• 대한수학회보
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• 제46권6호
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• pp.1151-1152
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• 2009

In this short notice, we prove a new result about the dth power residue symbol of function fields, by modifying the method of W. Kohnen in the paper published in Bull. Korean Math. Soc. 45 (2008), no. 2, 273-275.

• 대한수학회보
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• 제37권4호
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• pp.843-854
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• 2000

S. Turner has shown that a Neron symbol can be calculated from the values of K-meromorphic theta functions corresponding to divisors on K-holomorphic torus of strongly diagonal type. Using an isogeny to a K-holomorphic torus of strongly diagonal type, he constructed a Neron symbol on K-holomorphic torus of diagonal type. In this work, we provide a simple formula of the Neron symbol on the Tate curve. And then we construct the Neron symbol on K-holomorphic torus of diagonal or st rongly diagonal type without using isogenies.

• East Asian mathematical journal
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• 제32권1호
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• pp.35-41
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• 2016

We introduce formal symbols of product type and of minimum type and show that the formal power series representation for $e^p$ is a formal symbol of product type, where p is a formal symbol of minimum type.

• 한국수학사학회지
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• 제22권3호
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• pp.45-60
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• 2009

수학적 사고는 외적 기호에 의해 기호화되고, 역으로 이 기호는 사고의 형태를 결정한다. 기호는 - 대수학에서의 기호, 해석학에서의 기호 그리고 삼단논법을 검증해주는 다이어그램 - 수학연구에서 수행하는 사고 작용의 다양성을 반영하고 각각 발견법적 기능을 수행한다.

• 대한수학회논문집
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• 제34권2호
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• pp.533-542
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• 2019

We study commutants of Toeplitz operators acting on the Dirichlet space of the unit disk and prove that an operator in the Toeplitz algebra commuting with a Toeplitz operator with a nonconstant polynomial symbol must be a Toeplitz operator with an analytic symbol.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제16권1호
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• pp.79-90
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• 2012

This research investigated if the embodied symbol using a turtle metaphor in a microworld environment works as a cognitive tool to mediate the learning of combinatorics. It was found that students were able to not only count the number of cases systematically by using the embodied symbols in a situated problem regarding Permutation and Combination, but also find the rules and infer a concept of Combination through the activities manipulating the symbols. Therefore, we concluded that the embodied symbol, as a bridge that connects learners' concrete experiences with abstract mathematical concepts, can be applied to introduction of various mathematical concepts as well as a combinatorics concept.

• 디지털산업정보학회논문지
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• 제10권4호
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• pp.29-35
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• 2014

The formula contains up between the text and the structural information, as well as their mathematical symbols. Research on-line or off-line recognition formula is underway actively used in various fields, and various forms of the equation are implemented recognition system. Although many documents are included in the various formulas, it is not easy to enter a formula into the computer. Recognition of the expression is divided into two processes of symbol recognition and structural analysis. After analyzing the location information of each character is specified to recognize the effective area after each symbol, and to the structure analysis based on the proximity between the characters is recognized as an independent single formula. Furthermore, analyzing the relationship between the front and back each time a combination of the position relationship between each symbol, and then to add the symbol which was able to easily update the structure of the entire formula. In this paper, by using a scanner to scan the book formula was used to interpret the meaning of the recognized symbol has a relative size and location information of the expression symbol. An algorithm to remove the formulas for calculation of the number of formula is present at the same time is proposed. Using the proposed algorithms to scan the books in the formula in order to evaluate the performance verification as 100% separation and showed the recognition rate equation.

• ETRI Journal
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• 제42권6호
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• pp.859-871
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• 2020

A spectrally encapsulated (SE) orthogonal frequency-division multiplexing (OFDM) precoding scheme for wireless short packet transmission, which can suppress the out-of-band emission (OoBE) while maintaining the advantage of the cyclic prefix (CP)-OFDM, is proposed. The SE-OFDM symbol consists of a prefix, an inverse fast Fourier transform (IFFT) symbol, and a suffix generated by the head, center, and tail matrices, respectively. The prefix and suffix play the roles of a guard interval and suppress the OoBE, and the IFFT symbol has the same size as the discrete Fourier transform symbol in the CP-OFDM symbol and serves as an information field. Specifically, as the center matrix generating the IFFT symbol is orthogonal, data and pilot symbols can be allocated to any subcarrier without distinction. Even if the proposed precoder is required to generate OFDM symbols with spectral efficiency in the transmitter, a corresponding decoder is not required in the receiver. The proposed scheme is compared with CP-OFDM in terms of spectrum, OoBE, and bit-error rate.

• 충청수학회지
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• 제27권4호
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• pp.697-705
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• 2014

For a complex measure ${\mu}$ on B and $f{\in}L^2_a(B)$, the Toeplitz operator $T_{\mu}$ on $L^2_a(B,dv)$ with symbol ${\mu}$ is formally defined by $T_{\mu}(f)(w)=\int_{B}f(w)\bar{K(z,w)}d{\mu}(w)$. We will investigate properties of the Toeplitz operator $T_{\mu}$ with symbol ${\mu}$. We define the Toeplitz type operator $T^r_{\psi}$ with symbol ${\psi}$, $$T^r_{\psi}f(z)=c_r\int_{B}\frac{(1-{\parallel}w{\parallel}^2)^r}{(1-{\langle}z,w{\rangle})^{n+r+1}}{\psi}(w)f(w)d{\nu}(w)$$. We will also investigate properties of the Toeplitz type operator with symbol ${\psi}$.

• 대한수학회보
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• 제60권3호
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• pp.575-591
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• 2023

Motivated by several generalizations of the Pochhammer symbol and their associated families of hypergeometric functions and hypergeometric polynomials, by choosing to use a very generalized Pochhammer symbol, we aim to introduce certain extensions of the generalized Lauricella function F⁽ⁿ⁾_A and the Humbert's confluent hypergeometric function Ψ⁽ⁿ⁾ of n variables with, as their respective particular cases, the second Appell hypergeometric function F₂ and the generalized Humbert's confluent hypergeometric functions Ψ₂ and investigate their several properties including, for example, various integral representations, finite summation formulas with an s-fold sum and integral representations involving the Laguerre polynomials, the incomplete gamma functions, and the Bessel and modified Bessel functions. Also, pertinent links between the major identities discussed in this article and different (existing or novel) findings are revealed.