• Journal of Electrical Engineering and information Science
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• v.2 no.6
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• pp.56-63
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• 1997

Under most system assumptions, closed form solutions of performance measures for ATM switches with input queueing are not available. In this paper, we present expressions and bounds for the derivatives of cell loss probabilities with respect to the arrival rate evaluated at a zero arrival rate. These bounds are used to give an approximation by Taylor expansion, thereby providing an economical way to estimate cell loss probabilities in light traffic.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.997-1008
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• 2012

This work provides an alternative derivation of third order response functions in four wave mixing spectroscopy of multichromophoric macromolecular systems considering only single exciton states. For the case of harmonic oscillator bath linearly and diagonally coupled to exciton states, closed form expressions showing all the explicit time dependences are derived. These expressions can provide more solid physical basis for understanding 2-dimensional electronic spectroscopy signals. For more general cases of system-bath coupling, the quantum master equation (QME) approach is employed for the derivation of multistep time evolution equations for Green function-like operators. Solution of these equations is feasible at the level of 2nd order non-Markovian QME, and the new approach can account for inter-exciton coupling, dephasing, relaxation, and non-Markovian effects in a consistent manner.

• Particle and aerosol research
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• v.14 no.1
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• pp.1-8
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• 2018

The optical force on a perfectly reflecting sphere in a ray-optics regime is considered. With the assumption of geometric optics and a sphere smaller than the minimum waist of the illuminating beam, closed-form analytic expressions of the optical force are derived. Both axial and radial forces are expressed by a modified Bessel function of the first kind. The derived analytic expressions are compared to precise numerical computations of the exact optical force equations derived previously. In addition the error due to the small sphere assumption is estimated analytically.

• Journal of Korean Institute of Industrial Engineers
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• v.22 no.2
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• pp.179-188
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• 1996

We study n-class-based storage policy for an automated storage/retrieval system (AS/RS) and derive the closed form expressions of expected travel times under single command cycle. In order to confirm the correctness of the derivations, we consider both discrete and continuous storage racks, and show that the expressions for expected travel times of discrete rack converge to those of continuous one. We also derive the expected travel times when the coordinate locations for storages or retrievals are triangularly distributed and we try to solve class layout problem using the obtained results. Numerical examples are given in case of 3-class-based storage policy.

• Smart Structures and Systems
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• v.15 no.6
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• pp.1569-1582
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• 2015

Two hyperbolic displacement models are used for the bending response of simply-supported orthotropic laminated composite plates resting on two-parameter elastic foundations under mechanical loading. The models contain hyperbolic expressions to account for the parabolic distributions of transverse shear stresses and to satisfy the zero shear-stress conditions at the top and bottom surfaces of the plates. The present theory takes into account not only the transverse shear strains, but also their parabolic variation across the plate thickness and requires no shear correction coefficients in computing the shear stresses. The governing equations are derived and their closed-form solutions are obtained. The accuracy of the models presented is demonstrated by comparing the results obtained with solutions of other theories models given in the literature. It is found that the theories proposed can predict the bending analysis of cross-ply laminated composite plates resting on elastic foundations rather accurately. The effects of Winkler and Pasternak foundation parameters, transverse shear deformations, plate aspect ratio, and side-to-thickness ratio on deflections and stresses are investigated.

• Structural Engineering and Mechanics
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• v.8 no.3
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• pp.243-256
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• 1999

Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel's equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.

• Journal of Communications and Networks
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• v.8 no.3
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• pp.306-312
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• 2006

This paper studies theoretically the bit error rate (BER) performance of cooperative transmission using space-time block code (STBC) in a fully distributed manner. Specifically, we first propose a STBC-based cooperative signaling structure to make the cooperation of three single-antenna terminals possible. Then, we derive the closed-form BER expressions for both cooperation and noncooperation schemes under flat Rayleigh fading channel plus additive white Gaussian noise (AWGN). The validity of these expressions is verified by Monte-Carlo simulations. A variety of numerical and simulation results reveal that the cooperative transmission achieves higher diversity gain and better performance than the direct transmission for the same total transmit power.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.5
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• pp.2357-2380
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• 2019

In this paper, we investigate the impact of hardware impairments (HWIs) on the performance of a downlink massive MIMO system. We consider a single-cell system with maximum ratio transmission (MRT) as precoding scheme, and with all the HWIs characteristics such as phase noise, distortion noise, and amplified thermal noise. Based on the system model, we derive closed-form expressions for a typical user data rate under two scenarios: when a common local oscillator (CLO) is used at the base station and when separated oscillators (SLOs) are used. We also derive closed-form expressions for the downlink transmit power required for some desired per-user data rate under each scenario. Compared to the conventional system with ideal transceiver hardware, our results show that impairments of hardware make a finite upper limit on the user's downlink channel capacity; and as the number of base station antennas grows large, it is only the hardware impairments at the users that mainly limit the capacity. Our results also show that SLOs configuration provides higher data rate than CLO at the price of higher power consumption. An approach to minimize the effect of the hardware impairments on the system performance is also proposed in the paper. In our approach, we show that by reducing the cell size, the effect of accumulated phase noise during channel estimation time is minimized and hence the user capacity is increased, and the downlink transmit power is decreased.

• Geophysics and Geophysical Exploration
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• v.25 no.1
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• pp.38-43
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• 2022

In case axial symmetrical bodies with varying cross sections such as volcanic conduits and unexploded ordnance (UXO), it is efficient to approximate them by adding the response of thin disks perpendicular to the axis of symmetry. To compute the vector magnetic and magnetic gradient tensor respones by such bodies, it is necessary to derive an analytical expression of the circular disk. Therefore, in this study, we drive closed-form expressions of the vector magnetic and magnetic gradient tensor due to a circular disk. First, the vector magnetic field is obtained from the existing gravity gradient tensor using Poisson's relation where the gravity gradient tensor due to the same disk with a constant density can be transformed into a magnetic field. Then, the magnetic gradient tensor is derived by differentiating the vector magnetic field with respect to the cylindrical coordinates converted from the Cartesian coordinate system. Finally, both the vector magnetic and magnetic gradient tensors are derived using Lipschitz-Hankel type integrals based on the axial symmetry of the circular disk.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.13 no.1
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• pp.101-105
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• 2002

In this paper, the coupling windows of the dielectric resonator filter have been analyzed. The coupling factor which has been used to characterize the coupling window is represented by closed form expressions. The deviation of the coupling factor as the size of coupling window has been compared between calculated by presented method and measured ones. There are very closed agreements. The presented method can be applied not only to design dielectric resonator but also to design varactor tuned dielectric resonator filter so as that the passband bandwidth is constant within tuned ranges.