A Comparative Study of Dispersion Characteristics Determination of a Trapezoidally Corrugated Slow Wave Structure Using Different Techniques

The linear dispersion relation of a trapezoidally corrugated slow wave structure （TCSWS） is analyzed and presented. The size parameters of the TCSWS are chosen in such a way that they operate in the x-band frequency range. The dispersion relation is solved by utilizing the Rayleigh-Fourier method by expressing the radial function in terms of the Fourier series. A highly accurate synthetic technique is also applied to determine the complete dispersion characteristics from experimentally measured resonances （cold test）. Periodic structures resonate at specific frequencies when the terminals are shorted numerical calculation, synthetic technique and cold appropriately. The dispersion characteristics obtained from test are compared, and an excellent agreement is achieved.

Sliding behaviors of the trapezoidal roof rock block under a lateral dynamic disturbance

The surrounding rock of underground space is always affected by external dynamic disturbance from the side position,such as blasting vibration from a stope at the same level or seismic waves from adjacent strata.A series of laboratory tests,numerical simulations and theoretical analyses were carried out in this study to disclose the sliding mechanism of roof rock blocks under lateral disturbance.Firstly,the experiments on trapezoidal key block under various clamping loads and disturbance were conducted,followed by numerical simulations using the fast Lagrangian analysis of continua(FLAC3D).Then,based on the conventional wave propagation model and the classical shear-slip constitutive model,a theoretical model was proposed to capture the relative displacement between blocks and the sliding displacement of the key block.The results indicate that the sliding displacement of the key block increased linearly with the disturbance energy and decreased exponentially with the clamping load when the key block was disturbed to slide(without instability).Meanwhile,when the key block was disturbed to fall,two types of instability process may appear as immediate type or delayed type.In addition,the propagation of stress waves in the block system exhibited obvious low-velocity and lowfrequency characteristics,resulting in the friction reduction effect appearing at the contact interface,which is the essential reason for the sliding of rock blocks.The results can be applied to practical underground engineering and provide valuable guidance for the early detection and prevention of rockfalling disasters.

Composite Fractional Trapezoidal Rule with Romberg Integration

The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral operator.This would be achieved by first establishing a fractional-order version of the 2-point Trapezoidal rule and then by proposing another fractional-order version of the(n+1)-composite Trapezoidal rule.In particular,the so-called divided-difference formula is typically employed to derive the 2-point Trapezoidal rule,which has accordingly been used to derive a more accurate fractional-order formula called the(n+1)-composite Trapezoidal rule.Additionally,in order to increase the accuracy of the proposed approximations by reducing the true errors,we incorporate the so-called Romberg integration,which is an extrapolation formula of the Trapezoidal rule for integration,into our proposed approaches.Several numerical examples are provided and compared with a modern definition of the Riemann-Liouville fractional integral operator to illustrate the efficacy of our scheme.

Experimental,analytical and numerical studies on concrete encased trapezoidally web profiled cold-formed steel beams by varying depth-thickness ratio

Concrete encased with trapezoidally corrugated web profiled cold-formed steel beams are used worldwide to improve resistance toward fire and corrosion,higher load carrying capacity as well as significant increase in the bending stiffness by encasing concrete on the beam portion.The present work gives a detailed description on the experimental,analytical and numerical investigation on the flexural behavior of concrete encased trapezoidally corrugated web profiled cold-formed steel beams which were simply supported at both ends and subjected to two point symmetric loading.The flexural behavior of such structure has been experimentally tested to failure under pure bending.To find the effct of concrete encasement in the web,12 experiments were conducted by two different series.Beams having three different web corrugation angles of 0°,30°,and 45°with two different web depth-thickness(dw/tw)ratios of 60 and 80 were tested.Experimental results such as load-deflection relationship,ultimate capacity,load-strain relationship,moment-curvature curves,ductility and failure mode indices of the specimens are presented.From the static bending tests the concrete encased trapezoidally corugated web beam showed improved moment carrying capacity,ductility bchavior and the resistance to transverse deflections in comparison to concrete encased with plain web beam.Especially for the beams with concrete encased 30°trapezoidally corrugated web having(dw/tw)ratio 60 and 80,the loading capacity was improved about 54%and 67.3%and the ductility also increased about l.6 and 3.6 times,when compared to concrete encased beams with plain web.This research should contribute to the future engineering applications on seismic resistant structures and efficient usage of concrete encased with cold-formed steel beams by exhibiting its super elasto-plastic property.The analytical and numerical results showed good agreement with the experimental results at yield load,which indicates that the proposed analytical equations can be applied in predicting flexural strength accurately for such concrete encased trapezoidally corrugated web profiled cold-formed steel beams.

