diminish the amount of radionuclides that are available for transport to dose receptors or otherwise can be shown to reduce exposure of receptors to radiological releases. The total release fraction includes a fraction of airborne material that is respirable and could result in inhalation doses. This subset of the total release fraction is referred to as the respirable release fraction. Potential accidents may involve waste forms that are characterized as either bare (unconfined) fuel assemblies or confined fuel assemblies. The confined CSNF assemblies at the MGR are contained in shipping casks, canisters, or disposal containers (waste packages). In contrast to the bare fuel assemblies, the container that confines the fuel assemblies has the potential of providing an additional barrier for diminishing the total release fraction should the fuel rod cladding breach during an accident. However, this analysis will not take credit for this additional bamer and will establish only the total release fractions for bare unconfined CSNF assemblies, which may however be
Geographic Expansion of Lyme Disease in Michigan, 2000-2014.
Lantos, Paul M; Tsao, Jean; Nigrovic, Lise E; Auwaerter, Paul G; Fowler, Vance G; Ruffin, Felicia; Foster, Erik; Hickling, Graham
2017-01-01
Most Lyme disease cases in the Midwestern United States are reported in Minnesota and Wisconsin. In recent years, however, a widening geographic extent of Lyme disease has been noted with evidence of expansion eastwards into Michigan and neighboring states with historically low incidence rates. We collected confirmed and probable cases of Lyme disease from 2000 through 2014 from the Michigan Department of Health and Human Services, entering them in a geographic information system. We performed spatial focal cluster analyses to characterize Lyme disease expansion. We compared the distribution of human cases with recent Ixodes scapularis tick distribution studies. Lyme disease cases in both the Upper and Lower Peninsulas of Michigan expanded more than 5-fold over the study period. Although increases were seen throughout the Upper Peninsula, the Lower Peninsula particularly expanded along the Indiana border north along the eastern shore of Lake Michigan. Human cases corresponded to a simultaneous expansion in established I scapularis tick populations. The geographic distribution of Lyme disease cases significantly expanded in Michigan between 2000 and 2014, particularly northward along the Lake Michigan shore. If such dynamic trends continue, Michigan-and possibly neighboring areas of Indiana, Ohio, and Ontario, Canada-can expect a continued increase in Lyme disease cases.
Shrinkage and Expansive Strain of Concrete with Fly Ash and Expansive Agent
Institute of Scientific and Technical Information of China (English)
GAO Peiwei; LU Xiaolin; TANG Mingshu
2009-01-01
The effects of fly ash and MgO-type expansive agent on the shrinkage and expan-sive strain of concrete with high magnesia cement were investigated. The results show that high volumes of fly ash may reduce the shrinkage strain of concrete and inhibit the expansive strain of concrete with MgO-type expansive agent, but can not eliminate the shrinkage of concrete. MgO-type expansive agent may produce expansive strain and compensate the shrinkage strain of concrete, re-lieve the cracking risk, but the hydration product of magnesia tends to get together in paste and pro-duce expansive cracking of concrete with high magnesia content according to SEM observation.
Expansion Techniques for Collisionless Stellar Dynamical Simulations
Meiron, Yohai; Holley-Bockelmann, Kelly; Spurzem, Rainer
2014-01-01
We present GPU implementations of two fast force calculation methods, based on series expansions of the Poisson equation. One is the Self-Consistent Field (SCF) method, which is a Fourier-like expansion of the density field in some basis set; the other is the Multipole Expansion (MEX) method, which is a Taylor-like expansion of the Green's function. MEX, which has been advocated in the past, has not gained as much popularity as SCF. Both are particle-field method and optimized for collisionless galactic dynamics, but while SCF is a "pure" expansion, MEX is an expansion in just the angular part; it is thus capable of capturing radial structure easily, where SCF needs a large number of radial terms. We show that despite the expansion bias, these methods are more accurate than direct techniques for the same number of particles. The performance of our GPU code, which we call ETICS, is profiled and compared to a CPU implementation. On the tested GPU hardware, a full force calculation for one million particles took...
Deterministic ratchets for suspension fractionation
Kulrattanarak, T.
2010-01-01
Driven by the current insights in sustainability and technological development in biorefining natural renewable resources, the food industry has taken an interest in fractionation of agrofood materials, like milk and cereal crops. The purpose of fractionation is to split the raw material in sever
Financial Planning with Fractional Goals
M.H. Goedhart; J. Spronk (Jaap)
1995-01-01
textabstractWhen solving financial planning problems with multiple goals by means of multiple objective programming, the presence of fractional goals leads to technical difficulties. In this paper we present a straightforward interactive approach for solving such linear fractional programs with mult
Financial Planning with Fractional Goals
Goedhart, M.H.; Spronk, Jaap
1995-01-01
textabstractWhen solving financial planning problems with multiple goals by means of multiple objective programming, the presence of fractional goals leads to technical difficulties. In this paper we present a straightforward interactive approach for solving such linear fractional programs with multiple goal variables. The approach is illustrated by means of an example in financial planning.
Approximations of fractional Brownian motion
Li, Yuqiang; 10.3150/10-BEJ319
2012-01-01
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.
Investigations on Multiplication of Fractions.
Sai, Khoo Phon; Inder, Walter R. D.
1984-01-01
Three different models with continuous materials, discontinuous materials, and number lines were used to study the operation concept in six investigations on multiplication with fractions with pupils aged 11-12 in a Penang International School. All approaches could be understood by pupils, but they preferred the area and fractional models. (MNS)
Understanding Magnitudes to Understand Fractions
Gabriel, Florence
2016-01-01
Fractions are known to be difficult to learn and difficult to teach, yet they are vital for students to have access to further mathematical concepts. This article uses evidence to support teachers employing teaching methods that focus on the conceptual understanding of the magnitude of fractions.
Ejection Fraction Heart Failure Measurement
... Disease Venous Thromboembolism Aortic Aneurysm More Ejection Fraction Heart Failure Measurement Updated:Feb 15,2017 The ejection fraction ( ... failure This content was last reviewed April 2015. Heart Failure • Home • About Heart Failure • Causes and Risks for ...
Unwrapping Students' Ideas about Fractions
Lewis, Rebecca M.; Gibbons, Lynsey K.; Kazemi, Elham; Lind, Teresa
2015-01-01
Supporting students to develop an understanding of the meaning of fractions is an important goal of elementary school mathematics. This involves developing partitioning strategies, creating representations, naming fractional quantities, and using symbolic notation. This article describes how teachers can use a formative assessment problem to…
Wavelet-fractional Fourier transforms
Institute of Scientific and Technical Information of China (English)
Yuan Lin
2008-01-01
This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite-Ganssian functions.The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
Giant negative thermal expansion in magnetic nanocrystals.
