EXISTENCE OF TRIPLE POSITIVE SOLUTIONS OF A KIND OF SECOND-ORDER FOUR-POINT BVP

Zhao, Junfang,Ge, Weigao The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.1

Existence of Triple Positive Solutions of a Kind of Second-order Four-point BVP

Junfang Zhao 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1

In this paper, we considered the following four-point boundary value problem x“(t) + h(t)f(t,x(t), x‘(t)) = 0, 0 < t < 1 x‘(0) = ax<기호>, x’(1) = bx(η), where 0 <<기호> <η < 1, <기호>= ab<기호>- abη+a−b > 0, 0 < a <<기호> , 0 <b <<기호> . After the discussion of the Green function of the corresponding homogeneous system, we establish some criteria for the existence of positive solutions by using the generalized Leggett-William’'s fixed point theorem. The interesting point is the expression of the Green function, which is a difficulty for multi-point BVP. In this paper, we considered the following four-point boundary value problem x“(t) + h(t)f(t,x(t), x‘(t)) = 0, 0 < t < 1 x‘(0) = ax<기호>, x’(1) = bx(η), where 0 <<기호> <η < 1, <기호>= ab<기호>- abη+a−b > 0, 0 < a <<기호> , 0 <b <<기호> . After the discussion of the Green function of the corresponding homogeneous system, we establish some criteria for the existence of positive solutions by using the generalized Leggett-William’'s fixed point theorem. The interesting point is the expression of the Green function, which is a difficulty for multi-point BVP.

MULTIPLE SYMMETRIC POSITIVE SOLUTIONS OF A NEW KIND STURM-LIOUVILLE-LIKE BOUNDARY VALUE PROBLEM WITH ONE DIMENSIONAL p-LAPLACIAN

Junfang Zhao,Weigao Ge 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5

In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, (∅p(x'(t)))' + h(t)f(t, x(t), |x'(t)|) = 0, 0 < t < 1, x'(0) −δx(η) = 0, x'(1) + δx(η) = 0, where ∅p(s) = |s|p−2s, p > 1, δ > 0, 1 > η > ξ > 0, ξ +η= 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interestingpoint is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now. In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, (∅p(x'(t)))' + h(t)f(t, x(t), |x'(t)|) = 0, 0 < t < 1, x'(0) −δx(η) = 0, x'(1) + δx(η) = 0, where ∅p(s) = |s|p−2s, p > 1, δ > 0, 1 > η > ξ > 0, ξ +η= 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interestingpoint is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.

MULTIPLE SYMMETRIC POSITIVE SOLUTIONS OF A NEW KIND STURM-LIOUVILLE-LIKE BOUNDARY VALUE PROBLEM WITH ONE DIMENSIONAL p-LAPLACIAN

Zhao, Junfang,Ge, Weigao The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5

In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, $\{({\phi}_p(x'(t)))'+h(t)f(t,x(t),|x'(t)|)=0$, 0< t<1, $x'(0)-{\delta}x(\xi)=0,\;x'(1)+{\delta}x(\eta)=0$, where $\phi_p$ (s) = |s|$^{p-2}$, p > $\delta$ > 0, 1 > $\eta$ > $\xi$ > 0, ${\xi}+{\eta}$ = 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interesting point is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.

Ultrathin Biocompatible Electrospun Fiber Films for Self-Powered Human Motion Sensor

Gengrui Zhao,Shaobo Gong,Honggang Wang,Junfang Ren,Na Wang,Yawen Yang,Gui Gao,Shengsheng Chen,Linlin Li 한국정밀공학회 2021 International Journal of Precision Engineering and Vol.8 No.3

