We show that in two dimensions or higher, the Mordukhovich-loffe approximate subdifferential and Clarke subdifferential may differ almost everywhere for real-valued Lipschitz functions. Uncountably many Frechet differentiable vector-valued Lipschitz functions differing by more than constants can share the same Mordukhovich-Ioffe coderivatives. Moreover, the approximate Jacobian associated with ...

In this paper, we propose the spectral collocation method based on radial basis functions to solve the fractional Bagley-Torvik equation under uncertainty, in the fuzzy Caputo's H-differentiability sense with order ($1< nu < 2$). We define the fuzzy Caputo's H-differentiability sense with order $nu$ ($1< nu < 2$), and employ the collocation RBF method for upper and lower approximate solutions. ...

An approximate numerical mthod is presented for analysis and determination of modal characteristics in straight, pretwisted non-unifom helicopter blades. The analysis considers the coupled flapwise bending (out of plane), chordwise bending (in plane), and torsion vibration of both rotating and non-rotating blades. The proposed method is based on the integral expansion of Green functions (struct...

in the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. the basic assumption is that the class of functions that we investigate here, except the verification of dirichlet&apos;s principles, is concurrently able to be expanded in taylor&apos;s representation, over a particular interval o...

1. Abstract We present an incomplete series expansion (ISE) as a basis for function approximation. The ISE is expressed in terms of an approximate Hessian matrix which may contain second, third and even higher order ‘main’ or diagonal terms, but which excludes ‘interaction’ or off-diagonal terms. From the ISE, a family of approximate interpolating functions may be derived. The interpolating fun...

the railway transportation planning under the fuzzy environment is investigated in this paper. as a main result, a new modeling method, called minimum risk chance-constrained model, is presented based on the credibility measure. for the convenience ofs olving the mathematical model, the crisp equivalents ofc hance functions are analyzed under the condition that the involved fuzzy parameter...

In this paper, we discuss the statistical inference on the unknown parameters and reliability function of type-II extreme value (EVII) distribution when the observed data are progressively type-II censored. By applying EM algorithm, we obtain maximum likelihood estimates (MLEs). We also suggest approximate maximum likelihood estimators (AMLEs), which have explicit expressions. We provide Bayes ...

A large number of results in analysis of algorithms contain fluctuations. A typical result might read “The expected number of . . . for large n behaves like log2 n + constant + delta(log2 n), where delta(x) is a periodic function of period one and mean zero.” Examples include various trie parameters, approximate counting, probabilistic counting, radix exchange sort, leader election, skip lists,...