On the Hyers-Ulam-Rassias stability of Jensen's equation

Dongyan Zhang,Jian Wang 대한수학회 2009 대한수학회보 Vol.46 No.4

J. Wang [21] proposed a problem: whether the Hyers-Ulam- Rassias stability of Jensen’'s equation for the case p, q, r, s ∈(β,1/β)\{1} holds or not under the assumption that G and E are β-homogeneous F-space (0<β<1). The main purpose of this paper is to give an answer to Wang’'s problem. Furthermore, we proved that the stability property of Jensen’'s equation is not true as long as p or q is equal to β,1/β, or ¯β_(2)/β_(1) (0<β_(1),β_(2)≤1). J. Wang [21] proposed a problem: whether the Hyers-Ulam- Rassias stability of Jensen’'s equation for the case p, q, r, s ∈(β,1/β)\{1} holds or not under the assumption that G and E are β-homogeneous F-space (0<β<1). The main purpose of this paper is to give an answer to Wang’'s problem. Furthermore, we proved that the stability property of Jensen’'s equation is not true as long as p or q is equal to β,1/β, or ¯β_(2)/β_(1) (0<β_(1),β_(2)≤1).

DNA methylation and mRNA expression of COL6A3 in antler mesenchyme of female and male reindeer

Jian‑Cheng Zhai,Ruo‑Bing Han,Sheng‑Nan Wang,Qiang‑Hui Wang,Yan‑Ling Xia,Wei‑Shi Liu,Ya‑Jie Yin,He‑Ping Li 한국유전학회 2019 Genes & Genomics Vol.41 No.9

Backgroud Reindeer is the only deer species that both male and female produce antlers, which provides a particularly interesting case in studying the differences between antlers of the two sexes. Alpha 3(VI) Collagen Gene (COL6A3), forms a microfibrillar network associated with the structural integrity and biomechanical properties, has been found to be one of the differentially expressed genes in antler mesenchyme of female and male reindeer. Objective and Methods The promoter sequence of reindeer COL6A3 gene was obtained using the cloning technology and analyzed by the bioinformatics methods. Bisulfite sequencing PCR (BSP) was used to detect the methylation status of the COL6A3 promoter in reindeer antler mesenchyme. Real-time quantitative PCR was used to detect COL6A3 expression in the antler mesenchyme of female and male reindeer. Results Sequence analysis revealed that the reindeer COL6A3 partial promoter sequence was 983 bp including the possible promoter region at + 105 bp to + 155 bp. Homology and phylogenetic analysis indicated that the COL6A3 promoter of reindeer had the closest genetic distance with Bos taurus, Capra hircus and Ovis aries. BSP results indicated that the methylation level of COL6A3 promoter in the female reindeer antler mesenchyme was significantly higher than in the male. Correlating with increased methylation status, we also found that COL6A3 mRNA expression in female reindeer antler mesenchyme was significantly lower than in the male. Conclusion The higher methylation level of the COL6A3 gene in female reindeer antler mesenchyme coincides with decreased COL6A3 mRNA expression, thereby affecting the transposon silencing mechanism and possibly contributing to apparent differences of antlers in female and male reindeer.

ON THE HYERS-ULAM-RASSIAS STABILITY OF JENSEN'S EQUATION

Zhang, Dongyan,Wang, Jian Korean Mathematical Society 2009 대한수학회보 Vol.46 No.4

J. Wang [21] proposed a problem: whether the Hyers-Ulam-Rassias stability of Jensen's equation for the case p, q, r, s $\in$ ($\beta$, $\frac{1}{\beta}$) \ {1} holds or not under the assumption that G and E are $\beta$-homogeneous Fspace (0 < $\beta\;\leq$ 1). The main purpose of this paper is to give an answer to Wang's problem. Furthermore, we proved that the stability property of Jensen's equation is not true as long as p or q is equal to $\beta$, $\frac{1}{\beta}$, or $\frac{\beta_2}{\beta_1}$ (0 < $\beta_1,\beta_2\leq$ 1).

Path following of a surface ship sailing in restricted waters under wind effect using robust H_∞ guaranteed cost control

Wang, Jian-qin,Zou, Zao-jian,Wang, Tao The Society of Naval Architects of Korea 2019 International Journal of Naval Architecture and Oc Vol.11 No.1

The path following problem of a ship sailing in restricted waters under wind effect is investigated based on Robust $H_{\infty}$ Guaranteed Cost Control (RHGCC). To design the controller, the ship maneuvering motion is modeled as a linear uncertain system with norm-bounded time-varying parametric uncertainty. To counteract the bank and wind effects, the integral of path error is augmented to the original system. Based on the extended linear uncertain system, sufficient conditions for existence of the RHGCC are given. To obtain an optimal robust $H_{\infty}$ guaranteed cost control law, a convex optimization problem with Linear Matrix Inequality (LMI) constraints is formulated, which minimizes the guaranteed cost of the close-loop system and mitigates the effect of external disturbance on the performance output. Numerical simulations have confirmed the effectiveness and robustness of the proposed control strategy for the path following goal of a ship sailing in restricted waters under wind effect.

