51 
Twist or theory of immersions of surfaces in fourdimensional spheres and hyperbolic spacesFawley, Helen Linda January 1997 (has links)
Let f : S → S(^4) be an immersion of a Riemann surface in the 4sphere. The thesis begins with a study of the adapted moving frame of / in order to produce conditions for certain naturally defined lifts to SO(5)/U(2) and S0(5)T(^2) to be conformal, harmonic and holomorphic with respect to two different but naturally occuring almost complex structures. This approach brings together the results of a number of authors regarding lifts of conformal, minimal immersions including the link with solutions of the Toda equations. Moreover it is shown that parallel mean curvature immersions have hajmonic lifts into S0(5)/U(2).A certain natural lift of / into CP(^3), the twistor space of S(^4), is studied more carefully via an explicit description and in the case of / being a conformal immersion this gives a beautiful and simple formula for the lift in terms of a stereographic coordinate associated to /. This involves establishing explicitly the twotoone correspondence between elements of the matrix groups Sp(2) and SO(5) and working with quaternions. The formula enables properties of such lifts to be explored and in particular it is shown that the harmonic sequence of a harmonic lift is either finite or satisfies a certain symmetry property. Uniqueness properties of harmonic lifts are also proved. Finally, the ideas are extended to the hyperbolic space H(^4) and after an exposition of the twistor fibration for this case, a method for constructing superminimal immersions of surfaces into H'^ from those in S"' is given.

52 
A study of BesovLipschitz and TriebelLizorkin spaces using nonsmooth kernelsCandy, Timothy Lars January 2008 (has links)
We consider the problem of characterising BesovLipshitz and TriebelLizorkin
spaces using kernels with limited smoothness and decay. This extends the work of H.Q.
Bui et al in [4] and [5] from kernels in S to more general kernels, including the Poisson
kernel. We overcome the difficulty of defining the convolution of a general kernel with a
distribution by using the concept of a bounded distribution introduced by E. Stein [12].
The characterisations we obtain are valid for the full range of indices.

53 
On estimates of constants for maximal functionsIakovlev, Alexander January 2014 (has links)
In this work we will study HardyLittlewood maximal function and maximal operator, basing on both classical and most up to date works. In the first chapter we will give definitions for different types of those objects and consider some of their most important properties. The second chapter is entirely devoted to an overview of the fundamental properties of HardyLittlewood maximal function, which are strong (p, p) and weak (1, 1) inequalities. Here we list the most actual results on this inequalities in correspondence to the way the maximal function is defined. The third chapter presents the theorem on asymptotic behavior of the lower bound of the constant in the weaktype (1, 1) inequality for the maximal function associated with cubes of Rd, then the dimension d tends to infinity. In the last chapter a method forcomputing constant c, appearing in the main theorem of chapter 3, is given. / <p>QC 20140527</p>

54 
The assessment of waveform distortion in power systems : validation of methods based on singlepoint measurements / Duan SerfonteinSerfontein, Duan January 2011 (has links)
The portion of energy converted by nonlinear loads in the modern power system is
increasing due to the energyefficiency and sophistication possible with power
electronics. Higher voltage and energy ratings are continuously forthcoming. These
devices draw nonlinear currents resulting in voltage waveform distortion at the Point
of Common Coupling due to nonzero supply impedances between voltage source
and the PCC. With the increase in waveform distortion comes the demand for better
Quality of Supply management.
The verification and quantification of the origin of waveform distortion in a power
system is a continuous field of study and forms a critical part of the mitigation design.
Methods utilizing singlepoint measurements, usually taken at the Point of Common
Coupling, for the assessment of the harmonic distortion generated by loads are
continuously being published. It’s been proven by means of computer simulations
and laboratory experiments that in an interconnected network where multiple sources
of distortion exist that loads have the ability to exchange harmonic active power
between each other. This project investigates the latter statement by conducting
practical experiments to conclude that loads have the ability to exchange harmonic
active power and that multiple synchronized measurements should be taken to
assess the harmonic distortion due to a load.
Laboratory experiments are carried utilizing an acknowledged single point
measurement method. The results are compared to the direction of harmonic active
power obtained from utilizing multiple synchronized measurements. To further the
information obtained from the laboratory experiments, practical experiments were
conducted utilizing the same methods. The results obtained coincided with the
results of previously conducted experiments of which the results were published.
From the results obtained it was concluded that in an interconnected network where
multiple sources of distortion exist that loads have the ability to exchange harmonic
active power between each other. Furthermore it was proven that the single point
measurement method investigated presented inconsistent results. Ultimately it was
concluded that the reason for the inconsistency was due to the fact that loads have the ability to exchange harmonic active power and that the single point measurement
failed to acknowledge this. / Thesis (M.Ing. (Electrical and Electronic Engineering))NorthWest University, Potchefstroom Campus, 2012

55 
Geometry of Fourier transforms and restriction theoremsYamaguchi, Ryuji January 1981 (has links)
We say that a restriction theorem holds for a curve (gamma) (t) in (//R)('n) if for all f(epsilon) ((//R)('n)) and for some p and q, there is a constant C(,p,q) such that / (VBAR)(VBAR) f (VBAR) (,(gamma)) (VBAR)(VBAR) (,L('q)(du)) (LESSTHEQ) C(,p,q) (VBAR)(VBAR) f (VBAR)(VBAR) (,L('P)((//R)('n))). / In Chapter 1, we prove restriction theorems for noncompact plane curves with nonnegative affine curvature when 1 (LESSTHEQ) p < 4/3 and / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / There is an analogous result for space curves in the same chapter. / The Hilbert transform along the curve (gamma) is defined by / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / In Chapter 2, it is shown that when (gamma) has the rapidly decreasing positive affine curvature, H(,(gamma)) is a L('P)bounded operator for / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)

56 
The structure of the Banach algebra LUC(G)* /Owusu, Asubonteng. January 1900 (has links)
Thesis (M.Sc.)  Carleton University, 2006. / Includes bibliographical references (p. 4144). Also available in electronic format on the Internet.

57 
Constructions of harmonic maps between Hadamard manifolds /Ueno, Keisuke. January 2001 (has links)
Univ., Diss.Sendai.

58 
On the generalized radiation problem of A. WeinsteinLieberstein, H. Melvin. January 1956 (has links)
ThesisUniversity of Maryland. / Technical Note BN87. AFOSRTN56594, AD115 021. "Supported in part by U.S. Air Force under contract No. AF 18 (600)573."

59 
Bidrag til de generaliserede næstenperiodiske funktioners teoriFølner, Erling, January 1944 (has links)
ThesisCopenhagen.

60 
Timeharmonic and transient electromagnetic fields in spherical cavities with walls of arbitrary electrical propertiesButler, Chalmers M. January 1962 (has links)
Thesis (Ph. D.)University of WisconsinMadison, 1962. / Typescript. Vita. eContent providerneutral record in process. Description based on print version record. Includes bibliographical references (leaves [104]108).

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