Pointwise convergence of sequential Schr\"odinger means

We study pointwise convergence of the fractional Schr\"odinger means along sequences $t_n$ which converge to zero. Our main result is that bounds on the maximal function $\sup_{n} |e^{it_n(-\Delta)^{\alpha/2}} f|$ can be deduced from those on $\sup_{0<t\le 1} |e^{it(-\Delta)^{\alpha/2}} f|$ when $\{t_n\}$ is contained in the Lorentz space $\ell^{r,\infty}$. Consequently, our results provide seemingly optimal results in higher dimensions, which extend the recent work of Dimou-Seeger, and Li-Wang-Yan to higher dimensions. Our approach based on a localization argument also works for other dispersive equations and provides alternative proofs of previous results on sequential convergence

Pointwise convergence of sequential Schrödinger means

We study pointwise convergence of the fractional Schrödinger means along sequences tn that converge to zero. Our main result is that bounds on the maximal function supn|eitn(−Δ)α/2f| can be deduced from those on sup0<t≤1|eit(−Δ)α/2f| , when {tn} is contained in the Lorentz space ℓr,∞ . Consequently, our results provide seemingly optimal results in higher dimensions, which extend the recent work of Dimou and Seeger, and Li, Wang, and Yan to higher dimensions. Our approach based on a localization argument also works for other dispersive equations and provides alternative proofs of previous results on sequential convergence

Application of the Khorana score for cancer-associated thrombosis prediction in patients of East Asian ethnicity undergoing ambulatory chemotherapy

Background The Khorana score (KS) has not been well studied in East Asian cancer patients, who have different genetic backgrounds for inherited thrombophilia, body metabolism, and cancer epidemiology. Methods By using the Common Data Model, we retrospectively collected deidentified data from 11,714 consecutive newly diagnosed cancer patients who underwent first-line chemotherapy from December 2015 to December 2021 at a single institution in Korea, and we applied the KS for cancer-associated thrombosis (CAT) prediction. Age at diagnosis, sex, and use of highly thrombogenic chemotherapeutics were additionally investigated as potential risk factors for CAT development. Results By 6 months after chemotherapy initiation, 207 patients (1.77%) experienced CAT. Only 0.4% had a body mass index (BMI) ≥ 35 kg/m2 and changing the cutoff to 25 kg/m2 improved the prediction of CAT. Age ≥ 65 years and the use of highly thrombogenic chemotherapeutics were independently associated with CAT development. KS values of 1 ~ 2 and ≥ 3 accounted for 52.3% and 7.6% of all patients, respectively, and the incidence of CAT in these groups was 2.16% and 4.16%, respectively, suggesting a lower incidence of CAT in the study population than in Westerners. The KS component regarding the site of cancer showed a good association with CAT development but needed some improvement. Conclusion The KS was partially validated to predict CAT in Korean cancer patients undergoing modern chemotherapy. Modifying the BMI cutoff, adding other risk variables, and refining the use of cancer-site data for CAT risk prediction may improve the performance of the KS for CAT prediction in East Asian patients.This work was supported by the Technology Innovation Program (or Industrial Strategic Technology Development Program) (20004927, Upgrade of CDM based Distributed Biohealth Data Platform and Development of Verification Technology), funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea). The funder was not involved in any stage of the current study, including the design, data gathering, data analysis and interpretation, and decision to submit this work for publication

Sharp Sobolev regularity of a restricted X-ray transform

We study $L^p$-Sobolev regularity estimate for the restricted X-ray transforms generated by a nondegenerate curve. Making use of the inductive strategy in the recent work by the authors, we establish the sharp $L^p$-regularity estimates for the restricted X-ray transform in $\mathbb R^{d+1}$, $d\ge 3$. This extends the result due to Pramanik and Seeger in $\mathbb R^3$ to every dimension. We also obtain $L^p$-Sobolev regularity of the convolution averages over curves with the optimal regularity $\alpha=1/p$ for $p>2(d-1)