The vibrations' study to the burn gas exhaust fan from a thermoelectric power plant

The paper presents a diagnose analysis for an industrial fan having vertical axis rotation, which shows dangerous levels of vibration. The fan ejects the flue gases from a thermoelectric power plant. This is located and isolated on the roof of the power plant building by some elastic elements, in the form of some cassettes with coil springs. The cassettes are arranged symmetrically along the separation plane.The experimental research has been carried out in two steps. In the first step, we designed and we studied in laboratory a mathematical model to reproduce a real situation of the fan insulation. In the second step, we made experimental investigations on the spot. Comparing the measured vibration amplitudes to those obtained on mathematical model, we identified a hidden connection near one of cassettes with coil springs. The hidden connection has appeared during the cassettes mounting and so was created a mechanical asymmetry. Due to this, the dangerous levels of vibration have occurred and it was caused a temporary shutdown of the fan. The process for detecting and eliminating the mounting nonconformities it is presented in the paper.     

Temperature-induced assembly of semiconductor nanocrystals into fractal architectures and thermoelectric power properties in Au/Ge bilayer films

Fractal architectures of semiconductor nanocrystals were successfully achieved by temperature-induced assembly of semiconductor nanocrystals in gold/germanium (Au/Ge) bilayer films. New assessment strategies of fractal architectures are of fundamental importance in the development of micro/nano-devices. Temperature-dependent properties including resistivity and thermoelectric power (TEP) of Au/Ge bilayer films with self-similar fractal patterns were investigated in detail. Experimental results indicated that the microstructure of Au film plays an important role in the characteristics of Au/Ge bilayer films after annealing and the crystallization processes of amorphous Ge accompany by fractal formation of Ge nanocrystals via temperature-induced assembly. The appearance of fractal architectures has significantly influence on the TEP but little effect on the resistivity of the annealed bilayer film. By analysis of the data, we found that the values of superlocalization exponent are within 1.22 ? ξ ? 1.29, which are higher than expected for two-dimension fractal systems. The results provided possible evidence for the superlocalization on fractal architectures in Au/Ge bilayer films. The TEP measurements are considered a more effective method than the conductivity for investigating superlocalization in a percolating system.     

Measuring environmental efficiency of thermoelectric power plants: a common equilibrium efficient frontier DEA approach with fixed-sum undesirable output

China’s rapid development in economy has intensified many problems. One of the most important issues is the problem of environmental pollution. In this paper, a new DEA approach is proposed to measure the environmental efficiency of thermoelectric power plants, considering undesirable outputs. First, we assume that the total amount of undesirable outputs of any particular type is limited and fixed to current levels. In contrast to previous studies, this study requires fixed-sum undesirable outputs. In addition, the common equilibrium efficient frontier is constructed by using different input/output multipliers (or weights) for each different decision making unit (DMU), while previous approaches which considered fixed-sum outputs assumed a common input/output multiplier for all DMUs. The proposed method is applied to measure the environmental efficiencies of 30 thermoelectric power plants in mainland China. Our empirical study shows that half of the plants perform well in terms of environmental efficiency.

     

Specific surface area of mercuric sulphide

The specific surface area of mercuric sulphide (a) has been determined by three methods: (a) gas adsorption method (N₂ adsorption), (b) air permeability method and (c) microscopic method. The area values are compared. In the gas adsorption method, the effect of degassing temperature on the surface area of solid was studied. In the permeability method the porosity range over which the specific surface area remains constant was also determined.     

Theory of fractional order in generalized thermoelectric MHD

A new mathematical model of thermoelectric MHD theory has been constructed in the context of a new consideration of heat conduction with fractional orders. This model is applied to Stokes’ first problem for a conducting fluid with heat sources. Laplace transforms and state-space techniques [1] will be used to obtain the general solution for any set of boundary conditions. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some comparisons have been shown in figures to estimate the effects of the fractional order parameters on all the studied fields.     

On the power values of power sums

Using several currently available techniques, including Baker's method, Frey curves and modular forms, we prove that for odd values of k with 1?k<170, the equation

k¹+k²+?+xk=y2n     

Determination of lead by the precipitation of lead molybdate from a homogeneous solution by the diffusion method

A satisfactory quantitative method for the determination of lead as lead molybdate by precipitation from a homogeneous solution has been developed. The method employs the diffusion of ammonia into a solution containing lead and sodium molybdate in nitric acid medium. The precipitation of lead in the range of 28·0–280·0 mg is complete within 8–9 hours. Anions like sulphate, arsenate, phosphate, tungstate and chromate in moderate concentrations and cations such as Zn (II), Cu (II), Ni (II), Co (II), Mn (II), Cd (II), Hg (II), Ag (I), Ti (IV), As (V), Mg (II) and Al (III) do not contaminate the precipitate. The precipitate gets constant weight at 120°. This eliminated the ignition of the precipitate,i.e., the contamination of molybdic oxide by the precipitate was reduced.     

Transient heat transfer behavior of one-dimensional symmetric thermoelectric SMA actuators

The main purpose of this paper is to study the transient heat transfer behavior of one-dimensional symmetric thermoelectric Shape Memory Alloy (SMA) actuators, without assuming a small ratio between the layer thicknesses of SMA and semiconductor. For the transient heat transfer with a constant current density, it is proved that there is an upper bound for the current density so that the temperature distribution along the SMA layer is stable. For the transient cooling problem with a constant current density, it is proved that there is a lower bound for the current density so that the temperature at the interface between SMA and semiconductor layers is always decreasing to its stable state, and it may not be always decreasing if the current density is below the lower bound. Estimates for these bounds are derived. The physical implications of main results are also discussed.     

