• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• The Journal of Internal Korean Medicine
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• v.29 no.4
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• pp.856-870
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• 2008

Objectives : Consumption is a chronic wasting disease and major portion of Oriental Medicine's therapy. However, there is no standard diagnostic method for consumption that is $q{\grave{i}}-x{\bar{u}}$, $xu{\grave{e}}-x{\bar{u}}$, $yang-x{\bar{u}}$, $y{\bar{i}}n-x{\bar{u}}$. Methods : A questionnaire which includes symptoms and signs for diagnosis of $q{\grave{i}}-x{\bar{u}}$, $xu{\grave{e}}-x{\bar{u}}$, $yang-x{\bar{u}}$, $y{\bar{i}}n-x{\bar{u}}$ was evaluated by Delphi technique. Each question was valuated by interviewing 27 oriental medicine doctors. Then. we choose questions given over 5 points and reorganized some items according to the recommendations by interviewed-doctors. We then accessed the value of re-organized questions composing of the questionnaires. Conclusion : We finally chose each 9 items of $q{\grave{i}}-x{\bar{u}}$, $xu{\grave{e}}-x{\bar{u}}$, $yang-x{\bar{u}}$, $y{\bar{i}}n-x{\bar{u}}$'s questionnaire. Further study is necessary for modification of questionnaire by statistics and certification by clinical trial.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.603-617
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• 1997

Consider a Sobolev inner product on the space of polynomials such as $$ \phi(p,q) = \lambda p(c)q(c) + <\tau,p'(x)q'(x)> $$ where $\tau$ is a moment functional and c and $\lambda$ are real constants. We investigate properties of orthogonal polynomials relative to $\phi(\cdot,\cdot)$ and give necessary and sufficient conditions under which such Sobolev orthogonal polynomials satisfy a spectral type differential equation with polynomial coefficients.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.1-12
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• 2007

In this paper, we consider the q-Volkenborn integral of uniformly differentiable functions on the p-adic integer ring. By using this integral, we obtain the generating functions of twisted q-generalized Bernoulli numbers and polynomials. We find some properties of these numbers and polynomials.

• East Asian mathematical journal
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• v.27 no.3
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• pp.349-372
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• 2011

In this paper we define interval valued (${\in}$, ${\in}{\vee}q$)-fuzzy hquasi-ideals, interval valued (${\in}$, ${\in}{\vee}q$)-fuzzy h-bi-ideals, interval valued ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$)-fuzzy h-ideals, interval valued ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$)-fuzzy h-quasi-ideals, interval valued ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$)-fuzzy h-bi-ideals and characterize different classes of hemirings by the properties of these ideals.

• Journal of Advanced Navigation Technology
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• v.18 no.4
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• pp.341-346
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• 2014

This paper has presented the design and fabrication of phase correlator for wideband digital frequency discriminator (DFD) operating over the 6.0 to 18.0 GHz frequency range. Fabricated DFD phase correlator has been measured I or Q output signal, and analyzed frequency discrimination error. The operation of the proposed mixer type correlator has been analyzed by deriving some analytic equations. To design the phase correlator, this paper has modeled and simulated IQ mixer and 8-way power divider by using RF simulation tool. Designed phase correlator has fabricated and measured. The phase error and frequency discrimination error have been presented using by measured I and Q output signal. Over the 6.0~18.0 GHz range, the root mean square(RMS) phase error is $4.81^{\circ}$, RMS and frequency discrimination error is 1.49 MHz, RMS.

• Journal of the Korean Institute of Landscape Architecture
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• v.21 no.2
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• pp.50-67
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• 1993

