• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1531-1548
• /
• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• Kyungpook Mathematical Journal
• /
• v.62 no.3
• /
• pp.437-453
• /
• 2022

Unlike for polynomial rings, the notion of multiplication for the near-ring of polynomials is the substitution operation. This leads to somewhat surprising results. Let S be an abelian left near-ring with identity. The relation ~ on S defined by letting a ~ b if and only if ann_S(a) = ann_S(b), is an equivalence relation. The compressed zero-divisor graph 𝚪_E(S) of S is the undirected graph whose vertices are the equivalence classes induced by ~ on S other than [0]_S and [1]_S, in which two distinct vertices [a]_S and [b]_S are adjacent if and only if ab = 0 or ba = 0. In this paper, we are interested in studying the compressed zero-divisor graphs of the zero-symmetric near-ring of polynomials R₀[x] and the near-ring of the power series R₀[[x]] over a commutative ring R. Also, we give a complete characterization of the diameter of these two graphs. It is natural to try to find the relationship between diam(𝚪_E(R₀[x])) and diam(𝚪_E(R₀[[x]])). As a corollary, it is shown that for a reduced ring R, diam(𝚪_E(R)) ≤ diam(𝚪_E(R₀[x])) ≤ diam(𝚪_E(R₀[[x]])).

• International Journal of Stem Cells
• /
• v.16 no.2
• /
• pp.202-214
• /
• 2023

Background and Objectives: To investigate the role of exosomes from periodontal ligament cells (PDLCs) in bone marrow mesenchymal stem cell (BMSC) migration. Methods and Results: Human PDLCs were applied cyclic tension stretching. Exosomes were extracted from cultured PDLCs by ultracentrifugation, then characterized for their size, morphology and protein markers by NTA, TEM and western blotting. The process that PKH26-labeled exosomes taken up by BMSCs was assessed by confocal microscope. BMSC migration was examined by Transwell assay. Exosomes derived from PDLCs were identified. Cyclic tension stretch application on PDLCs can enhance the migration ability of BMSCs through exosomes. The exosomal miRNA expression profiles of unstretched and stretched PDLCs were tested by miRNA microarray. Four miRNAs (miR-4633-5p, miR-30c-5p, miR-371a-3p and let-7b-3p) were upregulated and six (miR-4689, miR-8485, miR-4655-3p, miR-4672, miR-3180-5p and miR-4476) were downregulated in the exosomes after stretching. Sixteen hub proteins were found in the miRNA-mRNA network. Gene Ontology and KEGG pathway analyses demonstrated that the target genes of differentially expressed exosomal miRNAs closely related to the PI3K pathway and vesicle transmission. Conclusions: The exosomes derived from cyclic tension-stretched PDLCs can promote the migration of BMSCs. Alternation of microRNA profiles provides a basis for further research on the regulatory function of the exosomal miRNAs of PDLCs during orthodontic tooth movement.

• Journal of applied mathematics & informatics
• /
• v.30 no.3_4
• /
• pp.623-633
• /
• 2012

Let {${\Omega}$, $\mathcal{F}$, P} be a probability space and {$X_n|n{\geq}1$} be a sequence of random variables defined on it. A finite sequence of random variables {$X_n|n{\geq}1$} is said to be conditionally negatively associated given $\mathcal{F}$ if for every pair of disjoint subsets A and B of {1, 2, ${\cdots}$, n}, $Cov^{\mathcal{F}}(f_1(X_i,i{\in}A),\;f_2(X_j,j{\in}B)){\leq}0$ a.s. whenever $f_1$ and $f_2$ are coordinatewise nondecreasing functions. We extend the H$\grave{a}$jek-R$\grave{e}$nyi-type inequality from negative association to conditional negative association of random variables. In addition, some corollaries are given.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.2165-2182
• /
• 2017

Let G be a group and $\mathbb{C}$ the field of complex numbers. Suppose ${\sigma}:G{\rightarrow}G$ is an endomorphism satisfying ${{\sigma}}({{\sigma}}(x))=x$ for all x in G. In this paper, we first determine the central solution, f : G or $G{\times}G{\rightarrow}\mathbb{C}$, of the functional equation $f(xy)+f({\sigma}(y)x)=2f(x)+2f(y)$ for all $x,y{\in}G$, which is a variant of the quadratic functional equation. Using the central solution of this functional equation, we determine the general solution of the functional equation f(pr, qs) + f(sp, rq) = 2f(p, q) + 2f(r, s) for all $p,q,r,s{\in}G$, which is a variant of the equation f(pr, qs) + f(ps, qr) = 2f(p, q) + 2f(r, s) studied by Chung, Kannappan, Ng and Sahoo in [3] (see also [16]). Finally, we determine the solutions of this equation on the free groups generated by one element, the cyclic groups of order m, the symmetric groups of order m, and the dihedral groups of order 2m for $m{\geq}2$.

• Communications for Statistical Applications and Methods
• /
• v.17 no.4
• /
• pp.507-513
• /
• 2010

Let {$X_i,-{\infty}$ < 1 < $\infty$} be a doubly infinite sequence of identically distributed and negatively associated random variables with mean zero and finite variance and {$a_i,\;-{\infty}$ < i < ${\infty}$} be an absolutely summable sequence of real numbers. Define a moving average process as $Y_n={\sum}_{i=-\infty}^{\infty}a_{i+n}X_i$, n $\geq$ 1 and $S_n=Y_1+{\cdots}+Y_n$. In this paper we prove that E|$X_1$|$^rh$($|X_1|^p$) < $\infty$ implies ${\sum}_{n=1}^{\infty}n^{r/p-2-q/p}h(n)E{max_{1{\leq}k{\leq}n}|S_k|-{\epsilon}n^{1/p}}{_+^q}<{\infty}$ and ${\sum}_{n=1}^{\infty}n^{r/p-2}h(n)E{sup_{k{\leq}n}|k^{-1/p}S_k|-{\epsilon}}{_+^q}<{\infty}$ for all ${\epsilon}$ > 0 and all q > 0, where h(x) > 0 (x > 0) is a slowly varying function, 1 ${\leq}$ p < 2 and r > 1 + p/2.

