role of the anterior cingulate cortex in extinction learning of avoidance behavior and in the retrieval of its extinction memory

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2012

Dominance of positivity of the Green's function associated to a perturbed polyharmonic dirichlet boundary value problem by pointwise estimates

Magdeburg, Univ., Fak. für Mathematik, Diss., 2015

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”.

Estudos sôbre o pneumococo: 4a. nota - Influência do pH do meio sôbre a formação da cápsula pelo pneumococo

One of the features of pneumococcus which has deserved the attention of investigators is the capsule. Since Pasteur, Chamberland and Roux (1881) several functions have been ascribed to it as well as peculiar properties. In the present paper, we take into consideration one only aspect of this problem; it is the relationship which there possibly may be between acidity of the culture medium and the power of capsule formation by pneumococcus. As it is known, this germ requires for its development 7.8 as an optimum pH, but maintains its biological activities down to 5.6. These variations do not take place without large alterations, particularly of the capsule, not only from the morphological but also from the chemical viewpoint. The diameter of the mucous envelopment of the pneumococcus decreases in proportion to the increase of acidity down to its complete extinction. This fact has been regarded by investigators as a biological feature inhe¬ring to the germ itself and as proceeding of self-defense. In an acid medium the existing capsule is destroyed and the germ does not produce it again; consequently, acidity inhibits the formation of the capsule. We tried to check how this phenomenon comes to pass and to elucidated it. As we know, the fundamental compound of the pneumococcus capsule is mucin. In the first place, we experimented the action of acidity on same in the following manner: Mucin extracted from bovine submaxillary gland is precipitated by HC1 at a determined concentration degree; the mucin dissolves again and precipi¬tates in function of this concentration. This property of mucin (solubility in acid medium) modifies a little the interpretation of the mechanism of disappearance of the capsule from the said germ in the culture medium. Indeed: The acidification of the medium consecutive to the growth of pneumococcus reduces the dimensions of the capsule until causing its com¬plete disappearance; but on transferring this strain to new optimum cultiva¬ting conditions the capsule appears again exhuberantly, at times as anteriorly, although with biased virulence. Linking these two facts we draw the following conclusions: Pneumo¬coccus does not lose its capacity of capsule formation in an acid medium; but mucin, whilst being produced, is entirely dissolved in this medium by the aid of acidity; we venture to state that, in spite of medium acidity, the capacity of capsule production is a constant feature of pneumococcus and that the disappearance of the capsule does not depend on the pneumococcus in itself when it produces smooth colonies, but on the chemical properties of mucin, mainly on its solubility in acid medium.

Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

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.

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.