NEW METHOD FOR MEASURING FUZZINESS IN ROUGH SETS

A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.

Shear resistance performance of steel-concrete-steel composite shear wall

For a deeper understanding of the shear resistance performance of the steel-concrete-steel composite shear wall, the main influence factors such as the thicknesses of the steel plates and the concrete, the strength grades of the concrete and the span-depth ratios of the composite wall, which have impacts on the shear resistance performance of the composite shear wail, are analyzed by the numerical simulation method. Meanwhile, the simplified calculation formulae of the initial elastic lateral-resisting stiffness and the shear bearing capacity of the composite shear wall are also proposed. The research shows that with the increase in the thicknesses of the steel plates and the concrete and the increase in the strength grades of the concrete, the shear performance of the shear wall improves obviously; the span-depth ratios of the composite wall have a significant effect on the initial elastic lateral- resisting stiffness, but a small effect on the shear bearing capacity. Comparing the results of the simplified calculation formulae with those of the nonlinear finite element method, it is obvious that the presented formulae are reasonable and meet the real force state of the structure. These conclusions can serve as a preliminary design reference for the steel-concrete- steel composite shear wall.

A Number Theoretic Function and Its Mean Value Computation

Let p be a prime, n be any positiv e integer, α(n,p) denotes the power of p in the factorization of n! . In this paper, we give an exact computing formula of the mean value ∑ n<Nα(n,p).

A n-fold Calculating Sieve Formula for Some Symmetric Sets

This paper introduces a method of sieve which can be to calculate the number of residues of the integers 1,2,...,2a sifted by n paiwise coprime numbers.

A new method determining safe thickness of karst cave roof under pile tip

Cave roofs are used to support pile foundation in many engineering projects. Accurate stability analysis method of cave roof under pile tip is important in order to ensure the safety of the pile foundation structure. Firstly the mechanical model to analysis the stability of cave roof under pile tip is founded aiming to solve the problems that the simplified mechanical model has. Secondly, the boundary of cave roof is simply supposed to be supported according to the integrity of the rock mass in the boundary of cave roof. Thirdly, based on the theory of plates and shells, the simplified model is calculated and the theoretical calculation formula to determine the safe thickness of cave roof under pile tip can be obtained when the edges of the cave roof are simply supported. In the end, the analysis of the practical engineering project proves the feasibility and the rationality of the method which can be a new method to calculate the safe thickness of cave roof under pile tip.

Dust removal efficiency of high pressure atomization in underground coal mine

To master theoretical calculation for dust removal efficiency of high pressure atomization in an underground coal mine, the corresponding atomization characteristics and dust removal efficiency were both comprehensively studied in theory by virtue of related theories of hydromechanics and aerosol.According to actual measurements of flow coefficients and atomization angles of X-type swirl nozzle,computational formula was derived for atomized particle sizes of such a nozzle in conjunction with relevant empirical equation. Moreover, a mathematical model for applying high pressure atomization to dust removal in underground coal mine was also established to deduce theoretical computation formula of fractional efficiency. Then, Matlab was adopted to portray the relation curve between fractional efficiency and influence factors. In addition, a theoretical formula was also set up for removal efficiency of respirable dust and total coal dust based on dust size and frequency distribution equations. In the end,impacts of dust characteristic parameters on various dust removal efficiencies were analyzed.

Nonhomogeneous(H,Q)-Process:The Backward and Forward Equations

As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonhomogeneous(H, Q) -process.