This study analyzed the distribution and structure of the vegetation landscape in Naejangsan National Park. The plant distribution was investigated using a field survey. There were 72 sites sampled using the clumpled sampling method. The data derived from the investigation was analyzed using the quantitative analysis of Bray-Curtis method. The analysis was performed by the classification of TWINSPAN. The ordination of DCA and RA was used for the species composition and successional trends. The results are as follows; 1. Quercus. serrata-Q. variabilis community as 21.76(16.49$\textrm{km}^2$), was the largest community in the actual vegetation of the Naejangsan National Park. The degree of green naturality index 8 area covered 64.8% of the study area and the index 6 area did 16%. 2. Classified by the ordination of DCA and environmental variables, such as the plant community was divided into seven groups according to the altitude and forming groups; Chamaecy Paris. pisifera-P.densiflora community, P.densiflora community, Q.variailis community, T.nuciofera-A.palmatum community. 3. Ther species diversity and evenness indices of C.pisifera-P.densiflora community, P.densiflora community appeared low but C.laxiflora communitywhich was the most stable community in the study area. 4. The similarity indices between Q.variabilis community and Q.serrata-Q.variabilis community were calculated 58.84%, but those between other communities were comparatively low level. 5. The successional trends of DBH class seem to be from C. pisifera-P.densiflora community, P.densiflora community to Quercus species community and from Q.variabilis community, Q.serrata-Q.variabilis community to Carpinus species community. 6. Results suggested that the successional trends in Naejangsan National Park; P.densiflora community\longrightarrowQ.variablilis community, Q.serrata-Q.variabilis community\longrightarrowC.laxiflora community in sequence.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.621-634
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• 2022

The scaled inverse of a nonzero element a(x) ∈ ℤ[x]/f(x), where f(x) is an irreducible polynomial over ℤ, is the element b(x) ∈ ℤ[x]/f(x) such that a(x)b(x) = c (mod f(x)) for the smallest possible positive integer scale c. In this paper, we investigate the scaled inverse of (xⁱ - x^j) modulo cyclotomic polynomial of the form Φ_p^s (x) or Φ_p^sq^t (x), where p, q are primes with p < q and s, t are positive integers. Our main results are that the coefficient size of the scaled inverse of (xⁱ - x^j) is bounded by p - 1 with the scale p modulo Φ_p^s (x), and is bounded by q - 1 with the scale not greater than q modulo Φ_p^sq^t (x). Previously, the analogous result on cyclotomic polynomials of the form Φ_2ⁿ (x) gave rise to many lattice-based cryptosystems, especially, zero-knowledge proofs. Our result provides more flexible choice of cyclotomic polynomials in such cryptosystems. Along the way of proving the theorems, we also prove several properties of {x^k}_k∈ℤ in ℤ[x]/Φ_pq(x) which might be of independent interest.

• Journal of dental hygiene science
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• v.14 no.4
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• pp.461-467
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• 2014

The objective of this study was to evaluate the impact of the Q-ray view, a novel optical device on reliability of assessing a tooth status by dental hygiene students in the training for dental hygiene process. Twenty patients were enrolled in this study. Oral examinations were conducted by both seventeen third-year dental hygiene students and a trained faculty member. Traditional visual inspection was performed in phase I and then re-examined with Q-ray view in phase II. Restoration codes and lesion codes for each tooth were recorded separately according to the predefined criteria. As a measure of reliability, percent agreement and Cohen's kappa were determined. Agreements for each intraoral regions and types of lesion and restoration were calculated. Paired t-test and Pearson chi-square test for two proportions were used to compare mean Cohen's kappa and percent agreement at each phase. For the lesion code, mean kappa values of phase II for intraoral regions were significantly greater than that of phase I (p=0.017). For the both of the lesion code and restoration code, percent agreements of phase II for each types of lesion and restoration were significantly greater than that of phase II (p<0.001 and p<0.001, respectively). Especially difference of percent agreements between phase I and II for incipient caries, caries and fracture were significant for the lesion code (p=0.046, p<0.001, and p=0.029, respectively) and for not restored or sealed, tooth-colored restoration were significant for the restoration code (p<0.001 and p=0.011, respectively). The reliability of assessing a tooth status was improved when the Q-ray view used in dental hygiene student with beginner level of expertise. Q-ray view can be a promising device for conducting and educating the dental hygiene process better.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.287-291
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• 1997

Assume $H_i : R_+ \times R_+ \to R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q \leq 1)$ hold for $t, u, v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $\Vert f(x+y) - f(x)f(y) \Vert \leq H_i (\Vert x \Vert, \Vert y \Vert)$ shall be investigated.