• Bulletin of the Korean Chemical Society
• /
• v.34 no.5
• /
• pp.1503-1507
• /
• 2013

The two major symptoms characterizing Alzheimer's disease are the formation of amyloid-${\beta}$ extracellular deposits in the form of senile plaques and intracellular neurofibrillary tangles (NFTs) that consist of pathological hyperphosphorylated tau protein aggregated into insoluble paired helical filaments (PHFs). Neurons of the central nervous system have appreciable amounts of tau protein, a microtubule-associated protein. To maintain an optimal operation of nerves, the microtubules are stabilized, which is necessary to support cell structure and cellular processes. When the modified tau protein becomes dysfunctional, the cells containing misfolded tau cannot maintain cell structure. One of the pathological hallmarks of Alzheimer's disease is hyperphosphorylated tau protein. This paper shows that the small heat shock protein from humans (Hsp27) reduces hyperphosphorylated tau and prevents hyperphosphorylated tau-induced cell death of the human neuroblastoma cell line SH-SY5Y.

• Communications of the Korean Mathematical Society
• /
• v.25 no.3
• /
• pp.457-475
• /
• 2010

In this paper, we have use a fuzzy bitopological space (X, $\tau_1$, $\tau_2$) to create a family $\tau_{ij}^s$ which is a supra fuzzy topology on X. Also, we introduce and study the concepts of r-($\tau_i$, $\tau_j$)-generalized fuzzy regular closed, r-($\tau_i$, $\tau_j$)-generalized fuzzy strongly semi-closed and r-($\tau_i$, $\tau_j$)-generalized fuzzy regular strongly semi-closed sets in fuzzy bitopological space in the sense of $\check{S}$ostak. Also, these classes of fuzzy subsets are applied for constructing several type of fuzzy closed mapping and some type of fuzzy separation axioms called fuzzy binormal, fuzzy mildly binormal and fuzzy almost pairwise normal.

• Journal of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.363-379
• /
• 2016

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] and the second Appell function [Appl. Math. Comput. 219 (2013), 8332-8337] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we introduce here the family of the incomplete generalized ${\tau}$-hypergeometric functions $2{\gamma}_1^{\tau}(z)$ and $2{\Gamma}_1^{\tau}(z)$. The main object of this paper is to study these extensions and investigate their several properties including, for example, their integral representations, derivative formulas, Euler-Beta transform and associated with certain fractional calculus operators. Further, we introduce and investigate the family of incomplete second ${\tau}$-Appell hypergeometric functions ${\Gamma}_2^{{\tau}_1,{\tau}_2}$ and ${\gamma}_2^{{\tau}_1,{\tau}_2}$ of two variables. Relevant connections of certain special cases of the main results presented here with some known identities are also pointed out.

• Bulletin of the Korean Mathematical Society
• /
• v.23 no.2
• /
• pp.91-102
• /
• 1986

A topological space (X,.tau.) is called invertible [7] if for each proper open set U in (X,.tau.) there exists a homoemorphsim h:(X,.tau.).rarw.(X,.tau.) such that h(X-U).contnd.U. Doyle and Hocking [7] and Levine [13], as well as others have investigated properties of invertible spaces. Recently, Crosseley and Hildebrand [5] have introduced the concept of semi-invertibility, which is weaker than that of invertibility, by replacing "homemorphism" in the definition of invertibility with "semihomemorphism", A space (X,.tau.) is said to be semi-invertible if for each proper semi-open set U in (X,.tau.) there exists a semihomemorphism h:(X,.tau.).rarw.(X,.tau.) such that h(X-U).contnd.U. The purpose of the present article is to introduce the class of almost-invertible spaces containing the class of semi-invertible spaces and to investigate its properties. One of the primary concerns will be to determine when a given local property in an almost-invertible space is also a global property. We point out that many of the results obtained can be applied in the cases of semi-invertible spaces and invertible spaces. For example, it is shown that if an invertible space (X,.tau.) has a nonempty open subset U which is, as a subspace, H-closed (resp. lightly compact, pseudocompact, S-closed, Urysohn, Urysohn-closed, extremally disconnected), then so is (X,.tau.).hen so is (X,.tau.).