Consolidation analysis of composite foundation with partially penetrated cement fly-ash gravel(CFG) piles under changing permeable boundary conditions

Based on the double-layered foundation theory, the composite ground with partially penetrated cement fly-ash gravel(CFG) piles was regarded as a double-layered foundation including the surface reinforced area and the underlying untreated stratum. Due to the changing permeability property of CFG piles, the whole consolidation process of the composite ground with CFG piles was divided into two stages, i.e., the early stage(permeable CFG pile bodies) and the later stage(impermeable pile bodies). Then, the consolidation equation of the composite foundation with CFG piles was established by using the Terzaghi one-dimensional consolidation theory. Consequently, the unified formula to calculate the excess pore water pressure was derived with the specific solutions for the consolidation degree of composite ground, reinforced area and underlying stratum under instant load obtained respectively. Finally, combined with a numerical example, influencing rules by main factors(including the replacement rate m, the treatment depth h1, the permeability coefficient Ks1, Kv2 and compression modulus Es1, Es2 of reinforced area and underlying stratum) on the consolidation property of composite ground with CFG piles were discussed in detail. The result shows that the consolidation velocity of underlying stratum is slower than that of the reinforced area. However, the consolidation velocity of underlying stratum is slow at first then fast as a result of the transferring of effective stress to the underlying stratum during the dissipating process of excess pore water pressure.

Rock burst induced by roof breakage and its prevention

Based on the research on rock burst phenomenon induced by the breakage of thick and hard roof around roadways and working faces in coal mines, a criterion of rock burst induced by roof breakage （RBRB） was proposed and the model was built. Through the model, a method calculating the varied stresses induced by roof breakage in support objects and coal body was proposed and a unified formula was derived for the calculation of stress increment on support objects and coal body under different breaking forms of roof. Whilst the formula for calculating dynamic load was derived by introducing dynamic index Kd. The formula was verified in Huating Mine by stress measurement. According to the formula for stress increment calculating, the sensitivities of dynamic load parameters were further studied. The results show that the thickness and breaking depth of roof, width of support objeet are the sensitive factors. Based on the discussion of the model, six associated effective methods for rock burst prevention are obtained.

Rules of distribution in a plastic zone of rocks surrounding a roadway affected by tectonic stress

In order to study the rules of distribution in a plastic zone of rocks, surrounding a roadway, affected by tectonic stress, we first analyzed the mechanics of a roadway affected by tectonic stress and derived a theoretical formula for the plastic zone of rocks surrounding a roadway. We also analyzed the distribution characteristics of the plastic zone under different levels of tectonic stress, vertical pressure, cohesion and friction angle of the surrounding rock. Secondly, we used numerical simulation to analyze the range and shape features of the plastic zone of rocks surrounding the roadway, given different tectonic stress levels. Finally we used a rock drilling detector to carry out field measurements on the broken state of rock surrounding the roadway at the –700 substation and channels in the Xinzhuang mine of the Shenhuo mining area. Given the measured ground stress, we analyzed the relationship between tectonic stress and the distribution of this plastic zone. Our results show that the range of the plastic zone at the top and bottom of the roadway increases with an increase in tectonic stress and this increase is especially obvious at the roadway corner.

Calculation of Thermodynamic Parameters for Freundlichand Temkin Isotherm Models

Derivation of the Freundlich and Temkin isotherm models from the kinetic adsorption/desorpt ion equations was carried out to calculate their thermodynamic equilibrium constants. The calculation formulae ofthree thermodynamic parameters, the standard molar Gibbs free energy change, the standard molar enthalpy change and the standard molar entropy change, of isothermal adsorption processes for Freundlich andTemkin isotherm models were deduced according to the relationship between the thermodynamic equilibriumconstats and the temperature.

Improved Z^(1/3) Law of Nuclear Charge Radius

An improved Z^1/3 law of nuclear charge radius is presented. The comparison between the calculated and experimental nuclear charge radii now available shows that this new formula is better than the other conventional formulae.

Thin-bed thickness calculation formula and its approximation using peak frequency

Quantitative thickness estimation below tuning thickness is a great challenge in seismic exploration. Most studies focus on the thin-beds whose top and bottom reflection coefficients are of equal magnitude and opposite polarity. There is no systematic research on the other thin-bed types. In this article, all of the thin-beds are classified into four types： thin-beds with equal magnitude and opposite polarity, thin-beds with unequal magnitude and opposite polarity, thin-beds with equal magnitude and identical polarity, and thin-beds with unequal magnitude and identical polarity. By analytical study, an equation describing the general relationship between seismic peak frequency and thin-bed thickness was derived which shows there is a Complex implicit non-linear relationship between them and which is difficult to use in practice. In order to solve this problem, we simplify the relationship by Taylor expansion and discuss the precision of the approximation formulae with different orders for the four types of thin-beds. Compared with the traditional amplitude method for thin-bed thickness calculation, the method we present has a higher precision and isn＇t influenced by the absolute value of top or bottom reflection coefficient, so it is convenient for use in practice.

