Search results for "Mathematica"
showing 10 items of 7971 documents
Tests for real and complex unit roots in vector autoregressive models
2014
The article proposes new tests for the number of real and complex unit roots in vector autoregressive models. The tests are based on the eigenvalues of the sample companion matrix. The limiting distributions of the eigenvalues converging to the unit eigenvalues turn out to be of a non-standard form and expressible in terms of Brownian motions. The tests are defined such that the null distributions related to eigenvalues +/-1 are the same. The tests for the unit eigenvalues with nonzero imaginary part are defined independently of the angular frequency. When the tests are adjusted for deterministic terms, the null distributions usually change. Critical values are tabulated via simulations. Al…
Residuenanalyse des Unabhängigkeitsmodells Zweier Kategorialer Variablen
1985
For the ‘cellwise’ analysis of independence of two categorial variables, Haberman (1973) proposes the method of ‘adjusted residuals’. Fuchs and Kenett (1980) use (the absolute value of) the maximal adjusted residual as a measure for the deviation from the null hypothesis.
Characteristic Functions and the Central Limit Theorem
2020
The main goal of this chapter is the central limit theorem (CLT) for sums of independent random variables (Theorem 15.37) and for independent arrays of random variables (Lindeberg–Feller theorem, Theorem 15.43). For the latter, we prove only that one of the two implications (Lindeberg’s theorem) that is of interest in the applications.
Dynamic copula models for the spark spread
2011
We propose a non-symmetric copula to model the evolution of electricity and gas prices by a bivariate non-Gaussian autoregressive process. We identify the marginal dynamics as driven by normal inverse Gaussian processes, estimating them from a series of observed UK electricity and gas spot data. We estimate the copula by modeling the difference between the empirical copula and the independent copula. We then simulate the joint process and price options written on the spark spread. We find that option prices are significantly influenced by the copula and the marginal distributions, along with the seasonality of the underlying prices.
Riemann-Type Definition of the Improper Integrals
2004
Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane's definition of the Lebesgue integral by imposing a Kurzweil-Henstock's condition on McShane's partitions.
Steady-state dynamic response of various hysteretic systems endowed with fractional derivative elements
2019
In this paper, the steady-state dynamic response of hysteretic oscillators comprising fractional derivative elements and subjected to harmonic excitation is examined. Notably, this problem may arise in several circumstances, as for instance, when structures which inherently exhibit hysteretic behavior are supplemented with dampers or isolators often modeled by employing fractional terms. The amplitude of the steady-state response is determined analytically by using an equivalent linearization approach. The procedure yields an equivalent linear system with stiffness and damping coefficients which are related to the amplitude of the response, but also, to the order of the fractional derivativ…
A Calvin Bestiary
2017
This paper compares a number of mathematical models for the Calvin cycle of photosynthesis and presents theorems on the existence and stability of steady states of these models. Results on five-variable models in the literature are surveyed. Next a number of larger models related to one introduced by Pettersson and Ryde-Pettersson are discussed. The mathematical nature of this model is clarified, showing that it is naturally defined as a system of differential-algebraic equations. It is proved that there are choices of parameters for which this model admits more than one positive steady state. This is done by analysing the limit where the storage of sugars from the cycle as starch is shut d…
Oxygen Consuming Regions in EMT60/Ro Multicellular Tumour Spheroids Determined by Nonlinear Regression Analysis of Experimental PO2 Profiles
1987
Malignant cells can be studied in vitro, in a tumour-like microenvironment, by growing multicellular tumour spheroids in culture (Sutherland, McCredie and Inch, 1971). Franko and Sutherland (1979) utilized diffusion theory to explain the viable rim thicknesses of spheroids measured histologically. Without PO2 profiles, however, an unequivocal interpretation of their results was not possible. Systematic studies of the PO2 profiles in spheroids have since been made with oxygen microelectrodes by several groups (Carlsson et al., 1979; Kaufman et al., 1981; Mueller-Klieser and Sutherland, 1982a,b). Based on these measurements, new analyses utilizing diffusion theory are being developed to chara…
Optimization of the breeder zone cooling tubes of the DEMO Water-Cooled Lithium Lead breeding blanket
2016
Abstract The determination of an optimal configuration for the breeder zone (BZ) cooling tubes is one of the most important issues in the DEMO Water-Cooled Lithium Lead (WCLL) breeding blanket R&D activities, since BZ cooling tubes spatial distribution should ensure an efficient heat power removal from the breeder, avoiding hotspots occurrence in the thermal field. Within the framework of R&D activities supported by the HORIZON 2020 EUROfusion Consortium action on the DEMO WCLL breeding blanket design, a campaign of parametric analyses has been launched at the Department of Energy, Information Engineering and Mathematical Models of the University of Palermo (DEIM), in close cooperation with…
A Density Functional Study of Open-Shell Cyclopentadienyl−Molybdenum(II) Complexes. A Comparison of Stabilizing Factors: Spin-Pairing, Mo−X π Bonding…
2000
International audience; The dissociation of PH3 from the 18-electron system CpMoX(PH3)3 to afford the corresponding 16-electron CpMoX(PH3)2 fragment has been investigated theoretically by density functional theory for X = H, CH3, F, Cl, Br, I, OH, and PH2. The product is found to prefer a triplet spin state for all X ligands except PH2, the singlet−triplet gap varying between 1.7 kcal/mol for OH to 8.7 kcal/mol for F. The Mo−PH3 bond dissociation energy to the 16-electron ground state varies dramatically across the series, from 4.5 kcal/mol for OH to 23.5 kcal/mol for H, and correlates with experimental observations on trisubstituted phosphine derivatives. Geometry-optimized spin doublet Cp…