Degree Powers of Minimally k-(edge)-connected Graphs

Let G be a graph on n vertices whose degree sequence is d_1≥…≥d_n.For a positive integer p,the degree power of G is defined by e_p(G)=∑_(i=1)~n d_i~p.In this paper,by majorization,we prove that for a minimally k-connected graph G of order n≥4k,it always holds e_2(G)≤kn(n-k)and the extremal graph is K_(k,n-k).Furthermore,we respectively determine the maximum degree powers among all minimally 2(3)-connected graphs and minimally 2-edgeconnected graphs,whose extremal graphs are also characterized.

Modifications in aroma characteristics of'Merlot'dry red wines aged in American,French and Slovakian oak barrels with different toasting degrees

Aging in oak barrels is widely used in enology which could bring flavor changes and aromatic complexity to wines.In the present study,the aroma compounds were analyzed from the‘Merlot’dry red wines,which were fermented in two types of fermenters(stainless steel tank and rotated oak barrel)and aged in six types of oak barrels(three geographic origins×two toasting degrees)for different time(0,3,6 and 9 months,respectively).Results showed that 30 volatiles were associated with barrels and increased during oak aging.The fermenters could influence the intensities of the toast,leathery,smoky,fruity,floral and caramel aromas.The concentration of whisky lactone,eugenol,cis-isoeugenol,and the intensities of the toast and spicy aromas were highest in the wines aged in American oak and were lowest in the wines aged in French oak barrels.The concentrations of guaiacol,syringol,trans-isoeugenol,furfural alcohol,vanilla,cis-whisky lactone enabled the medium toasting barrels to be distinguished from the light toasting ones.The compounds originating from the barrels could be used to distinguish the types of different barrels,but the other general grape-derived and fermentation-derived volatiles could not.The fermenters,oak species and toasting degrees of the barrels all had significant effects on the aroma profiles of the aged‘Merlot’dry red wines,but the influence of the geographic origin was not obvious.

Research on Condenser Deterioration Evolution Trend Based on ANP-EWM Fusion Health Degree

This study presents a proposed method for assessing the condition and predicting the future status of condensers operating in seawater over an extended period.The aim is to address the problems of scaling and corrosion,which lead to increased loss of cold resources.The method involves utilising a set of multivariate feature parameters associated with the condenser as input for evaluation and trend prediction.This methodology offers a precise means of determining the optimal timing for condenser cleaning,with the ultimate goal of improving its overall performance.The proposed approach involves the integration of the analytic network process with subjective expert experience and the entropy weightmethod with objective big data analysis to develop a fusion health degreemodel.The mathematical model is constructed quantitatively using the improved Mahalanobis distance.Furthermore,a comprehensive prediction model is developed by integrating the improved Informer model and Markov error correction.This model takes into account the health status of the equipment and several influencing factors,includingmultivariate feature characteristics.This model facilitates the objective examination and prediction of the progression of equipment deterioration trends.The present study involves the computation and verification of the field time series data,which serves to demonstrate the accuracy of the condenser health-related models proposed in this research.These models effectively depict the real condition and temporal variations of the equipment,thus offering a valuable method for determining the precise cleaning time required for the condenser.

Modelling rapid non-destructive test using light weight deflectometer on granular soils across different degrees of saturation

This study introduces an advanced finite element model for the light weight deflectometer(LWD),which integrates contact mechanics with fully coupled models.By simulating LWD tests on granular soils at various saturation levels,the model accurately reflects the dependence of the LWD modulus on dry density,water content,and effective stress.This model addresses and overcomes the limitations of previous finite element models for this specific problem.Simultaneously,this research presents the first experimentally validated fully coupled contact impact model.Furthermore,the research provides a comparative assessment of elastoplastic and nonlinear elastic models and contrasts an enriched node-tosegment method(developed in this study)with the more precise mortar technique for contact mechanics.These comparisons reveal unique advantages and challenges for each method.Moreover,the study underscores the importance of careful application of the LWD modulus,emphasising the need for sophisticated tools to interpret soil behaviour accurately.

