• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.6
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• pp.105-110
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• 2005

The linearized polynomial fan be regarded as a generalization of the identity function so that the inverse of the linearized polynomial is a generalization of e inverse function. Since the inverse function has so many good cryptographic properties, the inverse of the linearized polynomial is also a candidate of good Boolean functions. In particular, a construction method of vector resilient functions with high algebraic degree was proposed at Crypto 2001. But the analysis about the algebraic degree of the inverse of the linearized Polynomial. Hence we correct the inexact result and give the exact maximal algebraic degree.

• Kyungpook Mathematical Journal
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• v.18 no.1
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• pp.105-107
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• 1978

Considering the prime z-filters on a topological space X through the structures of the ring C(X) of continuous functions. a prime z-filter is uniquely determined by a primary z-ideal in the ring C(X), i. e., they have a one-to-one correspondence. Any primary ideal is contained in a unique maximal ideal in C(X). Denoting $\mathfrak{F}(X)$, $\mathfrak{Q}(X)$, 𝔐(X) the prime, primary-z, maximal spectra, respectively, $\mathfrak{Q}(X)$ is neither an open nor a closed subspace of $\mathfrak{F}(X)$.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.625-633
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• 1995

Classical Fatous' theorem asserts that the non-tangential limit of the Poisson integral of an integrals function on $[\pi, \pi]$ exists a.e.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.615-623
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• 1995

Consider a function m defined in $R^n$ and the associated convolution operator T given by the Fourier transform $\hat{T} = m\hat{f}$.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.189-195
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• 2014

Let X be a compact metric space, B be a unital commutative Banach algebra and ${\alpha}{\in}(0,1]$. In this paper, we first define the vector-valued (B-valued) ${\alpha}$-Lipschitz operator algebra $Lip_{\alpha}$ (X, B) and then study its structure and characterize of its maximal ideal space.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.855-890
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• 1999

Necessary and sufficient conditions on the weight functions u(.) and $\upsilon$(.) are derived in order that the fractional maximal operator $M\alpha,\;0\;\leq\;\alpha\;<\;1$, is bounded from the weighted amalgam space $\ell^s(L^p(\mathbb{R},\upsilon(x)dx)$ into $\ell^r(L^q(\mathbb{R},u(x)dx)$ whenever $1\leq s\leq r<\infty\;and\;1. The boundedness problem for the fractional intergral operator $I_{\alpha},0<\alpha\leq1$, is also studied.

• ETRI Journal
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• v.19 no.4
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• pp.389-401
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• 1997

In this paper, we consider the relationship between nonlinearity and correlation immunity of Boolean functions. In particular, we discuss the nonlinearity of correlation immune functions suggested by P. Camion et al. For the analysis of such functions, we present a simple method of generating the same set of functions, which makes it possible to construct correlation immune functions with controllable correlation immunity and nonlinearity. Also, we find a bound for the correlation immunity of functions having maximal nonlinearity.

• Management Science and Financial Engineering
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• v.22 no.1
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• pp.5-12
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• 2016

We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date. This can be avoided through compressing the processing time of the jobs with additional costs. We describe the compression cost as the convex or the concave function. The objective is to minimize the sum of the total penalty cost and the total compression cost. It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively. Thus, we consider the special cases such that the cost functions or maximal compression amounts of each job are identical. When the cost functions are convex, we show that the problem with the identical costs functions can be solved in strongly polynomial time. When the cost functions are concave, we show that the problem remains NP-hard even if the cost functions are identical, and develop the strongly polynomial approach for the case with the identical maximal compression amounts.

• Journal of the Korean Mathematical Society
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• v.26 no.1
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• pp.159-166
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• 1989

• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.36-40
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• 2013

The paper discusses the problem of how to allocate the fund to a large number of individuals in a higher school so as to bring a higher utility return based on the theory of uncertain set. Suppose that experts can assign each invested individual a corresponding nondecreasing membership function on a close interval I according to its actual level and developmental foreground. The membership degree at the fund $x{\in}I$ is called utility degree from fund x, and product (minimum) of utility degrees of distributed funds for all invested individuals is called united utility degree from the fund. Based on the above concepts, we present an uncertain optimization model, called Maximal United Utility Degree (or Maximal Membership Degree) model for fund distribution. Furthermore, we use nondecreasing polygonal functions defined on close intervals to structure a mathematical maximal united utility degree model. Finally, we design a genetic algorithm to solve these models.