GEOMETRIC QUANTIZATION OF ODD DIMENSIONAL SPIN^c MANIFOLDS

Wang, Jian,Wang, Yong Korean Mathematical Society 2012 대한수학회보 Vol.49 No.2

We prove a Guillemin-Sternberg geometric quantization formula for circle action on odd dimensional $spin^c$-manifolds. We prove two Kostant type formulas in this case. As a corollary, we get a cutting formula for the odd spinc quantization.

Prognostic Value of MGMT Promoter Methylation and TP53 Mutation in Glioblastomas Depends on IDH1 Mutation

Wang, Kai,Wang, Yin-Yan,Ma, Jun,Wang, Jiang-Fei,Li, Shao-Wu,Jiang, Tao,Dai, Jian-Ping Asian Pacific Journal of Cancer Prevention 2014 Asian Pacific journal of cancer prevention Vol.15 No.24

Several molecular markers have been proposed as predictors of outcome in patients with glioblastomas. We investigated the prognostic significance of $O^6$-methylguanine-DNA methyltransferase (MGMT) promoter methylation and TP53 mutation status dependent on isocitrate dehydrogenase 1 (IDH1) mutation in glioblastoma patients. A cohort of 78 patients with histologically confirmed glioblastomas treated with radiation therapy and chemotherapy were reviewed retrospectively. We evaluated the prognostic value of MGMT promoter methylation and TP53 mutation status with regard to progression-free survival (PFS) and overall survival (OS). It was revealed that mutations in IDH1, promoter methylation of MGMT, TP53 mutation, age, Karnofsky performance status (KFS), and extension of resection were independent prognostic factors. In patients with an IDH1 mutation, those with an MGMT methylation were associated with longer PFS (p=0.016) and OS (p=0.013). Nevertheless, the presence of TP53 mutation could stratify the PFS and OS of patients with IDH1 wild type (p=0.003 and 0.029 respectively, log-rank). The MGMT promoter methylation and TP53 mutation were associated with a favorable outcome of patients with and without mutant IDH1, respectively. The results indicate that glioblastomas with MGMT methylation or TP53 mutations have improved survival that may be influenced by IDH1 mutation status.

GEOMETRIC QUANTIZATION OF ODD DIMENSIONAL SPINc MANIFOLDS

Jian Wang,Yong Wang 대한수학회 2012 대한수학회보 Vol.49 No.2

We prove a Guillemin-Sternberg geometric quantization formula for circle action on odd dimensional $spin^c$-manifolds. We prove two Kostant type formulas in this case. As a corollary, we get a cutting formula for the odd spinc quantization.

Analytical behavior of built-up square concrete-filled steel tubular columns under combined preload and axial compression

Jian-Tao Wang,Fa-Cheng Wang 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.38 No.6

This paper numerically investigated the behavior of built-up square concrete-filled steel tubular (CFST) columns under combined preload and axial compression. The finite element (FE) models of target columns were verified in terms of failure mode, axial load-deformation curve and ultimate strength. A full-range analysis on the axial load-deformation response as well as the interaction behavior was conducted to reveal the composite mechanism. The parametric study was performed to investigate the influences of material strengths and geometric sizes. Subsequently, influence of construction preload on the full-range behavior and confinement effect was investigated. Numerical results indicate that the axial load-deformation curve can be divided into four working stages where the contact pressure of curling rib arc gradually disappears as the steel tube buckles; increasing width-to-thickness (B/t) ratio can enhance the strength enhancement index (e.g., an increment of 1.88% from B/t=40 to B/t=100), though ultimate strength and ductility are decreased; stiffener length and lip inclination angle display a slight influence on strength enhancement index and ductility; construction preload can degrade the plastic deformation capacity and postpone the origin appearance of contact pressure, thus making a decrease of 14.81%~27.23% in ductility. Finally, a revised equation for determining strain εscy corresponding to ultimate strength was proposed to evaluate the plastic deformation capacity of built-up square CFST columns.