Health effects of fruit juices and beverages with varying degrees of processing

The degree of processing is rarely considered an independent factor in the health effects of fruit juices and beverages(FJBs)consumption.In fact,the consumption of ultra-processed foods has been shown to pose health risks.In this study,we first integrated 4 systems used to classify the degree of food processing and then classified FJBs into three major categories,low(minimal),moderate and high.Second,we compared the differences in attitudes towards FJBs in dietary guidelines.Third,we integrated the results of existing epidemiological surveys,randomized controlled trials,and animal experiments to explore the health risks associated with consuming FJBs.Deepening the processing of FJBs has been found to lead to an increased risk of diseases.Dietary pattern,nutrients,addition agents and consumer preferences may be influential factors.Finally,we investigated whether there were any changes in the health benefits of 100%fruit juices produced by different processing methods.In conclusion,minimally/moderately processed 100%fruit juices provide more health benefits than highly processed fruit beverages.The results support the need to consider the extent of FJBs processing in future studies to adjust official nutritional recommendations for beverage consumption.

Wellbore Cleaning Degree and Hydraulic Extension in Shale Oil Horizontal Wells

The efficient development and exploitation of shale oil depends on long-distance horizontal wells. As the degreeof cleaning of the wellbore plays a key role in these processes, in this study, this problem is investigated experimentallyby focusing on the dimensionless cuttings bed height. A method is proposed to calculate the horizontalwellhydraulic extension taking into account the influence of the wellbore cleaning degree on the wellborepressure distribution and assess the effect of a variety of factors such as the bottom hole pressure, the circulatingpressure drop, the drilling pump performance and the formation properties. The analysis shows that the hydraulicextension of horizontal wells decreases with an increase in the cuttings bed height, and the higher the displacementof drilling fluid, the faster the hydraulic extension declines. The annular pressure drop of the horizontalsection increases with the increase of the cuttings bed height, resulting in a higher bottom-hole pressure. Severalarguments are provided to guide the safe drilling of shale oil horizontal wells and overcome the limits of currenttechnological approaches.

A related degree-based frequent pattern mining algorithm for railway fault data

It is of great significance to improve the efficiency of railway production and operation by realizing the fault knowledge association through the efficient data mining algorithm.However,high utility quantitative frequent pattern mining algorithms in the field of data mining still suffer from the problems of low time-memory performance and are not easy to scale up.In the context of such needs,we propose a related degree-based frequent pattern mining algorithm,named Related High Utility Quantitative Item set Mining(RHUQI-Miner),to enable the effective mining of railway fault data.The algorithm constructs the item-related degree structure of fault data and gives a pruning optimization strategy to find frequent patterns with higher related degrees,reducing redundancy and invalid frequent patterns.Subsequently,it uses the fixed pattern length strategy to modify the utility information of the item in the mining process so that the algorithm can control the length of the output frequent pattern according to the actual data situation and further improve the performance and practicability of the algorithm.The experimental results on the real fault dataset show that RHUQI-Miner can effectively reduce the time and memory consumption in the mining process,thus providing data support for differentiated and precise maintenance strategies.

Triad-displaced ULAs configuration for non-circular sources with larger continuous virtual aperture and enhanced degrees of freedom

Non-uniform linear array(NULA)configurations are well renowned due to their structural ability for providing increased degrees of freedom(DOF)and wider array aperture than uniform linear arrays(ULAs).These characteristics play a significant role in improving the direction-of-arrival(DOA)estimation accuracy.However,most of the existing NULA geometries are primarily applicable to circular sources(CSs),while they limitedly improve the DOF and continuous virtual aperture for noncircular sources(NCSs).Toward this purpose,we present a triaddisplaced ULAs(Tdis-ULAs)configuration for NCS.The TdisULAs structure generally consists of three ULAs,which are appropriately placed.The proposed antenna array approach fully exploits the non-circular characteristics of the sources.Given the same number of elements,the Tdis-ULAs design achieves more DOF and larger hole-free co-array aperture than its sparse array competitors.Advantageously,the number of uniform DOF,optimal distribution of elements among the ULAs,and precise element positions are uniquely determined by the closed-form expressions.Moreover,the proposed array also produces a filled resulting co-array.Numerical simulations are conducted to show the performance advantages of the proposed Tdis-ULAs configuration over its counterpart designs.

