Characteristics of Exponential FunctionsMath with H.Jones
Similar relations exist between exponential functions and their derivatives, but these do not appear to be well known, and are not described in any text-book I have been able to consult: reference is made in some text-books to the imaginary period of the exponential function. DOI: 10.1038/...
The symmetric nonnegative kernel related to the grand canonical partition function of large DNLSE systems is the product of two decaying exponential functions and a zero order modified Bessel function of the first kind (Eq. (9)). In the “second-order” approximation, we represent the modified...
Analysis of the charge-retention characteristics with the SEF and ILT In order to extract an accurate retention-time, while examining the recovery during each RM process, the stretched exponential function (SEF) is applied27. The general form of the SEF, i.e. F(t), is as follows, $${\...
The general analytical expression for the combination of power and exponential functions can be written as: (1)y(x)=Axα0exp[γ/|γ|(x/x0)γ], where y is the function, x is the argument, A and x0 are the constants, α and γ are the differential slope of function...
2) Relationships between runoff and sediment for each rainstorm event can be regressed by linear, power, logarithmic and exponential functions. Cluster Analysis is helpful in classifying runoff-erosion events and formulating soil conservation strategies for rainstorm erosion. 3) Response characteristics of...
special matrix functionsmatrix polynomialsorthogonal matrix polynomialsmatrix functional calculus15A6033C0533C4534A05The main goal of this paper is to describe certain convergence proper-14 ties of the exponential general basic sets of polynomials of several complex variables15 {PEm(z)} = {exp(Pm(z...
Therefore, the deformation coefficient is expressed as the product of a function of the effective confining pressure and porosity, the exponential function of the hydrate saturation rate, and the strain rate, [Math Processing Error]E50=f(\unicodex03C3c′,n)⋅exp(aSh)R\unicodex03B5am′, (9)...
Analysis has been carried out in the framework of the plane-wave impulse approximation. Quasielastic cross sections have been measured and experimental momentum distributions extracted. Theoretical fits to these distributions using simple Gaussian and exponential functions have been calculated and used to ...
entire function of the exponential typeFourier transformWe obtain the exact-by-order estimates of the approximation of functions from the classes S p , θΩ $$ {S}_{p,heta}^{\\\varOmega } $$ B (ℝ_( d )) in the space L ~( q )(ℝ_( d )), 1 < p < q < ∞, by ent...