In recent years, triboelectric nanogenerator (TENG) has been proven to be an effective and simple solution for self-powered wearable sensing, and a wide variety of materials and methods have been applied to TENG based sensors. In this study, an ultrathin fiber film with nanoporous brain-like structure (BUF) was obtained by cold-pressing the electrospun biocompatible fiber mats, and a wearable TENG sensor based on the BUF films that could sensitively detect human motion was demonstrated. This simply designed self-powered sensor was composed of Kapton as the shell and ultrathin, biocompatible poly L-lactic acid and ethyl cellulose (EC) fiber films as the triboelectric layers, prepared by convenient electrospinning method and cold-pressing. Compared to as-spun fiber mats, cold-pressed fiber membranes not only acquire overall compact structure but also remained porous surface morphology, which improved the triboelectric outputs and operational stability of TENG. Three TENGs were fabricated to evaluate the effects of different triboelectric layers on triboelectric outputs, and the BUF-TENG had the maximum triboelectric outputs (19 V, 630 nA at 3.5 Hz) and longer life than as-spun fiber mats based TENG. The BUF-TENG had linear relationship between triboelectric outputs and frequency, and sensitivities of 32.4, 0.94 and 0.22 V Hz−1 in the range of 0.1–0.35, 0.35–2 and 2–3.5 Hz, respectively. Moreover, a self-powered sensor based on the BUF-TENG was proposed to sensitively detect human walking state and limbs motion. With convenient preparation process and biocompatible materials, the BUF-TENG sensor could be a potential self-powered wearable and portable sensor in future health care and monitoring field.

POSITIVE SOLUTION FOR SYSTEMS OF NONLINEAR SINGULAR BOUNDARY VALUE PROBLEMS ON TIME SCALES

Chunmei Miao,Dehong Ji,Junfang Zhao,Weigao Ge,Jiani Zhang 한국수학교육학회 2009 純粹 및 應用數學 Vol.16 No.4

In this paper, we deal with the following system of nonlinear singular boundary value problems(BVPs) on time scale T [수식] where [수식] and [수식] may be singular at t = a, y = 0, and g(t, x) may be singular at t = a. The arguments are based upon a fixed-point theorem for mappings that are decreasing with respect to a cone. We also obtain the analogous existence results for the related nonlinear systems [수식], and [수식] satisfying similar boundary conditions.

Transcriptomic profiling reveals hepatic stem‐like gene signatures and interplay of miR‐200c and epithelial‐mesenchymal transition in intrahepatic cholangiocarcinoma

Oishi, Naoki,Kumar, Mia R.,Roessler, Stephanie,Ji, Junfang,Forgues, Marshonna,Budhu, Anuradha,Zhao, Xuelian,Andersen, Jesper B.,Ye, Qing‐,Hai,Jia, Hu‐,Liang,Qin, Lun‐,Xiu,Yamashita, Wiley Subscription Services, Inc., A Wiley Company 2012 Hepatology Vol.56 No.5

<P><B>Abstract</B></P><P>Intrahepatic cholangiocellular carcinoma (ICC) is the second most common type of primary liver cancer. However, its tumor heterogeneity and molecular characteristics are largely unknown. In this study, we conducted transcriptomic profiling of 23 ICC and combined hepatocellular cholangiocarcinoma tumor specimens from Asian patients using Affymetrix messenger RNA (mRNA) and NanoString microRNA microarrays to search for unique gene signatures linked to tumor subtypes and patient prognosis. We validated the signatures in an additional 68 ICC cases derived from Caucasian patients. We found that both mRNA and microRNA expression profiles could independently classify Asian ICC cases into two main subgroups, one of which shared gene expression signatures with previously identified hepatocellular carcinoma (HCC) with stem cell gene expression traits. ICC‐specific gene signatures could predict survival in Asian HCC cases and independently in Caucasian ICC cases. Integrative analyses of the ICC‐specific mRNA and microRNA expression profiles revealed that a common signaling pathway linking miR‐200c signaling to epithelial‐mesenchymal transition (EMT) was preferentially activated in ICC with stem cell gene expression traits. Inactivation of miR‐200c resulted in an induction of EMT, whereas activation of miR‐200c led to a reduction of EMT including a reduced cell migration and invasion in ICC cells. We also found that miR‐200c and neural cell adhesion molecule 1 (NCAM1) expression were negatively correlated and their expression levels were predictive of survival in ICC samples. NCAM1, a known hepatic stem/progenitor cell marker, was experimentally demonstrated to be a direct target of miR‐200c. Conclusion: Our results indicate that ICC and HCC share common stem‐like molecular characteristics and poor prognosis. We suggest that the specific components of EMT may be exploited as critical biomarkers and clinically relevant therapeutic targets for an aggressive form of stem cell‐like ICC. (H<SMALL>EPATOLOGY</SMALL> 2012;56:1792–1803)</P>