Zheng, X G; Kubozono, H; Yamada, H; Kato, K; Ishiwata, Y; Xu, C N
2008-12-01
Most solids expand when they are heated, but a property known as negative thermal expansion has been observed in a number of materials, including the oxide ZrW2O8 (ref. 1) and the framework material ZnxCd1-x(CN)2 (refs 2,3). This unusual behaviour can be understood in terms of low-energy phonons, while the colossal values of both positive and negative thermal expansion recently observed in another framework material, Ag3[Co(CN)6], have been explained in terms of the geometric flexibility of its metal-cyanide-metal linkages. Thermal expansion can also be stopped in some magnetic transition metal alloys below their magnetic ordering temperature, a phenomenon known as the Invar effect, and the possibility of exploiting materials with tuneable positive or negative thermal expansion in industrial applications has led to intense interest in both the Invar effect and negative thermal expansion. Here we report the results of thermal expansion experiments on three magnetic nanocrystals-CuO, MnF2 and NiO-and find evidence for negative thermal expansion in both CuO and MnF2 below their magnetic ordering temperatures, but not in NiO. Larger particles of CuO and MnF2 also show prominent magnetostriction (that is, they change shape in response to an applied magnetic field), which results in significantly reduced thermal expansion below their magnetic ordering temperatures; this behaviour is not observed in NiO. We propose that the negative thermal expansion effect in CuO (which is four times larger than that observed in ZrW2O8) and MnF2 is a general property of nanoparticles in which there is strong coupling between magnetism and the crystal lattice.
Fractional active disturbance rejection control.
Li, Dazi; Ding, Pan; Gao, Zhiqiang
2016-05-01
A fractional active disturbance rejection control (FADRC) scheme is proposed to improve the performance of commensurate linear fractional order systems (FOS) and the robust analysis shows that the controller is also applicable to incommensurate linear FOS control. In FADRC, the traditional extended states observer (ESO) is generalized to a fractional order extended states observer (FESO) by using the fractional calculus, and the tracking differentiator plus nonlinear state error feedback are replaced by a fractional proportional-derivative controller. To simplify controller tuning, the linear bandwidth-parameterization method has been adopted. The impacts of the observer bandwidth ωo and controller bandwidth ωc on system performance are then analyzed. Finally, the FADRC stability and frequency-domain characteristics for linear single-input single-output FOS are analyzed. Simulation results by FADRC and ADRC on typical FOS are compared to demonstrate the superiority and effectiveness of the proposed scheme.
Radiating subdispersive fractional optical solitons
Energy Technology Data Exchange (ETDEWEB)
Fujioka, J., E-mail: fujioka@fisica.unam.mx; Espinosa, A.; Rodríguez, R. F. [Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Mexico, DF 04510 (Mexico); Malomed, B. A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
2014-09-01
It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.
Mechanical Analogies of Fractional Elements
Institute of Scientific and Technical Information of China (English)
HU Kai-Xin; ZHU Ke-Qin
2009-01-01
A Fractional element model describes a special kind of viscoelastic material.Its stress is proportional to the fractional-order derivative of strain. Physically the mechanical analogies of fractional elements can be represented by spring-dashpot fractal networks. We introduce a constitutive operator in the constitutive equations of viscoelastic materials.To derive constitutive operators for spring-dashpot fractal networks, we use Heaviside operational calculus, which provides explicit answers not otherwise obtainable simply.Then the series-parallel formulas for the constitutive operator are derived. Using these formulas, a constitutive equation of fractional element with 1/2-order derivative is obtained.Finally we find the way to derive the constitutive equations with other fractional-order derivatives and their mechanical analogies.
Critical exponents from large mass expansion
Yamada, Hirofumi
2014-01-01
We perform estimation of critical exponents via large mass expansion under crucial help of delta-expansion. We address to the three dimensional Ising model at high temperature and estimate omega, the correction-to-scaling exponent, nu, eta and gamma in unbiased and self-contained manner. The results read at the highest 25th order expansion omega=0.8002, nu=0.6295, eta=0.0369 and gamma=1.2357. Estimation biased by omega=0.84(4) is also performed and proved to be in agreement with the summary of recent literatures.
ON CONVERGENCE OF WAVELET PACKET EXPANSIONS
Institute of Scientific and Technical Information of China (English)
Morten Nielsen
2002-01-01
It is well known that the-Walsh-Fourier expansion of a function from the block space ([0, 1 ) ), 1 ＜q≤∞, converges pointwise a.e. We prove that the same result is true for the expansion of a function from in certain periodixed smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1＜p＜∞, converges in norm and pointwise almost everywhere.
Extrudate Expansion Modelling through Dimensional Analysis Method
DEFF Research Database (Denmark)
A new model framework is proposed to correlate extrudate expansion and extrusion operation parameters for a food extrusion cooking process through dimensional analysis principle, i.e. Buckingham pi theorem. Three dimensionless groups, i.e. energy, water content and temperature, are suggested...... to describe the extrudates expansion. From the three dimensionless groups, an equation with three experimentally determined parameters is derived to express the extrudate expansion. The model is evaluated with whole wheat flour and aquatic feed extrusion experimental data. The average deviations...
Does cosmological expansion affect local physics?
Giulini, Domenico
2013-01-01
In this contribution I wish to address the question whether, and how, the global cosmological expansion influences local physics. I argue that a pseudo Newtonian picture can be quite accurate if ``expansion'' is taken to be an attribute of the inertial structure rather than of ``space'' in some substantivalist sense. This contradicts the often-heard suggestion to imagine cosmological expansion as that of ``space itself''. Regarding General Relativity, I emphasise the need for proper geometric characterisations in order to meaningfully compare localised systems in different spacetimes, like black holes in static and expanding environments. Examples of this sort are discussed in some detail to clearly map out the problems.
Some Improved Nonperturbative Bounds for Fermionic Expansions
Energy Technology Data Exchange (ETDEWEB)
Lohmann, Martin, E-mail: marlohmann@gmail.com [Universita di Roma Tre, Dipartimento di Matematica (Italy)
2016-06-15
We reconsider the Gram-Hadamard bound as it is used in constructive quantum field theory and many body physics to prove convergence of Fermionic perturbative expansions. Our approach uses a recursion for the amplitudes of the expansion, discovered in a model problem by Djokic (2013). It explains the standard way to bound the expansion from a new point of view, and for some of the amplitudes provides new bounds, which avoid the use of Fourier transform, and are therefore superior to the standard bounds for models like the cold interacting Fermi gas.
Hubble expansion is not a velocity
Ma, Yin-Zhe; Zhang, Shuang-Nan
2016-11-01
In this paper, we clarify the difference between the Hubble expansion and the Doppler shift pedagogically and illustrate both physically and mathematically why the Hubble expansion cannot be regarded as a velocity. Therefore, we suggest to replace the misleading word ‘recession velocity’ to be ‘Hubble recession’ to describe the cosmic expansion. We further derive how the peculiar velocity of a galaxy is related to its observed redshift and proper distance, which has practical use in the galaxy redshift and distance surveys.
Research progress of the fractional Fourier transform in signal processing
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.
Applications of (a,b)-continued fraction transformations
Katok, Svetlana
2011-01-01
We describe a general method of arithmetic coding of geodesics on the modular surface based on a two parameter family of continued fraction transformations studied previously by the authors. The finite rectangular structure of the attractors of the natural extension maps and the corresponding "reduction theory" play an essential role. In special cases, when an (a,b)-expansion admits a so-called "dual", the coding sequences are obtained by juxtaposition of the boundary expansions of the fixed points, and the set of coding sequences is a countable sofic shift. We also prove that the natural extension maps are Bernoulli shifts and compute the density of the absolutely continuous invariant measure and the measure-theoretic entropy of the one-dimensional map.
Algebraic determination of the evolutionary stable germination fraction.
