• Journal of Industrial Technology
• /
• v.4
• /
• pp.3-10
• /
• 1984

A new FDCT algorithm was developed. It needed only half numbers of the discrete output signals and made use of the prime factor FFT algorithm. The FDST algorithm of the second kind of DST was developed by use of the FDCT algorithm.

• The Pure and Applied Mathematics
• /
• v.23 no.4
• /
• pp.391-391
• /
• 2016

• Journal for History of Mathematics
• /
• v.12 no.2
• /
• pp.47-54
• /
• 1999

We introduce some historical facts on number theory, especially prime numbers and modular arithmetic. And then, with the viewpoint of computer arithmetic, residue number systems are considered as an alternate to positional number systems so that high performance and high speed computation can be achieved in a specified domain such as cryptography and digital signal processing.

• Journal of Integrative Natural Science
• /
• v.14 no.4
• /
• pp.159-161
• /
• 2021

In this article, we will study which prime numbers are represented by the principal form. p = x² + ny². We will also give some results related to the form of primes of the form x² + axy + y².

• Journal for History of Mathematics
• /
• v.24 no.4
• /
• pp.1-6
• /
• 2011

We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

• Nuclear Engineering and Technology
• /
• v.49 no.7
• /
• pp.1405-1413
• /
• 2017

To investigate the heat loads imposed on a reactor vessel through the natural convection of core melts in severe accidents, mass transfer experiments were performed based on the heat transfer/mass transfer analogy, using two- (2-D) and three-dimensional (3-D) facilities of various heights. The modified Rayleigh numbers ranged from $10^{12}$ to $10^{15}$, with a fixed Prandtl number of 2,014. The measured Nusselt numbers showed a trend similar to those of existing studies, but the absolute values showed discrepancies owing to the high Prandtl number of this system. The measured angle-dependent Nusselt numbers were analyzed for 2-D and 3-D geometries, and a multiplier was developed that enables the extrapolation of 2-D data into 3-D data. The definition of $Ra^{\prime}_H$ was specified for 2-D geometries, so that results could be extrapolated for 3-D geometries; also, heat transfer correlations were developed.

• International journal of advanced smart convergence
• /
• v.13 no.2
• /
• pp.35-43
• /
• 2024

In this paper, we propose two 127-bit LFSR (Linear Feedback Shift Register)-based OTP (One-Time Password) generators. One is a 9-digit decimal OTP generator with thirty taps, while the other is a 12-digit OTP generator with forty taps. The 9-digit OTP generator includes only the positions of Fibonacci numbers to enhance randomness, whereas the 12-digit OTP generator includes the positions of prime numbers and odd numbers. Both proposed OTP generators are implemented on an Arduino module, and randomness evaluations indicate that the generators perform well across six criteria and are straightforward to implement with Arduino.

• Journal of KIISE:Databases
• /
• v.33 no.1
• /
• pp.129-137
• /
• 2006

An XML labeling scheme is an efficient encoding method to determine the ancestor-descendant relationships of elements and the orders of siblings. Recently, many dynamic XML documents have appeared in the Web Services and the AXML(the Active XML), so we need to manage them with a dynamic XML labeling scheme. The prime number labeling scheme is a representative scheme which supports dynamic XML documents. It determines the ancestor-descendant relationships between two elements with the feature of prime numbers. When a new element is inserted into the XML document using this scheme, it has an advantage that an assigning the label of new element don't change the label values of existing nodes. But it has to have additional expensive operations and data structure for maintaining the orders of siblings. In this paper, we suggest the order number sharing method and algorithms categorized by the insertion positions of new nodes. They greatly minimize the existing method's sibling order maintenance cost.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.5
• /
• pp.1319-1334
• /
• 2020

In this paper, we study the basic theory of the category of graded w-Noetherian modules over a graded ring R. Some elementary concepts, such as w-envelope of graded modules, graded w-Noetherian rings and so on, are introduced. It is shown that: (1) A graded domain R is graded w-Noetherian if and only if R^g_𝔪 is a graded Noetherian ring for any gr-maximal w-ideal m of R, and there are only finite numbers of gr-maximal w-ideals including a for any nonzero homogeneous element a. (2) Let R be a strongly graded ring. Then R is a graded w-Noetherian ring if and only if R_e is a w-Noetherian ring. (3) Let R be a graded w-Noetherian domain and let a ∈ R be a homogeneous element. Suppose 𝖕 is a minimal graded prime ideal of (a). Then the graded height of the graded prime ideal 𝖕 is at most 1.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.6
• /
• pp.1981-1988
• /
• 2013

We say a positive integer n satisfies the Lehmer property if ${\phi}(n)$ divides n - 1, where ${\phi}(n)$ is the Euler's totient function. Clearly, every prime satisfies the Lehmer property. No composite integer satisfying the Lehmer property is known. In this article, we show that every composite integer of the form $D_{p,n}=np^n+1$, for a prime p and a positive integer n, or of the form ${\alpha}2^{\beta}+1$ for ${\alpha}{\leq}{\beta}$ does not satisfy the Lehmer property.