Keywords. Convexity, Schur-convexity, inequalities, Gamma functionWe consider necessary and sufficient conditions for the convexity of a function \\( x o f '(x) \\) in terms of some properties of the associated function of two variables F ( x , y ) = ( f ( y ) - f ( x )) / ...
you have full access to this open access article on complete monotonicity for several classes of functions related to ratios of gamma functions abstract let \(\vargamma (x)\) denote the classical euler gamma function. the logarithmic derivative \(\psi (x)=[\ln \vargamma (x)]'=\frac{\...
Two representations of the extended gamma functions $\Gamma^{2,0}_{0,2}[(b,x)]$ are proved. These representations are exploited to find a transformation relation between two Fox's $H$-functions. These results are used to solve Fox's $H$-function in terms of Meijer's $G$-function ...
The Laplace transform of a function f(t) is also denoted by L(f). It is known that some special functions can be represented as corresponding Laplace transforms, for example, Binet formula for gamma function:lnΓ(z)−(z−12)lnz+z−12ln(2π)=∫0∞(1et−1−1t+12...
For p prime, we give an explicit formula for Igusa's local zeta function associated to a polynomial mapping ${{bf f} = (f_1, ldots, f_t) : {bf Q}_p^{n} to ... B Bories - 《Manuscripta Mathematica》 被引量: 13发表: 2012年 Rectilinearization of semi-algebraic p-adic sets an...
Step 5: Triple-peak Lorentzian nonlinear fitting is performed to separate the spectra of CO2and HDO. Numerical least-squares optimization of the Lorentzian function is achieved by Levenberg–Marquardt method. Several database-based a priori constraints, including the relative strength of two HDO lines...
I prefer to use stamps because they give you a lot of composability. Erich Gamma, one of the Gang of Four authors who created Design Patterns, shared some interesting thoughts about interfaces in an interview with Bill Venners called “Leading-Edge Java Design Principles from Design Patterns: A...
1e. The uncertainly limit \({r}_{m}\), is estimated using\(\,{\rm{\gamma }}=\varDelta {E}_{{kin}}/{U}_{p} \sim 1\), where \(\varDelta {E}_{{kin}}\) is the statistical fluctuation of the electron kinetic energy, \(\varDelta {E}_{{kin}} \sim {E}_{{kin}}/\...
在地球物理学中,神经网络已被考虑用于modeling the dynamic process of seismic waveform inversion。为了模拟地震波传播,提出了一种理论指导的recurrent neural network(RNN); RNN 是专门为求解控制微分方程而设计的,其中一些参数被指定为控制物理方程中的物理参数。特别地,给定在时域离散化的波动方程,下一个时间步长的...
gamma是一个超参数,人工来设定 和logistic的对比图如下: 为了让smooth step function好在一张图里比较,这里的logistic function公式为L(x) = (1 + e−6x)−1 我寻思这玩意儿不就是hard activations 家族的吗? The hard sigmoid activation, defined as: if x < -2.5: return 0 if x > 2.5: return...