Valleriani, Angelo
2005-11-01
In this article, we consider a bet-hedging model with density dependence for germination behavior of dormant seeds. We show how to compute accurate values of the evolutionary stable germination fraction using a method based on expansion around the average seed bank size. The expansion is made up to the fourth order and is expressed in terms of the first four moments of the distribution of the year-to-year variation in the average yield per adult plant. This method leads to a simple algebraic equation, which can be solved without recurring to simulations of the seed bank dynamics. We first show the analytical derivation under general assumptions about the effect of density dependence. We then test our results with a numerical analysis where an explicit form of the density dependence has been taken.
Permutation entropy of fractional Brownian motion and fractional Gaussian noise
Energy Technology Data Exchange (ETDEWEB)
Zunino, L. [Centro de Investigaciones Opticas, C.C. 124 Correo Central, 1900 La Plata (Argentina); Departamento de Ciencias Basicas, Facultad de Ingenieria, Universidad Nacional de La Plata (UNLP), 1900 La Plata (Argentina); Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata (Argentina)], E-mail: lucianoz@ciop.unlp.edu.ar; Perez, D.G. [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso (PUCV), 23-40025 Valparaiso (Chile)], E-mail: dario.perez@ucv.cl; Martin, M.T. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CCT-CONICET), C.C. 727, 1900 La Plata (Argentina)], E-mail: mtmartin@fisica.unlp.edu.ar; Garavaglia, M. [Centro de Investigaciones Opticas, C.C. 124 Correo Central, 1900 La Plata (Argentina); Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata (Argentina)], E-mail: garavagliam@ciop.unlp.edu.ar; Plastino, A. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CCT-CONICET), C.C. 727, 1900 La Plata (Argentina)], E-mail: plastino@fisica.unlp.edu.ar; Rosso, O.A. [Centre for Bioinformatics, Biomarker Discovery and Information-Based Medicine, School of Electrical Engineering and Computer Science, The University of Newcastle, University Drive, Callaghan NSW 2308 (Australia); Chaos and Biology Group, Instituto de Calculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellon II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires (Argentina)], E-mail: oarosso@fibertel.com.ar
2008-06-30
We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays.
CHARACTERIZATION OF REACTIVE FORMATIONS: A VISION FOR THE CAPACITY EXPANSION
Directory of Open Access Journals (Sweden)
Danielly Vieira de Lucena
2013-12-01
Full Text Available All classes of clay minerals absorb water, but the smectite absorb much larger volumes than the other classes because of its expanded network. During the drilling of oil wells it is common for the detection of layers consisting of clay minerals high grade of hydration arranged in laminar packages. When in contact with water, the packets are separated clay as the water enters the basal spacing. This phenomenon is known as expansion or swelling. Given this, this paper aims to characterize shales in two regions of the country to explain the susceptibility of hydration of each of these formations. The characterization was done by making use of Exchange cation capacity (ECC, X-ray fluorescence (XRF, diferential thermal analysis (DTA, Thermogravimetry (TGA and X-ray diffraction (XRD. The results obtained showed that among the shales studied, those with the greatest degree of clay fractions (smectite in its composition showed higher swelling index according to the methodology of Foster.
Decomposition of fractional quantum Hall model states: product rule symmetries and approximations
Thomale, R.; Estienne, B.; Regnault, N.; Bernevig, B.A.
2011-01-01
We provide a detailed description of a product rule structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall (FQH) states derived recently, which we now extend to spin-singlet states. We show that the Haldane-Rezayi spin-singlet state can be obtained
Shrub expansion in SW Greenland
DEFF Research Database (Denmark)
Jørgensen, Rasmus Halfdan
from more southerly habitats are better adapted to climatic conditions in a warmer Greenland compared with local provenances. To answer the first question historical photographs of vegetation in SW Greenland (1898–1974) were compiled. The photos were repeated in 2010 and 2011 and 64 photo pairs were...... cropped into 133 smaller units and classified by aspect, substrate stability, muskoxen grazing and human disturbance. The photo material was evaluated by 22 experts with respect to changes in shrub cover. The results revealed a general shrub cover increase in the whole dataset, but also in a subset...... of firewood collection. A delayed reaction to the ending of the little ice age cannot be excluded, but seems rather unlikely considering other studies from Greenland. Effects of global warming in SW Greenland must be studied over even longer time periods than the 120 years of the current study. To answer...
A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
Akamatsu, Yukinao; Teaney, Derek
2016-01-01
We develop a set of kinetic equations for hydrodynamic fluctuations which are equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations can be coupled to existing second order hydrodynamic codes to incorporate the physics of these fluctuations. We first show that the kinetic response precisely reproduces the renormalization of the shear viscosity and the fractional power ($\\propto \\omega^{3/2}$) which characterizes equilibrium correlators of energy and momentum for a static fluid. Then we use the hydro-kinetic equations to analyze thermal fluctuations for a Bjorken expansion, evaluating the contribution of thermal noise from the earliest moments and at late times. In the Bjorken case, the solution to the kinetic equations determines the coefficient of the first fractional power of the gradient expansion ($\\propto 1/(\\tau T)^{3/2}$) for the expanding system. Numerically, we find that the contribution to the longitudinal pressure from hydrodynamic fluctuations is larger than second order hyd...
Dynamic Torque Calibration Unit
Agronin, Michael L.; Marchetto, Carl A.
1989-01-01
Proposed dynamic torque calibration unit (DTCU) measures torque in rotary actuator components such as motors, bearings, gear trains, and flex couplings. Unique because designed specifically for testing components under low rates. Measures torque in device under test during controlled steady rotation or oscillation. Rotor oriented vertically, supported by upper angular-contact bearing and lower radial-contact bearing that floats axially to prevent thermal expansion from loading bearings. High-load capacity air bearing available to replace ball bearings when higher load capacity or reduction in rate noise required.
Formation of an adherent hematopoietic expansion culture using fucoidan.
Irhimeh, Mohammad R; Fitton, J Helen; Ko, Kap-Hyoun; Lowenthal, Ray M; Nordon, Robert E
2011-09-01
Expansion of transplantable cord blood (CB) progenitors using a stroma requires provision of an exogenous cell source because of the low frequency of stromal precursor cells in CB. A simpler approach from a clinical regulatory perspective would be to provide synthetic extracellular matrix. The aim of this study was to characterize the effect on hematopoietic cell culture of fucoidan. The modulation of cytokine-driven hematopoietic cell expansion by fucoidan was investigated using two-level fractional and full factorial experimental designs. Mobilized peripheral blood (PB) CD34(+) cells were grown over 10 days in various combinations of FL, SCF, TPO, G-CSF, and SDF-1. Cultures were analyzed by immunophenotype. The effect of fucoidan on the divisional recruitment of CD34(+) cells was studied by CFDA-SE division tracking. Fucoidan was adsorbed by polystyrene to tissue culture plates and promoted formation of an adherent hematopoietic culture. Factorial design experiments with mobilized PB-CD34(+) cells showed that fucoidan reduced the production of CD34(+) cells and CD34(+)CXCR4(+) ratio but did not affect the production of monocytic, granulocytic, or megakaryocytic cells. The inhibitory effect of fucoidan on expansion of CB-CD34(+) cells was greater than mobilized PB. Division tracking analysis showed that CD34(+) cell generation times were lengthened by fucoidan. Fucoidan binds growth factors via their heparin-binding domain. The formation of an adherent hematopoietic culture system by fucoidan is most likely mediated by the binding of L-selectin and integrin-αMβ2 on myeloids. Fucoidan deserves further investigation as glycan scaffold that is suitable for immobilization of other matrix molecules thought to comprise blood stem cell niche.
