• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.87-99
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• 2007

In this paper, we consider the Sparre Andersen risk model modified by the inclusion of interest on the surplus. By using the techniques of Cai and Dickson [Ins.: Math. Econ. 32(2003)], we give the functional and also the exponential type upper bounds for the tail probability of the deficit at ruin. Some special cases are also discussed.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-667
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• 2011

A class of functions involving divided differences of the psi and tri-gamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving the ratio of two gamma functions and originating from the establishment of the best upper and lower bounds in Kershaw's double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in $\mathbb{R}^{n-1}$ and $\mathbb{R}^n$ respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.537-564
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• 2023

In this paper, we are mainly concerned with two-sided estimates for transition probabilities of symmetric Markov chains on ℤ^d, whose one-step transition probability is comparable to |x - y|^-dϕ_j (|x - y|)^-1 with ϕ_j being a positive regularly varying function on [1, ∞) with index α ∈ [2, ∞). For upper bounds, we directly apply the comparison idea and the Davies method, which considerably improves the existing arguments in the literature; while for lower bounds the relation with the corresponding continuous time symmetric Markov chains are fully used. In particular, our results answer one open question mentioned in the paper by Murugan and Saloff-Coste (2015).

• Journal of the Korean Operations Research and Management Science Society
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• v.29 no.4
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• pp.1-10
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• 2004

In this paper we study bounds for characteristics of stationary waiting times in (max, +)-linear systems with a Poisson arrival process. which are prevalent in manufacturing systems, kanban systems, cyclic and acyclic fork-and-join type systems, finite or infinite capacity tandem queues with various kinds of blocking, transportation systems, and telecommunication networks, and so on. Recently, some results on series expansion for characteristics, such as higher moments, Laplace transform, and tail probability, of transient and stationary waiting times in a class of (max, +)-linear systems via Taylor series expansions have been studied. In order to overcome the computational complexity in those results, we consider bounds for characteristics of stationary waiting times using valuable stochastic ordering results. Some numerical examples are also provided.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.789-795
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• 1999

Let $A_1$,A$_2$…, A\ulcorner and B$_1$,B$_2$…, B\ulcorner be two sequences of events on the same probability space. Let X= X\ulcorner(A) and Y-Y\ulcorner)(B), repectively, by the number of those A\ulcorner and B\ulcorner which oc-cur. We establish bivariate lower bounds on the distribution P(X$\geq$1, Y, $\geq$1)and P(X$\geq$i , $Y\geq$j)by linear combinations of the bino-mial moments S\ulcorner, \ulcorner, 1$\leq$i$\leq$j

• Journal of the Korean Statistical Society
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• v.19 no.1
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• pp.24-44
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• 1990

The purpose of this paper is to extend the idea of Tamhane and Bechhofer (1977, 1979) concerning the normal means problem to some general class of distributions. The key idea in Tamhane and Bechhofer is the derivation of the computable lower bounds on the probability of a correct selection. To derive such lower bounds, they used the specific covariance structure of a multivariate normal distribution. It is shown that such lower bounds can be obtained for a class of stochastically increasing distributions under certain conditions, which is sufficiently general so as to include the normal means problem as a special application. As an application of the general theory to the scale parameters problem, a two-stage elimination type procedure for selecting the population associated with the smallest variance from among several normal populations is proposed. The design constants are tabulated and the relative efficiencies are computed.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.725-742
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• 2021

The aim of this article is to estimate the coefficient bounds of certain subclasses of analytic functions. We claim that this is a novel and unique effort in combining the coefficient functional along with the new domains and the probability distributions which have not been found or are available in the literature of coefficients bounds. Here the authors analyze these bounds in the special domains associated with exponential function and sine function. Further we obtain Fekete-Szegö inequalities for the defined subclasses of analytic functions defined through Poisson distribution series and Pascal distribution series.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.29 no.6
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• pp.1259-1270
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• 2019

The upper bound of differential characteristic probability is mainly used to determine the number of rounds when constructing a block cipher. As the number of rounds affects the performance of block cipher, it is critical to evaluate the tight upper bound in the constructing process. In order to calculate the upper bound of differential characteristic probability, the previous searching methods for minimum number of active S-boxes constructed constraint equations for non-linear operations and linear operations, independently. However, in the case of BOGI design strategy, where linear operation is dependent on non-linear operation, the previous methods may present the less tight upper bound. In this paper, we exploit the properties of BOGI strategy to propose a new method to evaluate a tighter upper bound of differential characteristic probability than previous ones. Additionally, we mathematically proved the validity of our method. Our proposed method was applied to GIFT-64 and GIFT-128, which are based on BOGI strategy, and the upper bounds of differential characteristic probability were derived until 9 round. Previously, the upper bounds of differential characteristic probability for 7-round GIFT-64 and 9-round GIFT-128 were 2^-18.395 and 2^-26.885, respectively, while we show that the upper bounds of differential characteristic probability are more tight as 2^-19.81 and 2^-28.3, respectively.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.7A
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• pp.1080-1089
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• 1999

The union upper bounds to the bit error probability of maximum likelihood(ML) soft-decoding of parallel concatenated convolutional codes(PCCC) and serially concatenated convolutional codes(SCCC) can be evaluated through the weight enumerating function(WEF). This union upper bounds become the lower bounds of the BER achievable when iterative decoding is used. In this paper, to compute the WEF, an efficient error event search algorithm which is a combination of stack algorithm and bidirectional search algorithm is proposed. By computor simulation, it is shown that the union boounds obtained by using the proposed algorithm become the lower bounds to BER of concatenated convolutional codes with iterative decoding.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.509-525
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• 1999

In this paper we obtain sharp upper and lower bounds of samll ball and large deviation probabilities for the increments of Gaussian processes with stationary increments, whose results are essential to establish Chung type laws of iteratted logarithm.