Prime decompositions of knots in T2×I

AbstractThe famous H. Schubert theorem (1949) states that any nontrivial knot in S3 admits a decomposition into connected sum of prime factors, which are unique up to order. We prove a similar result for knots in T×I, where T is a two-dimensional torus. However, we only consider knots of geometric degree one, use a different type of connected summation, and take into account the order of prime factors

Aggregation kinetics at sedimentation: the impact of particles diffusion

We investigate the aggregation kinetics of sedimenting particles theoretically and numerically, using the advection-diffusion equation. Agglomeration, caused by both transport mechanisms (diffusion and advection), is important for small particles, like primary ash or soot particles in atmosphere, and large particles of equal or close size, where the advection mechanism is weak. For small Peclet numbers, which quantify the relative importance of diffusion and advection, we obtain the aggregation rates, as an expansion in Peclet numbers. For large Peclet numbers we use purely ballistic aggregation rates. Combining these results we obtain the rational approximant for the whole range of Peclet numbers. We also compute the aggregation rates by numerically solving the advection-diffusion equation. The results of the numerical simulations are in excellent agreement with the analytical theory for the studied Peclet numbers, varying by four orders of magnitude.Comment: 7 pages, 2 figures, 26 reference

Study of the machinability of an Inconel 625 composite with added NiTi-TiB2 fabricated by direct laser deposition

This work studies the process feasibility of milling a metal-matrix composite based on Inconel 625 with added NiTi-TiB2 fabricated by direct laser deposition. The composite is intended for manufacturing turbine blades and it has strength characteristics on par with those of Inconel 625. However, the addition of TiB2 has improved its heat and wear resistance. This material is new, and its machinability has not been studied. The new composite was milled with end mill cutters, and recommendations were worked out on the cutting speed, feed per tooth, cutter flank angle, as well as depth and width of milling. The wear of cutter teeth flank was more intense. After the flank wear land on the back surface of a tooth had reached 0.11–0.15 mm, there was a sharp increase in the forces applied which was followed by brittle fracture of the tooth. Milling at a speed of 25 m/min ensured 28 min of stable operation. However, afterwards the critical wear value of 0.11 mm was quickly approached at a cutting speed of 50 m/min, and critical wear followed after 14 min.я Dependencies of the cutting forces vs. time for all the selected cutting speeds and throughout the entire testing time period have a tendency to increase, which indicates the influence of cutter wear on the cutting forces. It was found that the durability of the cutters increases with an increase in the milling width and a decrease in the milling depth

Providing operating modes for Coriolis vibration gyroscopes with low-Q resonators

Coriolis vibration gyroscopes are a class of promising inertial primary information sensors that respond to the rotation of the resonator base through Coriolis inertial forces arising in the vibrating shell. Currently, two directions for the production of resonators for such gyroscopes have been developed: from quartz glass, a material with extremely low internal friction, and based on the processing of a metal alloy. When using the first direction, thanks to the high quality factor of quartz, it is possible to create navigation-class integrating gyroscopes. Existing samples of Coriolis vibration gyroscopes with metal resonators, as a rule, are angular velocity sensors. The problem of creating an integrating mode of a gyroscope with a metal resonator is associated with the low quality factor of metal alloys which usually does not exceed 35,000. With this value of quality factor, the duration of operation of the gyroscope in the angular deviation sensor mode will be several seconds. The paper presents methods for ensuring the functioning of Coriolis vibration gyroscopes, including the integrating gyroscope mode. A mathematical description of Coriolis vibration gyroscopes with a cylindrical cavity resonator is given based on the dynamic model of Dr. D. Lynch using the method of envelope amplitudes of oscillations. The mathematical model is supplemented with corrections that provide compensation for the dissipation of the resonator oscillations energy to implement the integrating mode of the gyroscope. The conditions for complete compensation of vibration energy dissipation are shown. A description of methods for exciting a standing wave in a resonator using periodic forcing and by creating self-oscillations is presented. It is shown that the duration of the transient excitation process is determined by the time constant of the resonator. The results of experimental studies of Coriolis vibration gyroscopes with a low-Q metal resonator are presented confirming the possibility of implementing an integrating mode of operation of the gyroscope. The initial excitation of the resonator oscillations is carried out by a self-oscillating circuit. According to the results of experimental studies, the quality factor of the metal resonator was increased by a factor of 17. The operating time of Coriolis vibrating gyroscopes has been equally increased. The possibility of constructing Coriolis vibration gyroscopes in the integrating gyroscope mode based on a low-Q metal resonator has been shown theoretically and experimentally. The solution to this problem was based on a circuitry method for increasing the quality factor. In principle, the quality factor of the resonator can be significantly increased compared to the figure achieved in the experiment. This will ensure a longer operating time of Coriolis vibration gyroscopes in the integrating mode

Dietary Fat Interacts with PCBs to Induce Changes in Lipid Metabolism in Mice Deficient in Low-Density Lipoprotein Receptor

