非线性奇异边值问题的正解

利用锥映射的不动点指数定量，研究了一类非线性奇异边值问题多个正解的存在性问题。在构造的解的存在条件之下，证明了奇异边值问题至少有两个正解的存在性定理。     

Ferromagnetism at 300 K in spin-coated films of Co doped anatase and rutile-TiO2

Thin films of Ti_1−xCo_xO₂ (x=0 and 0.03) have been prepared on sapphire substrates by spin-on technique starting from metalorganic precursors. When heat treated in air at 550 and 700 °C, respectively, these films present pure anatase and rutile structures as shown both by X-ray diffraction and Raman spectroscopy. Optical absorption indicate a high degree of transparency in the visible region. Such films show a very small magnetic moment at 300 K. However, when the anatase and the rutile films are annealed in a vacuum of 1×10⁻⁵ Torr at 500 and 600 °C, respectively, the magnetic moment, at 300 K, is strongly enhanced reaching 0.36μ_B/Co for the anatase sample and 0.68μ_B/Co for the rutile one. The ferromagnetic Curie temperature of these samples is above 350 K.     

Investigations of low- and high-spin states of <Superscript>132</Superscript>La

The fusion evaporation reaction ¹²²Sn(¹⁴N, 4n)¹³²La was used to populate the high-spin states of ¹³²La at the beam energy of 60 MeV. A new band consisting of mostly E2 transitions has been discovered. This band has the interesting links to the ground state 2^- and the isomeric state 6^-. A new transition of energy 351 keV connecting the low-spin states of the positive-parity band based on the πh _11/2 ⊗ νh _11/2 particle configuration, has been found. This has played a very important role in resolving the existing ambiguities and inconsistencies in the spin assignment of the band head. Received: 12 August 2002 / Accepted: 18 March 2003 / Published online: 7 May 2003     

190区超形变核中转动带的组态结构

通过系统研究A～190区超形变核中转动带的转动惯量、角动量顺排、旋称分裂随转动频率的变化规律, 结合我们用处理对力的粒子数守恒方法的计算结果, 对A～190区所有转动带的组态结构给出了一个整体的描述. 绝大多数超形变带都建立在强耦合轨道上, 例如中子[512]5/2, [624]9/2. 少数超形变带则建立在高j闯入轨道上, 即中子[761]3/2, [752]5/2. 根据我们提出的组态结构所进行的理论计算结果表明, A～190区所有转动带的一般行为、反常变化和带交叉都得到了满意的解释.     

Tunneling and EPR linewidths due to dislocations in Mn acetate

We compute the width and shape of the EPR and tunneling resonances due to dislocations in Mn₁₂ acetate crystals. Uncorrelated dislocations produce the Gaussian shape of resonances while dislocations bound in pairs produce the Lorentzian shape. We stress that the uniaxial spin Hamiltonian together with crystal defects can explain the totality of experimental data on Mn₁₂. Received 2 August 2001 / Received in final form 15 March 2002 Published online 17 September 2002     

On dimensional rigidity of bar-and-joint frameworks

Let V={1,2,…,n}. A mapping p:V→R^r, where p¹,…,pⁿ are not contained in a proper hyper-plane is called an r-configuration. Let G=(V,E) be a simple connected graph on n vertices. Then an r-configuration p together with graph G, where adjacent vertices of G are constrained to stay the same distance apart, is called a bar-and-joint framework (or a framework) in R^r, and is denoted by G(p). In this paper we introduce the notion of dimensional rigidity of frameworks, and we study the problem of determining whether or not a given G(p) is dimensionally rigid. A given framework G(p) in R^r is said to be dimensionally rigid iff there does not exist a framework G(q) in R^s for s?r+1, such that ∥qⁱ-q^j∥²=∥pⁱ-p^j∥² for all (i,j)∈E. We present necessary and sufficient conditions for G(p) to be dimensionally rigid, and we formulate the problem of checking the validity of these conditions as a semidefinite programming (SDP) problem. The case where the points p¹,…,pⁿ of the given r-configuration are in general position, is also investigated.     

Magnetism and magneto-transport studies in sonochemically prepared amorphous Co100−xPtx nano alloys

Bulk amorphous Co_(100−x)Pt_x (0≤x≤50) nano-alloys have been synthesized using high frequency ultrasound, displaying single domain (4-5 nm) behavior wherein weakly exchange-coupled particles lead to a field-dependent resistivity behavior. Magneto-resistivity is correlated to the order-disorder parameter in these powder compacts. The plot of Δρ/ρ₀ as a function of reduced magnetization indicates that all the systems are weakly exchange coupled.     

Lifetime study of high-spin states in 104,105In

In the neutron deficient isotopes _104,105In lifetimes of high spin states in the range from 0.5 ps to 600 ps have been measured in a coincidence recoil distance Doppler shift (RDDS) experiment. By combining the Doppler shift attenuation (DSA) and RDDS methods at few μm flight distances, the problem of delayed feeding has been avoided and very short lifetimes in the range 0.5–0.8 ps have been determined. Shell model calculations with strong restrictions for the neutron orbitals reveal good agreement with experimental level energies and still fair agreement for most measured B(M1) and B(E2) values. Received: 30 June 1998