Bayer-Macr\`i decomposition on Bridgeland moduli spaces over surfaces

We find a decomposition formula of the local Bayer-Macr\`i map for the nef line bundle theory on the Bridgeland moduli space over surface. If there is a global Bayer-Macr\`i map, such decomposition gives a precise correspondence from Bridgeland walls to Mori walls. As an application, we compute the nef cone of the Hilbert scheme $S^{[n]}$ of $n$-points over special kinds of fibered surface $S$ of Picard rank two.Comment: 23 page

Classification of full exceptional collections of line bundles on three blow-ups of P3\mathbb{P}^{3}

A fullness conjecture of Kuznetsov says that if a smooth projective variety $X$ admits a full exceptional collection of line bundles of length $l$, then any exceptional collection of line bundles of length $l$ is full. In this paper, we show that this conjecture holds for $X$ as the blow-up of $\mathbb{P}^{3}$ at a point, a line, or a twisted cubic curve, i.e. any exceptional collection of line bundles of length 6 on $X$ is full. Moreover, we obtain an explicit classification of full exceptional collections of line bundles on such $X$.Comment: 28 pages. To appear in Journal of the Korean Mathematical Society, A previous version with a different title appeared as [CGP17025] at https://cgp.ibs.re.kr/archive/preprints/201

Asymptotic behavior of bounded solutions for a system of neutral functional differential equations

AbstractConsider the system of neutral functional differential equations{(x1(t)−cx2(t−r))′=−F(x1(t))+G(x2(t−r)),(x2(t)−cx1(t−r))′=−F(x2(t))+G(x1(t−r)), where r>0, c∈[0,1), F, G∈C(R1) and F is strictly increasing on R1. It is shown that if F(x)⩾G(x) for all x∈R1 or F(x)⩽G(x) for all x∈R1, then every bounded solution of such a system tends to an equilibrium. Our results improve and extend some corresponding ones already known

Contractibility of space of stability conditions on the projective plane via global dimension function

We compute the global dimension function $\mathrm{gldim}$ on the principal component $\mathrm{Stab}^{\dag}(\mathbb{P}^2)$ of the space of Bridgeland stability conditions on $\mathbb{P}^2$. It admits $2$ as the minimum value and the preimage $\mathrm{gldim}^{-1}(2)$ is contained in the closure $\overline{\mathrm{Stab}^{\mathrm{Geo}}(\mathbb{P}^2)}$ of the subspace consisting of geometric stability conditions. We show that $\mathrm{gldim}^{-1}[2,x)$ contracts to $\mathrm{gldim}^{-1}(2)$ for any real number $x\geq 2$ and that $\mathrm{gldim}^{-1}(2)$ is contractible.Comment: 26 pages, 7 figures. Add a reference and update Section 4. Comments are welcome

Liver Imaging Reporting and Data System (LI-RADS) v2018: differential diagnostic value of ADC values for benign and malignant nodules with moderate probability (LR-3)

ObjectiveTo evaluate the usefulness of the apparent diffusion coefficient (ADC) in differentiating between benign and malignant LR-3 lesions classified by Liver Imaging Reporting and Data System 2018 (LI-RADS v2018).MethodsRetrospectively analyzed 88 patients with liver nodules confirmed by pathology and classified as LR-3 by LI-RADS. All patients underwent preoperative contrast-enhanced MR examination, and the following patient-related imaging features were collected: tumor size,nonrim APHE, nonperipheral “washout”, enhancing “capsule”, mild-moderate T2 hyperintensity, fat in mass, restricted diffusion, and nodule-in-nodule architecture. We performed ROC analysis and calculated the sensitivity and specificity.ResultsA total of 122 lesions were found in 88 patients, with 68 benign and 54 malignant lesions. The mean ADC value for malignant and benign lesions were 1.01 ± 0.15 × 103 mm2/s and 1.41 ± 0.31 × 103 mm2/s, respectively. The ADC value of malignant lesions was significantly lower than that of benign lesions, p < 0.0001. Compared with other imaging features, ADC values had the highest AUC (AUC = 0.909), with a sensitivity of 92.6% and a specificity of 74.1% for the differentiation of benign and malignant lesions.ConclusionsADC values are useful for differentiating between benign and malignant liver nodules in LR-3 classification, it improves the sensitivity of LI-RADS in the diagnosis of HCC while maintaining high specificity, and we recommend including ADC values in the standard interpretation of LI-RADSv2018

Classification of full exceptional collections of line bundles on three blow-ups of P 3

© 2019 Korean Mathematical Society. A fullness conjecture of Kuznetsov says that if a smooth projective variety X admits a full exceptional collection of line bundles of length l, then any exceptional collection of line bundles of length l is full. In this paper, we show that this conjecture holds for X as the blow-up of P 3 at a point, a line, or a twisted cubic curve, i.e., any exceptional collection of line bundles of length 6 on X is full. Moreover, we obtain an explicit classification of full exceptional collections of line bundles on such X11sciekc

Revision and psychometric evaluation of a fertility intention scale for young women with breast cancer in Chinese Mainland

Objective: Neglected fertility intentions affect the quality of life of young women with breast cancer. The purpose of this study was to revise the Taiwanese version of the Fertility Intention Scale and validate its psychometric properties among young women with breast cancer in Chinese Mainland. Methods: We performed a cross-sectional survey with young women with breast cancer at a Chinese cancer hospital to evaluate the psychometric properties of the Revised Fertility Intention Scale. A two-phase study was conducted: (1) revision of the scale and (2) evaluation of the scale's reliability and validity. Results: Six new items and one new dimension were added to the original 15 items and four dimensions, reliability and validity of the 21-item Revised Fertility Intention Scale were verified in a sample of 436 women in Chineses Mainland with breast cancer who were aged 18–40 years. The content validity index, results of factor analysis, convergent validity, and known-groups validity were acceptable, and the Cronbach's alpha and intraclass correlation coefficients supported the revised scale. Conclusions: The 21-item Revised Fertility Intention Scale has satisfactory reliability and validity for assessing fertility intentions among young women with breast cancer in Chinese Mainland. In clinical practice, nurses can use the scale to identify fertility intentions and associated factors in young women with breast cancer and develop feasible and effective oncofertility care measures

Association of self-compassion and body image disturbance among young breast cancer patients: Mediating effect of body surveillance and body shame

Objective: To examine whether body surveillance and body shame mediated the association between self-compassion and body image disturbance among young breast cancer patients. Methods: In this cross-sectional descriptive study, a total of 310 young women with breast cancer were recruited by convenience sampling. All of them completed self-report measurements of demographic and clinical characteristics, self-compassion scale, body image self-rating questionnaire for breast cancer and body surveillance scale, and body shame scale between September and December 2021 ​at a tertiary cancer hospital in Tianjin, China. Data analysis was performed with correlation analysis and structural equation modeling to verify relationships between key variables. Results: Less self-compassion was significantly associated with greater body image disturbance, while a positive correlation was found between body image disturbance, body surveillance, and body shame. Self-compassion indirectly negative predicted body image disturbance via the chain mediation of body surveillance and body shame. Conclusions: The links of self-compassion and body image disturbance were mediated by body surveillance and body shame. Reducing patients’ excessive body surveillance and body shame by improving their ability of self-compassion may be an effective measure to reduce body image disturbance