Revisiting Multiplication Area Models for Whole Numbers

We argue that there are two conceptually different area models for whole number multiplication: area-to-area model and lengths-to-area model depending on how multiplication operation is conceived: action on / change of an initial quantity, or operation / coordination of two quantities. These models complement each other to promote students’ conceptual understanding of whole number multiplication and help students extend their understanding of whole number multiplication to fraction multiplication

Revisiting Multiplication Area Models for Whole Numbers

We argue that there are two conceptually different area models for whole number multiplication: area-to-area model and lengths-to-area model depending on how multiplication operation is conceived: action on / change of an initial quantity, or operation / coordination of two quantities. These models complement each other to promote students’ conceptual understanding of whole number multiplication and help students extend their understanding of whole number multiplication to fraction multiplication

Growth of A Massive Black Hole Via Tidal Disruption Accretion

Stars that are tidally disrupted by the massive black hole (MBH) may contribute significantly to the growth of the MBH, especially in dense nuclear star clusters (NSCs). Yet, this tidal disruption accretion (TDA) of stars onto the MBH has largely been overlooked compared to the gas accretion (GA) channel in most numerical experiments until now. In this work, we implement a black hole growth channel via TDA in the high-resolution adaptive mesh refinement code Enzo to investigate its influence on a MBH seed's early evolution. We find that a MBH seed grows rapidly from $10^3\,\mathrm{M}_\odot$ to $\gtrsim 10^6\,\mathrm{M}_\odot$ in 200\,Myrs in some of the tested simulations. Compared to a MBH seed that grows only via GA, TDA can enhance the MBH's growth rate by up to more than an order of magnitude. However, as predicted, TDA mainly helps the early growth of the MBH (from $10^{3-4}\,\mathrm{M}_\odot$ to $\lesssim10^{5}\,\mathrm{M}_\odot$) while the later evolution is generally dominated by GA. We also observe that the star formation near the MBH is suppressed when TDA is most active, sometimes with a visible cavity in gas (of size $\sim$ a few pc) created in the vicinity of the MBH. It is because the MBH may grow expeditiously with both GA and TDA, and the massive MBH could consume its neighboring gas faster than being replenished by gas inflows. Our study demonstrates the need to consider different channels of black hole accretion that may provide clues for the existence of supermassive black holes at high redshifts.Comment: 17 pages, and 10 figure

ANTERIOR CRUCIATE LIGAMENT INJURY RISK FACTORS DIFFERENCES BETWEEN FEMALE DANCERS AND FEMALE SOCCER PLAYERS DURING SINGLE-LEGGED AND DOUBLE LEGGED LANDING TASKS

The purpose of this study was to compare ACL injury risk factors between female dancers and female soccer players during single-legged drop landing and double legged drop landing vertical jump tasks. Fifteen elite female soccer players and 45 professional female dancers (15 ballet, 15 modern, and 15 Korean dancers) were recruited to participate in this study. Two-way repeated measure of ANOVAs (participant groups & landing tasks, 4x2) were used. Female dancers landed with a significantly lower trunk flexion, trunk external rotation, knee external rotation, and knee valgus moment than those of female soccer players. Also, single-legged drop landing task demonstrated a higher trunk external rotation and knee valgus moment than those of double legged drop landing vertical jump task

Novel Pyrrolopyrimidine-Based α-Helix Mimetics: Cell- Permeable Inhibitors of Protein-Protein Interactions

This document is the Accepted Manuscript version of a Published Work that appeared in final form in the Journal of the American Chemical Society, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://doi.org/10.1021/ja108230s.There is considerable interest in developing nonpeptidic, small molecule α-helix mimetics to disrupt α-helix-mediated protein-protein interactions. Herein, we report the design of a novel pyrrolopyrimidine-based scaffold for such α-helix mimetics with increased conformational rigidity. We also developed a facile solid phase synthetic route, which is amenable to divergent synthesis of a large library. Using a fluorescence polarization-based assay, we identified cell permeable, dual MDMX/MDM2 inhibitors, demonstrating that the designed molecules can act as α-helix mimetics

Physical properties and biological effects of mineral trioxide aggregate mixed with methylcellulose and calcium chloride

Objectives: Methylcellulose (MC) is a chemical compound derived from cellulose. MTA mixed with MC reduces setting time and increases plasticity. This study assessed the influence of MC as an anti-washout ingredient and CaCl2 as a setting time accelerator on the physical and biological properties of MTA. Material and Methods: Test materials were divided into 3 groups; Group 1(control): distilled water; Group 2: 1% MC/CaCl2; Group 3: 2% MC/CaCl2. Compressive strength, pH, flowability and cell viability were tested. The gene expression of bone sialoprotein (BSP) was detected by RT-PCR and real­ time PCR. The expression of alkaline phosphatase (ALP) and mineralization behavior were evaluated using an ALP staining and an alizarin red staining. Results: Compressive strength, pH, and cell viability of MTA mixed with MC/CaCl2 were not significantly different compared to the control group. The flowability of MTA with MC/CaCI2 has decreased significantly when compared to the control (