Structural Carpentry in Qing Dynasty-A Framework for the Hierarchically Modularized Chinese Timber Structural Design

This article, by using mathematical expressions, offers a scientific framework for understanding how the grading system of Qing′s structural carpentry determines the design and construction in the grand style timber architecture.The Qing′s grand style timber structure, which is ready for prefabrication and assembly, is extremely hierarchical oriented and significantly standardized. The general procedure in designing a grand style timber structure is to start with the grade that defines the basic module (dou kou); next comes with the number of bracket set (cuan), the number of longitudinal bays and the number of purlins which affect its plan and cross section; thirdly choose a roof type that determines its longitudinal section and the facade as well. A series of formulae are conducted to help depict the layout, cross sectional roof curvature and special longitudinal treatments in 4 sloped and 9 spined roofs respectively.

Influences affecting the soil-water characteristic curve

The soil-water characteristic curve (SWCC) is the primary partially saturated soil information as its behavior and properties can be derived from it. Although there have been many studies of unsaturated soils and the SWCC, there is still no combined constitutive model that can simulate soil characteristics accurately. In cases when hydraulic hysteresis is dominant (e.g. under cyclic loading) it is particularly important to use the SWCC. In the past decades, several mathematical expressions have been proposed to model the curve. There are various influences on the SWCC as a source of information, so the curves obtained from conventional tests often cannot be directly applied; and the mathematical expressions from one scenario cannot be used to simulate another situation. The effects of void ratio, initial water content, stress state and high suction were studied in this work revealing that water content and stress state are more important than the other effects; but that the influences tend to decrease when suction increases. The van Genuchten model was modified to simulate better the changes in the degree of saturation at low values of suction. Predictions were compared with experimental results to determine the simulation capability of the model.

Seepage-stress coupling constitutive model of anisotropic soft rock

To provide a seepage-stress coupling constitutive model that can directly describe the seepage-stress coupling relationship, a series of one-dimensional seepage-stress coupling tests on two kinds of soft rock (argillaceous siltstone and brown mudstone) were performed by using an MTS-815.02 tri-axial rock mechanics test system, with which the stress-strain curves according to the seepage variation were obtained. Based on the experimental results and by employing Hooke's law, the formulation of the coefficient of strain-dependent permeability was presented and introduced to establish a coupling model. In addition, the mathematical expression and the incremental formulation for coupling model were advanced, in which five parameters that can be respectively determined by using the experimental results were included. The calculated results show that the proposed coupling model is capable of simulating the stress-strain relationship with considering the seepage-stress coupling in the nonlinear elastic stage of two kinds of soft rock.

Characteristics of a Terrain-Following Sigma Coordinate

This study quantifies the main characteristics of a terrain-following, G-coordinate through mathematical analyses of its covariant and contravariant basis vectors as well as the vertical coordinate of σ. A 3-D schematic of the σ-coordinate in a curvilinear coordinate system is provided in this study. The characteristics of the basis vectors were broken down into their ＂local vector charac- teristics＂ and ＂spatial distribution characteristics＂, and the exact expressions of the covariant; in addition, the con- travariant basis vectors of the G-coordinate used to eluci- date their detailed characteristics were properly solved. Through rewriting the expression of the vertical coordi- nate of G, a mathematical expression of all the cr-coor- dinate surfaces was found, thereby quantifying the so- called terrain-following characteristics and lack of flexi- bility to adjust the slope variation of G-coordinate sur- faces for the classic definition of G. Finally, an analysis on the range value of the vertical coordinate demonstrated that the general value range of G could be obtained by eliminating the G-coordinate surfaces below the Earth＇s surface. All these quantitative descriptions of the charac- teristics of G-coordinate were the foundation for improv- ing the G-coordinate or creating a new one.

Frame Detection Based on Cyclic Autocorrelation and Constant False Alarm Rate in Burst Communication Systems

Frame detection is important in burst communication systems for its contribu- tions in frame synchronization. It locates the information bits in the received data stream at receivers. To realize frame detection in the presence of additive white Gaussian noise （AWGN） and frequency offset, a constant false alarm rate （CFAR） detector is proposed through exploitation of cyclic autocorrelation feature implied in the preamble. The frame detection can be achieved prior to bit timing recovery. The threshold setting is independent of the signal level and noise level by utilizing CFAR method. Mathematical expressions is derived in AWGN channel by considering the probability of false alarm and probability of detection, separately. Given the probability of false alarm, the mathematical relationship between the frame detection performance and EJNo of received signals is established. Ex- perimental results are also presented in accor- dance with analysis.

