• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.493-511
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• 2009

Let $q\;{\geq}\;3$ be an odd integer and a be an integer coprime to q. Denote by N(a, q) the number of pairs of integers b, c with $bc\;{\equiv}\;a$ (mod q), $1\;{\leq}\;b$, $c\;{\leq}\;{\frac{q-1}{2}}$ and with b, c having different parity. The main purpose of this paper is to study the sum ${\sum}^{'q}_{a=1}\;\(N(a,\;q)\;-\;\frac{{\phi}(q)}{8}\)^2$ and obtain a sharp asymptotic formula.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1049-1064
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• 1997

We study the existence and uniqueness of nonnegative singular solution u(x,t) of the semilinear parabolic equation $$ u_t = \Delta u - a \cdot \nabla(u^q) = u^p, $$ defined in the whole space $R^N$ for t > 0, with initial data $M\delta(x)$, a Dirac mass, with M > 0. The exponents p,q are larger than 1 and the direction vector a is assumed to be constant. We here show that a unique singular solution exists for every M > 0 if and only if 1 < q < (N + 1)/(N - 1) and 1 < p < 1 + $(2q^*)$/(N + 1), where $q^* = max{q, (N + 1)/N}$. This result agrees with the earlier one for N = 1. In the proof of this result, we also show that a unique singular solution of a diffusion-convection equation without absorption, $$ u_t = \Delta u - a \cdot \nabla(u^q), $$ exists if and only if 1 < q < (N + 1)/(N - 1).

• Journal of Genetic Medicine
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• v.8 no.2
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• pp.119-124
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• 2011

Purpose: Supernumerary marker chromosome (SMC) could be associated with various phenotypic abnormalities based on the chromosomal origin of SMCs. The present study aimed to determine the genomic contents of SMCs using chromosomal microarray and to analyze molecular cytogenetic characterizations and clinical phenotypes in patients with SMCs. Materials and Methods: Among patients with SMCs detected in routine chromosomal analysis, SMCs originating from chromosome 15 were excluded from the present study. CGH-based oligonucleotide chromosomal microarray was performed in 4 patients. Results: The chromosomal origins of SMCs were identified in 3 patients. Case 1 had a SMC of 16.1 Mb in 1q21.1-q23.3. Case 2 showed 21 Mb gain in 19p13.11-q13.12. Case 3 had a 4.5 Mb-sized SMC rearranged from 2 regions of 2.5 Mb in 22q11.1-q11.21 and 2.0 Mb in 22q11.22-q11.23. Conclusion: Case 1 presented a wide range of phenotypic abnormalities including the phenotype of 1q21.1 duplication syndrome. In case 2, Asperger-like symptoms are apparently related to 19p12-q13.11, hearing problems and strabismus to 19p13.11 and other features to 19q13.12. Compared with cat-eye syndrome type I and 22q11.2 microduplication syndrome, anal atresia in case 3 is likely related to 22q11.1-q11.21 while other features are related to 22q11.22-q11.23. Analyzing SMCs using high-resolution chromosomal microarray can help identify specific gene contents and to offer proper genetic counseling by determining genotype-phenotype correlations.

• The Korean Journal of Food And Nutrition
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• v.22 no.4
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• pp.577-586
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• 2009

Aging is associated with decreased energy expenditure, thermogenesis and energy requirements. Maintenance of physical fitness of the elderly has been reported to reduce the rate at which the basal metabolic rate, muscle strength, skeletal muscle mass and bone density deteriorate. Skeletal muscle disease is known to increase the risk of physical disability and psychological problems. This study was conducted to investigate changes in disability, emotional problems, body compositions, obesity indices and nutrient intake levels according to physical fitness with the elderly in rural areas. According to the results, physical fitness was negatively related with Activities of Daily Living(ADL, p<0.05), Instrumental Activities of Daily Living(IADL, p<0.001), Body Mass Index(BMI, p<0.001) and abdominal obesity(p<0.05), while it showed a positive correlation with the General Self Efficacy Scale(GSES)(p<0.001) and nutrient intake(p<0.05). When changes in these factors were compared according to the range of quartile of the Fullerton Advanced Balance Scale(FAB Scale), GSES(Q1=35.3, Q2=43.5, Q3=53.2, Q4=51.9, p<0.001), BMI(Q1=36.1%, Q2=34.7%, Q3=33.2%, Q4=28.6%, p<0.01), abdominal obesity(Q1=1.02, Q2=0.99, Q3=0.97, Q4=0.94, p<0.001) and nutrient intake(Q1=71.1%, Q2=75.4%, Q3=80.6%, Q4=80.2%, p<0.05) differed significantly. Taken together, these results suggested that better physical fitness would lead to a reduction in negative factors including physical disability and obesity indices, but to an increase in positive factors such as GSES and nutrient intake. The results of this study are expected to be used as basic data for the development of programs to promote the health of the elderly in a local society.

