Dynamics of continued fractions and distribution of modular symbols

We formulate a thermodynamical approach to the study of distribution of modular symbols, motivated by the work of Baladi-Vall\'ee. We introduce the modular partitions of continued fractions and observe that the statistics for modular symbols follow from the behavior of modular partitions. We prove the limit Gaussian distribution and residual equidistribution for modular partitions as a vector-valued random variable on the set of rationals whose denominators are up to a fixed positive integer by studying the spectral properties of transfer operator associated to the underlying dynamics. The approach leads to a few applications. We show an average version of conjectures of Mazur-Rubin on statistics for the period integrals of an elliptic newform. We further observe that the equidistribution of mod $p$ values of modular symbols leads to mod $p$ non-vanishing results for special modular $L$-values twisted by a Dirichlet character.Comment: 42 page

Ultrahigh areal number density solid-state on-chip microsupercapacitors via electrohydrodynamic jet printing

Microsupercapacitors (MSCs) have garnered considerable attention as a promising power source for microelectronics and miniaturized portable/wearable devices. However, their practical application has been hindered by the manufacturing complexity and dimensional limits. Here, we develop a new class of ultrahigh areal number density solid-state MSCs (UHD SS-MSCs) on a chip via electrohydrodynamic (EHD) jet printing. This is, to the best of our knowledge, the first study to exploit EHD jet printing in the MSCs. The activated carbon-based electrode inks are EHD jet-printed, creating interdigitated electrodes with fine feature sizes. Subsequently, a drying-free, ultraviolet-cured solid-state gel electrolyte is introduced to ensure electrochemical isolation between the SS-MSCs, enabling dense SS-MSC integration with on-demand (in-series/in-parallel) cell connection on a chip. The resulting on-chip UHD SS-MSCs exhibit exceptional areal number density [36 unit cells integrated on a chip (area = 8.0 mm x 8.2 mm), 54.9 cells cm(-2)] and areal operating voltage (65.9 V cm(-2))

The factors affecting pregnancy outcomes in the second trimester pregnant women

Adequate nutrient intake during pregnancy is important to fetal and maternal health. The purpose of this study was to investigate the factors affecting birth weight and gestational age and to provide basic data to promote more favorable pregnancy outcomes. Data were collected from 234 pregnant women at two hospitals in Seoul. Demographic characteristics, anthropometric measurements and health related habits were obtained using a questionnaire at the hospital visit during the second trimester. Dietary intakes were estimated by 24 hour recall at the hospital visit during the second trimester. Data on pregnancy outcomes, including birth weights and gestational ages, were obtained from hospital records after delivery. Birth weights were divided into a low birth weight group (birth weight<3.1 kg), a normal birth weight group (3.1-3.6 kg) and a high birth weight group (>3.6 kg). Gestational ages were divided into tertiles according to the gestational age of the subjects: group 1 (<38.53 weeks), group 2 (38.53-40.00 weeks) and group 3 (>40.00 weeks). The number of family members was significantly lower in the low birth weight group than in the normal birth weight group (p<0.05). In the low birth weight group, pregnancy weight was significantly lower than in the high birth weight group (p<0.05). Health related habits were not significantly different among any of the groups. Intakes of fiber, phosphorous, iron, vitamin B6 and folic acid were significantly higher in the high birth weight group than the low birth weight group (p<0.05). Gestational age was not significantly affected by nutrient intakes, but birth weight was affected by nutrient intake in the results of this study. Therefore, the adequacy of nutrient intake is important for the improvement of pregnancy outcomes

Proto-Model of an Infrared Wide-Field Off-Axis Telescope

We develop a proto-model of an off-axis reflective telescope for infrared wide-field observations based on the design of Schwarzschild-Chang type telescope. With only two mirrors, this design achieves an entrance pupil diameter of 50 mm and an effective focal length of 100 mm. We can apply this design to a mid-infrared telescope with a field of view of 8 deg X 8 deg. In spite of the substantial advantages of off-axis telescopes in the infrared compared to refractive or on-axis reflective telescopes, it is known to be difficult to align the mirrors in off-axis systems because of their asymmetric structures. Off-axis mirrors of our telescope are manufactured at the Korea Basic Science Institute (KBSI). We analyze the fabricated mirror surfaces by fitting polynomial functions to the measured data. We accomplish alignment of this two-mirror off-axis system using a ray tracing method. A simple imaging test is performed to compare a pinhole image with a simulated prediction.Comment: 14 pages, 16 figure

Beyond slurry-cast supercapacitor electrodes: PAN/MWNT heteromat-mediated ultrahigh capacitance electrode sheets