There is evidence that dietary fat can modify the cytotoxicity of polychlorinated biphenyls (PCBs) and that coplanar PCBs can induce inflammatory processes critical in the pathology of vascular diseases. To test the hypothesis that the interaction of PCBs with dietary fat is dependent on the type of fat, low-density lipoprotein receptor–deficient (LDL-R(−/−)) mice were fed diets enriched with either olive oil or corn oil for 4 weeks. Half of the animals from each group were injected with PCB-77. Vascular cell adhesion molecule-1 (VCAM-1) expression in aortic arches was non-detectable in the olive-oil–fed mice but was highly expressed in the presence of PCB-77. PCB treatment increased liver neutral lipids and decreased serum fatty acid levels only in mice fed the corn-oil–enriched diet. PCB treatment increased mRNA expression of genes involved in inflammation, apoptosis, and oxidative stress in all mice. Upon PCB treatment, mice in both olive- and corn-oil–diet groups showed induction of genes involved in fatty acid degradation but with up-regulation of different key enzymes. Genes involved in fatty acid synthesis were reduced only upon PCB treatment in corn-oil–fed mice, whereas lipid transport/export genes were altered in olive-oil–fed mice. These data suggest that dietary fat can modify changes in lipid metabolism induced by PCBs in serum and tissues. These findings have implications for understanding the interactions of nutrients with environmental contaminants on the pathology of inflammatory diseases such as atherosclerosis

Down Syndrome: Age-Dependence of PiB Binding in Postmortem Frontal Cortex Across the Lifespan

Beta-amyloid (Aβ) deposition in brain accumulates as a function of age in people with Down syndrome (DS) with subsequent development into Alzheimer disease neuropathology, typically by 40 years of age. In vivo imaging using the Pittsburgh Compound B (PiB) ligand has facilitated studies linking Aβ, cognition, and dementia in DS. However, there are no studies of PiB binding across the lifespan in DS. The current study describes in vitro 3H-PiB binding in the frontal cortex of autopsy cases with DS compared to non-DS controls. Tissue from 64 cases included controls (N=25) and DS (N=39). In DS, 3H-PiB binding was significantly associated with age. After age 40 years in DS, 3H-PiB binding rose dramatically along with increasing individual variability. 3H-PiB binding correlated with the amount of Aβ42. Using fixed frontal tissue and fluorescent 6-CN-PiB, neuritic and cored plaques along with extensive cerebral amyloid angiopathy (CAA) showed 6-CN-PiB binding. These results suggest that cortical PiB binding as shown by positron emission tomography imaging reflects plaques and CAA in DS brain

HDL-Associated Estradiol Stimulates Endothelial NO Synthase and Vasodilation in an SR-BI–Dependent Manner

Cardiovascular diseases remain the leading cause of death in the United States. Two factors associated with a decreased risk of developing cardiovascular disease are elevated HDL levels and sex — specifically, a decreased risk is found in premenopausal women. HDL and estrogen stimulate eNOS and the production of nitric oxide, which has numerous protective effects in the vascular system including vasodilation, antiadhesion, and anti-inflammatory effects. We tested the hypothesis that HDL binds to its receptor, scavenger receptor class B type I (SR-BI), and delivers estrogen to eNOS, thereby stimulating the enzyme. HDL isolated from women stimulated eNOS, whereas HDL isolated from men had minimal activity. Studies with ovariectomized and ovariectomized/estrogen replacement mouse models demonstrated that HDL-associated estradiol stimulation of eNOS is SR-BI dependent. Furthermore, female HDL, but not male HDL, promoted the relaxation of muscle strips isolated from C57BL/6 mice but not SR-BI null mice. Finally, HDL isolated from premenopausal women or postmenopausal women receiving estradiol replacement therapy stimulated eNOS, whereas HDL isolated from postmenopausal women did not stimulate eNOS. We conclude that HDL-associated estrodial is capable of the stimulating eNOS. These studies establish a new paradigm for examining the cardiovascular effects of HDL and estrogen

Tunneling through a multigrain system: deducing the sample topology from the nonlinear conductance

We study a current transport through a system of a few grains connected with tunneling links. The exact solution is given for an arbitrarily connected double-grain system with a shared gate in the framework of the orthodox model. The obtained result is generalized for multigrain systems with strongly different tunneling resistances. We analyse the large-scale nonlinear conductance and demonstrate how the sample topology can be unambiguously deduced from the spectroscopy pattern (differential conductance versus gate-bias plot). We present experimental data for a multigrain sample and reconstruct the sample topology. A simple selection rule is formulated to distinguish samples with spectral patterns free from spurious disturbance caused by recharging of some grains nearby. As an example, we demonstrate experimental data with additional peaks in the spectroscopy pattern, which can not be attributed to coupling to additional grains. The described approach can be used to judge the sample topology when it is not guaranteed by fabrication and direct imaging is not possible.Comment: 13 pages (including 8 figures