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In this note, we study the largest matching roots of unicyclic graphs with a given number of fixed matching number. We also characterize the extremal graph with respect to the largest matching roots. In addition, we also study this problem on the trees with a given number of fixed matching number.

Digital electromagnetic transient simulation is an important means to analyze the operation, planning and control of power systems. Numerical integration algorithm is the core of electromagnetic transient simulation analysis. By analyzing the existing electromagnetic transient simulation methods of power systems, it is difficult to solve the numerical oscillation and decoupling problems, and the root matching method is proposed to solve such problems. From the perspectives of basic component modeling methods and basic simulation algorithms, the disadvantages of mainstream algorithms in solving electromagnetic oscillations are analyzed. Combining the calculation and simulation features in FPGA, the three-phase two-level inverter model of the power system built is verified.

Purpose To determine the cyclic displacement and ultimate failure loads of two clinically relevant suture configurations for repair of medial and lateral meniscus root tears. Methods A total of 10 matched pair fresh-frozen, human meniscus specimens were randomly assigned to either simple cinch or locking loop meniscus–suture fixation techniques for transtibial pull-out repair in either medial ( n  = 10 matched pairs) or lateral ( n  = 10 matched pairs) meniscal root tears. The menisci were subjected to cyclic tensioning at 10–30 N for 1000 cycles at 0.5 Hz, and then post-cycling load to failure was performed at a tensile rate of 0.5 mm/s. Results For both the medial and lateral meniscus, there was significantly less displacement with the cinch stitch at 100, 500 and 1000 cycle counts ( p  < 0.05). In respect to ultimate load, there was no significant difference in type of repair between the two suture configurations. When comparing ultimate load to failure from the medial to the lateral side, the ultimate load to failure was significantly greater for both suture configurations in the lateral meniscus root repair ( p  < 0.05). However, there was no significant difference in cyclic displacement between the medial and lateral meniscus. Conclusions The cinch stitch was significantly better at resisting displacement compared to the locking loop stitch configuration, and had similar ultimate load to failure. The lateral meniscus root repair construct has higher failure loads compared to the medial meniscus, independent of suture configuration.

The matching roots of a simple connected graph G are the roots of the matching polynomial which is defined as MGx=∑k=0n/2−1kmG,kxn−2k, where mG,k is the number of the k matchings of G. Let λ1G denote the largest matching root of the graph G. In this paper, among the unicyclic graphs of order n, we present the ordering of the unicyclic graphs with matching number 2 according to the λ1G values for n≥11 and also determine the graphs with the first and second largest λ1G values with matching number 3.

Here we generate up-to-date reference values of transthoracic echocardiographic aortic root dimensions matched by sex, age, and body surface area (BSA) derived from the population-based Hamburg City Health Study (HCHS) cohort. In 1687 healthy subjects (mean age 57.1 ± 7.7, 681 male and 1006 female), derived from the first prospectively-recruited 10,000 HCHS participants, dimensions of the aortic root were measured in systole and diastole using state-of-the-art 2-dimensional transthoracic echocardiography. Diameters were assessed at four levels: aortic annulus, Sinus of Valsalva, sinotubular junction, and ascending aorta. Female sex was associated with significantly smaller absolute aortic root dimensions, while indexing for BSA resulted in a reverse effect at all levels. There was a strong age dependency of all aortic root diameters as well as aortic annulus/sinotubular junction ratio for both sexes. Multivariate analysis revealed age, sex, weight, height, and BSA to be significant determinants of aortic root size. Finally, formulas were generated for the calculation of individual aortic root reference values considering age, sex, weight, and height. We provide population-based reference values of aortic root diameters based on a standardized transthoracic echocardiographic protocol of the population-based HCHS which may support the diagnosis, monitoring, and treatment of aortic root disease.

Wang, Cui, and Cioabă introduced the Laplacian matching root integral variation of a graph and proved that it cannot occur in one place. They also showed that the two-place variation is impossible for connected graphs satisfying \\(g(G)/c(G)>7/6\\), where \\(g(G)\\) is the girth and \\(c(G)\\) is the dimension of the cycle space, and conjectured that no connected graph admits such a two-place variation. In this paper, we confirm this conjecture. The proof combines a structural relation obtained in their paper with two new power-sum identities for Laplacian matching roots.

The prediction of vibration characteristics was studied in the mistuned bladed disk by the mobile interface prestressed component mode synthesis (CMS) superelement method. When the strongly, generally, and weakly coupling in the mistuned bladed disk, according to the results of the direct FEM method, the prediction accuracy of this method was verified and compared with the fixed-interface CMS method by using the relative error of dynamic frequency, vibration mode matching function, and dimensionless root mean square error of vibration amplitudes. It is pointed that for mistuned bladed disk in the strong coupling, the prediction accuracy of dynamic frequency and vibration amplitudes are higher by the mobile interface CMS method and the vibration modes are matched with the direct method. In weak coupling, the results of dynamic frequency and vibration modes predicted by the mobile interface CMS method and the fixed-interface CMS method are consistent with the direct method, but the vibration amplitudes’ prediction error of the mobile interface CMS method is lower than that of the fixed-interface CMS method. In general coupling, the mobile interface CMS method has higher dynamic frequency prediction accuracy at low order, and the two methods have comparable dynamic frequency prediction accuracy at high order. The vibration modes predicted by the two methods are matched with the direct FEM method, and the prediction accuracy of vibration amplitude by the mobile interface CMS method is better than that of the fixed-interface CMS method. The results indicate that the mobile interface CMS method could more accurately predict vibration characteristics of the mistuned bladed disk with different coupling degrees and could be an effective measurement for studying the vibration characteristics of the mistuned bladed disk system.

