The spores of Penicillium chrysogenum are of the noncoagulating type, and after spore germination a culture of disperse mycelia is obtained. In this study, it is shown that when the hyphal elements increase in size, they may agglomerate, and depending on the operating conditions, these agglomerates may develop into pellets with a dense core. The influence of initial spore concentration and agitation rate on agglomeration, leading to pellet formation, was studied. For a low concentration of spores in the inoculum, only a few hyphal elements agglomerate and pellets with a small diameter are obtained. At higher spore concentrations, many hyphal elements agglomerate and develop into large diameter pellets. Finally, at a very high spore concentration in the inoculum, the final hyphal element size is small and agglomerates therefore are not formed. With a high agitation rate, the agglomeration of hyphal elements is reduced. In a repeated fed-batch cultivation, where there was a shift from pellet morphology to disperse mycelia, it was found that there is no relation between macroscopic morphology and penicillin production by P. chrysogenum. The morphology was quantified throughout the repeated fed-batch cultivation, and both the pellet diameter and the concentration of pellets were affected by the agitation rate.

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Abstract. The PP-TSVD algorithm is a regularization algorithm based on the truncated singular value decomposition (TSVD) that computes piecewise polynomial (PP) solutions without any a priori information about, the locations of the break points. Here we describe an extension of this algorithm designed for two-dimensional inverse problems based on a Kronecker-product formulation. We illustrate its use in connection with deblurring of digital images with sharp edges, and we discuss its relations to total variation regularization. IntroductionIn this work we focus on discretizations of linear inverse problems in the form of square systems A z = b or overdetermined least squares systems min tIA z-bII2.These systems, which we denote discrete ill-posed problems, represent a wealth of applications of inverse problems; see, e.g., [6, §1.2]. Our main "tool" from linear algebra for analysis as well as computations is the singular value decomposition (SVD) of the coefficient matrix A. If we assume that A is m x n with m > n, then the SVD takes the formwhere ui and vi are the left, and right singular vectors which are orthonormal, and Gi are the singular values which are nonnegative and appearing in non-increasing order. In terms of the SVD, discrete ill-posed problems are characterized by having a coefficient matrix A whose singular values decay gradually to zero (in practice: until they hit a level determined by the machine precision).Standard methods for regularization of discrete ill-posed problems are Tikhonor regularization ~2 ilzll2 } (2) and truncated SVD (TSVD) minllzll2 subject to IIAk z -bll = min,

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