Derivation of Multiverse from Universal Wave Function Interpretation of String Theory

The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive power of this theory is rather limited. Furthermore, there are concerns that this theory will make it impossible to calculate some measured quantities, such as the masses of quarks and the electron. In this paper, we will show that a new development in string theory, the universal wave function interpretation of string theory, provides a way to derive the mathematical expression of the multiverse. We will demonstrate that the Weyl invariance existing in string theory indicates that our observed universe is a projection from a hologram. We will present how the laws of physics can be derived from this fact. Furthermore, we suggest it may also provide a way to calculate the masses of fundamental particles such as quarks and the electron.

Insurance ratemaking method for risk of construction diversion project

Based on analyzing risk factors of diversion project,synthetic risk rate and engineering insurance period,the frequency and distribution law of loss are researched on the grounds that foundation pit is submerged after diversion project ceases to be effective.And then,the standpoint that these total loss is subject to non-homogeneous compound Poisson processes is put forward.Furthermore,the collective risk model of the total loss about engineering insurance is established on the basis of construction diversion project risk.Ultimately,insurance ratemaking method for construction engineering risk and its mathematical expression are presented,which provides theoretical method for the insurance ratemaking of hydropower engineering to some extent.

Potentials of Cellular Vortex Element Modeling of Fluid Flow in Confined 2D Aquifer

Numerical methods such as finite difference, finite volume, finite element or hybrid methods have been globally used to successfully study fluid flow in porous stratum of which aquifers are typical examples. Those methods involve mathematical expressions which increases computation time with requirement of specific human expertise. In this paper, numerical models for single phase flow in 1D and 2D using the conservation of mass principles, Darcy＇s flow equation, equation of state, continuity equation and the STB/CFB （stock tank barrel/cubic feet barrel） balance were developed. The models were then recast into pressure vorticity equations using convectional algorithms. Derived equations were used to formulate transport equations which resemble the conventional vorticity transport equation. Formulated numerical models were used to investigate the daily instantaneous aquifer pressure drawdowns and pressure heads for 365 days. The developed equations were subsequently solved using cellular vortex element technique. The developed computer program was used to investigate confined aquifer of dimensions 10× 10 × 75 m with single vertex image. For the aquifer rate of 0.5 m3/s, 0.1 m3/s, 0.15 m3/s, 0.2 m3/s, 0.25 m3/s, 1.0 m3/s, 2.0 m3/s, 2.5 m3/s, 3.0 m3/s, 4.0 m3/s, the respective average head drawdowns and heads were, 1.127 ±0.0141 m, 1.317 ±0.0104 m, 1.412± 0.0041 m, 1.427 ± 0.116 m,1.527 ± 0.0141 m, 2.107 ± 0.0171 m, 2.197 ±0.0191 m, 3.007±0.0171 m, 3.127 ± 0.0041 m, 3.626 ± 0.0121 m, and 25 kN/m2, 35 kN/m2, 33 kN/m2, 5 kN/m2, 6 kN/m2, 11 kN/m2, 25 kN/m2, 42 kN/m2, 50 kN/m2, 62 kN/m2, respectively. Cellular vortex technique with relative little mathematics has been established to have recorded successes in numerical modeling of fluid flow in aquifer simulation.

FEM Edge Effect and Capacitance Evaluation on Cylindrical Capacitors

The purpose of this paper is to show the influence of the edge-effect on the electric field distribution, and hence on the inner capacitance and outer capacitance of a cylindrical capacitor surrounded by an insulating medium. To generalize the results, a two-dimensional axisymmetric finite element model of a cylindrical capacitor has been generated and the problem has been resolved taking into account the distance between the conductors for a complete set of dimensions. The available obtained results have been compared with previous published works. Finally, using statistical tools, the mathematical expression for computing the relationship between capacitance and insulation gap and cylindrical plates dimensions has been obtained.

Effect of Spatial Dimension and External Potential on Joule-Thomson Coefficients of Ideal Bose Gases

Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity, the analytical expressions of the Joule-Thomson coefficient （3TC） for an ideal Bose gas are derived in n-dimensional potential. The effect of the spatial dimension and the external potential on the JTC are discussed, respectively. These results show that： （i） For the free ideal Bose gas, when n/s ≤ 2 （n is the spatial dimension, s is the momentum index in the relation between the energy and the momentum）, and T → Tc （Tc is the critical temperature）, the JTC can obviously improve by means of changing the throttle valve＇s shape and decreasing the spatial dimension of gases. （ii） For the inhomogeneous external potential, the discriminant △= [1 - y∏^ni=1（kT/εi）^1/tiГ（1/ti＋1）] （k is the Boltzmann Constant, T is the thermodynamic temperature, ε is the external field＇s energy）, is obtained. The potential makes the JTC increase when △ 〉 0, on the contrary, it makes the JTC decrease when A 〈△. （iii） In the homogenous strong external potential, the JTC gets the maximum on the condition of kTεi〈〈1.

