New nondestructive method for three-dimensional photoelasticity

A new set of equations describing completely the optical phenomena in a model involving continuous rotation of secondary axes and secondary principal-stress differences are obtained. These are solved by Peano-Baker method using experimentally determined characteristic parameters for several wavelengths of light. Experimental verifications are obtained for a rectangular bar subjected to combined torsion and tension. Paper was presented at Third SESA International Congress on Experimental Mechanics held in Los Angeles, CA on May 13–18, 1973.

Quasi-three-dimensional elastic stresses in rotating disks

A method is presented to obtain stresses and displacements in rotating disks by taking into account the effect of out-of-plane restraint conditions at the hub. The stresses and displacements are obtained in a non-dimensional form, presented in the form of graphs and compared with the generalized plane stress solution.

An economical, adaptable and user-friendly drip-perfusion bioreactor system designed for in vitro three dimensional cell culturing

This research project investigated a bioreactor system capable of high density cell growth intended for use in regenerative medicine and protein production. The bioreactor was based on a drip-perfusion concept and constructed with minimal costs, readily available components, and straightforward processes for usage. This study involved the design, construction, and testing of the bioreactor where the results showed promising three dimensional cell growth within a polymer structure. The accessibility of this equipment and the capability of high density, three dimensional cell growth would be suitable for future research in pharmaceutical drug manufacturing, and human organ and tissue regeneration.

A new nondestructive method for three-dimensional photoelasticity

A new set of equations describing completely the optical phenomena in a model involving continuous rotation of secondary axes and secondary principal-stress differences are obtained. These are solved by Peano-Baker method using experimentally determined characteristic parameters for several wavelengths of light. Experimental verifications are obtained for a rectangular bar subjected to combined torsion and tension.

Quasi-three-dimensional elastic stresses in rotating disks

A method is presented to obtain stresses and displacements in rotating disks by taking into account the effect of out-of-plane restraint conditions at the hub. The stresses and displacements are obtained in a non-dimensional form, presented in the form of graphs and compared with the generalized plane stress solution.

Comprehensive Two-Dimensional Gas Chromatography: Instrumental and Methodological Development

Comprehensive two-dimensional gas chromatography (GC×GC) offers enhanced separation efficiency, reliability in qualitative and quantitative analysis, capability to detect low quantities, and information on the whole sample and its components. These features are essential in the analysis of complex samples, in which the number of compounds may be large or the analytes of interest are present at trace level. This study involved the development of instrumentation, data analysis programs and methodologies for GC×GC and their application in studies on qualitative and quantitative aspects of GC×GC analysis. Environmental samples were used as model samples. Instrumental development comprised the construction of three versions of a semi-rotating cryogenic modulator in which modulation was based on two-step cryogenic trapping with continuously flowing carbon dioxide as coolant. Two-step trapping was achieved by rotating the nozzle spraying the carbon dioxide with a motor. The fastest rotation and highest modulation frequency were achieved with a permanent magnetic motor, and modulation was most accurate when the motor was controlled with a microcontroller containing a quartz crystal. Heated wire resistors were unnecessary for the desorption step when liquid carbon dioxide was used as coolant. With use of the modulators developed in this study, the narrowest peaks were 75 ms at base. Three data analysis programs were developed allowing basic, comparison and identification operations. Basic operations enabled the visualisation of two-dimensional plots and the determination of retention times, peak heights and volumes. The overlaying feature in the comparison program allowed easy comparison of 2D plots. An automated identification procedure based on mass spectra and retention parameters allowed the qualitative analysis of data obtained by GC×GC and time-of-flight mass spectrometry. In the methodological development, sample preparation (extraction and clean-up) and GC×GC methods were developed for the analysis of atmospheric aerosol and sediment samples. Dynamic sonication assisted extraction was well suited for atmospheric aerosols collected on a filter. A clean-up procedure utilising normal phase liquid chromatography with ultra violet detection worked well in the removal of aliphatic hydrocarbons from a sediment extract. GC×GC with flame ionisation detection or quadrupole mass spectrometry provided good reliability in the qualitative analysis of target analytes. However, GC×GC with time-of-flight mass spectrometry was needed in the analysis of unknowns. The automated identification procedure that was developed was efficient in the analysis of large data files, but manual search and analyst knowledge are invaluable as well. Quantitative analysis was examined in terms of calibration procedures and the effect of matrix compounds on GC×GC separation. In addition to calibration in GC×GC with summed peak areas or peak volumes, simplified area calibration based on normal GC signal can be used to quantify compounds in samples analysed by GC×GC so long as certain qualitative and quantitative prerequisites are met. In a study of the effect of matrix compounds on GC×GC separation, it was shown that quality of the separation of PAHs is not significantly disturbed by the amount of matrix and quantitativeness suffers only slightly in the presence of matrix and when the amount of target compounds is low. The benefits of GC×GC in the analysis of complex samples easily overcome some minor drawbacks of the technique. The developed instrumentation and methodologies performed well for environmental samples, but they could also be applied for other complex samples.