Effect of periodic heat transfer on the transient thermal behavior of a convective-radiative fully wet porous moving trapezoidal fin

A moving trapezoidal profiled convective-radiative porous longitudinal fin wetted in a single-phase fluid is considered in the current article.The periodic variation in the fin base temperature is taken into account along with the temperature sensitive thermal conductivity and convective heat transfer coefficients.The modeled problem,which is resolved into a non-linear partial differential equation(PDE),is made dimensionless and solved by employing the finite difference method(FDM).The results are displayed through graphs and discussed.The effects of amplitude,frequency of oscillation,wet nature,Peclet number,and other relevant quantities on the distribution of temperature through the fin length and with the dimensionless time are investigated.It is deciphered that the periodic heat transfer gives rise to the wavy nature of the fin thermal profile against time.The analysis is beneficial in the design of fin structures for applications like solar collectors,space/airborne applications,and refrigeration industries.

High frequency doubling efficiency THz GaAs Schottky barrier diode based on inverted trapezoidal epitaxial cross-section structure

A high-performance terahertz Schottky barrier diode(SBD)with an inverted trapezoidal epitaxial cross-sectional structure featuring high varactor characteristics and reverse breakdown characteristics is reported in this paper.Inductively coupled plasma dry etching and dissolution wet etching are used to define the profile of the epitaxial layer,by which the voltage-dependent variation trend of the thickness of the metal-semiconductor contact depletion layer is modified.The simulation of the inverted trapezoidal epitaxial cross-section SBD is also conducted to explain the physical mechanism of the electric field and space charge region area.Compared with the normal structure,the grading coefficient M increases from 0.47 to 0.52,and the capacitance modulation ratio(C^(max)/C_(min))increases from 6.70 to 7.61.The inverted trapezoidal epitaxial cross-section structure is a promising approach to improve the variable-capacity ratio by eliminating the accumulation of charge at the Schottky electrode edge.A 190 GHz frequency doubler based on the inverted trapezoidal epitaxial cross-section SBD also shows a doubling efficiency of 35%compared to that 30%of a normal SBD.

Floyd-Warshall Algorithm Based on Picture Fuzzy Information

The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes.It works well for crisp weights,but the problem arises when weights are vague and uncertain.Let us take an example of computer networks,where the chosen path might no longer be appropriate due to rapid changes in network conditions.The optimal path from among all possible courses is chosen in computer networks based on a variety of parameters.In this paper,we design a new variant of the Floyd-Warshall algorithm that identifies an All-Pair Shortest Path(APSP)in an uncertain situation of a network.In the proposed methodology,multiple criteria and theirmutual associationmay involve the selection of any suitable path between any two node points,and the values of these criteria may change due to an uncertain environment.We use trapezoidal picture fuzzy addition,score,and accuracy functions to find APSP.We compute the time complexity of this algorithm and contrast it with the traditional Floyd-Warshall algorithm and fuzzy Floyd-Warshall algorithm.

Analysis of Friction and Heat Transfer Characteristics of Tubes with Trapezoidal Cut Twisted Tape Inserts

The thermo-hydraulic properties of circular tubes with a twisted tape inside(used accordingly to induce turbulence and enhance heat transfer through the tube wall)are described for Reynolds Numbers ranging from 830 to 1990.Tapes twisted with the three distinct twist ratios are considered,namely,6,4.4 and 3.Air is used as the working fluid in several tests.For the sake of comparison,the standard tube with no insert is also examined.It is shown that in the presence of the twisted tape,the‘frictional factor’,‘Nusselt Number’and the‘thermal performance factor’are much higher than those obtained for the plain tube.Moreover,the tapes having the lowest twist ratio,i.e.,3,are more effective than the others in terms of heat transfer augmentation.The‘thermal performance factor’is greater than one for all the twisted tapes used in the experiments,which confirms the enhanced performances of the heat exchanger and the related savings in terms of total energy.

Text Sentiment Analysis Based on Multi-Layer Bi-Directional LSTM with a Trapezoidal Structure

Sentiment analysis,commonly called opinion mining or emotion artificial intelligence(AI),employs biometrics,computational linguistics,nat-ural language processing,and text analysis to systematically identify,extract,measure,and investigate affective states and subjective data.Sentiment analy-sis algorithms include emotion lexicon,traditional machine learning,and deep learning.In the text sentiment analysis algorithm based on a neural network,multi-layer Bi-directional long short-term memory(LSTM)is widely used,but the parameter amount of this model is too huge.Hence,this paper proposes a Bi-directional LSTM with a trapezoidal structure model.The design of the trapezoidal structure is derived from classic neural networks,such as LeNet-5 and AlexNet.These classic models have trapezoidal-like structures,and these structures have achieved success in the field of deep learning.There are two benefits to using the Bi-directional LSTM with a trapezoidal structure.One is that compared with the single-layer configuration,using the of the multi-layer structure can better extract the high-dimensional features of the text.Another is that using the trapezoidal structure can reduce the model’s parameters.This paper introduces the Bi-directional LSTM with a trapezoidal structure model in detail and uses Stanford sentiment treebank 2(STS-2)for experiments.It can be seen from the experimental results that the trapezoidal structure model and the normal structure model have similar performances.However,the trapezoidal structure model parameters are 35.75%less than the normal structure model.