Modelling the diffusion of lead into drinking water

The use of lead in pipe networks, and the subsequent lead emissions into drinking water, is now a major concern to the European Union Member States. Computer simulation offers the possibility for achieving a greater understanding of the issues that relate to plumbosolvency control. An analytical and a numerical scheme for the diffusion of lead into drinking water within a pipe during a stagnation period are described. These have been validated by experimental work. Three models have been investigated to simulate the flow of water through a pipe. These flow models have been used in conjunction with the equation of mass transfer to simulate the concentration of lead at the tap. This has been used within a Monte Carlo framework in order to simulate a zone of properties. The zonal output data obtained consists of failure rates at specified lead standards. This data can be utilised to investigate and prioritise plumbosolvency control options, and substantially overcomes the severe limitations of sampling.     

On the power graph and the reduced power graph of a finite group

In this paper, for a finite group, we investigate to what extent its directed (resp. undirected) reduced power graph determines its directed power graph (resp. reduced power graph). Moreover, we investigate the determination of the orders of the elements of a finite group from its directed (resp. undirected) reduced power graph. Consequently, we show that some classes of finite groups are recognizable from their undirected reduced power graphs. Also, we study the relationship between the isomorphism classes of groups corresponding to the equivalence relations induced by the isomorphism of each of these graphs on the set of all finite groups.     

On the divisibility of power LCM matrices by power GCD matrices

Let S = {x ₁, ..., x _n } be a set of n distinct positive integers and e ⩾ 1 an integer. Denote the n × n power GCD (resp. power LCM) matrix on S having the e-th power of the greatest common divisor (x _i , x _j ) (resp. the e-th power of the least common multiple [x _i , x _j ]) as the (i, j)-entry of the matrix by ((x _i , x _j ) ^e ) (resp. ([x _i , x _j ] ^e )). We call the set S an odd gcd closed (resp. odd lcm closed) set if every element in S is an odd number and (x _i , x _j ) ∈ S (resp. [x _i , x _j ] ∈ S) for all 1 ⩽ i, j ⩽ n. In studying the divisibility of the power LCM and power GCD matrices, Hong conjectured in 2004 that for any integer e ⩾ 1, the n × n power GCD matrix ((x _i , x _j ) ^e ) defined on an odd-gcd-closed (resp. odd-lcm-closed) set S divides the n × n power LCM matrix ([x _i , x _j ] ^e ) defined on S in the ring M _n (ℤ) of n × n matrices over integers. In this paper, we use Hong’s method developed in his previous papers [J. Algebra 218 (1999) 216–228; 281 (2004) 1–14, Acta Arith. 111 (2004), 165–177 and J. Number Theory 113 (2005), 1–9] to investigate Hong’s conjectures. We show that the conjectures of Hong are true for n ⩽ 3 but they are both not true for n ⩾ 4. Research is partially supported by Program for New Century Excellent Talents in University, by SRF for ROCS, SEM, China and by the Lady Davis Fellowship at the Technion, Israel Research is partially supported by a UGC (HK) grant 2160210 (2003/05).     

On the power sequence of a fuzzy matrix convergent power sequence

The convergence of the power sequence of ann ×n fuzzy matrix has been studied. Some theoretical necessary and sufficient conditions have been established for the power sequence to be convergent generally. Furthermore, as one of our main concerns, the convergence index was studied in detail, especially for some special types of Boolean matrices. Also it has been established that the convergence index is bounded by (n ? 1)² + 1 from above for an arbitraryn ×n fuzzy matrix if its power sequence converges. Our method is concentrated on the limit behavior of the power sequence. It helped us to make our proofs be simpler and more direct than those in pure algebraic methods.     

On the power of interaction

LetIP[f(n)] be the class of languages recognized by interactive proofs withf(¦x¦) interactions. Babai [2] showed that all languages recognized by interactive proofs with a bounded number of interactions can be recognized by interactive proofs with only two interactions; i.e., for every constantk, IP[k] collapses toIP[2].In this paper, we give evidence that interactive proofs with an unbounded number of interactions may be more powerful than interactive proofs with a bounded number of interactions. We show that for any polynomially bounded polynomial time computable functionf(n) and anyg(n)=o(f(n)) there exists an oracleB such thatIP ^B [f(n)] ₌ IP ^B [g(n)].The techniques employed are extensions of the techniques for proving lower bounds on small depth circuits used in [6], [14] and [10].Research done while in the Department of Mathematics at M. I. T. and supported by an ONR graduate fellowship.Supported in part by NSF Grant DCR MCS8509905.Research done while at the Laboratory for Computer Science at M. I. T. and Supported by an IBM fellowship.     

On the distribution of the power generator

We present a new method to study the power generator of pseudorandom numbers modulo a Blum integer . This includes as special cases the RSA generator and the Blum-Blum-Shub generator. We prove the uniform distribution of these, provided that the period with fixed 0$"> and, under the same condition, the uniform distribution of a positive proportion of the leftmost and rightmost bits. This sharpens and generalizes previous results which dealt with the RSA generator, provided the period . We apply our results to deduce that the period of the binary sequence of the rightmost bit has exponential length.

     

On the power of white pebbles

We construct a family (G _p |p) of directed acyclic graphs such that any black pebble strategy forG _p requiresp ² pebbles whereas 3p+1 pebbles are sufficient when white pebbles are allowed.Supported by the National Science Foundation under contract no. DCR-8407256 and by the office of Naval Research under contract no. N0014-80-0517.     

The full power of the half-power

We use the complex square root to define a very simple homotopic invariant over the non-vanishing functions defined on the circle. As a consequence we provide easy proofs of the plane Brouwer fixed point theorem and the Fundamental Theorem of Algebra. The relation of this new invariant with the winding number and the Brouwer degree will be fully unveiled.