Voltammetric current–potential calculations using infinite series solution

2002 ◽  
Vol 4 (10) ◽  
pp. 803-807 ◽  
Author(s):  
Jan Mocak
Keyword(s):  
Infinite Series ◽  
Series Solution ◽  
Current Potential

scholarly journals Bivariate Infinite Series Solution of Kepler’s Equations

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 785
Author(s):  
Daniele Tommasini
Keyword(s):  
Parameter Space ◽  
Infinite Series ◽  
Iterative Procedure ◽  
Series Solution ◽  
Numerical Algorithms ◽  
Base Point ◽  
Series Solutions ◽  
Theoretical Interest ◽  
Analytical Computation ◽  
Derivatives Of

A class of bivariate infinite series solutions of the elliptic and hyperbolic Kepler equations is described, adding to the handful of 1-D series that have been found throughout the centuries. This result is based on an iterative procedure for the analytical computation of all the higher-order partial derivatives of the eccentric anomaly with respect to the eccentricity e and mean anomaly M in a given base point (ec,Mc) of the (e,M) plane. Explicit examples of such bivariate infinite series are provided, corresponding to different choices of (ec,Mc), and their convergence is studied numerically. In particular, the polynomials that are obtained by truncating the infinite series up to the fifth degree reach high levels of accuracy in significantly large regions of the parameter space (e,M). Besides their theoretical interest, these series can be used for designing 2-D spline numerical algorithms for efficiently solving Kepler’s equations for all values of the eccentricity and mean anomaly.

Transient distributions ensuing when ultracentrifugal equilibrium is disturbed by a substantial increase in speed

1968 ◽  
Vol 46 (8) ◽  
pp. 845-850 ◽  
Author(s):  
P. A. Charlwood
Keyword(s):  
Infinite Series ◽  
Series Solution ◽  
Rate Of Change ◽  
Rates Of Change ◽  
Interference Fringes ◽  
Lamm Equation

An infinite series solution to the Mason–Weaver approximation to the Lamm equation is given for the case in which a system at equilibrium in the ultracentrifuge is suddenly rotated at a considerably higher speed. The greatest rate of change of concentration occurs initially at the meniscus, but later the rate of change becomes less than that in the center of the column where initially it is relatively small. Curves are presented from which to calculate, for a wide variety of conditions, the time at which it is most advantageous to transfer the level of observation from the center of the column to the meniscus. The actual rates of change of concentration at these levels at these times are tabulated. Hence, in experiments of this type interference fringes can be identified unequivocally from a limited number of photographs.

Floquet-Based Analysis of General Responses of the Mathieu Equation

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Gizem Acar ◽  
Brian F. Feeny
Keyword(s):  
Infinite Series ◽  
Harmonic Balance ◽  
Series Solution ◽  
Floquet Theory ◽  
Harmonic Balance Method ◽  
Mathieu Equation ◽  
Periodic Part ◽  
Floquet Solution ◽  
Exponential Part ◽  
Stability Of The Solution

Solutions to the linear unforced Mathieu equation, and their stabilities, are investigated. Floquet theory shows that the solution can be written as a product between an exponential part and a periodic part at the same frequency or half the frequency of excitation. In the current work, an approach combining Floquet theory with the harmonic balance method is investigated. A Floquet solution having an exponential part with an unknown exponential argument and a periodic part consisting of a series of harmonics is assumed. Then, performing harmonic balance, frequencies of the response are found and stability of the solution is examined over a parameter set. The truncated solution is consistent with an existing infinite series solution for the undamped case. The truncated solution is then applied to the damped Mathieu equation and parametric excitation with two harmonics.

The variance of duration of stay in an absorbing Markov process

1978 ◽  
Vol 15 (02) ◽  
pp. 420-425
Author(s):  
Philip F. Rust
Keyword(s):  
Markov Process ◽  
Infinite Series ◽  
Series Solution ◽  
Initial State ◽  
Duration Of Stay ◽  
Transient States ◽  
Stationary Markov Process ◽  
Absorbing States

Given a stationary Markov process with s transient states and r absorbing states, a matrix infinite series solution is presented for the variance of duration of stay in state j within the interval [0, t), given initial state i. Closed forms are derived for absorbing states, and for transient states if eigenvalues are real and distinct. Several relationships among Markov matrices are presented.

Buckling of Isosceles Triangular Plates

1969 ◽  
Vol 73 (703) ◽  
pp. 604
Author(s):  
J. Lockwood Taylor
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Infinite Series ◽  
Series Solution ◽  
Technical Note ◽  
Buckling Load ◽  
Data Sheet ◽  
Trigonometrical Series ◽  
Equilateral Triangles ◽  
Isosceles Triangles

Application of a method suggested by my technical note on equilateral and semi-equilateral triangles has yielded values for the buckling coefficients for isosceles triangles which in some cases differ appreciably from those given on Data Sheet 02.04.06. The technical note quoted gives exact solutions in the form of a terminating trigonometrical series. When the triangle becomes isosceles, the series no longer terminates, but the infinite series solution, on insertion of the boundary conditions, gives an infinite determinant for the buckling load or eigenvalue. Evaluation of the determinant, or of a sufficient number of terms, was computed on a Univac 1107, with the following results, which have been converted to the notation of Data Sheet 02.04.06.

The Elastically Clamped Rectangular Plate With Arbitrary Lateral and Thermal Loading

1962 ◽  
Vol 29 (3) ◽  
pp. 578-580
Author(s):  
C. C. Chao ◽  
Max Anuliker
Keyword(s):  
Rectangular Plate ◽  
Thin Plate ◽  
Infinite Series ◽  
Series Solution ◽  
Thermal Loading ◽  
Plate Theory ◽  
Convergent Series ◽  
Clamped Plate ◽  
Simply Supported ◽  
Thin Plate Theory

Within the limits of classical thin-plate theory a variety of elementary problems have been solved for the rectangular plate3,4,5. In particular, the rectangular plate with edges simply supported or clamped has been dealt with at length and the solution to different loading cases given either in the form of a doubly infinite series or a single infinite series. In this paper a rapidly convergent series solution is outlined for the uniformly elastically clamped plate which is subjected to nonuniform lateral and thermal loading. The solution converges in the limit to those corresponding to the simply supported and rigidly clamped plate.

scholarly journals Series Solution for the Time-Fractional Coupled mKdV Equation Using the Homotopy Analysis Method

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
J. F. Gómez-Aguilar ◽  
H. Yépez-Martínez ◽  
R. F. Escobar-Jiménez ◽  
V. H. Olivares-Peregrino ◽  
J. M. Reyes ◽  
...  
Keyword(s):  
Infinite Series ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Time Derivative ◽  
Mkdv Equation ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Special Case ◽  
Integral Order ◽  
Fractional Equation

We present new analytical approximated solutions for the space-time fractional nonlinear partial differential coupled mKdV equation. A homotopy analysis method is considered to obtain an infinite series solution. The effectiveness of this method is demonstrated by finding exact solutions of the fractional equation proposed, for the special case when the limit of the integral order of the time derivative is considered. The comparison shows a precise agreement between these solutions.

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