Degree of Freedom Analysis for Holographic MIMO Based on a Mutual-Coupling-Compliant Channel Model

Degree of freedom(DOF)is a key indicator for spatial multiplexing layers of a wireless channel.Traditionally,the channel of a multiple-input multiple-output(MIMO)half-wavelength dipole array has a DOF that equals the antenna number.However,recent studies suggest that the DOF could be less than the antenna number when strong mutual coupling is considered.We utilize a mutual-coupling-compliant channel model to investigate the DOF of the holographic MIMO(HMIMO)channel and give a upper bound of the DOF with strong mutual coupling.Our numerical simulations demonstrate that a dense array can support more DOF per unit aperture as compared with a half-wavelength MIMO system.

Probability Distribution of China Aviation Network Average Degree of Edge Vertices and Its Evolutionary Trace Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of average degree of edge vertices of China aviation network were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the average degrees of edge vertices in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the average degree of edge vertices had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.

Probability Distribution of Ratio of China Aviation Network Edge Vertices Degree and Its Evolutionary Trace Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the ratio of edge vertices degree in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the ratio of edge vertices degree had linear probability distribution and the two parameters of the probability distribution had linear evolution trace.

Nonlinear Relationship and Its Evolutionary Trace between Node Degree and Average Path Length of China Aviation Network Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the node degree and the average path length of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the node average path length of China aviation network in 1988,1994,2001,2008 and 2015 was calculated.Through regression analysis,it was found that the node degree had a logarithmic relationship with the average length of node path,and the two parameters of the logarithmic relationship had linear evolutionary trace.Key word:China aviation network,complex network,node degree,average length of node path,logarithmic relationship,evolutionary trace.

Probability Distribution of Arithmetic Average of China Aviation Network Edge Vertices Nearest Neighbor Average Degree Value and Its Evolutionary Trace Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average degree values of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the arithmetic averages of edge vertices nearest neighbor average degree values of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the arithmetic average of edge vertices nearest neighbor average degree values had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.

Nonlinear Relationship and Its Evolutionary Trace between Average Degree and Average Path Length of Edge Vertices of China Aviation Network Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the average degree and the average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the average degree and average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Through regression analysis,it was found that the average degree had a logarithmic relationship with the average path length of edge vertices and the two parameters of the logarithmic relationship had linear evolutionary trace.

Numerical Study of a Three-Dimensional Laminar Flow in a Rectangular Channel with a 180-Degree Sharp Turn

This study presents a numerical analysis of three-dimensional steady laminar flow in a rectangular channel with a 180-degree sharp turn. The Navier-Stokes equations are solved by using finite difference method for Re = 900. Three-dimensional streamlines and limiting streamlines on wall surface are used to analyze the three-dimensional flow characteristics. Topological theory is applied to limiting streamlines on inner walls of the channel and two-dimensional streamlines at several cross sections. It is also shown that the flow impinges on the end wall of turn and the secondary flow is induced by the curvature in the sharp turn.

Trimming the Degrees of Freedom via a K^(+) Flux Rectifier for Safe and Long‑Life Potassium‑Ion Batteries

High degrees of freedom(DOF)for K^(+)movement in the electrolytes is desirable,because the resulting high ionic conductivity helps improve potassium-ion batteries,yet requiring support from highly free and flammable organic solvent molecules,seriously affecting battery safety.Here,we develop a K^(+)flux rectifier to trim K ion’s DOF to 1 and improve electrochemical properties.Although the ionic conductivity is compromised in the K^(+)flux rectifier,the overall electrochemical performance of PIBs was improved.An oxidation stability improvement from 4.0 to 5.9 V was realized,and the formation of dendrites and the dissolution of organic cathodes were inhibited.Consequently,the K||K cells continuously cycled over 3,700 h;K||Cu cells operated stably over 800 cycles with the Coulombic efficiency exceeding 99%;and K||graphite cells exhibited high-capacity retention over 74.7%after 1,500 cycles.Moreover,the 3,4,9,10-perylenetetracarboxylic diimide organic cathodes operated for more than 2,100 cycles and reached year-scale-cycling time.We fabricated a 2.18 Ah pouch cell with no significant capacity fading observed after 100 cycles.