Non-integer expansion embedding techniques for reversible image watermarking
Xiang, Shijun; Wang, Yi
2015-12-01
This work aims at reducing the embedding distortion of prediction-error expansion (PE)-based reversible watermarking. In the classical PE embedding method proposed by Thodi and Rodriguez, the predicted value is rounded to integer number for integer prediction-error expansion (IPE) embedding. The rounding operation makes a constraint on a predictor's performance. In this paper, we propose a non-integer PE (NIPE) embedding approach, which can proceed non-integer prediction errors for embedding data into an audio or image file by only expanding integer element of a prediction error while keeping its fractional element unchanged. The advantage of the NIPE embedding technique is that the NIPE technique can really bring a predictor into full play by estimating a sample/pixel in a noncausal way in a single pass since there is no rounding operation. A new noncausal image prediction method to estimate a pixel with four immediate pixels in a single pass is included in the proposed scheme. The proposed noncausal image predictor can provide better performance than Sachnev et al.'s noncausal double-set prediction method (where data prediction in two passes brings a distortion problem due to the fact that half of the pixels were predicted with the watermarked pixels). In comparison with existing several state-of-the-art works, experimental results have shown that the NIPE technique with the new noncausal prediction strategy can reduce the embedding distortion for the same embedding payload.
Surgically assisted rapid maxillary expansion in adults.
Pogrel, M A; Kaban, L B; Vargervik, K; Baumrind, S
1992-01-01
Twelve adults with maxillary width discrepancy of greater than 5 mm were treated by surgically assisted rapid maxillary expansion. The procedure consisted of bilateral zygomatic buttress and midpalatal osteotomies combined with the use of a tooth-borne orthopedic device postoperatively. Mean palatal expansion of 7.5 mm (range of 6 to 13 mm), measured in the first molar region, was achieved within 3 weeks in all patients. Expansion remained stable during the 12-month study period, with a mean relapse for the entire group of 0.88 +/- 0.48 mm. Morbidity was limited to mild postoperative discomfort. The results of this preliminary study indicated that surgically assisted rapid maxillary expansion is a safe, simple, and reliable procedure for achieving a permanent increase in skeletal maxillary width in adults. Further study is necessary to document the three-dimensional movements of the maxillary segments and long-term stability of the skeletal and dental changes.
High Falls generation station expansion approvals process
Energy Technology Data Exchange (ETDEWEB)
Litschko, C. [Lakeland Holding, Bracebridge, ON (Canada)
2005-07-01
Lakeland Holding Ltd. is the parent company for Lakeland Power Distribution Ltd., Bracebridge Generation Ltd., and Lakeland Energy Ltd. This PowerPoint presentation highlighted the High Falls generation expansion process. During construction of the High Falls plant, a concrete foundation was built beside the plant for future expansion. The expansion process involves building a 1,500 kilowatt generator to supply electricity to as many as 1600 households. The presentation described the context and background for the expansion and presented information on the water power generation plants. It presented site specifications as well as the approvals process by which final approval was granted in 2004. Observations and lessons learned from the approval process were identified. figs.
Origami Metamaterials for Tunable Thermal Expansion.
Boatti, Elisa; Vasios, Nikolaos; Bertoldi, Katia
2017-07-01
Materials with engineered thermal expansion, capable of achieving targeted area/volume changes in response to variations in temperature, are important for a number of aerospace, optical, energy, and microelectronic applications. While most of the proposed structures with engineered coefficient of thermal expansion consist of bi-material 2D or 3D lattices, here it is shown that origami metamaterials also provide a platform for the design of systems with a wide range of thermal expansion coefficients. Experiments and simulations are combined to demonstrate that by tuning the geometrical parameters of the origami structure and the arrangement of plates and creases, an extremely broad range of thermal expansion coefficients can be obtained. Differently from all previously reported systems, the proposed structure is tunable in situ and nonporous. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
An effective theory of accelerated expansion
Jimenez, Raul; Verde, Licia
2011-01-01
We work out an effective theory of accelerated expansion to describe general phenomena of inflation and acceleration (dark energy) in the Universe. Our aim is to determine from theoretical grounds, in a physically-motivated and model independent way, which and how many (free) parameters are needed to broadly capture the physics of a theory describing cosmic acceleration. Our goal is to make as much as possible transparent the physical interpretation of the parameters describing the expansion. We show that, at leading order, there are five independent parameters, of which one can be constrained via general relativity tests. The other four parameters need to be determined by observing and measuring the cosmic expansion rate only, H(z). Therefore we suggest that future cosmology surveys focus on obtaining an accurate as possible measurement of $H(z)$ to constrain the nature of accelerated expansion (dark energy and/or inflation).
On Learning Ring-Sum-Expansions
DEFF Research Database (Denmark)
Fischer, Paul; Simon, H. -U.
1992-01-01
The problem of learning ring-sum-expansions from examples is studied. Ring-sum-expansions (RSE) are representations of Boolean functions over the base {#123;small infinum, (+), 1}#125;, which reflect arithmetic operations in GF(2). k-RSE is the class of ring-sum-expansions containing only monomials...... of a 2-CNF and a 1-DNF. Finally the paper presents learning (on-line prediction) algorithms for k-RSE that are optimal with respect to the sample size (worst case mistake bound)...... of length at most k:. term-RSE is the class of ring-sum-expansions having at most I: monomials. It is shown that k-RSE, k>or=1, is learnable while k-term-RSE, k>2, is not learnable if RPnot=NP. Without using a complexity-theoretical hypothesis, it is proven that k-RSE, k>or=1, and k-term-RSE, k>or=2 cannot...
Zhang, Li; Fang, Qiaochu; Gabriel, Florence C; Szücs, Dénes
2014-01-01
Recent studies have indicated that people have a strong tendency to compare fractions based on constituent numerators or denominators. This is called componential processing. This study explored whether componential processing was preferred in tasks involving high stimuli variability and high contextual interference, when fractions could be compared based either on the holistic values of fractions or on their denominators. Here, stimuli variability referred to the fact that fractions were not monotonous but diversiform. Contextual interference referred to the fact that the processing of fractions was interfered by other stimuli. To our ends, three tasks were used. In Task 1, participants compared a standard fraction 1/5 to unit fractions. This task was used as a low stimuli variability and low contextual interference task. In Task 2 stimuli variability was increased by mixing unit and non-unit fractions. In Task 3, high contextual interference was created by incorporating decimals into fractions. The RT results showed that the processing patterns of fractions were very similar for adults and children. In task 1 and task 3, only componential processing was utilzied. In contrast, both holistic processing and componential processing were utilized in task 2. These results suggest that, if individuals are presented with the opportunity to perform componential processing, both adults and children will tend to do so, even if they are faced with high variability of fractions or high contextual interference.
Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials
Directory of Open Access Journals (Sweden)
Wu Guo-Cheng
2017-01-01
Full Text Available A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.
Directory of Open Access Journals (Sweden)
Özkan Güner
2014-01-01
Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.
Non-asymptotic fractional order differentiators via an algebraic parametric method
Liu, Dayan
2012-08-01
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.