New Physical and Chemical Constants and Prospects of Its Use for the Explicit Expression of Thermodynamic Functions

Based on the analysis of the Boltzmann＇s distribution in an infinitely high temperature found degeneration of the thermodynamic system in a purely informational with independently of each particle on its energy level, thus providing them full visibility of and the ability to calculate the maximum entropy in the Boltzmann formula S∞ = R·InNA = 455.251 J/（mol.K）. This value, when expressed in terms of fundamental constants, is itself a physical and chemical constants and mole monatomic ideal gas is unsurpassed in any studied temperature range. For complex substances this limit increases in direct proportion to their atomic. The existence of two limits entropy change--lower, equal to zero according to the third law of thermodynamics, and the top, equal to S∞, makes possible the explicit expression of the temperature dependence of the entropy in the form of an exponentialS=S∞exp[-5030.31p 2/5 /（M3/5T）]（5/2）r e/s∞. rather than in the form of a logarithmic dependence of the infinite by the approximateformula Sakura-Tetrode with which this the dependence is almost identical in the studied temperature range （100-10,000 K）, but not absurd negative entropy in the extrapolation formula Sakura-Tetrode absolute zero to the region and especially in the area of T → ∞where it turns S →∞.

Analysis of Heat Transfer Phenomenon in Magnetohydrodynamic Casson Fluid Flow Through Cattaneo–Christov Heat Diffusion Theory

Heat transport phenomenon of two-dimensional magnetohydrodynamie Casson fluid flow by employing Cattaneo-Christov heat diffusion theory is described in this work. The term of heat absorption/generation is incorporated in the mathematical modeling of present flow problem. The governing mathematical expressions are solved for velocity and temperature profiles using RKF 45 method along with shooting technique. The importance of arising nonlinear quantities namely velocity, temperature, skin-friction and temperature gradient are elaborated via plots. It is explored that the Casson parameter retarded the liquid velocity while it enhances the fluid temperature. Fhrther, we noted that temperature and thickness of temperature boundary layer are weaker in case of Cattaneo-Christov heat diffusion model when matched with the profiles obtained for Fourier＇s theory of heat flux.

Study on the effect of pressure on the equilibrium and stability of the solid-liquid interface in solidification of binary alloys

The equilibrium of the solid-liquid interface in pressurized solidification process of binary alloys was studied using the Gibbs theory, and the stability of the solid-liquid interface was discussed based on the consideration of the effects of pressure on the diffusion coefficient, the interface growth rate and tile equilibrium liquid composition. A mathematical description of the equi- librium status, the relationship of temperature, pressure, composition and interfacial tension was obtained, and further, a mathematical representation of the curvature radius of solid-liquid interface was developed, which facilitates a thorough understanding of the controlled variables of the interfacial stability.

An investigation of non-Newtonian fluid flow due to metachronal beating of cilia in a tube

The aim of this study is to explain theoretically the role of ciliary motion on the transport of epididymal fluid through the ductus efferentes of the male reproductive track. For this purpose, a mathematical model has been developed for the flow of a non-Newtonian fluid in an axisymmetric tube due to metachronal wave of cilia motion for the more realistic consequences. Carreau viscous fluid model is considered to see the rheological effects on the pumping characteristics of the flow. Regular perturbation method has been employed to obtain the analytical expressions for the stream function, the velocity field and a relation between the pressure difference and the volume flow rate. It is found that the volume flow rate is influenced significantly by Weissenberg number We and the cilia length parameter ε. The computational results are presented graphically to see the effects of various physical parameters. Finally, the analysis is applied and compared with the observed value of the flow rate of spermatic fluid in the ductus efferentes of the male reproductive track. The volume flow rate is reported closed to the estimated value 6 × 10^-3 ml/h in the human ductus efferentes when We = 0.5 and e is near by 0.25.

Academic Lexical Items in Economics Journal Papers

This paper reports a study into the use of lexical items in economics journal papers. The corpus in this study （EC） consisted of 907,380 running words from 120 journal papers randomly selected from economics journals which were written by native English speakers. The results showed that the Academic Word List （AWL） accounted for 12.74% of the tokens in EC and the distribution of AWL in EC was uneven. In the case study of the key words, only four out of nine key words ranked by keyness were AWL words, while the other five were from the General Service List （GSL）. Moreover, those nine key words together with other three key functional expressions were employed to fulfill discourse and rhetorical functions in academic writings. Pedagogical implications are also discussed within this paper.