On the fundamentals of coherence theory

In the thesis I study various quantum coherence phenomena and create some of the foundations for a systematic coherence theory. So far, the approach to quantum coherence in science has been purely phenomenological. In my thesis I try to answer the question what quantum coherence is and how it should be approached within the framework of physics, the metatheory of physics and the terminology related to them. It is worth noticing that quantum coherence is a conserved quantity that can be exactly defined. I propose a way to define quantum coherence mathematically from the density matrix of the system. Degenerate quantum gases, i.e., Bose condensates and ultracold Fermi systems, form a good laboratory to study coherence, since their entropy is small and coherence is large, and thus they possess strong coherence phenomena. Concerning coherence phenomena in degenerate quantum gases, I concentrate in my thesis mainly on collective association from atoms to molecules, Rabi oscillations and decoherence. It appears that collective association and oscillations do not depend on the spin-statistics of particles. Moreover, I study the logical features of decoherence in closed systems via a simple spin-model. I argue that decoherence is a valid concept also in systems with a possibility to experience recoherence, i.e., Poincaré recurrences. Metatheoretically this is a remarkable result, since it justifies quantum cosmology: to study the whole universe (i.e., physical reality) purely quantum physically is meaningful and valid science, in which decoherence explains why the quantum physical universe appears to cosmologists and other scientists very classical-like. The study of the logical structure of closed systems also reveals that complex enough closed (physical) systems obey a principle that is similar to Gödel's incompleteness theorem of logic. According to the theorem it is impossible to describe completely a closed system within the system, and the inside and outside descriptions of the system can be remarkably different. Via understanding this feature it may be possible to comprehend coarse-graining better and to define uniquely the mutual entanglement of quantum systems.

Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

Preparation, structural analysis and prebiotic potential of arabinoxylo-oligosaccharides

Arabinoxylo-oligosaccharides (AXOS) can be prepared enzymatically from arabinoxylans (AX) and AXOS are known to possess prebiotic potential. Here the structural features of 10 cereal AX were examined. AX were hydrolysed by Shearzyme® to prepare AXOS, and their structures were fully analysed. The prebiotic potential of the purified AXOS was studied in the fermentation experiments with bifidobacteria and faecal microbiota. In AX extracted from flours and bran, high amounts of a-L-Araf units are attached to the b-D-Xylp main chain, whereas moderate or low degree of substitution was found from husks, cob and straw. Nuclear magnetic resonance (NMR) spectroscopy showed that flour and bran AX contain high amounts of a-L-Araf units bound to the O-3 of b-D-Xylp residues and doubly substituted b-D-Xylp units with a-L-Araf substituents at O-2 and O-3. Barley husk and corn cob AX contain high amounts of b-D-Xylp(1→2)-a-L-Araf(1→3) side chains, which can also be found in AX from oat spelts and rice husks, and in lesser amounts in wheat straw AX. Rye and wheat flour AX and oat spelt AX were hydrolysed by Shearzyme® (with Aspergillus aculeatus GH10 endo-1,4-b-D-xylanase as the main enzyme) for the production of AXOS on a milligram scale. The AXOS were purified and their structures fully analysed, using mass spectrometry (MS) and 1D and 2D NMR spectroscopy. Monosubstituted xylobiose and xylotriose with a-L-Araf attached to the O-3 or O-2 of the nonreducing end b-D-Xylp unit and disubstituted AXOS with two a-L-Araf units at the nonreducing end b-D-Xylp unit of xylobiose or xylotriose were produced. Xylobiose with b-D-Xylp(1→2)-a-L-Araf(1→3) side chain was also purified. These AXOS were used as standards in further identification and quantification of corresponding AXOS from the hydrolysates in high-performance anion-exchange chromatography with pulsed amperometric detection (HPAEC-PAD) analysis. The prebiotic potential of AXOS was tested in in vitro fermentation experiments. Bifidobacterium adolescentis ATCC 15703 and B. longum ATCC 15707 utilized AXOS from the AX hydrolysates. Both species released L-arabinose from AXOS, but B. adolescentis consumed the XOS formed, whereas B. longum fermented the L-arabinose released. The third species tested, B. breve ATCC 15700, grew poorly on these substrates. When cultivated on pure AXOS, the bifidobacterial mixture utilized pure singly substituted AXOS almost completely, but no growth was detected with pure doubly substituted AXOS as substrates. However, doubly substituted AXOS were utilized from the mixture of xylose, XOS and AXOS. Faecal microbiota utilized both pure singly and doubly substituted AXOS. Thus, a mixture of singly and doubly substituted AXOS could function as a suitable, slowly fermenting prebiotic substance. This thesis contributes to the structural information on cereal AX and preparation of mono and doubly substituted AXOS from AX. Understanding the utilization strategies is fundamental in evaluating the prebiotic potential of AXOS. Further research is still required before AXOS can be used in applications for human consumption.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.

Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

Molecular Dynamics Simulations of Homogeneous Nucleation

Nucleation is the first step in a phase transition where small nuclei of the new phase start appearing in the metastable old phase, such as the appearance of small liquid clusters in a supersaturated vapor. Nucleation is important in various industrial and natural processes, including atmospheric new particle formation: between 20 % to 80 % of atmospheric particle concentration is due to nucleation. These atmospheric aerosol particles have a significant effect both on climate and human health. Different simulation methods are often applied when studying things that are difficult or even impossible to measure, or when trying to distinguish between the merits of various theoretical approaches. Such simulation methods include, among others, molecular dynamics and Monte Carlo simulations. In this work molecular dynamics simulations of the homogeneous nucleation of Lennard-Jones argon have been performed. Homogeneous means that the nucleation does not occur on a pre-existing surface. The simulations include runs where the starting configuration is a supersaturated vapor and the nucleation event is observed during the simulation (direct simulations), as well as simulations of a cluster in equilibrium with a surrounding vapor (indirect simulations). The latter type are a necessity when the conditions prevent the occurrence of a nucleation event in a reasonable timeframe in the direct simulations. The effect of various temperature control schemes on the nucleation rate (the rate of appearance of clusters that are equally able to grow to macroscopic sizes and to evaporate) was studied and found to be relatively small. The method to extract the nucleation rate was also found to be of minor importance. The cluster sizes from direct and indirect simulations were used in conjunction with the nucleation theorem to calculate formation free energies for the clusters in the indirect simulations. The results agreed with density functional theory, but were higher than values from Monte Carlo simulations. The formation energies were also used to calculate surface tension for the clusters. The sizes of the clusters in the direct and indirect simulations were compared, showing that the direct simulation clusters have more atoms between the liquid-like core of the cluster and the surrounding vapor. Finally, the performance of various nucleation theories in predicting simulated nucleation rates was investigated, and the results among other things highlighted once again the inadequacy of the classical nucleation theory that is commonly employed in nucleation studies.

Essays on Corporate Governance and the Quality of Disclosed Earnings: Across Transitional Europe

A growing body of empirical research examines the structure and effectiveness of corporate governance systems around the world. An important insight from this literature is that corporate governance mechanisms address the excessive use of managerial discretionary powers to get private benefits by expropriating the value of shareholders. One possible way of expropriation is to reduce the quality of disclosed earnings by manipulating the financial statements. This lower quality of earnings should then be reflected by the stock price of firm according to value relevance theorem. Hence, instead of testing the direct effect of corporate governance on the firm’s market value, it is important to understand the causes of the lower quality of accounting earnings. This thesis contributes to the literature by increasing knowledge about the extent of the earnings management – measured as the extent of discretionary accruals in total disclosed earnings - and its determinants across the Transitional European countries. The thesis comprises of three essays of empirical analysis of which first two utilize the data of Russian listed firms whereas the third essay uses data from 10 European economies. More specifically, the first essay adds to existing research connecting earnings management to corporate governance. It testifies the impact of the Russian corporate governance reforms of 2002 on the quality of disclosed earnings in all publicly listed firms. This essay provides empirical evidence of the fact that the desired impact of reforms is not fully substantiated in Russia without proper enforcement. Instead, firm-level factors such as long-term capital investments and compliance with International financial reporting standards (IFRS) determine the quality of the earnings. The result presented in the essay support the notion proposed by Leuz et al. (2003) that the reforms aimed to bring transparency do not correspond to desired results in economies where investor protection is lower and legal enforcement is weak. The second essay focuses on the relationship between the internal-control mechanism such as the types and levels of ownership and the quality of disclosed earnings in Russia. The empirical analysis shows that the controlling shareholders in Russia use their powers to manipulate the reported performance in order to get private benefits of control. Comparatively, firms owned by the State have significantly better quality of disclosed earnings than other controllers such as oligarchs and foreign corporations. Interestingly, market performance of firms controlled by either State or oligarchs is better than widely held firms. The third essay provides useful evidence on the fact that both ownership structures and economic characteristics are important factors in determining the quality of disclosed earnings in three groups of countries in Europe. Evidence suggests that ownership structure is a more important determinant in developed and transparent countries, while economic determinants are important determinants in developing and transitional countries.

Understorey vegetation as an indicator of forest site potential in Southern Finland.

The relationship between site characteristics and understorey vegetation composition was analysed with quantitative methods, especially from the viewpoint of site quality estimation. Theoretical models were applied to an empirical data set collected from the upland forests of southern Finland comprising 104 sites dominated by Scots pine (Pinus sylvestris L.), and 165 sites dominated by Norway spruce (Picea abies (L.) Karsten). Site index H100 was used as an independent measure of site quality. A new model for the estimation of site quality at sites with a known understorey vegetation composition was introduced. It is based on the application of Bayes' theorem to the density function of site quality within the study area combined with the species-specific presence-absence response curves. The resulting posterior probability density function may be used for calculating an estimate for the site variable. Using this method, a jackknife estimate of site index H100 was calculated separately for pine- and spruce-dominated sites. The results indicated that the cross-validation root mean squared error (RMSEcv) of the estimates improved from 2.98 m down to 2.34 m relative to the "null" model (standard deviation of the sample distribution) in pine-dominated forests. In spruce-dominated forests RMSEcv decreased from 3.94 m down to 3.16 m. In order to assess these results, four other estimation methods based on understorey vegetation composition were applied to the same data set. The results showed that none of the methods was clearly superior to the others. In pine-dominated forests, RMSEcv varied between 2.34 and 2.47 m, and the corresponding range for spruce-dominated forests was from 3.13 to 3.57 m.

Local approximability of max-min and min-max linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0. In a min-max LP, the objective is to minimise ρ subject to Ax ≤ ρ1, Cx ≥ 1, and x ≥ 0. The matrices A and C are nonnegative and sparse: each row ai of A has at most ΔI positive elements, and each row ck of C has at most ΔK positive elements. We study the approximability of max-min LPs and min-max LPs in a distributed setting; in particular, we focus on local algorithms (constant-time distributed algorithms). We show that for any ΔI ≥ 2, ΔK ≥ 2, and ε > 0 there exists a local algorithm that achieves the approximation ratio ΔI (1 − 1/ΔK) + ε. We also show that this result is the best possible: no local algorithm can achieve the approximation ratio ΔI (1 − 1/ΔK) for any ΔI ≥ 2 and ΔK ≥ 2.