The role of the Fox-Wright functions in fractional sub-diffusion of distributed order
Mainardi, Francesco
2007-01-01
The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin-Barnes integral representation. Such solution is proved to be related via a Laplace-type integral to the Fox-Wright functions. A series expansion is also provided in order to point out the distribution of time-scales related to the distribution of the fractional orders. The results of the time fractional diffusion equation of a single order are also recalled and then re-obtained from the general theory.
Institute of Scientific and Technical Information of China (English)
Xiao-jing LIU; Ji-zeng WANG; Xiao-min WANG; You-he ZHOU
2014-01-01
General exact solutions in terms of wavelet expansion are obtained for multi-term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ-ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.
Study on the Thermal Expansion and Thermal Cycling of AlNp/Al Composites
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The AIN particle reinforced aluminum matrix composites with 50% volume fraction were fabricated by squeeze-castingtechnology. The thermal expansion behavior and its response to thermal cycling were studied between 20C and400C. Compared with four theoretical models, the measured CTEs of the composite lie within the elastic boundsat lower temperature and elevated temperature, respectively. Strain hysteresis was observed between heating andcooling curves during cycling. This was attributed primarily to the anelastic behavior of the matrix induced by matrixresidual stresses.
Bell, Ian; Lemort, Vincent; Groll, E. A.; James E. Braun; King, Galen; Horton, W. Travis
2012-01-01
The use of liquid-flooding in the compression and expansion of non-condensable gas in scroll compressors and expanders enables the possibility of quasi-isothermal working processes. Liquid-flooded scroll machines were installed in a fully-instrumented Liquid-Flooded Ericsson Cycle test rig to conduct entire cycle performance tests. In addition, detailed compressor and expander performance data was obtained. Oil mass fractions of up to 92% and 76% were added to the gas entering the scroll comp...
Thermal expansion coefficient of binary semiconductors
Energy Technology Data Exchange (ETDEWEB)
Kumar, V.; Sastry, B.S.R. [Indian School of Mines, Dhanbad (India). Dept. of Electronics and Instrumentation
2001-07-01
The linear thermal expansion coefficient of tetrahedrally coordinated A{sup II}B{sup VI} and A{sup III}B{sup V} semiconductors has been calculated using plasmon energy data. A simple relation between the bond length and plasmon energy has been derived. The calculated values of thermal expansion coefficient and bond length have been compared with the experimental values and the values reported by different workers. An excellent experiment has been obtained between them. (orig.)
Cluster expansion in the canonical ensemble
Pulvirenti, Elena
2011-01-01
We consider a system of particles confined in a box $\\La\\subset\\R^d$ interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low density regime. The convergence is uniform in the volume and in the thermodynamic limit it reproduces Mayer's virial expansion providing an alternative and more direct derivation which avoids the deep combinatorial issues present in the original proof.
Index calculation by means of harmonic expansion
Imamura, Yosuke
2015-01-01
We review derivation of superconformal indices by means of supersymmetric localization and spherical harmonic expansion for 3d N=2, 4d N=1, and 6d N=(1,0) supersymmetric gauge theories. We demonstrate calculation of indices for vector multiplets in each dimensions by analysing energy eigenmodes in S^pxR. For the 6d index we consider the perturbative contribution only. We put focus on technical details of harmonic expansion rather than physical applications.
Optimized $\\delta$ expansion for relativistic nuclear models
Krein, G I; Peres-Menezes, D; Nielsen, M; Pinto, M B
1998-01-01
The optimized $\\delta$-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the $\\lambda \\phi^4$ model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the $\\delta$ expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations.
On storm weakening during substorm expansion phase
Directory of Open Access Journals (Sweden)
G. L. Siscoe
Full Text Available Iyemori and Rao recently presented evidence that the strength of a magnetic storm, as measured by -Dst, weakens, or its rate of growth slows, during the substorm expansion phase. Yet the expansion phase is known to inject energetic particles into the ring current, which should strengthen the storm. We propose to reconcile these apparently contradictory results by combining the virial theorem and a principle of energy partitioning between energy storage elements in a system with dissipation. As applied to the unloading description of the substorm expansion phase, the virial theorem states that -Dst is proportional to the sum of the total magnetic energy and twice the total kinetic energy in the magnetosphere including the tail. Thus if expansion phase involves converting magnetic energy stored in the tail into kinetic energy stored in the ring current, a drop in -Dst during expansion phase requires that less than half the drop in magnetic energy goes into the ring current, the rest going into the ionosphere. Indeed Weiss et al., have estimated that the energy dissipated in the ionosphere during expansion phase is twice that injected into the ring current. This conclusion is also consistent with the mentioned energy partitioning principle, which requires that more energy be dissipated than transferred between storage elements. While Iyemori and Rao's observations seem to contradict the hypothesis that storms consist at least in part of a sum of substorms, this mode of description might nonetheless be preserved by including the substorm's growth-phase contribution. Then the change in storm strength measured from before the growth phase to after the expansion phase is positive, even though the expansion phase alone makes a negative contribution.
Expansion of Bubbles in Inflationary Universe
Mohazzab, M.; Jabbari, M. M. Sheikh; Salehi, H.
1995-01-01
We show that particle production during the expansion of bubbles of true vacuum in the sea of false vacuum is possible and calculate the resulting rate. As a result the nucleated bubbles cannot expand due to the transfer of false vacuum energy to the created particles inside the bubbles. Therefore all the inflationary models dealing with the nucleation and expansion of the bubbles (including extended inflation) may not be viable.
Expansion of bubbles in inflationary universe
Mohazzab, M
1995-01-01
We show that particle production during the expansion of bubbles of true vacuum in the sea of false vacuum is possible and calculate the resulting rate. As a result the nucleated bubbles cannot expand due to the transfer of false vacuum energy to the created particles inside the bubbles. Therefore all the inflationary models dealing with the nucleation and expansion of the bubbles (including extended inflation) may not be viable.
Thermal Expansion Coefficients of Thin Crystal Films
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The formulas for atomic displacements and Hamiltonian of a thin crystal film in phonon occupation number representation are obtained with the aid of Green's function theory. On the basis of these results, the formulas for thermal expansion coefficients of the thin crystal film are derived with the perturbation theory, and the numerical calculations are carried out. The results show that the thinner films have larger thermal expansion coefficients.
Ferroelectric Fractional-Order Capacitors
Agambayev, Agamyrat
2017-07-25
Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.
On Generalized Fractional Differentiator Signals
Directory of Open Access Journals (Sweden)
Hamid A. Jalab
2013-01-01
Full Text Available By employing the generalized fractional differential operator, we introduce a system of fractional order derivative for a uniformly sampled polynomial signal. The calculation of the bring in signal depends on the additive combination of the weighted bring-in of N cascaded digital differentiators. The weights are imposed in a closed formula containing the Stirling numbers of the first kind. The approach taken in this work is to consider that signal function in terms of Newton series. The convergence of the system to a fractional time differentiator is discussed.
Fractional trajectories: Decorrelation versus friction
Svenkeson, A.; Beig, M. T.; Turalska, M.; West, B. J.; Grigolini, P.
2013-11-01
The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation of a fractional trajectory, that being an average over an ensemble of stochastic trajectories. Heretofore what has been interpreted as intrinsic friction, a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. We apply the general theory developed herein to the Lotka-Volterra ecological model, providing new insight into the final equilibrium state. The relaxation time to achieve this state is also considered.
