Entransy dissipation minimization for optimization of heat exchanger design

In this paper,by taking the water-water balanced counterflow heat exchanger as an example,the entransy dissipation theory is applied to optimizing the design of heat exchangers.Under certain conditions,the optimal duct aspect ratio is determined analytically.When the heat transfer area or the duct volume is fixed,analytical expressions of the optimal mass velocity and the minimal entransy dissipation rate are obtained.These results show that to reduce the irreversible dissipation in heat exchangers,the heat exchange area should be enlarged as much as possible,while the mass velocity should be reduced as low as possible.     

Simulation study of SVM-based approach in extracting parameters for electromagnetic detection of buried object

In this paper, a new method for extracting the parameters of buried object is proposed. The center position and dielectric properties of 2-D buried object are estimated by means of a regression technique based on support vector machine (SVM). The proposed method, after a proper training procedure, is able to reconstruct the center position and dielectric properties of a buried object inside a given investigation domain. Numerical simulation results indicate that SVM-based approach shows higher accuracy than the back-propagation neural networks (BPNN) algorithm.     

Control of the carrier-envelope phases of a synchronously pumped femtosecond optical parametric oscillator and its applications

The intrinsic synchronization, multi-color outputs and related carrier-envelope phases （CEP） among pulses bring advantages to synchronously pumped femtosecond optical parametric oscillators and the pumping sources for broadband frequency comb generation and ultrashort waveform coherent syn-thesis. In this paper, we discuss our latest research results in this field, which cover the following as-pects： the phase relationship and energy conservation law in an OPO and related experimental verifi-cation; control of the pumping Ti-sapphire femtosecond laser＇s CEP by self-referencing technology, and its repetition-rate locking by piezoelectric transducer （PZT）; CEP locking of the pulses from the OPO by beating the non-phase-matched visible outputs against pump supercontinuum to obtain a driving signal for a fast PZT on the OPO end mirror; the generation of a broadband frequency comb spanning from 400 nm to 2.4 μm with 1.2 kHz bandwidth; and the realization of coherent interference between phase controlled pump pulses and signal second harmonic pulses.     

Letters from William Burnside to Robert Fricke: automorphic functions,and the emergence of the Burnside Problem

Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of the Burnside Problem prior to its first publication. We present these letters as a whole to the public for the first time. We draw a picture of these two mathematicians and describe their activities leading to their correspondence. We thus gain an insight into their respective motivations, reactions, and attitudes, which may sharpen the current understanding of professional and social interactions of the mathematical community at the turn of the twentieth century. Dedicated to Heiko Harborth on the occasion of his seventieth birthday.     

Euler’s beta integral in Pietro Mengoli’s works

Beta integrals for several non-integer values of the exponents were calculated by Leonhard Euler in 1730, when he was trying to find the general term for the factorial function by means of an algebraic expression. Nevertheless, 70 years before, Pietro Mengoli (1626–1686) had computed such integrals for natural and half-integer exponents in his Geometriae Speciosae Elementa (1659) and Circolo(1672) and displayed the results in triangular tables. In particular, his new arithmetic–algebraic method allowed him to compute the quadrature of the circle. The aim of this article is to show how Mengoli calculated the values of these integrals as well as how he analysed the relation between these values and the exponents inside the integrals. This analysis provides new insights into Mengoli’s view of his algorithmic computation of quadratures.     

Giulio Racah and theoretical physics in Jerusalem

The present article considers Giulio Racah’s contributions to general physical theory and his establishment of theoretical physics as a discipline in Israel. Racah developed mathematical methods that are based on tensor operators and continuous groups. These methods revolutionized spectroscopy. Currently, these are essential research tools in atomic, nuclear and elementary particle physics. He himself applied them to modernizing theoretical atomic spectroscopy. Racah laid the foundations of theoretical physics in Israel. He educated several generations of Israeli physicists, and put Israel on the world map of physics.     

Newton's Easy Quadratures ``Omitted for the Sake of Brevity'