Rapid testing and prediction of soil–water characteristic curve of subgrade soils considering stress state and degree of compaction

The subgrade soil is generally in saturated or unsaturated condition. To analyze complex thermo-hydro-mechanical-chemical (THMC) behaviors of subgrade, it is essential to determine the soil–water characteristic curve (SWCC) that represents the relationship between matric suction and moisture content. In this study, a full-automatic rapid stress-dependent SWCC pressure-plate extractor was developed. Then, the influences of overburden stress and degree of compaction on the SWCC of subgrade soil such as high liquid limit silt (MH) and low liquid limit clay (CL) were analyzed. Accordingly, a new model taking into account the influences of overburden stress and degree of compaction based on the well-known Van Genuchten (VG) SWCC fitting model was presented and validated. The results show that with the increase of the degree of compaction and overburden stress, the saturated moisture content of subgrade soil decreases, while the air-entry value increases and the transition section curve becomes flat. The influences of the degree of compaction and overburden stress on the SWCC of MH is greater than that of CL. Meanwhile, there was a satisfactory agreement between the prediction and measurement, indicating a good performance of the new model for predicting the SWCC.

Theory of Approximate Reasoning in Two-Valued Predicate Logic Based on the Quasi-truth Degrees

Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the quasi-truth degrees of first-order formulae is discussed, and it is proved that there is no isolated point in the logic metric space (F, ρ ). Thus the pseudo-metric between first-order formulae is well defined to develop the study about approximate reasoning in the logic metric space (F, ρ ). Then, three different types of approximate reasoning patterns are proposed, and their equivalence under some condition is proved. This work aims at filling in the blanks of approximate reasoning in quantitative predicate logic.

Effect of modification degrees on the interfacial properties and EOR efficiency of amphiphilic Janus graphene oxide

Asymmetrically modified Janus graphene oxide(JGO)has attracted great attention due to its unique physical chemistry properties and wide applications.The modification degree of Janus nanosheets inevitably affects their interfacial activity,which is essential for their performances in enhanced oil recovery(EOR).In this study,the interfacial properties of Janus graphene oxide(JGO)with various modification degrees at liquid-liquid and liquid-solid interfaces were systematically evaluated via the measurements of interfacial tension(IFT),dilatational modulus,contact angle,and EOR efficiency was further assessed by core flooding tests.It is found that JGO-5 with higher modification degree exhibits the greater ability to reduce IFT(15.16 mN/m)and dilatational modulus(26 mN/m).Furthermore,JGO can construct interfacial and climbing film with the assistance of hydrodynamic power to effectively detach the oil from the rock surface and greatly enhance oil recovery.Moderately modified JGO-2 can highly improve recovery of residual crude oil(11.53%),which is regarded as the promising EOR agent in practical application.The present study firstly focuses on the effects of modification degrees on the JGO interfacial properties and proposes diverse EOR mechanisms for JGO with different modification degrees.

Influence of relative compaction and degree of saturation on the deformation characteristics of bentonite under freeze-thaw cycles

Bentonite,consisting of clay minerals of the montmorillonite group,has been widely used as an adsorbent and backfill material in nuclear waste disposal and groundwater remediation.It is challenging to use bentonite as a filling material in cold regions since bentonite is highly sensitive to thermal environmental changes,during which its bulk volume and microstructure change significantly.In this study,a series of one-dimensional and three-dimensional freeze-thaw tests were carried out within a closed system to investigate the influencing factors of the deformation of bentonite under freeze-thaw cycles.Results show that the initial soil water content greatly impacts bentonite's deformation during freeze-thaw cycles.For an initial higher degree of saturation(Sr),the expansion caused by the formation of ice lenses has a greater impact than the shrinkage induced by dehydration,ice-cementation,and so on.Conversely,bentonite tends to shrink at a lower degree of saturation during freezing.And the critical degree of saturation that determines bentonite's behavior of frost heave or frost shrinkage seems to be roughly 0.8.As the number of freeze-thaw cycles rises,initially uncompacted bentonite clay becomes more compacted,and initially compacted bentonite clay remains unchanged.