Fixed Point Theorems for Times Reasonable Expansive Mapping
Directory of Open Access Journals (Sweden)
Chen Chunfang
2008-01-01
Full Text Available Abstract Based on previous notions of expansive mapping, times reasonable expansive mapping is defined. The existence of fixed point for times reasonable expansive mapping is discussed and some new results are obtained.
Institute of Scientific and Technical Information of China (English)
王嵘; 苗登顺; 季吉
2011-01-01
Objective: To determine whether bone marrow mesenchymal stem cells (BM-MSCs) are presented in the different fractions of bone marrow cells and whether the efficiency of colony forming unit-fibroblastic (CFU-f) formed by BM-MSCs is regulated by 1,25(OH)2D3 and prostaglandin E2(PGE2). Methods:Total bone marrow cells or non-adherent bone marrow cells derived from total bone marrow cell cultures for 1 day were separated into the mononuclear cell fraction and the granulocyte/erythrocyte fraction or the mononuclear cell fraction, the granulocyte fraction and the erythrecyte fraction by density-gradient centrifugation and were cultured in the absence or presence of 10-8mol/L 1,25 (OH)2D3 or 10-7 mol/L PGE2 for 10 days. The resulting cells were stained with methylene blue and the number of CFU-f was counted. Results: ①The CFU-f formed by mononuclear cell fraction accounted for about 10％ of the total CFU-f, and CFU-f formed by granulocyte/erythrocyte fraction, granulocyte fraction and erythrocyte fraction accounted for about 90％ ,47％ and 35％ of the total CFU-f, respectively; ②The fractions derived from the non-adherent bone marrow cells accounted for about 71％ of the total CFU-f, which was more than those formed by the fractions derived from total bone marrow cells;③ Treatment of 1 ,25(OH)2D3 and PGE2 enhanced the CFU-f formation of the mononuclear fraction and the granulocyte fraction derived from total bone marrow cells and the mononuclear cell fraction, the granulocyte fraction and the erythrocyte fraction derived from non-adherent bone marrow cells. Conclusion: Our results indicate that BM-MSCs are presented in the different fractions of bone marrow cells,and 1 ,25(OH)2D3 and PGE2 play a rele in stimulating proliferation of BM-MSCs.%目的:研究骨髓间充质干细胞(BM-MSCs)是否存在于骨髓不同组份中,以及其成纤维细胞集落形成单位(CFU-f)形成效率是否受1,25二羟基维生素D3[1,25(OH)2D3]和前列腺素E2(PGE2)的
Expansive Soil Crack Depth under Cumulative Damage
Directory of Open Access Journals (Sweden)
Bei-xiao Shi
2014-01-01
Full Text Available The crack developing depth is a key problem to slope stability of the expansive soil and its project governance and the crack appears under the roles of dry-wet cycle and gradually develops. It is believed from the analysis that, because of its own cohesion, the expansive soil will have a certain amount of deformation under pulling stress but without cracks. The soil body will crack only when the deformation exceeds the ultimate tensile strain that causes cracks. And it is also believed that, due to the combined effect of various environmental factors, particularly changes of the internal water content, the inherent basic physical properties of expansive soil are weakened, and irreversible cumulative damages are eventually formed, resulting in the development of expansive soil cracks in depth. Starting from the perspective of volumetric strain that is caused by water loss, considering the influences of water loss rate and dry-wet cycle on crack developing depth, the crack developing depth calculation model which considers the water loss rate and the cumulative damages is established. Both the proposal of water loss rate and the application of cumulative damage theory to the expansive soil crack development problems try to avoid difficulties in matrix suction measurement, which will surely play a good role in promoting and improving the research of unsaturated expansive soil.
Thermal expansion of doped lanthanum gallates
Indian Academy of Sciences (India)
K T Jacob; S Jain; V S Saji; P V K Srikanth
2010-08-01
Thermal expansion of several compositions of Sr and Mg-doped LaGaO3 including an -site deficient composition (La0.9Sr0.1)0.98(Ga0.8Mg0.2)O2.821 were measured in the temperature range from 298 to 1273 K. The effect of doping on thermal expansion was studied by varying the composition at one site of the perovskite structure (either or ), while keeping the composition at the other site invariant. Thermal expansion varied nonlinearly with temperature and exhibited an inflexion between 550 and 620 K, probably related to the change in crystal structure from orthorhombic to rhombohedral. The dependence of average thermal expansion coefficient (av) on the dopant concentration on either or site of the perovskite structure was found to be linear, when the composition at the other site was kept constant. Mg doping on the -site had a greater effect on the average thermal expansion coefficient than Sr doping on the -site. Cation deficiency at the -site decreases thermal expansion when compositions at both sites are held constant.
New Ultraspherical Wavelets Spectral Solutions for Fractional Riccati Differential Equations
Directory of Open Access Journals (Sweden)
W. M. Abd-Elhameed
2014-01-01
Full Text Available We introduce two new spectral wavelets algorithms for solving linear and nonlinear fractional-order Riccati differential equation. The suggested algorithms are basically based on employing the ultraspherical wavelets together with the tau and collocation spectral methods. The main idea for obtaining spectral numerical solutions depends on converting the differential equation with its initial condition into a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. For the sake of illustrating the efficiency and the applicability of our algorithms, some numerical examples including comparisons with some algorithms in the literature are presented.
Schaub, Maryellen
2016-01-01
The emergence and transformation of kindergarten in the United States is the quintessential example of the irrepressibility of schooling expansion, the ever-greater institutionalization of education in children's lives, and the rise in formal education's emphasis on cognitive skills among young children. This article explores the cultural…
Solutions of fractional diffusion problems
Directory of Open Access Journals (Sweden)
Rabha W. Ibrahim
2010-10-01
Full Text Available Using the concept of majorant functions, we prove the existence and uniqueness of holomorphic solutions to nonlinear fractional diffusion problems. The analytic continuation of these solutions is studied and the singularity for two cases are posed.
Australia's Next Top Fraction Model
Gould, Peter
2013-01-01
Peter Gould suggests Australia's next top fraction model should be a linear model rather than an area model. He provides a convincing argument and gives examples of ways to introduce a linear model in primary classrooms.
Fractional Dynamics of Relativistic Particle
Tarasov, Vasily E
2011-01-01
Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to a non-potential four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u_{\\mu} u^{\\mu}+c^2=0, where c is a speed of light in vacuum. In the general case, the fractional dynamics of relativistic particle is described as non-Hamiltonian and dissipative. Conditions for fractional relativistic particle to be a Hamiltonian system are considered.
Physcicists rewarded for 'fractional electrons'
Ball, P
1998-01-01
The 1998 Nobel prize for physics has been awarded to Horst Stormer, Daniel Tsui and Robert Laughlin.Stormer and Tsui were the first to observe the fractional quantum Hall effect and Laughlin provided the theory shortly afterwards (1 page).
