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TOPOLOGICAL AND COMBINATORIAL PROPERTIES OF NEIGHBORHOOD AND CHESSBOARD COMPLEXESZeckner, Matthew 01 January 2011 (has links)
This dissertation examines the topological properties of simplicial complexes that arise from two distinct combinatorial objects. In 2003, A. Björner and M. de Longueville proved that the neighborhood complex of the stable Kneser graph SGn,k is homotopy equivalent to a k-sphere. Further, for n = 2 they showed that the neighborhood complex deformation retracts to a subcomplex isomorphic to the associahedron. They went on to ask whether or not, for all n and k, the neighborhood complex of SGn,k contains as a deformation retract the boundary complex of a simplicial polytope. Part one of this dissertation provides a positive answer to this question in the case k = 2. In this case it is also shown that, after partially subdividing the neighborhood complex, the resulting complex deformation retracts onto a subcomplex arising as a polyhedral boundary sphere that is invariant under the action induced by the automorphism group of SGn,2. Part two of this dissertation studies simplicial complexes that arise from non-attacking rook placements on a subclass of Ferrers boards that have ai rows of length i where ai > 0 and i ≤ n for some positive integer n. In particular, enumerative properties of their facets, homotopy type, and homology are investigated.
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The palaeomagnetic significance of the Bushveld Complex and related 2 Ga magnetic rocks in ancient continental entitiesLetts, Shawn Andrew 26 May 2008 (has links)
The Kaapvaal Craton was the scene of two major magmatic events around 2.0 Ga,
namely the Bushveld Complex and the Phalaborwa Complex. Both complexes
have been the subject of numerous palaeomagnetic studies during and prior to the
1980s. Despite these studies, systematic inconstancies for emplacement ages, in
particular for the Bushveld Complex, have been found between the
palaeomagnetic findings and well constrained ages. The greatest concern with the
Bushveld Complex results are the large spread in pole positions previously
determined for the different zones. This has been interpreted in prior studies to
indicate that the Bushveld Complex was emplaced and cooled below the Curie
temperature of magnetite over a time span of 50 my. The results obtained
previously for the Phalaborwa Complex appear to be out of position (~16°) with
respect to those for the Bushveld Complex. This is of concern because new
geochronological data show that the Rustenburg Layered Suite of the Bushveld
Complex was emplaced approximately 1 my after the Phalaborwa Complex.
These inconsistencies have prompted the current re-investigation of the
palaeomagnetic results for both the Bushveld Complex and the Phalaborwa
Complex.
New palaeomagnetic data collected from all zones of the Rustenburg Layered
Suite from the Eastern, Northern and Western Lobes of the Bushveld Complex,
yielded palaeomagnetic poles that eliminated the spread in the apparent polar
wander path. This observation is in agreement with precise age data, constraining
the time period of emplacement of the complex to ~ 6 my. Resulting beddingcorrected
high blocking components from all zones produced better groupings,
thereby supporting a primary magnetic signature and indicating that the complex
was intruded in a near-horizontal position. Dual polarities identified within each
zone of the complex and positive reversal tests have identified one of the oldest
known reversals of the Earth’s magnetic field.
iii
Palaeomagnetic data from the Phalaborwa Complex have produced a pole position
that is in close proximity to those obtained from the coeval Bushveld Complex.
In an attempt to achieve a better understanding of tectonic events occurring in the
Kaapvaal Craton a number of dual polarity dykes within the Bushvled and
Phalaborwa Complexes were palaeomagnetic analysed. Results revealed that the
acquired pole positions are in agreement with ~1.9 Ga dykes, indicating the
possibility that the dykes occurring in both complexes are part of the same
magmatic event.
Palaeopoles generated during this study were used in refining the Kaapvaal Craton
apparent polar wander path around 2.0 Ga, and in conjunction with other welldefined
2.0 Ga poles for the Kaapvaal Craton, a robust cratonic pole was produced
that was used in Precambrian palaeographic reconstructions with emphasis on the
postulated Vaalbara continent and the Columbia supercontinent. Palaeomagnetic
reconstruction derived in this study has cast doubt on the existence of the
Vaalbara continent at 2.0 Ga. Although, some support is given to the existence of
the Columbia supercontinent at the same period.
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First principles and effective theory approaches to dynamics of complex networksDehmamy, Nima 13 February 2016 (has links)
This dissertation concerns modeling two aspects of dynamics of complex networks: (1)
response dynamics and (2) growth and formation.
