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In the paper, the authors 1. establish general expressions of series expansions of $ (\arcsin x)^\ell $ for $ \ell\in\mathbb{N} $; 2. find closed-form formulas for the sequence $ \begin{equation*} {\rm{B}}_{2n,k}\biggl(0,\frac{1}{3},0,\frac{9}{5},0,\frac{225}{7},\dotsc, \frac{1+(-1)^{k+1}}{2}\frac{[(2n-k)!!]^2}{2n-k+2}\biggr), \end{equation*} $ where $ {\rm{B}}_{n, k} $ denotes the second kind Bell polynomials; 3. derive series representations of generalized logsine functions. The series expansions of the powers $ (\arcsin x)^\ell $ were related with series representations for generalized logsine functions by Andrei I. Davydychev, Mikhail Yu. Kalmykov, and Alexey Sheplyakov. The above sequence represented by special values of the second kind Bell polynomials appeared in the study of Grothendieck's inequality and completely correlation-preserving functions by Frank Oertel.

We propose a general expression for plasma extraction transit-time oscillations (PETT-Oscs) from silicon-bipolar power semiconductor devices. PETT-Oscs are generated when the transition time for the hole to fly into the depletion region and be accelerated by the electric field harmonizes with the resonant frequency of the loops through stray inductances and p-n junction capacitances. A physical model of PETT leads to an expression that takes into account its dependence on voltage and dopant density. The average carrier speed in the depletion region and the junction temperature dependence are fitted to the experimental results. The validity of the proposed general expression for PETT-Osc is verified successfully through state-of-the-art insulated-gate bipolar transistor module design. PETT-Osc from the package is estimated to generate at the typical operating conditions. The expression guiding the prevention method for PETT-Osc and the completed module does not show PETT-Osc in the operational range. The expression indicates the existence of PETT-Osc outside of the operational range, although it does not appear in the voltage and current for the collector or the gate. However, precise measurement using an antenna revealed the presence of PETT-Osc at the predicted conditions. [ABSTRACT FROM AUTHOR]

The container relocation problem (CRP) for ports worldwide has been a highly significant research topic because of its contribution to the improvement of yard-running efficiency. It can be defined as a sequence that allows each container to be extracted with the least number of relocations when identical containers in a cluster have been stacked in a block. This study differs from previous research mainly in five aspects: (1) a two-level goal programming model for CRP is presented that can help in understanding of this problem and provide a solid theoretical ground for this research; (2) because of the NP time hardness of the CRP, heuristic rules are proposed to reduce hunting space by the way of dividing solution space; (3) an improved path optimum algorithm (I-POA) is proposed to reduce unfeasible solutions and find a high-quality solution for any three-dimensional case in a shorter running time; (4) the numerical experiments show that the algorithm proposed in this research achieves better performance than similar algorithms because of its higher levels of efficiency and more robust property; and (5) a general expression for the utilization level of the storage area and the number of relocations is proposed to check the reliability of the result by conducting a sensitivity analysis. Based on this research, the following conclusion can be obtained: I-POA possesses significant practical value in the improvement of intelligent resource scheduling standards of coastal container ports worldwide. [ABSTRACT FROM AUTHOR]

An adaptive force model is proposed to achieve better performance between the accuracy and the speed of cloth simulation in three-dimensional (3D) space. The proposed force model can be expressed with a general mathematical form demonstrated by the distance between the clothing and the human body. This paper defines how a continuous adaptive area can be established with a shape "block". It is clarified that, within a specific block, a force model is expressed with the gravity of the clothing, the forces of the adjacent blocks and the anti-force of the human body to the block. In this manner, the force model of the desired clothing can be obtained through a general mathematical expression. The simulations and experimental results demonstrate that the acceptable clothing simulation in 3D space can be achieved with higher speed by saving about 20.2% runtime, and the efficiency of the proposed scheme can be verified. [ABSTRACT FROM AUTHOR]

In this paper, we develop a general first-order perturbation theory of the propagation of a signal in an optical fiber in the presence of amplification and Kerr nonlinearity, valid for arbitrary pulse shapes. We obtain a general expression of the sampled signal after optical filtering, coherent detection, and optimal sampling. We include intrachannel and as well as interchannel nonlinear effects. We obtain simplified expressions in the case in which the accumulated dispersion is high (equivalent to the far-field limit in paraxial optics). This general theory is applied in detail to the special case of spectral-efficient sinc pulses. This exercise shows that the characteristics of the neighboring wavelength-division multiplexed channels are essential in determining the nonlinear impairments. [ABSTRACT FROM PUBLISHER]