Why Is an Integral an Accurate Value?

The derivative and integral in calculus are both exact values. To explain this reason, the integration interval can be infinitely subdivided. The difference in area between curved trapezoids and rectangles can be explained by the theory of higher-order infinitesimal, leading to the conclusion that the difference between the two is an infinitesimal value. From this, it can be inferred that the result obtained by integration is indeed an accurate value.

Modeling of Coupled Heat and Mass Transfer in a Trapezoidal Porous Bed on a Grid

We investigate heat and mass transfer in an isosceles trapezoidal cavity, filled with charcoal considered as a granular porous medium. The Darcy-Brinkman-Forchheimer flow model is coupled to the energy and mass equations with the assumption of non-thermal equilibrium. These equations are discretized by the finite volume method with an offset mesh and then solved by the line-by-line method of Thomas. The coupling between pressure and velocity is obtained by Semi-Implicit Method for Pressure Linked Equations. (SIMPLE) algorithm. The results show that the temperature in the cavity increases when the inclination angle of the sides walls decreases. The 15° inclination is selected as being able to offer better thermal performance in the cookstove combustion chamber.

Arithmetic Operations of Generalized Trapezoidal Picture Fuzzy Numbers by Vertex Method

In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.

Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems

Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.

Assessment of gas and dust explosion in coal mines by means of fuzzy fault tree analysis

During the past decade, coal dust and gas explosions have been the most two serious types of disasters in China, threatening the lives of miners and causing significant losses in terms of national property. In this paper, an evaluation model of coal dust and gas explosions was constructed based on a fuzzy fault tree by taking the Xingli Coal Mine as a research site to identify the risk factors of coal dust and gas explosions.Furthermore, the hazards associated with such explosions were evaluated for this particular coal mine.After completing an on-site investigation, the fuzzy probabilities of basic events were obtained through expert scoring, and these expert opinions were then aggregated as trapezoidal fuzzy numbers to calculate the degrees of importance of all basic events. Finally, these degrees of importance were sorted. According to the resulting order, the basic events with higher probabilities were determined to identify key hazards in the daily safety management of this particular coal mine. Moreover, effective measures for preventing gas and coal dust explosions were derived. The fuzzy fault tree analysis method is of high significance in the analysis of accidental coal mine explosions and provides theoretical guidance for improving the efficiency of coal mine safety management in a scientific and feasible manner.

Meshless Method for Analysis of Permeable Breakwaters in the Proximity of A Vertical Wall

In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves and in the proximity of a vertical wall. Both single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with appropriate mixed type boundary conditions, and solved numerically using the ISBM. To model the permeability of the breakwaters fully absorbing boundary conditions are assumed. Numerical results are presented in terms of hydrodynamic quantities of the reflection coefficients. These are firstly validated against the results of a multi-domain boundary element method(BEM) developed independently for a previous study. The agreement between the results of the two methods is excellent. The coefficients of reflection are then computed and discussed for a variety of structural conditions including the breakwaters height, width, spacing, and absorbing permeability. Effects of the proximity of the vertical plane wall are also investigated. The breakwater's width is found to have only marginal effects compared with its height. Permeability tends to decrease the minimum reflections. These coefficients show periodic variations with the spacing relative to the wavelength. Trapezoidal breakwaters are found to be more cost-effective than the rectangular breakwaters. Dual breakwater systems are confirmed to perform much better than single structures.

Predictive model for stage-discharge curve in compound channels with vegetated floodplains

The governing equation of the discharge per unit width, derived from the flow continuity equation and the momentum equation in the vegetated compound chan- nel, is established. The analytical solution to the discharge per unit width is presented, including the effects of bed friction, lateral momentum transfer, drag force, and secondary flows. A simple＇ but available numerical integral method, i.e., the compound trapezoidM formula, is used to calculate the approximate solutions of the sub-area discharge and the total discharge. A comparison with the published experimental data from the U. K. Flood Channel Facility （UK-FCF） demonstrates that this model is capable of predicting not only the stage-discharge curve but also the sub-area discharge in the vegetated com- pound channel. The effects of the two crucial parameters, i.e., the divided number of the integral interval and the secondary flow coefficient, on the total discharge are discussed and analyzed.

