Trees with the most subtrees -- an algorithmic approach

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in applications. The number of subtrees in the extremal cases constitute sequences which are of interest to number theorists. The structures which maximize or minimize the number of subtrees among general trees, binary trees and trees with a given maximum degree have been identified previously. Most recently, results of this nature are generalized to trees with a given degree sequence. In this note, we characterize the trees which maximize the number of subtrees among trees of a given order and degree sequence. Instead of using theoretical arguments, we take an algorithmic approach that explicitly describes the process of achieving an extremal tree from any random tree. The result also leads to some interesting questions and provides insight on finding the trees close to extremal and their numbers of subtrees.Comment: 12 pages, 7 figures; Journal of combinatorics, 201

Effects of benthic algae on release of soluble reactive phosphorus from sediments: a radioisotope tracing study

AbstractTo evaluate the effect of benthic algae on soluble reactive phosphorus (SRP) release from sediments in shallow lakes, experiments on SRP release with and without benthic algae in sediment cores and an experiment on SRP uptake by benthic algae were conducted using the radioisotope (32P) tracing method. The dissolved oxygen (DO) concentration in sediment cores was also investigated. The results show that benthic algae effectively reduce the release of SRP from sediments to overlying water. The uptake of SRP by benthic algae, which is the direct way in which benthic algae affect the SRP release from sediments, is low in filtered water and increases with the SRP concentration. However, in the experiment, the increased uptake rate lasted for a short time (in one hour), and after that it returned to a low rate. Benthic algae make the DO concentration and the oxic layer thickness increased, which can indirectly reduce the SRP release from sediments. These findings indicate that benthic algae can reduce the SRP release from sediments in both direct and indirect ways. It seems that the indirect way also plays an important role in reducing the SRP release from sediments

2,2′-[(4,6-Dinitro-1,3-phenyl­ene)dioxy]diacetic acid hemihydrate

The skeletons of both independent mol­ecules of the carboxylic acid hemihydrate, C10H8N2O10·0.5H2O, are approximately planar [maximum deviations 0.642 (3) and 0.468 (1) Å]. The deviations arise from the twisting of the nitro groups with respect to the aromatic rings [dihedral angles = 3.24 (2) and 27.01 (1), and 7.87 (1) and 16.37 (2)° in the two molecules]. The crystal structure features inter­molecular O—H⋯O hydrogen bonds, which the link the dicarboxylic acid and water mol­ecules into a supra­molecular layer network

Poly[diethyl­enetriammonium [aquadi-μ2-sulfato-sulfatocerium(III)]]

A new organically templated open-framework cerium sulfate, {(C4H16N3)[Ce(SO4)3(H2O)]}n, was hydro­thermally synthesized. The CeIII cation is nine-coordinated by nine O atoms, including one water mol­ecule. Two of the SO4 groups afford one monodentate and bidentate linkages as the bridge to connect adjacent CeIII cations, while the third SO4 group attaches the CeIII cation in a bidentate mode. The crystal structure consists of layers composed of eight-membered-ring networks formed by four CeO9 polyhedra and four SO4 tetra­hedra. The triply protonated diethyl­enetriamine cations are located between adjacent layers and connect the layers via hydrogen bonds

Multi-axis fatigue loading system of wind turbine blade and vibration coupling characteristics

This paper presents a new method which focuses on the multi-axis fatigue loading mode for wind turbine blade and aims to shorten the fatigue loading cycle. The whole test scheme is design for the measurement of fatigue loading system. The two leading sources of fatigue loading system are asymmetric arrangement in the space. In addition, its vibration mathematical model is derived according to the Lagrange equation. The numerical simulation model is developed by means of Matlab Simulink. The vibration coupling characteristics including motor revolution speed, phase and amplitude of wind turbine blade is obtained. Moreover, the trajectory of wind turbine blade is obtained. Finally, a multi-axis fatigue loading platform for small wind turbine blade is built for the proposed study. The on-site test showed that if the revolution speeds of the two loading sources is the same as the natural frequency of wind turbine blade, the revolution speed, the phase angle of motor and the blade trajectory were relative changed smoothly. Thus, the amplitude of blade is state and the largest. Otherwise when the revolution speed of motor is different with the natural frequency of blade, the revolution speeds and phase angle of the two loading sources fluctuated largely. The above conclusion provided the theoretical basis for the subsequent decoupling control algorithm of multi-axis fatigue loading test

Inhibitory Effects of Various Ratios of Polysaccharides/Alkaloids from Rhizome of Coptis chinensis Franch on α-Glucosidase

Purpose: To investigate the inhibitory effects of various ratios of polysaccharides/ alkaloids from the rhizome of Coptis chinensis Franch (RCC) on α-glucosidase.Methods: The polysaccharides (PSD) and alkaloids (ALK) from RCC were prepared using the water extraction and alcohol precipitation method and Reinecke’s salt precipitation method, respectively. Subsequently, the α glucosidase inhibitory effects of PSD, ALK, and PSD/ALK at various ratios were evaluated spectrophotometrically in vitro.Results: With a half maximal inhibitory concentration (IC50) value of 171.67 μg/mL, ALK showed higher α-glucosidase inhibitory activity than PSD (IC50 = 296.89 μg/mL). In addition, the polysaccharides/alkaloids (PSD/ALK) at the ratio of 3:1 exhibited stronger α-glucosidase inhibitory activity (IC50 = 160.9 μg/mL) than PSD, ALK and PSD/ALK at ratios of 1:3 (IC50 = 394.78 μg/mL), 1:2 (IC50 = 185.18 μg/mL), 1:1 (IC50 = 350.51 μg/mL), and 2:1 (IC50 = 229.16 μg/mL).Conclusion: The results obtained suggest that PSD/ALK (3:1) possesses the strongest α-glucosidase inhibitory effect and may be considered as a candidate agent in future anti-diabetes drug development.Keywords: Coptis chinensis, Polysaccharides, Alkaloids, α-Glucosidase, Antidiabeti