Multipliers of Sobolev spaces

Let Wm,p denote the Sobolev space of functions on Image n whose distributional derivatives of order up to m lie in Lp(Image n) for 1 less-than-or-equals, slant p less-than-or-equals, slant ∞. When 1 < p < ∞, it is known that the multipliers on Wm,p are the same as those on Lp. This result is true for p = 1 only if n = 1. For, we prove that the integrable distributions of order less-than-or-equals, slant1 whose first order derivatives are also integrable of order less-than-or-equals, slant1, belong to the class of multipliers on Wm,1 and there are such distributions which are not bounded measures. These distributions are also multipliers on Lp, for 1 < p < ∞. Moreover, they form exactly the multiplier space of a certain Segal algebra. We have also proved that the multipliers on Wm,l are necessarily integrable distributions of order less-than-or-equals, slant1 or less-than-or-equals, slant2 accordingly as m is odd or even. We have obtained the multipliers from L1(Image n) into Wm,p, 1 less-than-or-equals, slant p less-than-or-equals, slant ∞, and the multiplier space of Wm,1 is realised as a dual space of certain continuous functions on Image n which vanish at infinity.

Formal description, compression and transformation of digital pictures

This paper describes the application of vector spaces over Galois fields, for obtaining a formal description of a picture in the form of a very compact, non-redundant, unique syntactic code. Two different methods of encoding are described. Both these methods consist in identifying the given picture as a matrix (called picture matrix) over a finite field. In the first method, the eigenvalues and eigenvectors of this matrix are obtained. The eigenvector expansion theorem is then used to reconstruct the original matrix. If several of the eigenvalues happen to be zero this scheme results in a considerable compression. In the second method, the picture matrix is reduced to a primitive diagonal form (Hermite canonical form) by elementary row and column transformations. These sequences of elementary transformations constitute a unique and unambiguous syntactic code-called Hermite code—for reconstructing the picture from the primitive diagonal matrix. A good compression of the picture results, if the rank of the matrix is considerably lower than its order. An important aspect of this code is that it preserves the neighbourhood relations in the picture and the primitive remains invariant under translation, rotation, reflection, enlargement and replication. It is also possible to derive the codes for these transformed pictures from the Hermite code of the original picture by simple algebraic manipulation. This code will find extensive applications in picture compression, storage, retrieval, transmission and in designing pattern recognition and artificial intelligence systems.

Determination of the optically equivalent model in three-dimensional photoelasticity

Any stressed photoelastic medium can be reduced to an optically equivalent model consisting of a linear retarder, with retardation 1 and principal axis at azimuth 1, and a pure rotator of power 2. The paper describes two simple methods to determine these quantities experimentally. Further, a method is described to overcome the problem of rotational effects in scattered-light investigations. This new method makes use of the experimentally determined characteristic parameters

A parametric differentiation version with finite-difference scheme applicable to a class of problems in boundary layer flow with massive blowing

A numerical procedure, based on the parametric differentiation and implicit finite difference scheme, has been developed for a class of problems in the boundary-layer theory for saddle-point regions. Here, the results are presented for the case of a three-dimensional stagnation-point flow with massive blowing. The method compares very well with other methods for particular cases (zero or small mass blowing). Results emphasize that the present numerical procedure is well suited for the solution of saddle-point flows with massive blowing, which could not be solved by other methods.

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.