Optimal control of a Stefan problem with gradient-based methods in FEniCS

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Masterarbeit, 2016

The orthogonal subcategory problem in homotopy theory

It is known that, in a locally presentable category, localization exists with respect to every set of morphisms, while the statement that localization with respect to every (possibly proper) class of morphisms exists in locally presentable categories is equivalent to a large-cardinal axiom from set theory. One proves similarly, on one hand, that homotopy localization exists with respect to sets of maps in every cofibrantly generated, left proper, simplicial model category M whose underlying category is locally presentable. On the other hand, as we show in this article, the existence of localization with respect to possibly proper classes of maps in a model category M satisfying the above assumptions is implied by a large-cardinal axiom called Vopënka's principle, although we do not know if the reverse implication holds. We also show that, under the same assumptions on M, every endofunctor of M that is idempotent up to homotopy is equivalent to localization with respect to some class S of maps, and if Vopënka's principle holds then S can be chosen to be a set. There are examples showing that the latter need not be true if M is not cofibrantly generated. The above assumptions on M are satisfied by simplicial sets and symmetric spectra over simplicial sets, among many other model categories.

Periodic orbits of the planar collision restricted 3-body problem

Using the continuation method we prove that the circular and the elliptic symmetric periodic orbits of the planar rotating Kepler problem can be continued into periodic orbits of the planar collision restricted 3–body problem. Additionally, we also continue to this restricted problem the so called “comets orbits”.

A topological proof that surface relators are test words

Vegeu el resum a l'inici del document del fitxer adjunt.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Bribe-proof rules in the division problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compensate another agent to misrepresent his preference and, after an appropriate redistribution of their shares, each obtain a strictly preferred share. We characterize all bribe-proof rules as the class of efficient, strategy-proof, and weak replacement monotonic rules. In addition, we identify the functional form of all bribe-proof and tops-only rules.

A maximal domain of preferences for tops-only rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.

Mitsuda's reactions: induced by BCG in the normal Rhesus ("Macacca mulatta")

The reversals of Mitsuda's reactions induced by BCG have been objected to based on the possiblem interference of other determination causes of the phenomenon: tuberculous primo-infections, communicants of unsuspected leprosy, revearsals due to other causes, such as anti-diphteric and anti-tetanic vaccination, etc. In order to study the problem, we have used Rhesus monkeys (Macaca mulatta), which were reared in isolation, in an attempt to avoid the referred to interferences. Prior to the experiments, all animals were tested and found negative to radiograph, tuberculin and lepromin tests and were then submitted to the application of BCG vaccine (from 1 to 3 days old), in different doses and by different via. At different times, after the application of BCG, they were again submitted to the radiographic, tuberculin and lepromin tests. In the tables I to IV the experiences were summarised. From the experiments, the following conclusions were reached: 1 - From 12 Rhesus that received BCG 11 showed reversals of the Mitsuda reaction (91.7%). 2 - These reverseals took place both in tests effected shortly after BCG (from 6 days to 2 months), and tests effected much later (from 7 to 12 months after BCG). 3 - Some differences were found in the results, according to the dosis and the application via of the BCG. a) - The testicular and peritonela via (0,02g) were the only that determined strong positive Mitsuda's reactions (+++). b) - By oral via, animals that received high dosis (0.6g and 1.2 g), there resulted uniform and regular reversals, even though of low intensity (+); but from those who got small doses (0.2 g.) one showed no reversals in all tests, and the other presented reversals in the 2nd and 3rd tests only, also with low positivity (+). 4) In the 2nd and 3rd Mitsuda's reactions in the same animals, positivity was always precocious (generally within 48 hours), one getting the impression that there occurs a sensibilization of the animal body by the antigen with the repetition of the tests, even though the intensity of the reaction always remains the same. This precocious reaction (Fernandez type) occurs both shortly and long time after the application of the BCG. Its precocity depends not of the antigen only because the first Mitsuda's reaction after the BCG application occurs after some time and seems not influenced by the control lepromin test effected on the Rhesus before the BCG. 5) On the control group, the animals which received a.a.f. bacilli suspensions (Mycobacterium sp.; M. avium, and M. smegmatis), did not show reverseals of the Mitsuda's reaction. Two Rhesus, however, which received dead BCG (120ºC autoclave 1 hour), one intradermically (0.006 g) and the other orally (1.2 g), did both present reversals of the Mitsuda's reaction, with weak positivity (+). In all animals of the control-group, the allergic reactions were found negative. 6) Strong local inflammatory reactions were observed in the Rhesus that had received living BCG by intradermal via, and in the one submitted to multipunctures, there occurred the formation of a large caseous abcess. 7) The allergic tuberculinic and infratuberculinic reactions appeared dissociated from the Mitsuda's reactions: sometimes they are more precocious, occurring before of the lepromin test; on other occasions they disappear, when the Mitsuda's reactions still persist; and finally, they may be absent, when the latter occur, especially after the oral application of the BCG. 8) In Rhesus which received BCG by testicular and peritonela via, in the infratuberculinic test (0.1 ml of total BCG extract), besides the classic answer, which occurs between 48 and 96 hours, one could observe a delayed answer (15 to 20 days), represented by a non-erythematous nodule, which persists for 11-14 days.

Subjective income expectations, canonical models and income risk

Expectations are central to behaviour. Despite the existence of subjective expectations data, the standard approach is to ignore these, to hypothecate a model of behaviour and to infer expectations from realisations. In the context of income models, we reveal the informational gain obtained from using both a canonical model and subjective expectations data. We propose a test for this informational gain, and illustrate our approach with an application to the problem of measuring income risk.

On Boas-Type Problem

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α(0 & α & 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of modulus of continuity. The aim of this paper is to obtain Boas-type theorems for generalized Lipschitz classes. To define generalized Lipschitz classes we use the concept of modulus of smoothness of fractional order.

Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.