Linear change of variable in normal systems

1973 ◽  
Vol 7 (3) ◽  
pp. 384-387
Author(s):  
J. Derral Mulholland
Keyword(s):  
Linear Change ◽  
Change Of Variable

scholarly journals Some Basic 𝑑-Orthogonal Polynomial Sets

2005 ◽  
Vol 12 (4) ◽  
pp. 583-593
Author(s):  
Ali Zaghouani
Keyword(s):  
Orthogonal Polynomial ◽  
Recurrence Relation ◽  
Generating Function ◽  
Linear Change ◽  
Change Of Variable

Abstract The purpose of this paper is to study the class of polynomial sets which are at the same time 𝑑-orthogonal and 𝑞-Appell. By a linear change of variable, the resulting set reduces to 𝑞-Al-Salam–Carlitz polynomials, for 𝑑 = 1. Various properties of the obtained polynomials are singled out: a generating function, a recurrence relation of order 𝑑 + 1. We also explicitly express a 𝑑-dimensional functional for which the d-orthogonality holds.

scholarly journals Linear change of variable in normal systems

1973 ◽  
Vol 8 (1) ◽  
pp. 152-152
Author(s):  
J. Derral Mulholland
Keyword(s):  
Linear Change ◽  
Change Of Variable

scholarly journals Pyrolysis and Oxidation of PAN in Dry Air. Thermoanalytical Methods

1970 ◽  
Vol 17 (1) ◽  
pp. 38-42
Author(s):  
Anna BIEDUNKIEWICZ ◽  
Pawel FIGIEL ◽  
Marta SABARA
Keyword(s):  
Temperature Increase ◽  
Heating Rates ◽  
Linear Change ◽  
Dry Air ◽  
Isothermal Conditions ◽  
Gaseous Products ◽  
Heterogeneous Processes ◽  
Temperature Ranges ◽  
Higher Temperature ◽  
Kinetics Of

The results of investigations on pyrolysis and oxidation of pure polyacrylonitrile (PAN) and its mixture with N,N-dimethylformamide (DMF) under non-isothermal conditions at linear change of samples temperature in time are presented. In each case process proceeded in different way. During pyrolysis of pure PAN the material containing mainly the product after PAN cyclization was obtained, while pyrolysis of PAN+DMF mixture gave the product after cyclization and stabilization. Under conditions of measurements, in both temperature ranges, series of gaseous products were formed.For the PAN-DMF system measurements at different samples heating rates were performed. The obtained results were in accordance with the kinetics of heterogeneous processes theory. The process rates in stages increased along with the temperature increase, and TG, DTG and HF function curves were shifted into higher temperature range. This means that the process of pyrolysis and oxidation of PAN in dry air can be carried out in a controlled way.http://dx.doi.org/10.5755/j01.ms.17.1.246

Improved correlation dimension estimates through change of variable

1992 ◽  
Vol 163 (4) ◽  
pp. 269-274 ◽  
Author(s):  
M. Lefranc ◽  
D. Hennequin ◽  
P. Glorieux
Keyword(s):  
Correlation Dimension ◽  
Change Of Variable

scholarly journals r-Dependence in Two-Point Orientation Coherence Functions

2000 ◽  
Vol 34 (4) ◽  
pp. 233-241
Author(s):  
Peter R. Morris
Keyword(s):  
Correlation Function ◽  
Weight Function ◽  
Bessel Functions ◽  
Unit Weight ◽  
Experimental Procedure ◽  
Change Of Variable

Functions are derived, which are orthonormal on the range r=0, 1, with weight function corresponding to the distribution of r in a typical experimental procedure for measurement of the two-point orientation–coherence (or orientation–correlation) function. These are obtained by making an appropriate change of variable in spherical Bessel functions, orthonormal on the range r=0, 1, with unit weight function. The effects of weight function and change of variable on the functions are considered.

Associations Between Change Over Time in Pandemic-Related Stress and Change in Physical Activity

2021 ◽  
pp. 1-8
Author(s):  
Kathryn E. Wilson ◽  
Andrew Corbett ◽  
Andrew Van Horn ◽  
Diego Guevara Beltran ◽  
Jessica D. Ayers ◽  
...  
Keyword(s):  
Physical Activity ◽  
Stress Reduction ◽  
Activity Levels ◽  
Latent Growth ◽  
Linear Change ◽  
Change Over Time ◽  
Trajectories Of Change ◽  
Related Stress ◽  
The Relationship ◽  
Over Time

