• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.427-438
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• 2005

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.433-442
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• 2022

Let N^(q) be an arithmetic table of a negative exponent polynomial with q-commuting variables. We study sequential properties of diagonal sums of N^(q). We first device a q-coefficient table $\hat{N}$ of N^(q), find sequences of diagonal sums over $\hat{N}$, and then retrieve the findings of $\hat{N}$ to N^(q). We also explore recurrence rules of s-slope diagonal sums of N^(q) with various s and q.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.75-80
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• 2024

In this paper, we study some dynamics of the uniform limits of sequences in dynamical systems on a noncompact metric space. We show that if a sequence of homeomorphisms on a noncompact metric space has the uniform ergodic shadowing property, then the uniform limit also has the ergodic shadowing property. Then we apply this result to nonwandering maps.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.97-102
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the Pareto distribution. Let ｛$X_n,n\qeq1$｝be a sequence of independent and identically distributed random variables with a common continuous distribution function(cdf) F($chi$) and probability density function(pdf) f($chi$). Let $Y_n\;=\;mas{X_1,X_2,...,X_n}$ for $ngeq1$. We say $X_{j}$ is an upper record value of {$X_{n},n\geq1$}, if $Y_{j}$＞$Y_{j-1}$,j＞1. The indices at which the upper record values occur are given by the record times ${u( n)}n,\geq1$, where u(n) = min{j｜j ＞u(n-l), $X_{j}$＞$X_{u(n-1)}$,n\qeq2$ and u(l) = 1. Suppose $X{\epsilon}PAR(\frac{1}{\beta},\frac{1}{\beta}$ then E$(\frac{{X^\tau}}_{u(m)}}{{X^{s+1}}_{u(n)})\;=\;\frac{1}{s}E$ E$(\frac{{X^\tau}}_{u(m)}{{X^s}_{u(n-1)}})$ - $\frac{(1+\betas)}{s}E(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}}$ and E$(\frac{{X^{\tau+1}}_{u(m)}}{{X^s}_{u(n)}})$ = $\frac{1}{(r+1)\beta}$ [E$(\frac{{X^{\tau+1}}}_u(m)}{{X^s}_{u(n-1)}})$ - E$(\frac{{X^{\tau+1}}_u(m)}}{{X^s}_{u(n-1)}})$ - (r+1)E$(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}})$]

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.15-22
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the power distribution. Let {$X_n$, $n{\geq}1$} be a sequence of independent an identically distributed random variables with a common continuous distribution function(cdf) $F(x)$ and probability density function(pdf) $f(x)$. Let $Y_n=max\{X_1,X_2,{\cdots},X_n\}$ for $n{\geq}1$. We say $X_j$ is an upper record value of {$X_n$, $n{\geq}1$}, if $Y_j$ > $Y_{j-1}$, $j$ > 1. The indices at which the upper record values occur are given by the record times {$u(n)$}, $n{\geq}1$, where $u(n)=min\{j{\mid}j>u(n-1),X_j>X_{u(n-1)},n{\geq}2\}$ and $u(1)=1$. Suppose $X{\in}POW(0,1,{\theta})$ then $$E\left(\frac{X^r_{u(m)}}{X^{s+1}_{u(n)}}\right)=\frac{\theta}{s}E\left(\frac{X^r_{u(m)}}{X^s_{u(n-1)}}\right)+\frac{(s-\theta)}{s}E\left(\frac{X^r_{u(m)}}{X^s_{u(n)}\right)\;and\;E\left(\frac{X^{r+1}_{u(m)}}{X^s_{u(n)}}\right)=\frac{\theta}{n+1}\left[E\left(\frac{X^{r+1}_{u(m-1)}}{X^s_{u(n+1)}}\right)-E\left(\frac{X^{r+1}_{u(m)}}{X^s_{u(n-1)}}\right)+\frac{r+1}{\theta}E\left(\frac{X^r_{u(m)}}{X^s_{u(n)}}\right)\right]$$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.983-991
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• 2013

