Binaries Wandering Around Supermassive Black Holes Due To Gravito-electromagnetism

Extreme-mass-ratio inspirals (EMRIs) are important sources for space-borne gravitational-wave (GW) detectors. Such a source normally consists of a stellar-mass black hole (BH) and a Kerr supermassive BH (SMBH), but recent astrophysical models predict that the small body could also be a stellar-mass binary BH (BBH). A BBH reaching several gravitational radii of a SMBH will induce rich observable signatures in the waveform, but the current numerical tools are insufficient to simulate such a triple system while capturing the essential relativistic effects. Here we solve the problem by studying the dynamics in a frame freely falling alongside the BBH. Since the BBH is normally non-relativistic and much smaller than the curvature radius of the Kerr background, the evolution in the free-fall frame reduces to essentially Newtonian dynamics, except for a perturbative gravito-electromagnetic (GEM) force induced by the curved background. We use this method to study the BBHs on near-circular orbits around a SMBH and track their evolution down to a distance of $2-3$ gravitational radii from the SMBH. Our simulations reveal a series of dynamical effects which are not shown in the previous studies using conventional methods. The most notable one is a radial oscillation and azimuthal drift of the BBH relative to the SMBH. These results provide new insight into the evolution and detection of the EMRIs containing BBHs.Comment: 12 pages, 10 figures. Comments welcome

On mixed Ramsey numbers

AbstractFor a graph theoretic parameter f, an integer m and a graph H, the mixed Ramsey number v(f; m; H) is defined as the least positive integer p such that if G is any graph of order p, then either f(G)⩾m or Ḡ contains a subgraph isomorphic to H. Let ϱ denote vertex linear arboricity and let H be any connected graph of order n. In this note we show that v(ϱ; m; H) = 1 + (n + np(H) − 2)(m − 1), where np(H) is the path partition number of H

Prevention and Control Strategies and Mechanism Analysis for Risk Derivative of Coal Energy Supply Chain

AbstractThis paper analyzes the risk derived source of the coordinated development between the coal production, coal transportation, power generation, coal-powered energy to the electricity supply chain; coal production, coal transportation, power generation, electricity supply to the investment risk between incremental development, incremental development cost risk, price risk mechanism of delivery of development; the risk prevention and control of coal production, coal transportation, power generation, power supply to the electricity supply chain

A note on the total chromatic number of Halin graphs with maximum degree 4

AbstractIn this paper, we prove that χT(G) = 5 for any Halin graph G with Δ(G) = 4, where Δ(G) and χT(G) denote the maximal degree and the total chromatic number of G, respectively

Some properties of Ramsey numbers

AbstractIn this paper, some properties of Ramsey numbers are studied, and the following results are presented. 1.(1) For any positive integers k1, k2, …, km l1, l2, …, lm (m > 1), we have r ∏i=1m ki + 1, ∏i=1m li + 1 ≥ ∏i=1m [ r (ki + 1,li + 1) − 1] + 1.2.(2) For any positive integers k1, k2, …, km, l1, l2, …, ln , we have r ∑i=1m ki + 1, ∑j=1n lj + 1 ≥ ∑i=1m∑j=1n r (ki + 1,lj + 1) − mn + 1. Based on the known results of Ramsey numbers, some results of upper bounds and lower bounds of Ramsey numbers can be directly derived by those properties

Trichlorophenyl-benzoxime induces apoptosis in human colon carcinoma cells via activation of mitochondria dependent pathway

Purpose: To determine the apoptotic effect of trichlorophenyl-benzoxime (TCPB) on colorectal cancer (CRC) cells, and to elucidate the mechanism of action. Methods: Colon carcinoma cell lines (DLD-1 and HT-29) were used in this study. The cells were cultured in Dulbecco's modified Eagle's medium (DMEM) supplemented with 10 % fetal bovine serum (FBS) and 1 % penicillin/streptomycin at 37 ˚C in an atmosphere of 5 % CO2 and 95 % air. When the cells attained 60 - 70 % confluency, they were treated with serum-free medium and graded concentrations of TCPB (1.0 – 6.0 μM) for 24 h. Cell viability and apoptosis were assessed using 3-(4, 5-dimethylthiazol-2-yl) 2, 5-diphenyltetrazolium bromide (MTT) and flow cytometric assays, respectively. Western blotting and 2', 7' dichlorofluorescein diacetate (DCFH DA) assays were used for the determination of expression levels of apoptotic proteins, and levels of reactive oxygen species (ROS), respectively. Results: Treatment of DLD-1 and HT-29 cells with TCPB led to significant and dose-dependent reductions in their viability, as well as significant and dose-dependent increases in the number of apoptotic cells (p < 0.05). Treatment of HT-29 cells with TCPB led to significant increases in the population of cells in the G0/G1 phase, but significant reduction of cell proportion in S and G2/M phases (p < 0.05). It also significantly and dose-dependently upregulated the expressions of caspase-3 and bax, down-regulation of the expression of bcl-2 (p < 0.05). TCPB treatment upregulated the expressions of p53, cytochrome c (cyt c), procaspase-3, and procaspase-9, but down-regulated the expression of pAkt dose-dependently (p < 0.05). The expression of Akt in HT-29 cells was not significantly affected by TCPB (p > 0.05). However, TCPB significantly enhanced the cleavage of PARP1, and significantly and dose-dependently increased the levels of ROS in HT-29 cells (p < 0.05). Conclusion: These results suggest that TCPB exerts apoptotic effect on CRC cells via activation of mitochondria-dependent pathway, and thus can be suitably developed for the management of colon cancer

A Multiobjective Robust Scheduling Optimization Mode for Multienergy Hybrid System Integrated by Wind Power, Solar Photovoltaic Power, and Pumped Storage Power

Wind power plant (WPP), photovoltaic generators (PV), cell-gas turbine (CGT), and pumped storage power station (PHSP) are integrated into multienergy hybrid system (MEHS). Firstly, this paper presents MEHS structure and constructs a scheduling model with the objective functions of maximum economic benefit and minimum power output fluctuation. Secondly, in order to relieve the uncertainty influence of WPP and PV on system, robust stochastic theory is introduced to describe uncertainty and propose a multiobjective stochastic scheduling optimization mode by transforming constraint conditions with uncertain variables. Finally, a 9.6 MW WPP, a 6.5 MW PV, three CGT units, and an upper reservoir with 10 MW·h equivalent capacity are chosen as simulation system. The results show MEHS system can achieve the best operation result by using the multienergy hybrid generation characteristic. PHSP could shave peak and fill valley of load curve by optimizing pumping storage and inflowing generating behaviors based on the load supply and demand status and the available power of WPP and PV. Robust coefficients can relieve the uncertainty of WPP and PV and provide flexible scheduling decision tools for decision-makers with different risk attitudes by setting different robust coefficients, which could maximize economic benefits and minimize operation risks at the same time