The integral representation of fractionally exponential functions and their application to dynamic problems of linear viscoelasticity, J Appl Mech Tech Phys 1970; 11: 100-107.S.I. Meshkov, The integral represen
In previous sections, we learned the properties and rules for both exponential and logarithmic functions. We have seen that any exponential function can be written as a logarithmic function and vice versa. We have used exponents to solve logarithmic equations and logarithms to solve e...
Exponential Functions and Real Life Problems:指数函数与现实生活中的问题 热度: 指数函数的应用2 热度: 相关推荐 ApplicationoftheStretchedExponentialFunctiontoFluorescence LifetimeImaging K.C.BennyLee,*J.Siegel,*S.E.D.Webb,*S.Le´veˆque-Fort,*M.J.Cole,*R.Jones,*K.Dowling,* M.J.Lever...
Hereris the modulus of thecomplex numberandθis the argument. Therefore, theexponential formis simply another way of writing thepolar form. The advantage of the exponential form is its simplicity. For circular motion, at constantangular velocity, it can represent the motion both in the real and...
The following figure shows a graph of a representative exponential decay function.Figure 2. An example of exponential decay.Let’s look at a physical application of exponential decay. Newton’s law of cooling says that an object cools at a rate proportional to the difference between the ...
Problems Simplify the following expressions as much as possible. 1. 16a 8 b 12 ( ) 3 4 2. 144 1/2 x !3 16 3/4 x 7 ( ) 0 3. a 2/3 b !3/4 c 7/8 a !1/3 b 1/4 c 1/8 Find each of the indicated function values. ...
However, there is no analytical expression for its Fourier transform because of the unusual mathematical behavior of the stretched-exponential function. Numerical approximations to the frequency-domain description of the stretched-exponential model have had limited success due to problems originating from ...
The “Type II” sums are Dirichlet convolutions involving a factor supported on a range and is quite easy to deal with; the “Type ” terms are Dirichlet convolutions that resemble (non-degenerate portions of) the divisor function, formed from convolving together portions of . The “Type ”...
Chemical-disordered materials have a wide range of applications whereas the determination of their structures or configurations is one of the most important and challenging problems. Traditional methods are extremely inefficient or intractable for large
Assume that there exist a function V∈ν0{1,2} and a scalar λ≥0 such that the following conditions hold: Exponential stability of generalized impulsive stochastic delay differential equations In this section, we shall apply the Razumikhin-type theorems established in the previous section to ...