On small bases for which 1 has countably many expansions

Let $q\in(1,2)$. A $q$-expansion of a number $x$ in $[0,\frac{1}{q-1}]$ is a sequence $(\delta_i)_{i=1}^\infty\in\{0,1\}^{\mathbb{N}}$ satisfying $$x=\sum_{i=1}^\infty\frac{\delta_i}{q^i}.$$ Let $\mathcal{B}_{\aleph_0}$ denote the set of $q$ for which there exists $x$ with a countable number of $q$-expansions, and let $\mathcal{B}_{1, \aleph_0}$ denote the set of $q$ for which $1$ has a countable number of $q$-expansions. In \cite{Sidorov6} it was shown that $\min\mathcal{B}_{\aleph_0}=\min\mathcal{B}_{1,\aleph_0}=\frac{1+\sqrt{5}}{2},$ and in \cite{Baker} it was shown that $\mathcal{B}_{\aleph_0}\cap(\frac{1+\sqrt{5}}{2}, q_1]=\{ q_1\}$, where $q_1(\approx1.64541)$ is the positive root of $x^6-x^4-x^3-2x^2-x-1=0$. In this paper we show that the second smallest point of $\mathcal{B}_{1,\aleph_0}$ is $q_3(\approx1.68042)$, the positive root of $x^5-x^4-x^3-x+1=0$. Enroute to proving this result we show that $\mathcal{B}_{\aleph_0}\cap(q_1, q_3]=\{ q_2, q_3\}$, where $q_2(\approx1.65462)$ is the positive root of $x^6-2x^4-x^3-1=0$.Comment: 14 pages, 2 figure

A simple method for deriving functional MSCs and applied for osteogenesis in 3D scaffolds

We describe a simple method for bone engineering using biodegradable scaffolds with mesenchymal stem cells derived from human induced-pluripotent stem cells (hiPS-MSCs). The hiPS-MSCs expressed mesenchymal markers (CD90, CD73, and CD105), possessed multipotency characterized by tri-lineages differentiation: osteogenic, adipogenic, and chondrogenic, and lost pluripotency – as seen with the loss of markers OCT3/4 and TRA-1-81 – and tumorigenicity. However, these iPS-MSCs are still positive for marker NANOG. We further explored the osteogenic potential of the hiPS-MSCs in synthetic polymer polycaprolactone (PCL) scaffolds or PCL scaffolds functionalized with natural polymer hyaluronan and ceramic TCP (PHT) both in vitro and in vivo. Our results showed that these iPS-MSCs are functionally compatible with the two 3D scaffolds tested and formed typically calcified structure in the scaffolds. Overall, our results suggest the iPS-MSCs derived by this simple method retain fully osteogenic function and provide a new solution towards personalized orthopedic therapy in the future

CPUE Estimation and Standardization Based on VMS: A Case Study for Squid-Jigging Fishery in the Equatorial of Eastern Pacific Ocean

Different fisheries, even the same fishery, use different ways of quantifying fishing efforts such as the number of vessels, days, voyages, and hooks. In squid-jigging fisheries, fishing hours, fishing days, and the number of vessels are valid units for calculating the catch per unit effort (CPUE). A vessel monitoring system (VMS) provides vessel position data with high spatial and temporal resolution and offers the possibility to quantify the CPUE at a finer scale. Using the squid fishery in the equatorial waters of the eastern Pacific as a case study, the CPUE was evaluated and standardized based on VMS data. The drifting operating points of the squid fishing vessels were filtered by the speed threshold, solar radiation, and operating time setting methods, leading to the number of fishing hours per day, and the nominal CPUE was calculated by combining the catch data obtained from logbooks. Then, the generalized linear model (GLM) and generalized additive model (GAM) were applied to conduct CPUE standardization considering spatiotemporal factors and environmental variables including sea surface temperature (SST), sea surface salinity (SSS), sea surface height (SSH), and chlorophyll-a (Chl_a). The results showed that month, latitude, SST, SSH, and Chl-a all have a high significant effect on CPUE as demonstrated through the significance test conducted by GLM. The GAM including the significant factors was judged to be the best model according to the AIC guidelines. The latitude range for high CPUE in the fishery was 3°S~0°S, SST range 24~25 °C, SSH range 4~8 m, and Chl_a range 0.15~0.20 mg/m3. In addition, the nominal and standardized CPUEs were compared based on fishing hours and fishing days. The results indicated that the two types of CPUEs were highly related hence there was no significant difference

Are Ecosystem Services Provided by Street Trees at Parcel Level Worthy of Attention? A Case Study of a Campus in Zhenjiang, China

Street trees in urban areas have positive impacts on the environment, such as climate regulation, air purification, and runoff mitigation. However, the ecosystem services (ES) provided by street trees at the parcel level remain a notable gap in the existing literature. This study quantified the ES benefits provided by street trees at Jiangsu University in Zhenjiang, China, which could represent the parcel level. A widely applied model, i-Tree Eco, was used to evaluate the ES, including carbon storage, carbon sequestration, pollutant removal, rainwater runoff reduction, and their economic value. We also analyzed how these are affected by the structure of tree species. The results revealed that the 10 most abundant species accounted for 84.3% of the total number of trees, with an unstable structure of species composition. A reasonable age proportion was important since a lower proportion of young trees may make future benefit outputs unstable. The annual economic value provided by ES was USD 205,253.20, with an average of USD 79.90 per tree. Platanus orientalis had the highest single plant benefit, indicating that the management pattern of street trees could be adapted in different environments to maximize benefits. Thus, street trees at the parcel level should receive more attention with strategic planning and management in order to maximize the ES and their economic value