In the 1687 Principia, Newton gave a solution to the direct problem (given the orbit and center of force, find the central force) for a conic-section with a focal center of force (answer: a reciprocal square force) and for a spiral orbit with a polar center of force (answer: a reciprocal cube force). He did not, however, give solutions for the two corresponding inverse problems (given the force and center of force, find the orbit). He gave a cryptic solution to the inverse problem of a reciprocal cube force, but offered no solution for the reciprocal square force. Some take this omission as an indication that Newton could not solve the reciprocal square, for, they ask, why else would he not select this important problem? Others claim that ``it is child's play' for him, as evidenced by his 1671 catalogue of quadratures (tables of integrals). The answer to that question is obscured for all who attempt to work through Newton's published solution of the reciprocal cube force because it is done in the synthetic geometric style of the 1687 Principia rather than in the analytic algebraic style that Newton employed until 1671. In response to a request from David Gregory in 1694, however, Newton produced an analytic version of the body of the proof, but one which still had a geometric conclusion. Newton's charge is to find both ``the orbit' and ``the time in orbit.' In the determination of the dependence of the time on orbital position, t(r), Newton evaluated an integral of the form ∫dx/x <sup>n</sup> to calculate a finite algebraic equation for the area swept out as a function of the radius, but he did not write out the analytic expression for time t = t(r), even though he knew that the time t is proportional to that area. In the determination of the orbit, θ (r), Newton obtained an integral of the form ∫dx/√(1−x<sup>2</sup>) for the area that is proportional to the angle θ, an integral he had shown in his 1669 On Analysis by Infinite Equations to be equal to the arcsin(x). Since the solution must therefore contain a transcendental function, he knew that a finite algebraic solution for θ=θ(r) did not exist for ``the orbit' as it had for ``the time in orbit.' In contrast to these two solutions for the inverse cube force, however, it is not possible in the inverse square solution to generate a finite algebraic expression for either ``the orbit' or ``the time in orbit.' In fact, in Lemma 28, Newton offers a demonstration that the area of an ellipse cannot be given by a finite equation. I claim that the limitation of Lemma 28 forces Newton to reject the inverse square force as an example and to choose instead the reciprocal cube force as his example in Proposition 41. (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith     

Mean Motions in Ptolemy’s <Emphasis Type="Italic">Planetary Hypotheses</Emphasis>

In the Planetary Hypotheses, Ptolemy summarizes the planetary models that he discusses in great detail in the Almagest, but he changes the mean motions to account for more prolonged comparison of observations. He gives the mean motions in two different forms: first, in terms of ‘simple, unmixed’ periods and next, in terms of ‘particular, complex’ periods, which are approximations to linear combinations of the simple periods. As a consequence, all of the epoch values for the Moon and the planets are different at era Philip. This is in part a consequence of the changes in the mean motions and in part due to changes in Ptolemy’s time in the anomaly, but not the longitude or latitude, of the Moon, the mean longitude of Saturn and Jupiter, but not Mars, and the anomaly of Venus and Mercury, the former a large change, the latter a small one. The pattern of parameter changes we see suggests that the analyses that yielded the Planetary Hypotheses parameters were not the elegant trio analyses of the Almagest but some sort of serial determinations of the parameters based on sequences of independent observations.     

Preparation of Zn-doped TiO2 nanotubes electrode and its application in pentachlorophenol photoelectrocatalytic degradation

Zn-doped titanium oxide （TiO2） nanotubes electrode was prepared on a titanium plate by direct anodic oxidation and immersing method in sequence. Field emission scanning electron microscopy （FESEM） showed that the Zn-doped TiO2 nanotubes were well aligned and organized into high density uniform arrays with diameter ranging from 50 to 90 nm. The length and the thickness were about 200 and 15 nm respectively. TiO2 anatase phase was identified by X-ray diffraction （XRD）. X-ray photoelectronspectroscopy （XPS） indicated that Zn ions were mainly located on the surface of TiO2 nanotubes in form of ZnO clusters. Compared with TiO2 nanotubes electrode, about 20 nm red shift in the spectrum of UV-vis absorption was observed. The degradation of pentachlorophenol （PCP） in aqueous solution under the same condition （initial concentration of PCP： 20 mg/L; concentration of Na2SO4：0.01 mol/L and pH： 7.03） was carried out using Zn-doped TiO2 nanotubes electrode and TiO2 nanotubes electrode. The degradation rates of PCP using Zn-doped TiO2 nanotubes electrode were found to be twice and 5.8 times as high as that using TiO2 nanotubes electrode by UV radiation （400 μw/cm^2） and visible light radiation （4500 μw/cm^2）, respectively. 73.5% of PCP was removed using Zn-doped TiO2 nanotubes electrode against 45.5% removed using TiO2 nanotubes electrode in 120 min under UV radiation. While under visible light radiation, the degradation efficiency of PCP was 18.4% using Zn-doped TiO2 nanotubes electrode against 3.2% using TiO2 nanotubes electrode in 120 min. The optimum concentration of Zn doping was found to be 0.909%. The PCP degradation efficiencies of the 10 repeated experiments by Zn-doped TiO2 nanotubes electrode were rather stable with the deviation within 3.0%.     

Provable Efficient Certificateless Group Key Exchange Protocol

Certificateless public key cryptography （CL-PKC） avoids the inherent escrow of identity-based cryptography and does not require certificates to guarantee the authenticity of public keys. Based on CL-PKC, we present an efficient constant-round group key exchange protocol, which is provably secure under the intractability of computation Diffie-Hellman problem. Our protocol is a contributory key exchange with perfect forward secrecy and has only two communication rounds. So it is more efficient than other protocols. Moreover, our protocol provides a method to design efficient constant-round group key exchange protocols and most secret sharing schemes could be adopted to construct our protocol.