Commercial SNF Accident Release Fractions
Energy Technology Data Exchange (ETDEWEB)
J. Schulz
2004-11-05
The purpose of this analysis is to specify and document the total and respirable fractions for radioactive materials that could be potentially released from an accident at the repository involving commercial spent nuclear fuel (SNF) in a dry environment. The total and respirable release fractions are used to support the preclosure licensing basis for the repository. The total release fraction is defined as the fraction of total commercial SNF assembly inventory, typically expressed as an activity inventory (e.g., curies), of a given radionuclide that is released to the environment from a waste form. Radionuclides are released from the inside of breached fuel rods (or pins) and from the detachment of radioactive material (crud) from the outside surfaces of fuel rods and other components of fuel assemblies. The total release fraction accounts for several mechanisms that tend to retain, retard, or diminish the amount of radionuclides that are available for transport to dose receptors or otherwise can be shown to reduce exposure of receptors to radiological releases. The total release fraction includes a fraction of airborne material that is respirable and could result in inhalation doses; this subset of the total release fraction is referred to as the respirable release fraction. Accidents may involve waste forms characterized as: (1) bare unconfined intact fuel assemblies, (2) confined intact fuel assemblies, or (3) canistered failed commercial SNF. Confined intact commercial SNF assemblies at the repository are contained in shipping casks, canisters, or waste packages. Four categories of failed commercial SNF are identified: (1) mechanically and cladding-penetration damaged commercial SNF, (2) consolidated/reconstituted assemblies, (3) fuel rods, pieces, and debris, and (4) nonfuel components. It is assumed that failed commercial SNF is placed into waste packages with a mesh screen at each end (CRWMS M&O 1999). In contrast to bare unconfined fuel assemblies, the
Concurrent fractional and equilibrium crystallisation
Sha, Lian-Kun
2012-06-01
This paper proposes the concept of concurrent fractional and equilibrium crystallisation (CFEC) in a multi-phase magmatic system in light of experimental results on diffusivities of elements and other species in minerals and melts. A group of equations are presented to describe how the concentrations of an element or isotope change in fractionated solid, equilibrated solid, melt, liquid, and gas phases, as well as in magma, as a function of distribution coefficients and mass fractions during the CFEC process. CFEC model is a generalised and unified formulation that is valid, not only for pure fractional crystallisation (FC) and perfect equilibrium crystallisation (EC) singly, as two of its limiting end-member cases, but also for the geologically more important process of concurrent fractional and equilibrium crystallisation. The concept that both fractional and equilibrium crystallisation can operate concurrently in a magmatic system, for a given element, among different minerals, and even within different-sized crystal grains of the very same mineral phase, is of fundamental importance in deepening our current understanding of magmatic differentiation processes. CFEC probably occurs more frequently in the natural world than either pure fractional or perfect equilibrium crystallisation alone, as a result of the interplay of varying diffusivities of elements under diverse physicochemical conditions, different residence time and growth rates of mineral phases in magmas, and varying grain sizes within each phase and among different phases. The marked systematic variations in trace element concentrations in the melts of the Bishop Tuff have long been perplexing and difficult to reconcile with existing models of differentiation. CFEC, which is able to better explain the scatter trends in a systematic way than fractional crystallisation, is considered to be the cause.
The Periodogram of fractional processes
Velasco, Carlos
2007-01-01
We analyse asymptotic properties of the discrete Fourier transform and the periodogram of time series obtained through (truncated) linear filtering of stationary processes. The class of filters contains the fractional differencing operator and its coefficients decay at an algebraic rate, implying long-range-dependent properties for the filtered processes when the degree of integration α is positive. These include fractional time series which are nonstationary for any value of the memory param...
Magnesium isotope fractionation during carbonatite magmatism at Oldoinyo Lengai, Tanzania
Li, Wang-Ye; Teng, Fang-Zhen; Halama, Ralf; Keller, Jörg; Klaudius, Jurgis
2016-06-01
To investigate the behaviour of Mg isotopes during carbonatite magmatism, we analyzed Mg isotopic compositions of natrocarbonatites and peralkaline silicate rocks from Oldoinyo Lengai, Tanzania. The olivine melilitites from the vicinity of Oldoinyo Lengai have homogeneous and mantle-like Mg isotopic compositions (δ26Mg of -0.30 to -0.26‰), indicating limited Mg isotope fractionation during mantle melting. The highly evolved peralkaline silicate rocks not related to silicate-carbonatite liquid immiscibility, including phonolites from the unit Lengai I, combeite-wollastonite nephelinites (CWNs) from the unit Lengai II A and carbonated combeite-wollastonite-melilite nephelinites (carbCWMNs), have δ26Mg values (from -0.25 to -0.10‰) clustered around the mantle value. By contrast, the CWNs from the unit Lengai II B, which evolved from the silicate melts that were presumably generated by silicate-carbonatite liquid immiscibility, have heavier Mg isotopes (δ26Mg of -0.06 to +0.09‰). Such a difference suggests Mg isotope fractionation during liquid immiscibility and implies, based on mass-balance calculations, that the original carbonatite melts at Lengai were isotopically light. The variable and positive δ26Mg values of natrocarbonatites (from +0.13 to +0.37‰) hence require a change of their Mg isotopic compositions subsequent to liquid immiscibility. The negative correlations between δ26Mg values and contents of alkali and alkaline earth metals of natrocarbonatites suggest Mg isotope fractionation during fractional crystallization of carbonatite melts, with heavy Mg isotopes enriched in the residual melts relative to fractionated carbonate minerals. Collectively, significant Mg isotope fractionation may occur during both silicate-carbonatite liquid immiscibility and fractional crystallization of carbonatite melts, making Mg isotopes a potentially useful tracer of these processes relevant to carbonatite petrogenesis.
Likelihood Inference for a Nonstationary Fractional Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
values Xº-n, n = 0, 1, ..., under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values......This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d - b; where d = b > 1/2 are parameters to be estimated. We model the data X¿, ..., X¿ given the initial...... are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to ?find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II...
Likelihood inference for a nonstationary fractional autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
values X0-n, n = 0, 1,...,under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values......This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d-b; where d ≥ b > 1/2 are parameters to be estimated. We model the data X1,...,XT given the initial...... are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II....
A Collocation Method for Solving Fractional Riccati Differential Equation
Directory of Open Access Journals (Sweden)
Yalçın Öztürk
2013-01-01
Full Text Available We have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation with delay term. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. In addition, illustrative examples are presented to demonstrate the effectiveness of the proposed method. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.
Structural Perspectives on the Evolutionary Expansion of Unique Protein-Protein Binding Sites.
Goncearenco, Alexander; Shaytan, Alexey K; Shoemaker, Benjamin A; Panchenko, Anna R
2015-09-15
Structures of protein complexes provide atomistic insights into protein interactions. Human proteins represent a quarter of all structures in the Protein Data Bank; however, available protein complexes cover less than 10% of the human proteome. Although it is theoretically possible to infer interactions in human proteins based on structures of homologous protein complexes, it is still unclear to what extent protein interactions and binding sites are conserved, and whether protein complexes from remotely related species can be used to infer interactions and binding sites. We considered biological units of protein complexes and clustered protein-protein binding sites into similarity groups based on their structure and sequence, which allowed us to identify unique binding sites. We showed that the growth rate of the number of unique binding sites in the Protein Data Bank was much slower than the growth rate of the number of structural complexes. Next, we investigated the evolutionary roots of unique binding sites and identified the major phyletic branches with the largest expansion in the number of novel binding sites. We found that many binding sites could be traced to the universal common ancestor of all cellular organisms, whereas relatively few binding sites emerged at the major evolutionary branching points. We analyzed the physicochemical properties of unique binding sites and found that the most ancient sites were the largest in size, involved many salt bridges, and were the most compact and least planar. In contrast, binding sites that appeared more recently in the evolution of eukaryotes were characterized by a larger fraction of polar and aromatic residues, and were less compact and more planar, possibly due to their more transient nature and roles in signaling processes.
