Area Inequalities for Embedded Disks Spanning Unknotted Curves

We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bounds the area of an embedded disk spanning the curve in terms of two parameters: the length L of the curve and the thickness r (maximal radius of an embedded tubular neighborhood) of the curve. For fixed length, the expression giving the upper bound on the area grows exponentially in 1/r^2. In the direction of lower bounds, we give a sequence of length one curves with r approaching 0 for which the area of any spanning disk is bounded from below by a function that grows exponentially with 1/r. In particular, given any constant A, there is a smooth, unknotted length one curve for which the area of a smallest embedded spanning disk is greater than A.Comment: 31 pages, 5 figure

An experimental evaluation of the performance deficit of an aircraft engine starter turbine

An experimental investigation was made to determine the reasons for the low aerodynamic performance of a 13.5 centimeter tip diameter aircraft engine starter turbine. The investigation consisted of an evaluation of both the stator and the stage. An approximate ten percent improvement in turbine efficiency was obtained when the honeycomb shroud over the rotor blade tips was filled to obtain a solid shroud surface

Pole Dancing: 3D Morphs for Tree Drawings

We study the question whether a crossing-free 3D morph between two straight-line drawings of an $n$-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the two given drawings are two-dimensional and at the one in which they are three-dimensional. In the former setting we prove that a crossing-free 3D morph always exists with $O(\log n)$ steps, while for the latter $\Theta(n)$ steps are always sufficient and sometimes necessary.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Field-Tuning of the electron and hole populations in the ruthenate Bi_3Ru_3O_11

Experiments on the Hall coefficient R_H and heat capactity C reveal an unusual, compensated electronic ground state in the ruthenate Bi_3Ru_3O_11. At low temperature T, R_H decreases linearly with magnetic field |H| for fields larger than the field scale set by the Zeeman energy. The results suggest that the electron and hole populations are tuned by H in opposite directions via coupling of the spins to the field. As T is decreased below 5 K, the curve C(T)/T vs. T^2 shows an anomalous flattening consistent with a rapidly growing Sommerfeld parameter \gamma(T). We discuss shifts of the electron and hole chemical potentials by H to interpret the observed behavior of R_H.Comment: 5 pages, 6 figures, reference adde

Influence of heat pressure steaming (HPS) on the mechanical and physical properties of common oak wood.

Common oak (Quercus robur) was thermally treated applying a heat pressure steaming procedure. Physical and mechanical properties of treated and untreated samples were investigated extensively. Swelling, water absorption, water vapour resistance, porosity and thermal conductivity were tested and the mechanical properties of tensile, bending and compression strength and of Young’s modulus (static and dynamic) as well as Poisson’s ratio and shear modulus were determined. The tests were carried out in the standard climate 20 °C and 65 % relative humidity and also in all three anatomical main directions: longitudinal, radial and tangential. The equilibrium moisture content at 20 °C and 65 % relative humidity for HPS (heat pressure steamed) oak (determined in adsorption test) was 6.7 % and for untreated oak 9.1 %. Swelling in longitudinal direction was not affected: a reduction of 17 and 10 % could be observed in radial and tangential direction, respectively. The porosity of the treated samples was 53.9 % in comparison to the untreated samples with 51.0 %. The thermal conductivity depending on the modification procedure changed only slightly which was related to the different densities of the samples. The water vapour resistance of the modified samples increases compared to the untreated samples. The values are double (dry-cup) respectively three times (wet-cup) higher than those of the reference samples. The elastic properties were not influenced by heat pressure steaming. The MOE does not show a significant change depending on the treatment. Bending and tensile strength of HPS oak decrease. In longitudinal direction, the tensile strength drops by 26 % and the bending strength by 25 %.ISSN:0018-3768ISSN:1436-736

A 4-Base-Pair Core-Enclosing Helix in Telomerase RNA Is Essential for Activity and for Binding to the Telomerase Reverse Transcriptase Catalytic Protein Subunit

The telomerase ribonucleoprotein (RNP) counters the chromosome end replication problem, completing genome replication to prevent cellular senescence in yeast, humans, and most other eukaryotes. The telomerase RNP core enzyme is composed of a dedicated RNA subunit and a reverse transcriptase (telomerase reverse transcriptase [TERT]). Although the majority of the 1,157-nucleotide (nt) Saccharomyces cerevisiae telomerase RNA, TLC1, is rapidly evolving, the central catalytic core is largely conserved, containing the template, template-boundary helix, pseudoknot, and core-enclosing helix (CEH). Here, we show that 4 bp of core-enclosing helix is required for telomerase to be active in vitro and to maintain yeast telomeres in vivo, whereas the DeltaCEH and 1- and 2-bp alleles do not support telomerase function. Using the CRISPR/nuclease-deactivated Cas9 (dCas9)-based CARRY (CRISPR-assisted RNA-RNA-binding protein [RBP] yeast) two-hybrid assay to assess binding of our CEH mutant RNAs to TERT, we find that the 4-bp CEH RNA binds to TERT but the shorter-CEH constructs do not, consistent with the telomerase activity and in vivo complementation results. Thus, the CEH is essential in yeast telomerase RNA because it is needed to bind TERT to form the core RNP enzyme. Although the 8 nt that form this 4-bp stem at the base of the CEH are nearly invariant among Saccharomyces species, our results with sequence-randomized and truncated-CEH helices suggest that this binding interaction with TERT is dictated more by secondary than by primary structure. In summary, we have mapped an essential binding site in telomerase RNA for TERT that is crucial to form the catalytic core of this biomedically important RNP enzyme