• Journal of Information Technology Applications and Management
• /
• v.17 no.3
• /
• pp.121-134
• /
• 2010

Past studies in e-commerce loyalty were mostly focused on the effects of customer satisfaction and trust on loyalty toward online vendors. Few studies investigated the impacts of switching barriers, whilst they are widely proven to affect customer loyalty in offline commerce. Even in a handful of studies that did deal with switching barriers, their treatment of the subject remained at best superficial. This may have to do with the fact that switching costs in e-commerce could be comparatively negligible, as switching to another online vendor often involves one simple mouse click. In this study, we investigated the impact of switching barriers on loyalty under the e-commerce context. Furthermore, the extent of switching barriers which could be affected by those positive factors (most constructs were adopted from IDT) was also examined. The statistical testing results revealed that combined model which includes both the positive factors and the switching barriers explains the loyalty formation process more strongly ($R^2$ = 0.543) than each separated models ($R^2$ = 0.468 for positive factor only model, and $R^2$ = 0.365 for switching barrier only model). While only the two switching barriers such as convenience and emotional were shown to be statistically significant, we found that trust strongly influences customer's emotional barrier, let alone direct impact on loyalty, which thereby influences loyalty. The results offer insights for better understanding switching barriers in e-commerce related applications.

• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.641-648
• /
• 1994

Let M be a minimally immersed closed hypersurface in $S^{n+1}$, II the second fundamental form and $S = \Vert II \Vert^2$. It is well known that if $0 \leq S \leq n$, then $S \equiv 0$ or $S \equiv n$ and totally geodesic hypersheres and Clifford tori are the only possible minimal hypersurfaces with $S \equiv 0$ or $S \equiv n$ ([6], [2]). From these results, Chern suggested some questions on the study of compact minimal hypersurfaces on the sphere with S =constant: what are the next possible values of S to n, and does in the ambient sphere\ulcorner By the way, S is defined extrinsically but, in fact, it is an intrinsic invariant for the minimal hypersurface, i.e., S = n(n-1) - R, where R is the scalar, curvature of M. Some partial answers have been obtained for dim M = 3: Assuming $M^3 \subset S^4$ is closed and minimal with S =constant, de Almeida and Brito [1] proved that if $R \geq 0$ (or equivalently $S \leq 6$), then S = 0, 3 or 6, Peng and Terng ([5]) proved that if M has 3 distint principal curvatures, then S = 6, and in [3] Chang showed that if there exists a point which has two distinct principal curvatures, then S = 3. Hence the problem for dim M = 3 is completely done. For higher dimensional cases, not much has been known and these problems seem to be very hard without imposing some more conditions on M.

• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.687-700
• /
• 1994

Throughout this paper we will let H denote the complete Heyting algebra ($H, \vee, \wedge, *$) with order reversing involution *. 0 and 1 denote the supermum and the infimum of $\emptyset$, respectively. Given any set X, any element of $H^X$ is called H-fuzzy set (or, simply f.set) in X and will be denoted by small Greek letters, such as $\mu, \nu, \rho, \sigma$. $H^X$ inherits a structure of H with order reversing involution in natural way, by definding $\vee, \wedge, *$ pointwise (sam notations of H are usual). If $f$ is a map from a set X to a set Y and $\mu \in H^Y$, then $f^{-1}(\mu)$ is the f.set in X defined by f^{-1}(\mu)(x) = \mu(f(x))$. Also for $\sigma \in H^X, f(\sigma)$ is the f.set in Y defined by $f(\sigma)(y) = sup{\sigma(x) : f(x) = y}$ ([4]). A preorder R on a set X is reflexive and transitive relation on X, the pair (X,R) is called preordered set. A map $f$ from a preordered set (X, R) to another one (Y,T) is said to be preorder preserving (inverting) if for $x,y \in X, xRy$ implies $f(x)T f(y) (resp. f(y)Tf(x))$. For the terminology and notation, we refer to [10, 11, 13] for category theory and [7] for H-fuzzy semitopogenous spaces.

• Journal of the Korean Mathematical Society
• /
• v.54 no.5
• /
• pp.1379-1410
• /
• 2017

Kang and Ko introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4. Let $R=k[w_0,\;w_1,\;w_2,\;{\ldots},\;w_m]$ be the polynomial ring over an algebraically closed field k with indetermiantes $w_l$ and deg $w_l=1$, and $I_i$ a homogeneous perfect ideal of grade 3 with type $t_i$ defined by a skew-symmetrizable matrix $G_i(1{\leq}t_i{\leq}4)$. We show that for m = 2 the Hilbert function of the zero dimensional standard k-algebra $R/I_i$ is determined by CI-sequences and a Gorenstein sequence. As an application of this result we show that for i = 1, 2, 3 and for m = 3 a Gorenstein sequence $h(R/H_i)=(1,\;4,\;h_2,\;{\ldots},\;h_s)$ is unimodal, where $H_i$ is the sum of homogeneous perfect ideals $I_i$ and $J_i$ which are geometrically linked by a homogeneous regular sequence z in $I_i{\cap}J_i$.