Quality evaluation of cortex berberidis from different geographical origins by simultaneous high performance liquid chromatography combined with statistical methods

Purpose: To develop an effective method for evaluating the quality of Cortex berberidis from different geographical origins.Methods: A simple, precise and accurate high performance liquid chromatography (HPLC) method was first developed for simultaneous quantification of four active alkaloids (magnoflorine, jatrorrhizine, palmatine, and berberine) in Cortex berberidis obtained from Qinghai, Tibet and Sichuan Provinces of China. Method validation was performed in terms of precision, repeatability, stability, accuracy, and linearity. Besides, partial least squares discriminant analysis (PLS-DA) and one-way analysis of variance (ANOVA) were applied to study the quality variations of Cortex berberidis from various geographical origins.Results: The proposed HPLC method showed good linearity, precision, repeatability, and accuracy. The four alkaloids were detected in all samples of Cortex berberidis. Among them, magnoflorine (36.46 - 87.30 mg/g) consistently showed the highest amounts in all the samples, followed by berberine (16.00 - 37.50 mg/g). The content varied in the range of 0.66 - 4.57 mg/g for palmatine and 1.53 - 16.26 mg/g for jatrorrhizine, respectively. The total content of the four alkaloids ranged from 67.62 to 114.79 mg/g. Moreover, the results obtained by the PLS-DA and ANOVA showed that magnoflorine level and the total content of these four alkaloids in Qinghai and Tibet samples were significantly higher (p < 0.01) than those in Sichuan samples.Conclusion: Quantification of multi-ingredients by HPLC combined with statistical methods provide an effective approach for achieving origin discrimination and quality evaluation of Cortex berberidis. The quality of Cortex berberidis closely correlates to the geographical origin of the samples, with Cortex berberidis samples from Qinghai and Tibet exhibiting superior qualities to those from Sichuan.Keywords: Tibetan medicine, Cortex berberidis, Origin discrimination, Quality evaluation, Magnoflorine, Palmatine, Berberine, Jatrorrhizin

Antimicrobial and molecular interaction studies on derivatives of curcumin against Streptococcus pneumoniae which caused pneumonia

Background: The antimicrobial properties and molecular interaction analysis of curcumin and its derivatives against three different strains of Streptococcus pneumoniae (Penicillin-susceptible, Penicillin-intermediate and Penicillin-resistant) are studied. Results: These properties were analyzed based on the measurement of the inhibition zone, minimum inhibitory concentration (MIC), and rate of kill revealed that curcumin monoglucoside, curcumin diglucoside and curcumin possessed strong antimicrobial properties even on the Penicillin-resistant strains. Additionally, the molecular docking simulation analyses against Penicillin Binding Protein of S. pneumoniae also confirm that these compounds docked at the active site of the enzyme. Further, the molecular dynamics simulation validates the conformational stability of the docked ligand\u2013protein complexes in the dynamic environment. Conclusion: curcumin monoglucoside, curcumin diglucoside and curcumin can be prescribed for treatment against Penicillin-resistant S. pneumoniae

Goal-directed fluid optimization based on stroke volume variation and cardiac index during one-lung ventilation in patients undergoing thoracoscopy lobectomy operations: a pilot study

OBJECTIVES: This pilot study was designed to utilize stroke volume variation and cardiac index to ensure fluid optimization during one-lung ventilation in patients undergoing thoracoscopic lobectomies. METHODS: Eighty patients undergoing thoracoscopic lobectomy were randomized into either a goal-directed therapy group or a control group. In the goal-directed therapy group, the stroke volume variation was controlled at 10%±1%, and the cardiac index was controlled at a minimum of 2.5 L.min-1.m-2. In the control group, the MAP was maintained at between 65 mm Hg and 90 mm Hg, heart rate was maintained at between 60 BPM and 100 BPM, and urinary output was greater than 0.5 mL/kg-1/h-1. The hemodynamic variables, arterial blood gas analyses, total administered fluid volume and side effects were recorded. RESULTS: The PaO2/FiO2-ratio before the end of one-lung ventilation in the goal-directed therapy group was significantly higher than that of the control group, but there were no differences between the goal-directed therapy group and the control group for the PaO2/FiO2-ratio or other arterial blood gas analysis indices prior to anesthesia. The extubation time was significantly earlier in the goal-directed therapy group, but there was no difference in the length of hospital stay. Patients in the control group had greater urine volumes, and they were given greater colloid and overall fluid volumes. Nausea and vomiting were significantly reduced in the goal-directed therapy group. CONCLUSION: The results of this study demonstrated that an optimization protocol, based on stroke volume variation and cardiac index obtained with a FloTrac/Vigileo device, increased the PaO2/FiO2-ratio and reduced the overall fluid volume, intubation time and postoperative complications (nausea and vomiting) in thoracic surgery patients requiring one-lung ventilation