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     

Controlling rough paths

We formulate indefinite integration with respect to an irregular function as an algebraic problem which has a unique solution under some analytic constraints. This allows us to define a good notion of integral with respect to irregular paths with Hölder exponent greater than 1/3 (e.g. samples of Brownian motion) and study the problem of the existence, uniqueness and continuity of solution of differential equations driven by such paths. We recover Young's theory of integration and the main results of Lyons’ theory of rough paths in Hölder topology.     

A priori estimates and existence of positive solutions for strongly nonlinear problems

In this paper we study the existence of positive solutions for a nonlinear Dirichlet problem involving the m-Laplacian. The nonlinearity considered depends on the first derivatives; in such case, variational methods cannot be applied. So, we make use of topological methods to prove the existence of solutions. We combine a blow-up argument and a Liouville-type theorem to obtain a priori estimates. Some Harnack-type inequalities which are needed in our reasonings are also proved.     

Estimation of growth rate in unidirectionally solidified multicrystalline silicon by the growth-induced striation method

Multicrystalline silicon was grown by unidirectional solidification method using the accelerated crucible rotation technique. The application of the accelerated crucible rotation technique in unidirectional solidification method induced growth striations across the axial direction of the grown crystal. This striation pattern was observed from carbon concentration distribution, obtained by using Fourier transform infrared spectroscopy. The generated striation pattern was found to be weak and discontinuous. Some striations were absent, probably due to back melting, caused during each crucible rotation. From the growth striations and applied time period in crucible rotation, the growth rate was estimated by using Fourier transformation analysis.     

The role of As2O3 on the stability and some physical properties of PbO-Sb2O3 glasses

PbO-Sb₂O₃ glasses added with different concentrations of As₂O₃ (10-55 mol%) were prepared to understand their IR spectra, elastic properties (Young's modulus E, Shear modulus G, microhardness H), optical absorption and dielectric properties (constant ε, loss tan δ, ac conductivity σ_ac over a moderately wide range of frequency and temperature and breakdown strength in air medium at room temperature). Results have indicated that the structure of the PbO-Sb₂O₃-As₂O₃ glass is more rigid when the concentration of As₂O₃ is around 40 mol%.     

On-line cysteine modification for protein analysis: new probes for electrochemical tagging nanospray mass spectrometry

A series of electrogenerated selective electrophiles based on substituted benzoquinones has been characterized as tags for l-cysteine and cysteine residues in proteins. The electrophiles are generated electrochemically from the corresponding hydroquinones. It is shown from mass spectrometry analysis that the electrogenerated benzoquinone can tag the biomolecules. The rate constants pertaining to the addition of l-cysteine onto the electrogenerated benzoquinones have been determined using electrochemical techniques. The substitution patterns have been unraveled leading to the assessment of site-specific rate constants. It is shown that the rate constants are primarily dependent on the electronic nature of the substituents as expressed by the Hammett substitution constant. The apparent tagging yields observed for l-cysteine in nanospray mass spectrometry experiments do not correspond to the yields expected from the electrochemical study, as the ionisation efficiencies are highly dependent on the tag. Finally, the on-line tagging has been tested using β-lactoglobulin A and myoglobin. Based on these results, it is concluded that the tagging reaction is selective towards cysteine when it takes place in the nanospray interface. The results show that the methodology presented can be used for a rapid characterization and identification of reactive sites in biomolecules.     

A Novel Model for Protein Immobilization on Microspheres

The immobilization of proteins, especially receptor proteins commonly used in high through-put screening of drugs (HTS), have received great attention in recent years. There are many successful isothermal models for describing the adsorption of protein onto solid surface, such as Langmuir model, Bi-Langmuir model, Fowler model, Freundlich model, Freundlich-Langmuir model and Tekmin model etc. In all these models, Langmuir model was the most favorable one model accepted by many researchers, but the experimental results showed that it was not entirely fit to all adsorption behaviors. So new models were required for describing protein adsorption onto microspheres in different conditions.In our research, a novel isothermal model, including Langmuir and other adsorbing behaviors was presented basing on the holding degree of surface active sites and the interaction styles of protein immobilization. In Langmuir model, the adsorbing amount of protein was described as [PS] =Km[P]/1 + K[P], where [PS] was the concentration of adsorbed protein, [P] was the concentration of freeprotein at equilibrium state, and Km and K was constant. According to the interactions of protein and ligands, there were three patterns in the interactions of protein and ligands. On the similar assumption that the interaction of protein and microspheres were three styles, and based on the definition of the holding degree of surface active sites (Y), three adsorption behaviors could be described as Y K[ P ]φ/ K[P]φ+1 or ln K + φ ln[P] =ln(Y/1-Y) in which [P] was the concentration of free protein at equilibrium state, and φ and K was constant. Different scale of φ presented different adsorption behaviors, especially when φ was 1, the adsorption behavior was Langmuir adsorbing model. Figure I indicated the different adsorbing results in different adsorption behaviors (φ＞1, φ＜1,and φ=1).     

The existence of Thom classes

In this paper we consider the category of unstable modules over the Steenrod algebra. We prove the existence of finite primary decompositions in this category. Moreover, we prove the existence of Thom classes in noetherian unstable modules, i.e., elements that generate cyclic unstable submodules that are closed under the action of the Steenrod algebra. This in turn leads to the proof of the prime filtration theorem in the category of noetherian unstable modules. As an application we present a proof of the Landweber-Stong conjecture (now a theorem by D. Bourguiba and S. Zarati) that does not make use of the classification of injectives.     

On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form

We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12].     

Multilevel a posteriori error analysis for reaction–convection–diffusion problems

We present a new approach to the a posteriori error analysis of stable Galerkin approximations of reaction–convection–diffusion problems. It relies upon a non-standard variational formulation of the exact problem, based on the anisotropic wavelet decomposition of the equation residual into convection-dominated scales and diffusion-dominated scales. The associated norm, which is stronger than the standard energy norm, provides a robust (i.e., uniform in the convection limit) control over the streamline derivative of the solution. We propose an upper estimator and a lower estimator of the error, in this norm, between the exact solution and any finite dimensional approximation of it. We investigate the behaviour of such estimators, both theoretically and through numerical experiments. As an output of our analysis, we find that the lower estimator is quantitatively accurate and robust.