Background: Physical activity (PA) mitigated psychological distress during the initial weeks of the COVID-19 pandemic, yet not much is known about whether PA had effects on stress in subsequent months. We examined the relationship between change over time in COVID-related stress and self-reported change in PA between March and July 2020. Methods: Latent growth modeling was used to examine trajectories of change in pandemic-related stress and test their association with self-reported changes in PA in an international sample (n = 679). Results: The participants reported a reduction in pandemic-related stress between April and July of 2020. Significant linear (factor mean = −0.22) and quadratic (factor mean = 0.02) changes (Ps < .001) were observed, indicating a deceleration in stress reduction over time. Linear change was related to change in PA such that individuals who became less active during the pandemic reported less stress reduction over time compared with those who maintained or increased their PA during the pandemic. Conclusions: Individuals who experienced the greatest reduction in stress over time during the pandemic were those who maintained their activity levels or became more active. Our study cannot establish a causal relationship between these variables, but the findings are consistent with other work showing that PA reduces stress.

ON THE VALUATION OF DERIVATIVES WITH SNAPSHOT RESET FEATURES

2008 ◽  
Vol 11 (08) ◽  
pp. 905-941 ◽  
Author(s):  
ERIC C. K. YU ◽  
WILLIAM T. SHAW
Keyword(s):  
Convertible Bonds ◽  
Convertible Bond ◽  
Put Options ◽  
Risk Characteristics ◽  
Black Scholes ◽  
Barrier Type ◽  
Simple Change ◽  
Discontinuous Nature ◽  
Change Of Variable ◽  
Digital Options

We propose a general approach that requires only a simple change of variable that keeps the valuation of call and put options (convertible bonds) with strike (conversion) price resets two-dimensional in the classical Black–Scholes setting. A link between reset derivatives, compound options and "discrete barrier" type options, when there is one reset is then discussed, from which we analyze the risk characteristics of reset derivatives, which can be significantly different from their vanilla counterparts. We also generalize the prototype reset structure and show that the delta and gamma of a convertible bond with reset can both be negative. Finally, we show that the "waviness" property found in the delta and gamma of some reset derivatives is due to the discontinuous nature of the reset structure, which is closely linked to digital options.

scholarly journals Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jaume Llibre ◽  
Yuzhou Tian
Keyword(s):  
Hamiltonian Systems ◽  
Homogeneous Polynomial ◽  
First Integral ◽  
Liouville Integrability ◽  
Linear Change ◽  
Change Of Variables ◽  
Polynomial First Integral ◽  
Homogeneous Potentials

<p style='text-indent:20px;'>We characterize the meromorphic Liouville integrability of the Hamiltonian systems with Hamiltonian <inline-formula><tex-math id="M2">\begin{document}$ H = \left(p_1^2+p_2^2\right)/2+1/P(q_1, q_2) $\end{document}</tex-math></inline-formula>, being <inline-formula><tex-math id="M3">\begin{document}$ P(q_1, q_2) $\end{document}</tex-math></inline-formula> a homogeneous polynomial of degree <inline-formula><tex-math id="M4">\begin{document}$ 4 $\end{document}</tex-math></inline-formula> of one of the following forms <inline-formula><tex-math id="M5">\begin{document}$ \pm q_1^4 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M6">\begin{document}$ 4q_1^3q_2 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M7">\begin{document}$ \pm 6q_1^2q_2^2 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M8">\begin{document}$ \pm \left(q_1^2+q_2^2\right)^2 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M9">\begin{document}$ \pm q_2^2\left(6q_1^2-q_2^2\right) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M10">\begin{document}$ \pm q_2^2\left(6q_1^2+q_2^2\right) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M11">\begin{document}$ q_1^4+6\mu q_1^2q_2^2-q_2^4 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M12">\begin{document}$ -q_1^4+6\mu q_1^2q_2^2+q_2^4 $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M13">\begin{document}$ \mu&gt;-1/3 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M14">\begin{document}$ \mu\neq 1/3 $\end{document}</tex-math></inline-formula>, and <inline-formula><tex-math id="M15">\begin{document}$ q_1^4+6\mu q_1^2q_2^2+q_2^4 $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M16">\begin{document}$ \mu \neq \pm 1/3 $\end{document}</tex-math></inline-formula>. We note that any homogeneous polynomial of degree <inline-formula><tex-math id="M17">\begin{document}$ 4 $\end{document}</tex-math></inline-formula> after a linear change of variables and a rescaling can be written as one of the previous polynomials. We remark that for the polynomial <inline-formula><tex-math id="M18">\begin{document}$ q_1^4+6\mu q_1^2q_2^2+q_2^4 $\end{document}</tex-math></inline-formula> when <inline-formula><tex-math id="M19">\begin{document}$ \mu\in\left\{-5/3, -2/3\right\} $\end{document}</tex-math></inline-formula> we only can prove that it has no a polynomial first integral.</p>

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