Negative thermal expansion materials: technological key for control of thermal expansion.
Takenaka, Koshi
2012-02-01
Most materials expand upon heating. However, although rare, some materials contract upon heating. Such negative thermal expansion (NTE) materials have enormous industrial merit because they can control the thermal expansion of materials. Recent progress in materials research enables us to obtain materials exhibiting negative coefficients of linear thermal expansion over -30 ppm K(-1). Such giant NTE is opening a new phase of control of thermal expansion in composites. Specifically examining practical aspects, this review briefly summarizes materials and mechanisms of NTE as well as composites containing NTE materials, based mainly on activities of the last decade.
Xenon fractionation in porous planetesimals.
Zahnle, K; Pollack, J B; Kasting, J F
1990-01-01
The distinctively fractionated Xe on Mars and Earth may have its root in a common source from which both planets accreted. We begin with Ozima and Nakazawa's hypothesis that terrestrial Xe fractionation was caused by gravitational separation of adsorbed solar nebular gases inside large porous planetesimals. We point out that Xe would have been trapped as the planetesimal grew and pores were squeezed shut by lithostatic pressure. We show that enough fractionated Xe to supply the Earth could have been trapped this way. The degree of fractionation is controlled by the lithostatic pressure at the pore-closing front and so would have been roughly the same for all large planetesimals. The predicted degree of fractionation agrees well with that preserved in terrestrial and martian Xe. Relative to Xe, this source is strongly depleted in other noble gases. In contrast to the original Ozima and Nakazawa hypothesis, our hypothesis predicts the observed fractionation, and it allows planetary accretion to occur after the dissipation of the solar nebula. The required planetesimals are large, representing a class of object now extinct in the solar system.
Energy Technology Data Exchange (ETDEWEB)
Santos, Maria Clara de C. dos; Seidl, Peter R.; Guimaraes, Maria Jose O.C. [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Escola de Quimica
2008-07-01
With the growth of the national and worldwide economy, there has been a considerable increase in demand for polyolefins, thus requiring an increase in the production of basic petrochemicals (primarily ethane and propane). Due the quality of the national oil, heavy and poor in light derivatives, it is necessary investments in processes of conversion of heavy fractions with intent to maximize production these olefins and alternative raw materials for obtaining these petrochemicals The possible alternatives studied were the expansion of the core petrochemical, changes in the refinery processing units and the construction of COMPERJ, the latter being a example of alternative that can change the current scenario. The work aims to the simulation of process units of COMPERJ with the intention of evaluate which solutions like COMPERJ can best meet the growing market of polyolefins. (author)
Institute of Scientific and Technical Information of China (English)
胡益民; 李国庆; 张家龙
2015-01-01
无模型自适应控制（MFAC）不依赖受控系统的机理模型，只利用其输入输出（I/O）数据实现控制，近年来得到快速发展。本文用拟牛顿算法（BFGS）改进了MIMO系统MFAC算法的参数输入方法，以减少达到稳定操作的计算次数和调整时间，某30×104 t·a−1气体分馏装置的应用表明，面对操作波动，改进后的MFAC能较快地实现操作稳定和质量达标；且由于不超调，塔底再沸和塔顶冷却负荷小，因而能耗低。%In recent years, model-free adaptive control (MFAC) harvests a rapid development because it does not require the mathematical model and only uses the input/output data of the controlled system. In this paper the Quasi-Newton Methods (BFGS) was used to revamp the parameter input of MFAC of MIMO systems, resulting in less iterative calculating number of times and adjusting time. The application in a gas fractionation unit with an annual processing capacity of 0.3 Mt showed that MFAC can reach propylene quality target and steady operation rapidly with less energy consumption due to the minimum heating and cooling duties when facing operation fluctuation.
Fractional characteristic times and dissipated energy in fractional linear viscoelasticity
Colinas-Armijo, Natalia; Di Paola, Mario; Pinnola, Francesco P.
2016-08-01
In fractional viscoelasticity the stress-strain relation is a differential equation with non-integer operators (derivative or integral). Such constitutive law is able to describe the mechanical behavior of several materials, but when fractional operators appear, the elastic and the viscous contribution are inseparable and the characteristic times (relaxation and retardation time) cannot be defined. This paper aims to provide an approach to separate the elastic and the viscous phase in the fractional stress-strain relation with the aid of an equivalent classical model (Kelvin-Voigt or Maxwell). For such equivalent model the parameters are selected by an optimization procedure. Once the parameters of the equivalent model are defined, characteristic times of fractional viscoelasticity are readily defined as ratio between viscosity and stiffness. In the numerical applications, three kinds of different excitations are considered, that is, harmonic, periodic, and pseudo-stochastic. It is shown that, for any periodic excitation, the equivalent models have some important features: (i) the dissipated energy per cycle at steady-state coincides with the Staverman-Schwarzl formulation of the fractional model, (ii) the elastic and the viscous coefficients of the equivalent model are strictly related to the storage and the loss modulus, respectively.
Fractional Order Digital Differentiator Design Based on Power Function and Least squares
Kumar, Manjeet; Rawat, Tarun Kumar
2016-10-01
In this article, we propose the use of power function and least squares method for designing of a fractional order digital differentiator. The input signal is transformed into a power function by using Taylor series expansion, and its fractional derivative is computed using the Grunwald-Letnikov (G-L) definition. Next, the fractional order digital differentiator is modelled as a finite impulse response (FIR) system that yields fractional order derivative of the G-L type for a power function. The FIR system coefficients are obtained by using the least squares method. Two examples are used to demonstrate that the fractional derivative of the digital signals is computed by using the proposed technique. The results of the third and fourth examples reveal that the proposed technique gives superior performance in comparison with the existing techniques.
Institute of Scientific and Technical Information of China (English)
Hongmei Zhang; Fawang Liu
2007-01-01
In this paper, the space-time Riesz fractional partial differential equations with periodic conditions are considered. The equations are obtained from the integral partial differential equation by replacing the time derivative with a Caputo fractional derivative and the space derivative with Riesz potential. The fundamental solutions of the space Riesz fractional partial differential equation (SRFPDE) and the space-time Riesz fractional partial differential equation (STRFPDE) are discussed, respectively. Using methods of Fourier series expansion and Laplace transform, we derive the explicit expressions of the fundamental solutions for the SRFPDE and the STRFPDE, respectively.
Crystal fractionation in the SNC meteorites: Implications for sample selection
Treiman, Allan H.
1988-01-01
Almost all rock types in the SNC meteorites are cumulates, products of magma differentiation by crystal fractionation (addition or removal of crystals). If the SNC meteorites are from the surface of Mars or near subsurface, then most of the igneous units on Mars are differentiated. Basaltic units probably experienced minor to moderate differientation, but ultrabasic units probably experienced extreme differentiation. Products of this differentiation may include Fe-rich gabbro, pyroxenite, periodotite (and thus serpentine), and possibly massive sulfides. The SNC meteorites include ten lithologies (three in EETA79001), eight of which are crystal cumulates. The other lithologies, EETA79001 A and B are subophitic basalts.