New insights in the treatment of acromioclavicular separation

A direct force on the superior aspect of the shoulder may cause acromioclavicular(AC) dislocation or separation. Severe dislocations can lead to chronic impairment, especially in the athlete and high-demand manual laborer. The dislocation is classified according to Rockwood. Types Ⅰ?and Ⅱ are treated nonoperatively, while types Ⅳ, Ⅴ and Ⅵ are generally treated operatively. Controversy exists regarding the optimal treatment of type Ⅲ dislocations in the high-demand patient. Recent evidence suggests that these should be treated nonoperatively initially. Classic surgical techniques were associated with high complication rates, including recurrent dislocations and hardware breakage. In recent years, many new techniques have been introduced in order to improve the outcomes. Arthroscopic reconstruction or repair techniques have promising short-term results. This article aims to provide a current concepts review on the treatment of AC dislocations with emphasis on recent developments.

Experimental Study of Wave Attenuation in Trapezoidal Floating Breakwaters

A comprehensive experimental study was carried out on the regular wave attenuation with a trapezoidal pontoontype floating breakwater(FB) in deep water. The functionalities of two simple FB geometries consist of a rectangle and a trapezoid with the slope of 60° were investigated under the wave attack. A two-dimensional wave flume was used in the experiment; the incident, transmitted waves, mooring line forces and motion responses of the floating breakwaters were measured. Also the influence of the sea state conditions(incident wave height and wave period)and structural parameters(draught of the structure) were investigated using the trapezoidal FB. Our experimental results indicated that the trapezoidal FB significantly reduced the wave transmission and mooring line force when compared with rectangular FBs. A new formula was developed in order to predict the value of the transmission coefficient in trapezoidal FBs with the slope of 60°. Experimental data showed to be consistent with the results of the formula.

Application of pole-zero cancellation circuit in nuclear signal filtering and shaping algorithm

In radiation measurement and digital nuclear spectrum systems,traditional nuclear signal processing circuits in nuclear electronics have been gradually replaced by digital algorithm modules with the application of highperformance programmable hardware logic devices(such as FPGA or DSP).Referring to the digital realization method of inverse RC integral circuit systems,the function of the pole-zero cancellation(PZC)circuit was analyzed,a new modified cascade equivalent model of PZC was established,and the time-domain digital PZC(DPZC)recursive algorithm was derived in detail in this study.Two parameters kIand k_(D)are included in the new algorithm,where kIshould match the exponential decay time constant of the input signal to realize the pole-zero compensation,while the decay time constant of the output signal can be changed with the adjustable parameter k_(D)(which is larger than the decay time constant of the input signal).Based on the new DPZC algorithm module,two trapezoidal(triangular)shaping filters were designed and implemented.The amplitude–frequency characteristics of the output signal of the proposed trapezoidal shaping algorithm and the convolution trapezoidal shaping algorithm were compared,with fixed peaking time.The results show that the trapezoidal shaping algorithm based on DPZC can better suppress high-frequency noise.Finally,based on the Na I(Tl)scintillator(u75 mm×75 mm)detector and^(137)Cs source,the effect of the k_(D)value on the energy resolution of the DPZC trapezoidal(triangular)shaping algorithm was studied.The experimental results show that,with an increase in k_(D),the energy resolution of the system improved and reached the maximum when k_(D)was greater than 10,and the optimal energy resolution of the system was 7.72%.

Dynamic Characteristics of Double-Helical Planetary Gear Sets Under Time-Varying Mesh Stiffness

Internal and external meshes are two of primary excitation sources which induce vibration while double-helical planetary gear sets are in transmission. Based on the analysis of tooth movement principle,three cases of mesh stiffness are derived via investigating the length of action lines,and catalogued in terms of β < β0,β = β0and β > β_0. The simulation demonstrates mesh stiffness between gear pairs performs as a trapezoid waveform( TW) and changes along with the line of action simultaneously,total mesh stiffness comes from the superposition of each engaged gear. While governing equations of motion contained 16 DOFs( degree of freedom) are constructed and effectively solved through the combination of numerical approaches. Comparing with sinusoidal waveform mesh stiffness( SW),the results show that dynamical factors and perturbation under the excitation of TW( β < β_0) are greater and remarkable than that from SW,with respect to the mean dynamic factors about 1. 51 and 1. 28,respectively. The fluctuation response between ring- planet( R- P) is stronger than sun-planet( S-P) which is also validated by both approach studies,frequency spectra analyses identifies larger distinct rotational resonance and more frequencies under TW excitation.