Eigenvalue approach to study the effect of rotation and relaxation time in generalized magneto-thermo-viscoelastic medium in one dimension

The fundamental equations of the problems of generalized thermoelasticity with one relaxation parameter including heat sources in infinite rotating magneto-thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace transform domain for a one dimensional problem. These equations have been solved by the eigenvalue approach to determine deformations, stress, and temperature. The results have been compared to those available in the existing literature. The graphs have been drawn to show the effect of rotation in the medium.     

一些特殊图类乘积的离散度

连通图的离散度是用s(G)来表示的,s(G)=max{ω(G-S)-|S|:ω(G-S)>1,SV(G)}.给出了两个完全图乘积的和一个完全图与路的乘积的离散度.还给出了两个完全图乘积的坚韧度.     

A note on the computational complexity of graph vertex partition

A stable set of a graph is a vertex set in which any two vertices are not adjacent. It was proven in [A. Brandstädt, V.B. Le, T. Szymczak, The complexity of some problems related to graph 3-colorability, Discrete Appl. Math. 89 (1998) 59-73] that the following problem is NP-complete: Given a bipartite graph G, check whether G has a stable set S such thatG-Sis a tree. In this paper we prove the following problem is polynomially solvable: Given a graph G with maximum degree 3 and containing no vertices of degree 2, check whether G has a stable set S such thatG-Sis a tree. Thus we partly answer a question posed by the authors in the above paper. Moreover, we give some structural characterizations for a graph G with maximum degree 3 that has a stable set S such that G-S is a tree.     

Electrical detection of nuclear spin echoes

We show, via a straightforward calculation, that it is feasible to detect nuclear spin echoes in a ferromagnetic thin film by electrical means. The detection scheme is based on the deflection of the electronic magnetization when the nuclear magnetization reforms during an echo. This deflection is observed as a time-dependent magnetoresistive signal.     

Magnetic and electrical transport properties of delta-doped amorphous Ge:Mn magnetic semiconductors

We report on the growth and characterization of delta-doped amorphous Ge:Mn diluted magnetic semiconductor thin films on GaAs (0 0 1) substrates. The fabricated samples exhibit different magnetic behaviors, depending on the Mn doping concentration. The Curie temperature was found to be dependent on both the Mn doping concentration and spacing between the doping layers. A sharp drop in magnetization and rise in resistivity are observed at low temperature in samples with high Mn doping concentrations, which is also accompanied by a negative thermal remanent magnetization (TRM) in the higher temperature range. The temperature at which the magnetization starts to drop and the negative TRM appears show a correlation with the Mn doping concentration. The experimental results are discussed based on the formation of ferromagnetic regions at high temperature and antiferromagnetic coupling between these regions at low temperature.     

A graphical approach to computing Selmer groups of congruent number curves

Let E _n:y ²=x ³−n ² x denote the family of congruent number elliptic curves. Feng and Xiong (2004) equate the nontriviality of the Selmer groups associated with E _n to the presence of certain types of partitions of graphs associated with the prime factorization of n. In this paper, we extend the ideas of Feng and Xiong in order to compute the Selmer groups of E _n. 2000 Mathematics Subject Classification Primary—11G05; Secondary—14H52, 14H25, 05C90     

Precise measurement of magnetic moment of short-lived β-emitting nuclei12B ( I π=1+, T 1/2=20.18 ms)

The spin polarized β-emitting nuclei¹²B (I ^π=1⁺,T _1/2=20.18 ms) were produced by the nuclear reaction¹¹B(d, p)¹²B and by the selection technique of the incident deuteron energy and the¹²B recoil angle following the nuclear reaction. The nuclear magnetic moment of the short-lived nuclei¹²B was measured by β-NMR with the β-NMR and β-NQR setup established for the first time in China. The nuclear magnetic moment of¹²B was determined to be μ=0.99993±0.00048 nm org=0.99993±0.00048 after the precise correction of the Knight shift.     

Novel radical‐responsive MRI contrast agent based on paramagnetic liposomes

A novel, radical responsive MRI contrast agent based on a gadolinium chelate conjugated to a liposome through a disulfide linker was synthesized, with the aim of pursuing the in vivo mapping of radicals. The liposome was prepared by incorporating a thiol‐activated phospholipid, which was subsequently reacted with a gadolinium chelate containing a free thiol group. The long reorientational motion of the supramolecular adduct endows the paramagnetic agent with a relaxivity significantly higher than that of the free complex. The disulfide bond represents a radical‐sensitive moiety and a large decrease in contrast efficacy (T₁ relaxivity) is shown upon its cleavage. A preliminary assessment of the system was made by means of in vitro gamma‐irradiation and thiol–disulfide bond exchange with dithiothreitol. Both methods showed a clear dose‐dependent decrease in T₁‐relaxivity. Copyright © 2003 John Wiley & Sons, Ltd.     

Optimally Stable Multivariate Bases

We show that the tensor product B-spline basis and the triangular Bernstein basis are in some sense best conditioned among all nonnegative bases for the spaces of tensor product splines and multivariate polynomials, respectively. We also introduce some new condition numbers which are analogs of component-wise condition numbers for linear systems introduced by Skeel.     

Stark's conjecture over complex cubic number fields

Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark's conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) and coupling this information with the Fincke-Pohst algorithm applied to certain quadratic forms leads to a significant reduction in search time for finding Stark units in larger extensions (where the conjecture is still unproven). Stark's conjecture is verified in each case for these Stark units in larger extensions and explicit generating polynomials for abelian extensions over complex cubic base fields, including Hilbert class fields, are obtained from the minimal polynomials of these new Stark units.