A particularly challenging class of networks are ones in which both nodes and links are
evolving over time – the most prominent example is a financial network. In the first part
of the dissertation we present a model for the response dynamics in networks near a metastable
point. We start with a Landau-Ginzburg approach and show that the most general
lowest order Lagrangians for dynamical weighted networks can be used to derive conditions
for stability under external shocks. Using a closely related model, which is easier to solve
numerically, we propose a powerful and intuitive set of equations for response dynamics
of financial networks. We find the stability conditions of the model and find two phases:
“calm” phase , in which changes are sub-exponential and where the system moves to a new,
close-by equilibrium; “frantic” phase, where changes are exponential, with negative blows
resulting in crashes and positive ones leading to formation of "bubbles". We empirically
verify these claims by analyzing data from Eurozone crisis of 2009-2012 and stock markets.
We show that the model correctly identifies the time-line of the Eurozone crisis, and in the stock market data it correctly reproduces the auto-correlations and phases observed in the
data.
The second half of the dissertation addresses the following question: Do networks that
form due to local interactions (local in real space, or in an abstract parameter space) have
characteristics different from networks formed of random or non-local interactions? Using
interacting fields obeying Fokker-Planck equations we show that many network characteristics
such as degree distribution, degree-degree correlation and clustering can either be
derived analytically or there are analytical bounds on their behaviour. In particular, we
derive recursive equations for all powers of the ensemble average of the adjacency matrix.
We analyze a few real world networks and show that some networks that seem to form from
local interactions indeed have characteristics almost identical to simulations based on our
model, in contrast with many other networks.
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NMR spectroscopic studies of binding and exchange in rhenium alkane complexesLawes, Douglas John, Chemistry, Faculty of Science, UNSW January 2008 (has links)
The transition metal complexes cyclopentadienylrhenium tricarbonyl [CpRe(CO)3, Cp = cyclopentadienyl] and (isopropylcyclopentadienyl)rhenium tricarbonyl [(i-PrCp)Re(CO)3, i-Pr = isopropyl] were photolysed in alkanes at low temperature and the resulting alkane complexes, of the general formula Cp'Re(CO)2(alkane) (Cp' = Cp or (i-PrCp)), were studied using NMR spectroscopy. Characteristic proton chemical shifts (δ) and couplings (3JHH) were observed for alkane complexes of several linear, branched and cyclic alkanes of up to eight carbons. Alkanes with chemically distinct methyl (CH3) and/or methylene (CH2) units were observed alternatively binding through each unit to rhenium. No bound methine unit was observed. Large C-H coupling constants (1JCH) were observed for protons of several bound CH3 and CH2 units, indicating the bound C-H is intact. These species are, thus, alkane sigma (σ) complexes, wherein the alkane has an agostic (M-H-C, 3 centre 2 electron) interaction with the rhenium centre. The CH3 binding mode of (i-PrCp)Re(CO)2(1-pentane) was elucidated; sequential deuteration in the bound CH3 revealed an equilibrium isotope effect (EIE) in the remaining proton/s, confirming that only one C-H has an agostic interaction with rhenium at any instant . NMR parameters δ(1H) (-8.22), δ(13C) ( 42.4) and 1JCH (85 Hz) for the complexed C-H reveal it is unequivocally intact and yet strongly interacting with the rhenium centre, hallmarks for the agostic interaction. Intramolecular exchange was identified between pentane complex isomers Cp'Re(CO)2(1-pentane), Cp'Re(CO)2(2-pentane) and Cp'Re(CO)2(3-pentane). Equilibrium constants were determined, revealing a preference for CH2 binding over CH3. The inequivalent hydrogens found in methylene groups of cyclohexane at low temperature permitted simultaneous observation of axial and equatorial C-H protons of a bound CH2 in CpRe(CO)2(cyclohexane); an EIE, upon deuteration, indicated rapid exchange between complexed C-H bonds in the bound CH2 unit. The rhenium centre was found to prefer complexation of the axial C-H bond, over the equatorial, with K ~2.9. Intermolecular exchange of alkane ligands with free solvent was directly observed, in the competitive complexation of the [CpRe(CO)2] fragment to different alkanes in binary mixtures. The preference cyclohexane > cyclopentane > pentane > isobutane was established and equilibrium constants determined. The kinetics were followed by NMR and modelled, revealing rate constants; decay rates were also determined.
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Weighted Bergman Kernel Functions and the Lu Qi-keng ProblemJacobson, Robert Lawrence 2012 May 1900 (has links)
The classical Lu Qi-keng Conjecture asks whether the Bergman kernel function for every domain is zero free. The answer is no, and several counterexamples exist in the literature. However, the more general Lu Qi-keng Problem, that of determining which domains in Cn have vanishing kernels, remains a difficult open problem in several complex variables. A challenge in studying the Lu Qi-keng Problem is that concrete formulas for kernels are generally difficult or impossible to compute. Our primary focus is on developing methods of computing concrete formulas in order to study the Lu Qi-keng Problem.