Bioenergy crops have a secondary benefit if they increase soil organic C (SOC) stocks through capture and allocation below-ground. The effects of four genotypes of short-rotation coppice willow (Salix spp., ‘Terra Nova’ and ‘Tora’) and Miscanthus (M. × giganteus (‘Giganteus’) and M. sinensis (‘Sinensis’)) on roots, SOC and total nitrogen (TN) were quantified to test whether below-ground biomass controls SOC and TN dynamics. Soil cores were collected under (‘plant’) and between plants (‘gap’) in a field experiment on a temperate agricultural silty clay loam after 4 and 6 years’ management. Root density was greater under Miscanthus for plant (up to 15.5 kg m−3) compared with gap (up to 2.7 kg m−3), whereas willow had lower densities (up to 3.7 kg m−3). Over 2 years, SOC increased below 0.2 m depth from 7.1 to 8.5 kg m−3 and was greatest under Sinensis at 0–0.1 m depth (24.8 kg m−3). Miscanthus-derived SOC, based on stable isotope analysis, was greater under plant (11.6 kg m−3) than gap (3.1 kg m−3) for Sinensis. Estimated SOC stock change rates over the 2-year period to 1-m depth were 6.4 for Terra Nova, 7.4 for Tora, 3.1 for Giganteus and 8.8 Mg ha−1 year−1 for Sinensis. Rates of change of TN were much less. That SOC matched root mass down the profile, particularly under Miscanthus, indicated that perennial root systems are an important contributor. Willow and Miscanthus offer both biomass production and C sequestration when planted in arable soil.

PurposeOsteophytes are common radiographic markers of osteoarthritis. However, they are not accurately depicted using conventional imaging, thus hampering surgical interventions that rely on pre-operative images. Studies have shown that ultrasound (US) is promising at detecting osteophytes and monitoring the progression of osteoarthritis. Furthermore, three-dimensional (3D) ultrasound reconstructions may offer a means to quantify osteophytes. The purpose of this study was to compare the accuracy of osteophyte depiction in the knee joint between 3D US and conventional computed tomography (CT).MethodsEleven human cadaveric knees were pre-screened for the presence of osteophytes. Three osteoarthritic knees were selected, and then, 3D US and CT images were obtained, segmented, and digitally reconstructed in 3D. After dissection, high-resolution structured light scanner (SLS) images of the joint surfaces were obtained. Surface matching and root mean square (RMS) error analyses of surface distances were performed to assess the accuracy of each modality in capturing osteophytes. The RMS errors were compared between 3D US, CT and SLS models.ResultsAverage RMS error comparisons for 3D US versus SLS and CT versus SLS models were 0.87 mm ± 0.33 mm (average ± standard deviation) and 0.95 mm ± 0.32 mm, respectively. No statistical difference was found between 3D US and CT. Comparative observations of imaging modalities suggested that 3D US better depicted osteophytes with cartilage and fibrocartilage tissue characteristics compared to CT.ConclusionUsing 3D US can improve the depiction of osteophytes with a cartilaginous portion compared to CT. It can also provide useful information about the presence and extent of osteophytes. Whilst algorithm improvements for automatic segmentation and registration of US are needed to provide a more robust investigation of osteophyte depiction accuracy, this investigation puts forward the potential application for 3D US in routine diagnostic evaluations and pre-operative planning of osteoarthritis.

Gas turbine engines have several advantages over piston reciprocating engines, such as higher output per unit volume, reduced vibration, rapid acceleration and deceleration, high power output, and clean exhaust gases. As a result, their use for propulsion in ships has been steadily increasing. However, gas turbine engines exhibit significant parameter variations depending on the rotational speed, making the design of controllers to ensure system stability while achieving satisfactory control performance, a very challenging task. In this paper, a novel CEM-based 2-DOF PID controller design technique is proposed to ensure the stability of a gas turbine engine while improving tracking and disturbance rejection performance. The proposed controller consists of a PID controller focused on enhancing disturbance rejection performance and a set-point filter to improve tracking performance. The set-point filter is composed of gains from the controller and a single weighting factor. When tuning the gains of the controller, the maximum sensitivity is considered to maintain an appropriate balance between system stability and response performance. The key novelty of this study can be summarized in two main points. One is that the controller is designed by matching characteristic equations, and by setting the roots of the desired characteristic equation as multipoles, the gains of the PID controller can be tuned with only one adjusting variable, making the tuning of the 2-DOF controller easier. The other is that the controller parameters are tuned based on maximum sensitivity, thus taking into account the robust stability of the control system. To demonstrate the feasibility of the proposed method, simulations are conducted for four scenarios using various performance indices.