A note on q-analogue of Boole polynomials

In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.Comment: 11 page

Barnes-type Daehee polynomials

In this paper, we consider Barnes-type Daehee polynomials of the first kind and of the second kind. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.Comment: 34 page

Linear differential equations for families of polynomials

Abstract In this paper, we present linear differential equations for the generating functions of the Poisson-Charlier, actuarial, and Meixner polynomials. Also, we give an application for each case

Degenerate r-truncated Stirling numbers

For any positive integer $r$, the $r$-truncated (or $r$-associated) Stirling number of the second kind $S_{2}^{(r)}(n, k)$ enumerates the number of partitions of the set $\{1, 2, 3, \dots, n\}$ into $k$ non-empty disjoint subsets, such that each subset contains at least $r$ elements. We introduce the degenerate $r$-truncated Stirling numbers of the second kind and of the first kind. They are degenerate versions of the $r$-truncated Stirling numbers of the second kind and of the first kind, and reduce to the degenerate Stirling numbers of the second kind and of the first kind for $r = 1$. Our aim is to derive recurrence relations for both of those numbers

Toward Data-Driven Digital Therapeutics Analytics: Literature Review and Research Directions

With the advent of Digital Therapeutics (DTx), the development of software as a medical device (SaMD) for mobile and wearable devices has gained significant attention in recent years. Existing DTx evaluations, such as randomized clinical trials, mostly focus on verifying the effectiveness of DTx products. To acquire a deeper understanding of DTx engagement and behavioral adherence, beyond efficacy, a large amount of contextual and interaction data from mobile and wearable devices during field deployment would be required for analysis. In this work, the overall flow of the data-driven DTx analytics is reviewed to help researchers and practitioners to explore DTx datasets, to investigate contextual patterns associated with DTx usage, and to establish the (causal) relationship of DTx engagement and behavioral adherence. This review of the key components of data-driven analytics provides novel research directions in the analysis of mobile sensor and interaction datasets, which helps to iteratively improve the receptivity of existing DTx.Comment: This paper has been accepted by the IEEE/CAA Journal of Automatica Sinic

Effects of dodecacalcium heptaaluminate content on the setting time, compressive strength, alkalinity, and cytocompatibility of tricalcium silicate cement

Objective: This study aimed to investigate the effects of dodecacalcium hepta-aluminate (C12A7) content on some physicochemical properties and cytocompatibility of tricalcium silicate (C3S) cement using human dental pulp cells (hDPCs). Material and Methods: High purity C3S cement was manufactured by a solid phase method. C12A7 was mixed with the cement in proportions of 0, 5, 8, and 10 wt% (C12A7-0, -5, -8, and -10, respectively). Physicochemical properties including initial setting time, compressive strength, and alkalinity were evaluated. Cytocompatibility was assessed with cell viability tests and cell number counts. Statistical analysis was performed by using one-way analysis of variance (ANOVA) and Tukey’s test (p<0.05). Results: The initial setting time of C3S-based cement was shorter in the presence of C12A7 (p<0.05). After 1 day, C12A7-5 showed significantly higher compressive strength than the other groups (p<0.05). After 7 days, the compressive strength of C12A7-5 was similar to that of C12A7-0, whereas other groups showed strength lower than C12A7-0. The pH values of all tested groups showed no significant differences after 1 day (p>0.05). The C12A7-5 group showed similar cell viability to the C12A7-0 group (p>0.05), while the other experimental groups showed lower values compared to C12A7-0 group (p<0.05). The number of cells grown on the C12A7-5 specimen was higher than that on C12A7-8 and -10 (p<0.05). Conclusions: The addition of C12A7 to C3S cement at a proportion of 5% resulted in rapid initial setting time and higher compressive strength with no adverse effects on cytocompatibility

Alternative Embryo Transfer on Day 3 or Day 5 for Reducing the Risk of Multiple Gestations

Purpose: This study was carried out to reduce the possibility of high-order multiple gestations and the failure of embryo transfer by determining their replacement date based on the number and quality of 2-day embryos. Methods: All zygotes were cocultured with cumulus cells in 10 ¹l of YS medium containing 10% human follicular fluid (hFF) for 48 or 96 hr. In period I, all embryos were transferred on day 3 (1032 cycles). In period II, the embryos were transferred on either day 3 or day 5 by determining their replacement date based on the number and quality of 2-day embryos: there were 2701 patients in whom embryos were replaced on day 3 (in the case that the number of zygotes was less than eight and the number of good-quality embryos was less than three) and 1952 patients less than 40 years old in whom embryos were replaced on day 5 (in the case that the number of zygotes was eight or more and/or the number of good-quality embryos was three or more). On the other hand, patients who were 40 years old or more were alloted to day 3 transfer cycles, regardless of the number and quality of the 2-day embryos, due to the possibility of their not producing blastocyst-stage embryos in vitro. Results: The number of embryos transferred in period II was 2.9 ± 0.6, while that in period I was 3.7 ± 0.5. The multiple pregnancy rate was significantly decreased in period II (30.7%) compared to that (49.6%) in period I, while the pregnancy and implantation rates in period II (36.1 and 16.4%, respectively) were not lower than those (34.9 and 16.1%, respectively) in period I. The rate of triplet or more gestations was significantly minimized in period II (2.3%) compared to that in period I (26.5%). Conclusions: We propose that determination of the date on which embryos should be transferred based on the number and quality of embryos on day 2 may help to maintain an acceptable pregnancy rate, while minimizing embryo transfer failure and high-order multiple gestations