An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? transformation formula.     

Condensed Cramer rule for some restricted quaternion linear equations

In this paper, we derive an alternative more condensed Cramer rule for the unique solution of some restricted left and right systems of quaternion linear equations. The findings of this paper extend some known results in the literature.     

NFZ-10工业辐照电子直线加速器

 研制的电子直线加速器NFZ 10的辐照加工能力相当于30PBq的60Co源,电子束能量为4～12MeV,平均束功率为3kW,扫描宽度为1m,能量不稳定度≤±0.5%,束流不稳定度≤±0.6%,扫描不均匀度≤±2.5%。NFZ-10加速器已被用于辐照各种电力半导体器件,一年多来运行稳定可靠并获得较好的经济效益。     

beta-Barrel transmembrane proteins: Geometric modelling, detection of transmembrane region, and structural properties

The location of the membrane lipid bilayer relative to a transmembrane protein structure is important in protein engineering. Since it is not present on the determined structures, it is essential to automatically define the membrane embedded protein region in order to test mutation effects or to design potential drugs. beta-Barrel transmembrane proteins, present in nature as outer membrane proteins (OMPs), comprise one of the two transmembrane protein fold classes. Lately, the number of their determined structures has increased and this enables the implementation and evaluation of structure-based annotation methods and their more comprehensive study. In this paper, we propose two new algorithms for (i) the geometric modelling of beta-barrels and (ii) the detection of the transmembrane region of a beta-barrel transmembrane protein. The geometric modelling algorithm combines a non-linear least square minimization method and a genetic algorithm in order to find the characteristics (axis, radius) of a shape with axial symmetry which best models a beta-barrel. The transmembrane region is detected by profiling the external residues of the beta-barrel along its axis in terms of hydrophobicity and existence of aromatic and charged residues. TbB-Tool implements these algorithms and is available in . A non-redundant set of 22 OMPs is used in order to evaluate the algorithms implemented and the results are very satisfying. In addition, we quantify the abundance of all amino acids and the average hydrophobicity for external and internal beta-stranded residues along the axis of beta-barrel, thus confirming and extending other researchers' results.     

Precoloring extension on unit interval graphs

In the precoloring extension problem a graph is given with some of the vertices having preassigned colors and it has to be decided whether this coloring can be extended to a proper k-coloring of the graph. Answering an open question of Hujter and Tuza [Precoloring extension. III. Classes of perfect graphs, Combin. Probab. Comput. 5 (1) (1996) 35-56], we show that the precoloring extension problem is NP-complete on unit interval graphs.     

Generalized Navier-Stokes equations with initial data in local Q-type spaces

In this paper, we establish a link between Leray mollified solutions of the three-dimensional generalized Navier-Stokes equations and mild solutions for initial data in the adherence of the test functions for the norm of . This result applies to the usual incompressible Navier-Stokes equations.     

Weighted estimates for a class of multilinear fractional type operators

In this paper, a class of multiple fractional type weights is defined as

     

Identification of stiffness, dissipation and input parameters of randomly excited non-linear systems: Capability of restricted potential models (RPM)

A dynamic identification technique in the time domain for time invariant systems under random external forces is presented. This technique is based on the use of the class of restricted potential models (RPM), which are characterized by a non-linear stiffness and a special form of damping, that is a product of the input power spectral density (PSD) matrix and the velocity gradient of a non-linear function of the total mechanical energy. By applying stochastic differential calculus and by specific analytical manipulations, some algebraic equations, depending on the response statistics and on the mechanic parameters that characterize RPM, are obtained. These equations can be used for the dynamic identification of the above mechanic parameters once the response statistics of the system to be identified are evaluated. The proposed technique allows one to identify single-degree-of-freedom or multi-degrees-of-freedom systems in the case of unmeasurable input. Further, the probabilistic characteristics of the external forces can be completely estimated in terms of PSD matrix.