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  • 41A15  (4)
  • Antigens, Differentiation, T-Lymphocyte/analysis  (1)
  • B-splines  (1)
  • 1
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    In vivo modulation of cytolytic activity and Thy-1 expression in TCR-gamma delta+ intraepithelial lymphocytes (1989)
    American Association for the Advancement of Science (AAAS)
    Details
    Publication Date: 1989-03-31
    Description: Although the functional aspects of the alpha beta T cell antigen receptor (TCR) found on most peripheral T cells are well described, the function of the gamma delta TCR remains unclear. Murine intraepithelial lymphocytes (IEL) of the small intestine are CD8+, express the gamma delta TCR, and are constitutively lytic. Fresh IEL from germ-free mice had no lytic activity. Moreover, whereas IEL from normal mice are 30 to 50 percent Thy-1+, IEL from germ-free did not express Thy-1. Acclimation of germ-free mice to nonsterile conditions resulted in the generation of Thy-1+ IEL and induction of lytic activity. Thus CD8+ TCR-gamma delta IEL were regulated by externally derived stimuli via a specific functional interaction between IEL and gut-associated antigens.〈br /〉〈span class="detail_caption"〉Notes: 〈/span〉Lefrancois, L -- Goodman, T -- New York, N.Y. -- Science. 1989 Mar 31;243(4899):1716-8.〈br /〉〈span class="detail_caption"〉Author address: 〈/span〉Department of Cell Biology, Upjohn Company, Kalamazoo, MI 49001.〈br /〉〈span class="detail_caption"〉Record origin:〈/span〉 〈a href="http://www.ncbi.nlm.nih.gov/pubmed/2564701" target="_blank"〉PubMed〈/a〉
    Keywords: Animals ; Antigens/immunology ; Antigens, CD8 ; Antigens, Differentiation, T-Lymphocyte/analysis ; Antigens, Surface/*analysis/immunology ; Antigens, Thy-1 ; *Cytotoxicity, Immunologic ; Epithelial Cells ; Germ-Free Life ; Immunosorbent Techniques ; Intestine, Small/*cytology ; Mice ; Mice, Inbred BALB C ; Mice, Inbred C57BL ; Receptors, Antigen, T-Cell/analysis/*immunology ; Signal Transduction ; T-Lymphocytes/*immunology
    Print ISSN: 0036-8075
    Electronic ISSN: 1095-9203
    Topics: Biology , Chemistry and Pharmacology , Computer Science , Medicine , Natural Sciences in General , Physics
    Published by American Association for the Advancement of Science (AAAS)
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  • 2
    Electronic Resource
    Electronic Resource
    On the Cholesky factorization of the Gram matrix of locally supported functions (1995)
    Springer
    BIT 35 (1995), S. 233-257 
    Details
    ISSN: 1572-9125
    Keywords: Cholesky factorization ; Gram matrix ; orthogonal splines ; B-splines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Cholesky factorization of bi-infinite and semi-infinite matrices is studied and in particular the following is proved. If a bi-infinite matrixA has a Cholesky factorization whose lower triangular factorL and its lower triangular inverse decay exponentially away from the diagonal, then the semi-infinite truncation ofA has a lower triangular Cholesky factor whose elements approach those ofL exponentially. This result is then applied to studying the asymptotic behavior of splines obtained by orthogonalizing a large finite set of B-splines, in particular identifying the limiting profile when the knots are equally spaced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01737164
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  • 3
    Electronic Resource
    Electronic Resource
    Some properties of bivariate Bernstein-Schoenberg operators (1987)
    Springer
    Constructive approximation 3 (1987), S. 123-130 
    Details
    ISSN: 1432-0940
    Keywords: Bernstein-Schoenberg operator ; Bernstein polynomial ; MultivariateB-spline ; Asymptotic error ; 41A15 ; 41A63
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The bivariate Bernstein-Schoenberg operatorV T of degreem, introduced in [5], is a spline approximation operator that generalizes the Bernstein polynomial operatorB m . It is shown here that for a convex functionf,f≤V T (f)≤B m (f). This result is then used to show that for a twice differentiable functiong, the asymptotic error limm(V T (g)-g) depends only on the asymptotic error for quadratic polynomials. The latter is evaluated explicitly in the special circumstances thatV T is, in a sense, asymptotically close toB m .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01890558
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  • 4
    Electronic Resource
    Electronic Resource
    Closed surfaces defined from biquadratic splines (1991)
    Springer
    Constructive approximation 7 (1991), S. 149-160 
    Details
    ISSN: 1432-0940
    Keywords: 41A15 ; 41A05 ; 41A63 ; Closed surface ; Biquadratic B-spline ; Rectangular patch complex
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In order to construct closed surfaces with continuous unit normal, this paper studies certain spaces of spline functions on meshes of four-sided faces. The functions restricted to the faces are biquadratic polynomials or, in certain special cases, bicubic polynomials. A basis is constructed of positive functions with “small” support which sum to 1 and reduce to tensor-product biquadratic B-splines away from certain “singular” vertices. It is also shown that the space is suitable for interpolating data at the midpoints of the faces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01888151
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  • 5
    Electronic Resource
    Electronic Resource
    Asymptotic formulas for multivariate Bernstein-Schoenberg operators (1995)
    Springer
    Constructive approximation 11 (1995), S. 439-453 
    Details
    ISSN: 1432-0940
    Keywords: 41A15 ; 41A36 ; 41A63 ; Bernstein-Schoenberg operator ; simplex spline ; asymptotic error
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study an approximation operator of Bernstein-Schoenberg type which employs multivariate B-splines and was introduced in [2]. By first considering its action on convex functions, we derive a general formula of Voronovskaya type for the asymptotic error as the degree tends to infinity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01208431
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  • 6
    Electronic Resource
    Electronic Resource
    Wavelet bases for a set of commuting unitary operators (1993)
    Springer
    Advances in computational mathematics 1 (1993), S. 109-126 
    Details
    ISSN: 1572-9044
    Keywords: Hilbert space ; commuting unitary operators ; Riesz basis ; wandering subspaces ; multiresolution approximation ; duality principle ; box splines ; 41A15 ; 42C15 ; 47B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let (U=U 1, ...,U d ) be an orderedd-tuple of distinct, pairwise commuting, unitary operators on a complex Hilbert space ℋ, and letX:={x 1, ...,x r } ⊂ ℋ such that $$U^{\mathbb{Z}^d } X: = \{ U_1^{n_1 } \ldots U_d^{n_d } x_j :(n_1 , \ldots ,n_d ) \in \mathbb{Z}^d ,j = 1, \ldots ,r\} $$ is a Riesz basis of the closed linear spanV 0 of $$U^{\mathbb{Z}^d } X$$ . Suppose there is unitary operatorD on ℋ such thatV 0 ⊂D V 0 =:V 1 andU n D=DU An for alln ∈ ℤ d , whereA is ad ×d matrix with integer entries and Δ := det(A) ≠ 0. Then there is a subset Λ inV 1, withr(Δ − 1) vectors, such that $$U^{\mathbb{Z}^d } (\Gamma )$$ is a Riesz basis ofW 0, the orthogonal complement ofV 0 inV 1. The resulting multiscale and decomposition relations can be expressed in a Fourier representation by one single equation, in terms of which the duality principle follows easily. These results are a consequence of an extension, to a set of commuting unitary operators, of Robertson's Theorems on wandering subspace for a single unitary operator [24]. Conditions are given in order that $$U^{\mathbb{Z}^d } (\Gamma )$$ is a Riesz basis ofW 0. They are used in the construction of a class of linear spline wavelets on a four-direction mesh.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02070823
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