The kernel for the annulus was historically the first counterexample to the Lu Qi-keng Conjecture. We locate the zeros of the kernel for the annulus more precisely than previous authors. We develop a theory giving a formula for the weighted kernel on a general planar domain with weight the modulus squared of a meromorphic function. A consequence of this theory is a technique for computing explicit, closed-form formulas for such kernels where the weight is associated to a meromorphic kernel with a finite number of zeros on the domain. For kernels associated to meromorphic functions with an arbitrary number of zeros on the domain, we obtain a weighted version of the classical Ramadanov's Theorem which says that for a sequence of nested bounded domains exhausting a limiting domain, the sequence of associated kernels converges to the kernel associated to the limiting domain. The relationship between the zeros of the weighted kernels and the zeros of the corresponding unweighted kernels is investigated, and since these weighted kernels are related to unweighted kernels in C^2, this investigation contributes to the study of the Lu Qi-keng Problem. This theory provides a much easier technique for computing certain weighted kernels than classical techniques and provides a unifying explanation of many previously known kernel formulas. We also present and explore a generalization of the Lu Qi-keng Problem.
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Spectroscopic and theoretical studies of charge-transfer complexes.Larkindale, John Peter January 1971 (has links)
No description available.
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NMR spectroscopic studies of binding and exchange in rhenium alkane complexesLawes, Douglas John, Chemistry, Faculty of Science, UNSW January 2008 (has links)
The transition metal complexes cyclopentadienylrhenium tricarbonyl [CpRe(CO)3, Cp = cyclopentadienyl] and (isopropylcyclopentadienyl)rhenium tricarbonyl [(i-PrCp)Re(CO)3, i-Pr = isopropyl] were photolysed in alkanes at low temperature and the resulting alkane complexes, of the general formula Cp'Re(CO)2(alkane) (Cp' = Cp or (i-PrCp)), were studied using NMR spectroscopy. Characteristic proton chemical shifts (δ) and couplings (3JHH) were observed for alkane complexes of several linear, branched and cyclic alkanes of up to eight carbons. Alkanes with chemically distinct methyl (CH3) and/or methylene (CH2) units were observed alternatively binding through each unit to rhenium. No bound methine unit was observed. Large C-H coupling constants (1JCH) were observed for protons of several bound CH3 and CH2 units, indicating the bound C-H is intact. These species are, thus, alkane sigma (σ) complexes, wherein the alkane has an agostic (M-H-C, 3 centre 2 electron) interaction with the rhenium centre. The CH3 binding mode of (i-PrCp)Re(CO)2(1-pentane) was elucidated; sequential deuteration in the bound CH3 revealed an equilibrium isotope effect (EIE) in the remaining proton/s, confirming that only one C-H has an agostic interaction with rhenium at any instant . NMR parameters δ(1H) (-8.22), δ(13C) ( 42.4) and 1JCH (85 Hz) for the complexed C-H reveal it is unequivocally intact and yet strongly interacting with the rhenium centre, hallmarks for the agostic interaction. Intramolecular exchange was identified between pentane complex isomers Cp'Re(CO)2(1-pentane), Cp'Re(CO)2(2-pentane) and Cp'Re(CO)2(3-pentane). Equilibrium constants were determined, revealing a preference for CH2 binding over CH3. The inequivalent hydrogens found in methylene groups of cyclohexane at low temperature permitted simultaneous observation of axial and equatorial C-H protons of a bound CH2 in CpRe(CO)2(cyclohexane); an EIE, upon deuteration, indicated rapid exchange between complexed C-H bonds in the bound CH2 unit. The rhenium centre was found to prefer complexation of the axial C-H bond, over the equatorial, with K ~2.9. Intermolecular exchange of alkane ligands with free solvent was directly observed, in the competitive complexation of the [CpRe(CO)2] fragment to different alkanes in binary mixtures. The preference cyclohexane > cyclopentane > pentane > isobutane was established and equilibrium constants determined. The kinetics were followed by NMR and modelled, revealing rate constants; decay rates were also determined.
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Synthesis, reactivities and electrochemistry of ruthenium and osmium oxo complexes with polypyridine ligands /Leung, Wai-ho, Wilkie. January 1989 (has links)
Thesis (Ph. D.)--University of Hong Kong, 1990.
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Spectroscopic and theoretical studies of charge-transfer complexes.Larkindale, John Peter January 1971 (has links)
No description available.
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Oedipus in the cave : metaphors of seeing in modern drama and film /Roof, Judith A. (Judith Ann) January 1984 (has links)
No description available.
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