Reaction of N-acylthioureas with electrophilic reagents : Synthesis of 1,3,5-oxadiazinium salts, 1,3,5-thiadiazinium salts, 1,2,4-dithiazolium salts and benzothiazoles

N-Acylthioureas 1 can be easily transformed into 2,4-diamino-6-aryl-1,3,5-oxadiazinium salts 12, 2,4-diamino-6-aryl-1,3,5-thiadiazinium salts 13,3-amino-5-aryl-1,2,4-dithiazolium salts 19 and 2-acylimino-benzothiazolines 22, respectively by reaction with different electrophiles. The structure of the compounds prepared is confirmed by analytical data as well as by chemical transformations.     

Stability and robustness of collocation methods for Abel-type integral equations

Summary We study stability aspects of collocation methods for Abel-type integral equations of the first kind using piecewise polynomials. These collocation methods may be formulated as projection methods. Stability is defined as the boundedness of the sequence of projectors in their natural setting. Robustness is essentially the optimal asymptotic insensitivity to perturbations in the data. We show that stability and robustness are equivalent for the above collocation methods. This allows us to obtain optimal error estimates for some methods that are well-known to be robust. We also present numerical results for some methods which appear to be robust.Research supported in part by the United States Army under Contract No. DAAG 29-83-K-0109     

Geometric Analysis and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets

Due to its unequalled advantages, the magnetic resonance imaging (MRI) modality has truly revolutionized the diagnosis and evaluation of pathology. Because many morphological anatomic details that may not be visualized by other high tech imaging methods can now be readily shown by diagnostic MRI, it has already become the standard modality by which all other clinical imaging techniques are measured. The unique quantum physical basis of the MRI modality combined with the imaging capabilities of current computer technology has made this imaging modality a target of interdisciplinary interest for clinicians, physicists, biologists, engineers, and mathematicians. Due to the fact that MRI scanners perform corticomorphic processing, this modality is by far more complex than all the other high tech clinical imaging techniques. The purpose of this paper is to outline a phase coherent wavelet approach to Fourier transform MRI. It is based on distributional harmonic analysis on the Heisenberg nilpotent Lie group G and the associated symplectically invariant symbol calculus of pseudodifferential operators. The contour and contrast resolution of MRI scans which is controlled by symplectic filter bank processing gives the noninvasive MRI modality superiority over X-ray computed tomography (CT) in soft tissue differentiation.     

G2 PREDICTION OF THE ENTHALPIES OF FORMATION FOR SOME DIATOMIC CATIONS AND NEUTRALS

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Isogroups of differential ideals of vector-valued differential forms: Application to partial differential equations

An older geometric technique for the study of invariance groups of partial differential equations, originally proposed by one of the authors and F. B. Estabrook, is generalized and extended to problems involving exterior equations for vector-valued or Lie algebra-valued exterior differential forms. Use of the method is demonstrated in the study of the symmetry groups of the two-dimensional Dirac equation and the full Yang-Mills free-field equations in Minkowski spacetime.     

Convergence of Newton-like-iterative methods

Summary Newton-like methods in which the intermediate systems of linear equations are solved by iterative techniques are examined. By applying the theory of inexact Newton methods radius of convergence and rate of convergence results are easily obtained. The analysis is carried out in affine invariant terms. The results are applicable to cases where the underlying Newton-like method is, for example, a difference Newton-like or update-Newton method.     

A compact F-space not co-absolute with βN−N

We show that if every Parovi?enko space of weight $\text{c}$ is co-absolute with $\text{β}\text{N}\text{?}\text{N}$, then .