一个包含Smarandache函数的方程

对于任意正整数n,我们用S(n)表示Smarandache函数,即S(n)=min{m:n|m!}.本文的主要目的是运用初等方法研究方程∑_(d|n)S(d)=n的可解性,并给出它的所有正整数解.     

von Neumann代数中套子代数上的Lie同构

本文给出因子von Neumann代数中的幂等算子在广义Lie积下的一个刻画; 得到因子von Neumann代数中套子代数的幂等算子在Lie积下的一个特征．作为应用, 研究了因子von Neumann代数中套子代数上的Lie同构,并证明因子von Neumann 代数中套子代数之间的Lie同构,要么是同构与广义迹之和,要么是负反同构与广义迹之和．     

Boiling heat transfer characteristics of nanofluids in a flat heat pipe evaporator with micro-grooved heating surface

An experimental study was performed to understand the nucleate boiling heat transfer of water–CuO nanoparticles suspension (nanofluids) at different operating pressures and different nanoparticle mass concentrations. The experimental apparatus is a miniature flat heat pipe (MFHP) with micro-grooved heat transfer surface of its evaporator. The experimental results indicate that the operating pressure has great influence on the nucleate boiling characteristics in the MFHP evaporator. The heat transfer coefficient and the critical heat flux (CHF) of nanofluids increase greatly with decreasing pressure as compared with those of water. The heat transfer coefficient and the CHF of nanofluids can increase about 25% and 50%, respectively, at atmospheric pressure whereas about 100% and 150%, respectively, at the pressure of 7.4 kPa. Nanoparticle mass concentration also has significant influence on the boiling heat transfer and the CHF of nanofluids. The heat transfer coefficient and the CHF increase slowly with the increase of the nanoparticle mass concentration at low concentration conditions. However, when the nanoparticle mass concentration is over 1.0 wt%, the CHF enhancement is close to a constant number and the heat transfer coefficient deteriorates. There exists an optimum mass concentration for nanofluids which corresponds to the maximum heat transfer enhancement and this optimum mass concentration is 1.0 wt% at all test pressures. The experiment confirmed that the boiling heat transfer characteristics of the MFHP evaporator can evidently be strengthened by using water/CuO nanofluids.     

A high-resolution MAS NMR study on the potential catalysts Mo/HBeta for olefin metathesis: The interaction of Mo species with HBeta zeolite

The interfacial interaction of Mo species with the HBeta zeolite was studied by multinuclear MAS NMR, XRD and N₂ adsorption. As proved by the quantitative ²⁷Al MAS NMR, this interaction is so strong as to dealuminate the framework of HBeta, and leads to a new peak appearing at −14 ppm, which indicates the formation of crystalline Al₂(MoO₄)₃. This can also be detected by XRD measurements when the Mo loading is as high as 9.0 wt.%. The corresponding quantitative ²⁹Si and ¹H MAS NMR spectra show that the amount of silanols and Brønsted acidic sites decrease obviously with increasing Mo loading. This also reveals an interaction between Mo species and HBeta support through an oxygen bridge resulting from condensation with the hydroxyls on the support. At higher Mo loadings, the interaction is so strong that it results in an extraction of aluminum from the zeolite framework, and subsequently appearance of Al₂(MoO₄)₃ and loss of Brønsted acidic sites. These can be correlated to the low catalytic activity of Mo/HBeta in metathesis of ethylene and 2-butylene to propylene.     

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequcncies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields(NSMC)on Cayley trees are studied.In the proof,a new technique for the study of strong liinit theorems of Markov chains is extended to the case of Markov chain fields.The asymptotic equiparti- tion properties with almost everywhere(a.e.)convergence for NSMC on Cayley trees are obtained.     

DIRICHLET BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER QUASI-LINEAR DIFFERENTIAL EQUATIONS WITH CHANGING SIGN NONLINEARITIES

This paper is concerned with the existence of positive solutions of two-point Dirichlet singular and nonsingular boundary problems for second-order quasi-linear differential equations with changing sign nonlinearities.     

Synthesis and Structural Characterization of Adduct [La(NO_3)_3·4H_2O]·2(BQEB)

Differentkindsofopenchaincrownethershavebeensynthesizedasthemodelcompoundsofionophoresandtheirinteractionswithsodium,potassiumandrareearthionshavealsobeenstudiedl'z.PanshowedCe(III)yieldedalf1complexwithl,8-bis(8'-quinolyloxy)-3,6-dioxaandtheCe(IIl)ioncoordinatedbothtoetheroxygenandquinolinenitrogenatoms3.TUmInleridentifiedtwolanthanidenitratecomplexeshavingastoichiometryof3:2(3RE:2L)'.InordertostUdythefunctionsofbothquinolineandbenzenering,introducedintothepolyetherchain,a1inearpolyether…     

Decisive Role of Symmetry in Structures of Three-Body Systems

A three-body system of identical particles is considered in order to demonstrate that the quantum-mechanical symmetry plays a decisive role in determining microscopic structures. Received March 14, 1994; revised July 29, 1994; accepted for publication October 19, 1994     

(4S)-4-羧基杂氮硅三环的合成

利用L-N,N-双(β-羟乙基)丝氨酸及L-N,N-双(β-羟乙基)苏氨酸与三乙氧基硅烷或氯烷基三乙氧基硅烷反应合成了具有手性的(4S)-4-羧基杂氮硅三环(1～5),并运用IR、~1HNMR、EI-MS等手段表征了结构。证据显示存在着贯穿笼状结构的N→Si配键。     

Indirect Flow Injection Chemiluminescence Method for the Determination of Tetracycfines Using Cu（]I） as a Probe Ion

This paper reported an indirect flow injection chemiluminescence （FI-CL） method for the determination of the drugs tetracycline （TC）, chlortetracycline （CTC） and oxytetracycline（OTC） using Cu（ Ⅱ ） as a probe ion. The CL reaction was induced on-line and after injection of the sample the negative peaks appeared as a result of complexation. The method was applied to the determination of TCs in pharmaceuticals and human urine with recoveries in the range95-105%.