For each real number $n$ > 6, we prove that there is a sequence $\{pk(n,z)\}^{\infty}_{k=1}$ of fourth degree self-reciprocal polynomials such that the zeros of $p_k(n,z)$ are all simple and real, and every $p_{k+1}(n,z)$ has the largest (in modulus) zero ${\alpha}{\beta}$ where ${\alpha}$ and ${\beta}$ are the first and the second largest (in modulus) zeros of $p_k(n,z)$, respectively. One such sequence is given by $p_k(n,z)$ so that $$p_k(n,z)=z^4-q_{k-1}(n)z^3+(q_k(n)+2)z^2-q_{k-1}(n)z+1$$, where $q_0(n)=1$ and other $q_k(n)^{\prime}s$ are polynomials in n defined by the severely nonlinear recurrence $$4q_{2m-1}(n)=q^2_{2m-2}(n)-(4n+1)\prod_{j=0}^{m-2}\;q^2_{2j}(n),\\4q_{2m}(n)=q^2_{2m-1}(n)-(n-2)(n-6)\prod_{j=0}^{m-2}\;q^2_{2j+1}(n)$$ for $m{\geq}1$, with the usual empty product conventions, i.e., ${\prod}_{j=0}^{-1}\;b_j=1$.

• BMB Reports
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• v.40 no.2
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• pp.135-141
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• 2007

Conjugation of the methyl group at the fifth carbon of cytosines within the palindromic dinucleotide 5'-CpG-3' sequence (DNA methylation) is the best studied epigenetic mechanism, which acts together with other epigenetic entities: histone modification, chromatin remodeling and microRNAs to shape the chromatin structure of DNA according to its functional state. The cancer genome is frequently characterized by hypermethylation of specific genes concurrently with an overall decrease in the level of 5-methyl cytosine, the pathological implication of which to the cancerous state has been well established. While the latest genome-wide technologies have been applied to classify and interpret the epigenetic layer of gene regulation in the physiological and disease states, the epigenetic testing has also been seriously explored in clinical practice for early detection, refining tumor staging and predicting disease recurrence. This critique reviews the latest research findings on the use of DNA methylation in cancer diagnosis, prognosis and staging/classification.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.9
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• pp.727-735
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• 2003

The determination of completion time constitutes an important step in developing algorithms for short-term production scheduling. Existing completion time algorithms of multi-product batch processes often assume that intermediate storage tanks are always available when it is needed. In this paper, we consider a serial multi-product batch plants with ZW and NIS policy intermediate storge tank. We limit storage residence time and allocated products in the intermediate storage tank to minimize the quality change of the stored material as well as to reduce the clearing time during product change. A set of recurrence relations is suggested to calculate the completion times for the given batch sequence of products on all processing units. Also analytic solution for the suggested model is solved by a graphical method. The effectiveness of these results is proved by a few illustrative examples.

• Journal of Chest Surgery
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• v.32 no.11
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• pp.1036-1041
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• 1999

Background: To know the clinical aspects of varicose vein and the effectiveness of operative treatment, the patients who had been operated during the five and a half years were reviewed. Material and Method: From September 1993 to February 1999, 227 patients with varicose vein were operated upon. These patients were reviewed with history taking, physical examination, laboratory tests, operation and follow up visits at an out patient department. Result: The ages of the patients were from 20 to 69 years, mean 40.2 years. varicose veins. Occupations of the patients include housewives, store or factory owners, cooks, waiter or waitresses in a restaurant, salary men(women), teachers, hair stylists, professional athletes, in sequence, most of them require standing all day long. The 126 women had experienced child birth, among them 116 patients delivered more than 2 babies. All patients had protruding leg veins as the symptom. Most of them(61%) had pain. Other additional symptoms were heaviness, heatness, tingling, cramp, fatigue, etc. 68.3% of the patients had the symptoms for more than 10 years. Anatomical location of varicose vein was in long saphenous vein in 157 patients, in small saphenous vein in 27, and in other regions(combined or perforating vein) in 43 patients. There was no operative mortality. There were 2 patients who underwent reoperation due to recurrence during this study period. In one patient, it recurred in the distal perforating vein in small saphenous vein. The other patient had recurrence at the saphenofemoral junction in groin. The patients are doing well after the reoperation, but a long term observation is needed. Conclusion: Clinical aspects of varicose vein were reviewed. For the patients with varicose vein who had saphenofemoral regurgitation, operative treatment seemed to bea safe and effective modality of treatment.

• The Journal of the Acoustical Society of Korea
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• v.35 no.1
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• pp.42-48
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• 2016

Since a variety of sound occur in same place and similar sound occurs in other places, the performance of acoustic scene classification is not guaranteed in case of insufficient training data. A Bag of Words (BOW) based histogram feature is foreseen as a method to overcome the problem. However, since the histogram features is made by using a feature distribution, the ordering of sequence of features is ignored. A temporal information such as periodicity and stationarity are also important for acoustic scene classification. In this paper, temporal features about a periodicity and a stationarity are extracted by using a recurrent quantification analysis. In the experiment, performance of the proposed method is shown better than other baseline methods.