An Effective Guidewire Looping Technique for the Recanalization of Occlusive Segments of Infrapopliteal Vessels

Jian-bo Wang,Jun-gong Zhao,Ming-hua Li,Yue-qi Zhu,Jue Wang,Pei-lei Zhang 대한영상의학회 2010 Korean Journal of Radiology Vol.11 No.4

Objective: To determine the efficacy, safety and primary follow-up results of a guidewire looping technique for the treatment of infrapopliteal arteries. Materials and Methods: From October 2006 to May 2008, an intraluminal angioplasty of the infrapopliteal arteries was attempted in 200 consecutive patients. Altogether, 417 infrapopliteal lesions, with lengths varying from 2 cm to 32 cm, were treated as part of this study, including 305 lesions in the anterior tibial arteries, 89 in the posterior tibial arteries, and 23 in the peroneal arteries. The ‘U’-shaped guidewire technique was attempted in 393 lesions from 361 limbs. The tip of a hydrophilic 0.035-inch guidewire was formed into a ‘U’ shape with the aid of a 4-Fr catheter and collateral branch vessel to recanalize the completely occluded long segment lesions. Results: A successful angioplasty with at least one artery recanalized directly to the malleolar or dorsal foot was achieved in 322 limbs (89%). The looping technique had a success rate of 90% (352 of 393 lesions). After the procedure, the rest pain was relieved in 58 of 69 patients, while 207 of 245 limbs (85%) showed improvement for intermittent claudication. Complete wound healing was noted in 21 of 54 patients, while 20 of 54 patients showed an improvement in the wound size or depth. A total of 38 major immediate procedure-related complications were noted, including retroperitoneal hematoma, distal emboli, and vessel rupture. Conclusion: The results of this study suggests that the guidewire looping technique is a safe and effective method for the recanalization of the occluded lesions in infrapopliteal vessels. Objective: To determine the efficacy, safety and primary follow-up results of a guidewire looping technique for the treatment of infrapopliteal arteries. Materials and Methods: From October 2006 to May 2008, an intraluminal angioplasty of the infrapopliteal arteries was attempted in 200 consecutive patients. Altogether, 417 infrapopliteal lesions, with lengths varying from 2 cm to 32 cm, were treated as part of this study, including 305 lesions in the anterior tibial arteries, 89 in the posterior tibial arteries, and 23 in the peroneal arteries. The ‘U’-shaped guidewire technique was attempted in 393 lesions from 361 limbs. The tip of a hydrophilic 0.035-inch guidewire was formed into a ‘U’ shape with the aid of a 4-Fr catheter and collateral branch vessel to recanalize the completely occluded long segment lesions. Results: A successful angioplasty with at least one artery recanalized directly to the malleolar or dorsal foot was achieved in 322 limbs (89%). The looping technique had a success rate of 90% (352 of 393 lesions). After the procedure, the rest pain was relieved in 58 of 69 patients, while 207 of 245 limbs (85%) showed improvement for intermittent claudication. Complete wound healing was noted in 21 of 54 patients, while 20 of 54 patients showed an improvement in the wound size or depth. A total of 38 major immediate procedure-related complications were noted, including retroperitoneal hematoma, distal emboli, and vessel rupture. Conclusion: The results of this study suggests that the guidewire looping technique is a safe and effective method for the recanalization of the occluded lesions in infrapopliteal vessels.

Layer speciation and electronic structure investigation of freestanding hexagonal boron nitride nanosheets.

Wang, Jian,Wang, Zhiqiang,Cho, Hyunjin,Kim, Myung Jong,Sham, T K,Sun, Xuhui RSC Pub 2015 Nanoscale Vol.7 No.5

<P>Chemical imaging, thickness mapping, layer speciation and polarization dependence have been performed on single and multilayered (up to three layers and trilayered nanosheets overlapping to form 6 and 9 layers) hexagonal boron nitride (hBN) nanosheets by scanning transmission X-ray microscopy. Spatially-resolved XANES directly from freestanding regions of different layers has been extracted and compared with sample normal and 30 tilted configurations. Notably a double feature σ* excitonic state and a stable high energy σ* state were observed at the boron site in addition to the intense π* excitonic state. The boron projected σ* DOS, especially the first σ* exciton, is sensitive to surface modification, particularly in the single layered hBN nanosheet which shows more significant detectable contaminants and defects such as tri-coordinated boron/nitrogen oxide. The nitrogen site has shown very weak or no excitonic character. The distinct excitonic effect on boron and nitrogen was interpreted to the partly ionic state of hBN. Bulk XANES of hBN nanosheets was also measured to confirm the spectro-microscopic STXM result. Finally, the unoccupied electronic structures of hBN and graphene were compared.</P>