and Applied Analysis 3 For each complex number x,ΨP x define a linear mapping of C|N| into C. If anyNj is zero, Ψ i,j P is the empty matrix for all i and the corresponding column of matrices in ΨP is absent. If Nj 0 for all j,ΨP x is defined to be the unique linear mapping of {0} C0 into C; its matrix representation is then the empty matrix. In particular consider ΨP x ( x4 2x2 1 − 2x 3x4 2x 4x3 )

The performance of an 8-noded hexahedron C1* element in elasticity is investigated. Three translational displacements and their derivatives as strain in each direction are considered as degrees of freedom (d.o.f.’s) at each node. The geometric mapping is enforced using a C0 element with no derivative as nodal d.o.f.’s . The stiffness matrix of the element is also computed using a transformation...

This paper presents a novel approach for fault type estimation in power systems. The Fault type estimation is the first step to estimate instantaneous voltage, voltage sag magnitude and duration in a three-phase system at fault duration. The approach is based on time-domain state estimation where redundant measurements are available. The current based model allows a linear mapping between the m...

This paper presents a new formulation for mapping algorithms into linear systolic arrays. The closed-form necessary and suucient mapping conditions are derived to identify mappings without computation connicts and data link collisions. These mapping conditions are easy to check because their constituent variables are the space-time mapping matrix and the problem size parameters. The design of o...

An important problem in physical mapping is to test the consecutive ones property of a (0,1)-matrix: that is, whether it is possible to permute the columns so that each row of the resulting matrix has the ones occur in a consecutive block. This is useful, for example, in probe hybridization for cosmid clones and in the STS content mapping of YAC library. The linear time algorithm by Booth and L...

Introduction This clinical report assesses the feasibility of 3-D ultrashort echo time enhanced T2* (UTE-T2*) mapping of cartilage in vivo and examines the sensitivity of UTE-T2* to early cartilage degeneration compared to arthroscopic grading as the standard. UTE-T2* mapping is sensitive to changes in short-T2 signal (T2 <10ms) and may provide improved sensitivity to subtle matrix alterations,...

Association-mapping methods promise to overcome the limitations of linkage-mapping methods. The main objectives of this study were to (i) evaluate various methods for association mapping in the autogamous species wheat using an empirical data set, (ii) determine a marker-based kinship matrix using a restricted maximum-likelihood (REML) estimate of the probability of two alleles at the same locu...

Introduction The B1 transmit field inhomogeneity represents a serious problem in whole-body high field MRI (≥3T). B1 shimming based on measured B1 maps is a promising approach to cope with this problem and represents the primary application for parallel transmission at this point in time [1,2]. However, B1 mapping is still an error-prone and time consuming process [3], potentially resulting in ...