Phenomenon of Resonance in a Two-Mode Laser with an Input Additive Signal

Exact formulas for the power spectrum and signal-to-noise ratio (SNR) with periodic additive signal arecalculated in the linear system.Then the phenomenon of resonance is studied in detail.We show that resonancepeak and suppressed valley exist in the curves of the SNR versus the coefficient of self-saturation, the net gain and thecross-coupling coefficient of the laser system.

Matrix porosity calculation in volcanic and dolomite reservoirs and its application

Matrix porosity calculations of fractured and vuggy reservoirs, such as volcanics and weathered dolomite, are one of the problems urgently needed to solve in well-log evaluation. In this paper, we first compare the an empirical formula for porosity calculation from full diameter rhyolite core experiments with the matrix porosity formulas commonly used. We discuss the applicability of the empirical formula in fractured and vuggy reservoirs, such as intermediate-basic volcanics and weathered dolomite. Based on core analysis data, the error distribution of the calculated porosity of our empirical formula and the other porosity formulas in these reservoirs are given. The statistical error analysis indicates that the our empirical formula provides a higher precision than the other porosity formulas. When the porosity is between 1.5% and 15%, the acoustic experiment formula can be used not only for acidic volcanics but also in other fractured and vuggy reservoirs, such as intermediate-basic volcanics and weathered dolomite. Moreover, the formula can reduce the effects of borehole enlargement and rock alteration on porosity computation.

Wheel slip-sinkage and its prediction model of lunar rover

In order to investigate wheel slip-sinkage problem, which is important for the design, control and simulation of lunar rovers, experiments were carried out with a wheel-soil interaction test system to measure the sinkage of three types of wheels in dimension with wheel lugs of different heights and numbers under a series of slip ratios (0-0.6). The curves of wheel sinkage versus slip ratio were obtained and it was found that the sinkage with slip ratio of 0.6 is 3-7 times of the static sinkage. Based on the experimental results, the slip-sinkage principle of lunar's rover lugged wheels (including the sinkage caused by longitudinal flow and side flow of soil, and soil digging of wheel lugs) was analyzed, and corresponding calculation equations were derived. All the factors that can cause slip sinkage were considered to improve the conventional wheel-soil interaction model, and a formula of changing the sinkage exponent with the slip ratio was established. Mathematical model for calculating the sinkage of wheel according to vertical load and slip ratio was developed. Calculation results show that this model can predict the slip-sinkage of wheel with high precision, making up the deficiency of Wong-Reece model that mainly reflects longitudinal slip-sinkage.

Evaluation of standard liver volume formulae for Chinese adults

AIM:To evaluate different standard liver volume (SLV) formula and verify the applicability of the formulae for Chinese adults.METHODS: Data from 70 cases of living donor liver transplantation (LDLT) performed at our transplantation centers between January 2008 and April 2009 were analyzed. SLV was estimated using our recently reported formula [the Chengdu formula: SLV (mL)=11.5×body weight (kg) + 334] and other reported formulae used for Chinese adults. Actual intraoperative liver volumes were obtained from a review of the patients' medical records.RESULTS: The actual right liver volume was not significantly different from the estimated right liver volume determined by the Chengdu formula, but was significantly smaller than estimates using the Heinemann, Urata, Vauthey, and Lee formulae (P<0.01), and signif icantly larger than estimates using the Fan formula (P<0.05).CONCLUSION: The Chengdu formula was demonstrated to be reliable by its application in LDLT.