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.39-49
• /
• 2004

Let G be a simple graph and let $\={G}$ denotes its complement. We say that G is integral if its spectrum consists entirely of integers. If $\overline{aK_{a}\;{\bigcup}\;{\beta}K_{b}}$ is integral we show that it belongs to the class of integral graphs $[\frac{kt}{\tau}\;{x_0}\;+\;\frac{mt}{\tau}\;z}\;K_{(t+{\ell}n)+{\ell}m}\;\bigcup\;[\frac{kt}{\tau}\;{y_0}\;+\;\frac{(t\;+\;{\ell}n)k\;+\;{\ell}m}{\tau}\;z]n\;K_{em)$, where (i) t, k, $\ell$, m, $n\;\in\;\mathbb{N}$ such that (m, n) = 1, (n,t) = 1 and ($\ell,\;t$) = 1 ; (ii) $\tau\;=\;((t\;+\;{\ell}n)k\;+\;{\ell}m,\;mt)$ such that $\tau\;$\mid$kt$; (iii) ($x_0,\;y_0$) is a particular solution of the linear Diophantine equation $((t\;+\;{\ell}n)k\;+\;{\ell}m)x\;-\;(mt)y\;=\;\tau\;and\;(iv)\;z\;{\geq}\;{z_0}$ where $z_{0}$ is the least integer such that $(\frac{kt}{\tau}\;{x_0}\;+\;\frac{mt}{\tau}\;{z_0})\;\geq\;1\;and\;(\frac{kt}{\tau}\;{y_0}\;+\;\frac{(t+{\ell}n)k+{\ell}m}{\tau}\;{z_0})\;\geq\;1$.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.34 no.4
• /
• pp.1181-1190
• /
• 2014

In this study, the erosional parameters for deposit beds were quantitatively estimated domestically for the first time through the erosion tests using an annular flume. Four erosion tests were carried out for the deposit beds with different consolidation structures, which were obtained by consolidating the kaolinite slurries for a given time durations. Results of erosion tests showed that the bed shear strength ${\tau}_s$ increased with the consolidation time and bed depth. The erosion rate ${\epsilon}$ was also shown to be related well with the excess shear stress ${\tau}_b-{\tau}_s$ which was given by the difference between flow shear stress ${\tau}_b$ and bed shear strength ${\tau}_s$. While the logarithm of the erosion rate was linearly related with the excess shear stress as ${\tau}_b-{\tau}_s{\geq}0.1N/m^2$, however, the erosion rate decreased rapidly with it when ${\tau}_b-{\tau}_s{\leq}0.1N/m^2$. These erosion test results were also shown to be good enough to verify by comparing with the test results from previous studies and a new equation was suggested to describe the erosion rate more well in the region of ${\tau}_b-{\tau}_s{\leq}0.1N/m^2$.

• Journal of the Korean Mathematical Society
• /
• v.31 no.4
• /
• pp.633-643
• /
• 1994

Let us consider the initial-value problem of dimension m: $$ \frac{d\tau}{d}y(\tau) = f(\tau, Y(\tau)), y(0) = y_0, \tau \geq 0, (1.1) $$ Where $ = (f_1, f_2, \cdots, f_m) and y = (y_1, y_2, \cdots, y_m)$.

• BMB Reports
• /
• v.51 no.6
• /
• pp.265-273
• /
• 2018

Tau protein is encoded in the microtubule-associated protein tau (MAPT) gene and contributes to the stability of microtubules in axons. Despite of its basic isoelectric point and high solubility, tau is often found in intraneuronal filamentous inclusions such as paired helical filaments (PHFs), which are the primary constituent of neurofibrillary tangles (NFTs). This pathological feature is the nosological entity termed "tauopathies" which notably include Alzheimer's disease (AD). A proteinaceous signature of all tauopathies is hyperphosphorylation of the accumulated tau, which has been extensively studied as a major pharmacological target for AD therapy. However, in addition to phosphorylation events, tau undergoes a number of diverse posttranslational modifications (PTMs) which appear to be controlled by complex crosstalk. It remains to be elucidated which of the PTMs or their combinations have pro-aggregation or anti-aggregation properties. In this review, we outline the consequences of and communications between several key PTMs of tau, such as acetylation, phosphorylation, and ubiquitination, focusing on their roles in aggregation and degradation. We place emphasis on the structure of tau protofilaments from the human AD brain, which may be good targets to modulate etiological PTMs which cause tau aggregation.

• Journal of applied mathematics & informatics
• /
• v.9 no.2
• /
• pp.667-677
• /
• 2002

In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.725-736
• /
• 2009

We define a (${\tau}_i$, ${\tau}_j$)-fuzzy strongly preopen set on a fuzzy bitopological space and characterize a fuzzy pairwise strong precontinuous mapping and a fuzzy pairwise strong preopen mapping(a fuzzy pairwise strong preclosed mapping) on a fuzzy bitopological space.