• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.133-147
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• 2021

Our aim in this paper is to derive several new monotonicity properties and functional inequalities of some functions involving the q-gamma, q-digamma and q-polygamma functions. More precisely, some classes of functions involving the q-gamma function are proved to be logarithmically completely monotonic and a class of functions involving the q-digamma function is showed to be completely monotonic. As applications of these, we offer upper and lower bounds for this special functions and new sharp upper and lower bounds for the q-analogue harmonic number harmonic are derived. Moreover, a number of two-sided exponential bounding inequalities are given for the q-digamma function and two-sided exponential bounding inequalities are then obtained for the q-tetragamma function.

• Structural Engineering and Mechanics
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• v.31 no.1
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• pp.113-116
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• 2009

• Korean Journal of Materials Research
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• v.11 no.5
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• pp.372-377
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• 2001

A theory developed in Part I has been applied to calculate effective elastic and thermoelastic moduli of particle-strengthened, unidirectionally fiber-reinforced, and layered composites. For the unidirectional fiber composites the effect of fiber aspect ratio is taken into account. The analytical solutions obtained to the effective elastic moduli are compared with some of existing expressions and the following results are found. The effective bulk and shear moduli of the particle strengthened composites coincide with Korner's expressions, which correspond with the lower bounds of Hanshin and Shtrikman. The same expressions as the lower bounds of Hill and Hanshin are obtained for five independent moduli of the aligned continuous fiber composites, four of which coincide with Hanshin and Rosen's exact solutions for 'composite cylinder assemblage'.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.169-181
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• 2007

Applying the properties of Hadamard core for totally nonnegative matrices, we give new lower bounds of the determinant for Hadamard product about matrices in Hadamard core and totally nonnegative matrices, the results improve Oppenheim inequality for tridiagonal oscillating matrices obtained by T. L. Markham.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.12C
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• pp.1150-1156
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• 2006

In this paper we derive some lower bounds on the linear complexity and upper bounds on the 1-error linear complexity over $F_p$ of M-ary Sidel'nikov sequences of period $p^m-1$ when $M\geq3$ and $p\equiv{\pm}1$ mod M. In particular, we exactly compute the 1-error linear complexity of ternary Sidel'nikov sequences when $p^m-1$ and $m\geq4$. Based on these bounds we present the asymptotic behavior of the normalized linear complexity and the normalized 1-error linear complexity with respect to the period.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.1
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• pp.193-214
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• 2017

In this paper, we study the problem of network utility maximization in a CSMA based multi-hop wireless network. Existing work in this aspect typically adopted continuous time Markov model for performance modelling, which fails to consider the channel conflict impact in actual CSMA networks. To maximize the utility of a CSMA based wireless network with channel conflict, in this paper, we first model its weighted network capacity (i.e., network capacity weighted by link queue length) and then propose a distributed link scheduling algorithm, called CSMA based Maximal-Weight Scheduling (C-MWS), to maximize the weighted network capacity. We derive the upper and lower bounds of network utility based on C-MWS. The derived bounds can help us to tune the C-MWS parameters for C-MWS to work in a distributed wireless network. Simulation results show that the joint optimization based on C-MWS can achieve near-optimal network utility when appropriate algorithm parameters are chosen and also show that the derived utility upper bound is very tight.

• Journal of Communications and Networks
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• v.17 no.3
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• pp.231-240
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• 2015

To facilitate the base station planning in high speed railway communication systems, it is necessary to consider the functional relationships between the base station transmit power and space parameters such as train velocity and cell radius. Since these functions are able to present some inherent system properties determined by its spatial topology, they will be referred to as the power-space functions in this paper. In light of the fact that the line-of-sight path persists the most power of the received signal of each passing train, this paper considers the average transmission rate and bounds on power-space functions based on the additive white Gaussian noise channel (AWGN) model. As shown by Monte Carlo simulations, using AWGN channel instead of Rician channel introduces very small approximation errors, but a tractable mathematical framework and insightful results. Particularly, lower bounds and upper bounds on the average transmission rate, as well as transmit power as functions of train velocity and cell radius are presented in this paper. It is also proved that to maintain a fixed amount of service or a fixed average transmission rate, the transmit power of a base station needs to be increased exponentially, if the train velocity or cell radius is increased, respectively.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.1-10
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• 1999

When the component proportions in mixture experiments are restricted by lower and upper bounds multicollinearity appears all too frequently. The ridge regression can be used to stabilize the coefficient estimates in the fitted model. I propose a graphical method for evaluating the mixture component effects of ridge regression estimator with respect to the prediction variance and the prediction bias.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.13-20
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• 2004

A more general version of diffusivity based on total variation of density is defined and an information inequality for median-unbiased estimation is presented. The resulting information inequality can be interpreted as an analogue of the Bhattacharyya system of lower bounds for mean-unbiased estimation. A condition on which the information bound is achieved is also given.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.149-160
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• 2010

Let $W(x)={\prod}_{k=1}^m{\mid}x-x_k{\mid}^{{\gamma}_k}{\cdot}{\exp}(-{\mid}x{\mid}^{\alpha})$. Associated with the weight W, upper and lower bounds of the generalized Christoffel functions for generalized nonnegative polynomials are obtained.