• Childhood Kidney Diseases
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• v.16 no.1
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• pp.46-50
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• 2012

C1q nephropathy is a distinct clinicopathologic entity, characterized by mesangial immunoglobulin and complement deposits, predominantly C1q, with no evidence for systemic lupus erythematosus. Clinically it may present as nephrotic syndrome and non-nephrotic proteinuria per se or associated with microscopic hematuria, gross hematuria, hypertension, or renal insufficiency. So far there is only one report about a familial case of C1q nephropathy (in two sisters). We present two cases of familial C1q nephropathy with nephrotic syndrome which was steroid resistant, but partially remitted with cyclosporine.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.39-46
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• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1303-1314
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• 2011

We consider meromorphic solutions of q-difference equations of the form $$\sum_{j=o}^{n}a_j(z)f(q^jz)=a_{n+1}(z),$$ where $a_0(z)$, ${\ldots}$, $a_{n+1}(z)$ are meromorphic functions, $a_0(z)a_n(z)$ ≢ 0 and $q{\in}\mathbb{C}$ such that 0 < |q| ${\leq}$ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0 < |q| < 1 and n = 2. Some growth estimates for meromorphic solutions are also given in the cases 0 < |q| < 1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q| = 1.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.1
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• pp.21-32
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• 2002

In this paper, for any prime q, new cyclic difference sets with Singer parameter equation omitted are constructed by using the q-ary sequences (d-homogeneous functions) of period $q_n$-1. When q is a power of 3, new cyclic difference sets with Singer parameter equation omitted are constructed from the ternary sequences of period $q_n$-1 with ideal autocorrealtion found by Helleseth, Kumar and Martinsen.

• Journal of the Korean Geophysical Society
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• v.5 no.3
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• pp.211-218
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• 2002

The reversed two station method (RSTM) devised by Chun et al. (1987) is widely used to obtain $Q_{Lg}^{-1}$ for Lg wave data with hypocentral distance greater than 90 km. By applying RSTM to the Lg data of central South Korea with hypocentral distance between 95 and 381 km, we obtained high $Q_{Lg}^{-1}$. The value of $Q_{Lg}^{-1}$ is very similar with that of southeastern S. Korea, which is derived from the same method for similar distances. The studied hypocentral range seems to distort $Q_{Lg}^{-1}$ to high value because decay rate in this range is higher than 0.5, which is typical decay rate of surface wave.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• v.26 no.3
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• pp.245-253
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• 2000

The development and progression of oral cancer is associated with an accumulation of multiple genetic alterations through the multistep processes. Comparative genomic hybridization(CGH), newly developed cytogenetic and molecular biologic technique, has been widely accepted as a useful method to allow the detection of genetic imbalance in solid tumors and the screening for chromosome sites frequently affected by gains or losses in DNA copy number. The authors examined 19 primary oral squamous cell carcinomas using CGH to identify altered chromosome regions that might contain novel oncogenes and tumor suppressor genes. Interrelationship between these genetic aberrations detected and major oncogenes and tumor suppressor genes previously recognized in carcinogenesis of oral cancers was studied. 1. Changes in DNA copy number were detected in 14 of 19 oral cancers (78.9%, mean: 5.58, range: $3{\sim}13$). High level amplification was present in 4 cases at 9p23, $12p21.1{\sim}q13.1$, 3q and $8q24{\sim}24.3$. Fourteen cases(78.9%, mean: 3.00, range: $1{\sim}8$) showed gains of DNA copy number and 12 cases(70.5%, mean: 2.58, range: $1{\sim}9$) revealed losses of DNA copy number. 2. The most common gains were detected on 3q(52.6%), 5p(21.0%), 8q(21.0%), 9p(21.0%), and 11q(21.0%). The losses of DNA copy number were frequently occurred at 9p(36.8%), 17q(36.8%), 13q(26.3%), 4p(21.0%) and 9p(21.0%). 3. The minimal common regions of gains were repeatedly observed at $3q24{\sim}26.7$, $3q27{\sim}29$, $1q22{\sim}31$, $5p12{\sim}13.3$, $8q23{\sim}24$, and 11q13.1-13.3. The minimal common regions of losses were detected at $9q11{\sim}21.3$, 17p31, $13q22{\sim}34$, and 14p16. 4. In comparison of CGH results with tumor stages, the lower stage group showed more frequent gain at 3q, 5q, 9p, and 14q, whereas gains at 1q($1q22{\sim}31$) and 11q($11q13.1{\sim}13.3$) were mainly detected in higher stage group. The loss at $13q22{\sim}34$ was exclusively detected in higher stage. The results indicate that the most frequent genetic alterations in the development of oral cancers were gains at $3q24{\sim}26.3$, $1q22{\sim}31$, and $5p12{\sim}13.3$ and losses at $9q11{\sim}21.3$, 17p31, and 13q. It is suggested that genetic alterations manifested as gains at $3q24{\sim}26.3$, $3q27{\sim}29$, $5p12{\sim}13.3$ and 5p are associated with the early progression of oral cancer. Gains at $1q22{\sim}31$ and $11q13.1{\sim}13.3$ and loss at 13q22-34 could be involved in the late progression of oral cancers.