Supercapacitors (SCs) have garnered considerable attention as an appealing power source for forthcoming smart energy era. An ultimate challenge facing the SCs is the acquisition of higher energy density without impairing their other electrochemical properties. Herein, we demonstrate a new class of polyacrylonitrile (PAN)/multi-walled carbon tube (MWNT) heteromat-mediated ultrahigh capacitance electrode sheets as an unusual electrode architecture strategy to address the aforementioned issue. Vanadium pentoxide (V2O5) is chosen as a model electrode material to explore the feasibility of the suggested concept. The heteromat V2O5 electrode sheets are produced through one-pot fabrication based on concurrent electrospraying (for V2O5 precursor/MWNT) and electrospinning (for PAN nanofiber) followed by calcination, leading to compact packing of V2O5 materials in intimate contact with MWNTs and PAN nanofibers. As a consequence, the heteromat V2O5 electrode sheets offer three-dimensionally bicontinuous electron (arising from MWNT networks)/ion (from spatially reticulated interstitial voids to be filled with liquid electrolytes) conduction pathways, thereby facilitating redox reaction kinetics of V2O5 materials. In addition, elimination of heavy metallic foil current collectors, in combination with the dense packing of V2O5 materials, significantly increases (electrode sheet-based) specific capacitances far beyond those accessible with conventional slurry-cast electrodes.ope

Enhanced cardiac expression of two isoforms of matrix metalloproteinase-2 in experimental diabetes mellitus.

BackgroundDiabetic cardiomyopathy (DM CMP) is defined as cardiomyocyte damage and ventricular dysfunction directly associated with diabetes independent of concomitant coronary artery disease or hypertension. Matrix metalloproteinases (MMPs), especially MMP-2, have been reported to underlie the pathogenesis of DM CMP by increasing extracellular collagen content.PurposeWe hypothesized that two discrete MMP-2 isoforms (full length MMP-2, FL-MMP-2; N-terminal truncated MMP-2, NTT-MMP-2) are induced by high glucose stimulation in vitro and in an experimental diabetic heart model.MethodsRat cardiomyoblasts (H9C2 cells) were examined to determine whether high glucose can induce the expression of the two isoforms of MMP-2. For the in vivo study, we used the streptozotocin-induced DM mouse heart model and age-matched controls. The changes of each MMP-2 isoform expression in the diabetic mice hearts were determined using quantitative real-time polymerase chain reaction (qRT-PCR). Immunohistochemical stains were conducted to identify the location and patterns of MMP-2 isoform expression. Echocardiography was performed to compare and analyze the changes in cardiac function induced by diabetes.ResultsQuantitative RT-PCR and immunofluorescence staining showed that the two MMP-2 isoforms were strongly induced by high glucose stimulation in H9C2 cells. Although no definite histologic features of diabetic cardiomyopathy were observed in diabetic mice hearts, left ventricular systolic dysfunction was determined by echocardiography. Quantitative RT-PCR and IHC staining showed this abnormal cardiac function was accompanied with the increases in the mRNA levels of the two isoforms of MMP-2 and related to intracellular localization.ConclusionTwo isoforms of MMP-2 were induced by high glucose stimulation in vitro and in a Type 1 DM mouse heart model. Further study is required to examine the role of these isoforms in DM CMP

Fishbone-Associated Actinomycosis of the Anterior Cervical Space: A Diagnostic Dilemma

We report the imaging and pathologic findings of fishbone-associated actinomycosis of the anterior cervical space in a 57-year-old man, misdiagnosed preoperatively as a malignancy originating from thyroglossal duct cyst. CT revealed an enhancing mass containing a small abscess pocket and two sharp linear calcifications within it, which infiltrated into the strap muscle. Pathologic examination demonstrated two fishbones within the actinomycotic abscess. Fishbone-associated actinomycosis should be considered when a cervical mass contains sharp linear calcifications

Effect of Total Leaf Numbers on the Growth and Fruit Quality in Muskmelon Plants Showing Leaf Yellowing Symptoms

This study was conducted to evaluate the influence of total leaf numbers on the growth, net formation of fruits, and occurrence of leaf yellowing symptoms (LYS) in muskmelon plants. The growth and development of LYS on muskmelon plants having 25, 30, and 35 fully expanded leaves on the vine were compared to those of the control plant having 20 leaves. Plant height, leaf area, root fresh weight, and root dry weight increased as the number of leaves increased. Plants with 35 leaves showed the greatest plant growth. Net photosynthetic rate was positively related to increasing leaf numbers with plants having over 25 leaves showing the greatest photosynthetic rates. On the other hand, there were no significant differences in chlorophyll content and root activity among treatments with different leaf numbers. The ratio of LYS infection was also greater in plants having 25-30 leaves, than in those having leaf numbers. Plants with different leaf numbers and LYS infection showed a variation in fruit quality, although LYS did not significantly affect fruit quality except net index. The plants having 20 leaves that showed LYS developed fruits that had significantly smaller flesh (mesocarp) thickness than, the plants having greater numbers of leaves. The higher sugar contents of fruits were found in the plants having 35 leaves whether they showed LYS (12.1°Bx) or not (12.5°Bx). Therefore, leaving more than 25 healthy leaves per plant was recommended for minimizing damage from LYS.OAIID:oai:osos.snu.ac.kr:snu2015-01/104/0000027607/11ADJUST_YN:NEMP_ID:A075898DEPT_CD:517CITE_RATE:0FILENAME:(이희주)effect_of_total_leaf_numbers_on_the_growth_and_fruit_quality_in_muskmelon_plants_showing_leaf_yell··.pdfDEPT_NM:식물생산과학부CONFIRM: