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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Advances in computational mathematics 7 (1997), S. 455-545 
    ISSN: 1572-9044
    Keywords: subdivision ; refinable functions ; regularity ; multiwavelets ; 39B12 ; 41A15 ; 41A25 ; 65D99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Advances in computational mathematics 12 (2000), S. 335-362 
    ISSN: 1572-9044
    Keywords: ideal bases ; Gröbner bases ; multivariate polynomials ; interpolation ; systems of polynomial equations ; 65D05 ; 65H10 ; 13P10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The H-basis concept allows, similarly to the Gröbner basis concept, a reformulation of nonlinear problems in terms of linear algebra. We exhibit parallels of the two concepts, show properties of H-bases, discuss their construction and uniqueness questions, and prove that n polynomials in n variables are, under mild conditions, already H-bases. We apply H-bases to the solution of polynomial systems by the eigenmethod and to multivariate interpolation.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Advances in computational mathematics 3 (1995), S. 219-237 
    ISSN: 1572-9044
    Keywords: Lagrange interpolation ; finite difference ; algorithm ; Primary ; 41A05 ; 41A10 ; 65D05 ; 65D10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper is concerned with the practical implementation of two methods to compute the solution of polynomial interpolation problems. In addition to a description of the implementation, practical results and several improvements will be discussed, focusing on speed and robustness of the algorithms under consideration.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 33 (1989), S. 1330-1342 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The disruption of native and recombinant strains of Escherichia coli was studied using a high-pressure homogenizer (Microfluidizer). The cells were grown in both batch and continuous fermentations. Cell suspensions ranging from 4 to 175 g dry wt/L were investigated at disruption pressures ranging from 30-95 MPa and at up to five passes. For both types of cells, the fraction of cells disrupted was dependent on the growth rate and concentration of the cells, the disruption pressure, and the number of passes through the disrupter. A model is presented that correlates the fractional disruption with these operating variables. The recombinant strain disrupted more readily than the native strain; 95 to 98% disruption of the former was achieved in two to three passes at a pressure of 95 MPa.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 59 (1998), S. 128-128 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: No abstract.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 57 (1998), S. 306-313 
    ISSN: 0006-3592
    Keywords: Halomonas elongata ; osmotic shock ; fed-batch ; compatible solutes ; ectoine ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A novel biotechnological process called “bacterial milking” has been established for the production of compatible solutes using the Gram-negative bacterium Halomonas elongata. Following a high-cell-density fermentation which provided biomass up to 48 g cell dry weight per liter, we applied alternating osmotic shocks in combination with crossflow filtration techniques to harvest the compatible solutes ectoine and hydroxyectoine. H. elongata, like other halophilic or halotolerant microorganisms, produces compatible solutes in response to the salinity of the medium. When transferred to a low salinity medium (osmotic downshock), H. elongata cells rapidly released their solutes to achieve osmotic equilibrium. Subsequent reincubation in a medium of higher salt concentration resulted in resynthesis of these compatible solutes and - after a defined regeneration time - the procedure could be repeated. By repeatedly performing this “bacterial milking” process (at least nine times) we were able to produce large amounts of ectoines with a biomass productivity of 155 mg of ectoine per cycle per gram cell dry weight. Further purification of the products was achieved by a simple two-step procedure based on cation exchange chromatography and crystallization. The principles described in this article may also be useful for the production of other low-molecular-weight compounds. © 1998 John Wiley & Sons, Inc. Biotechnol Bioeng 57: 306-313, 1998.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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