Comportamento do Heterocromossômio em alguns Ortópteros do Brasil

In the present paper the behavior of the heterochromoso-mes in the course of the meiotic divisions of the spermatocytes in 15 species of Orthoptera belonging to 6 different families was studied. The species treated and their respective chromosome numbers were: Phaneropteridae: Anaulacomera sp. - 1 - 2n = 30 + X, n +15+ X and 15. Anaulacomera sp. - 2 - 2n - 30 + X, n = 15+ X and 15. Stilpnochlora marginella - 2n = 30 + X, n = 15= X and 15. Scudderia sp. - 2n = 30 + X, n = 15+ X and 15. Posldippus citrifolius - 2n = 24 + X, n = 12+X and 12. Acrididae: Osmilia violacea - 2n = 22+X, n = 11 + X and 11. Tropinotus discoideus - 2n = 22+ X, n = 11 + X and 11. Leptysma dorsalis - 2n = 22 + X, n = 11-J-X and 11. Orphulella punctata - 2n = 22-f X, n = 11 + X and 11. Conocephalidae: Conocephalus sp. - 2n = 32 + X, n = 16 + X and 16. Proscopiidae: Cephalocoema zilkari - 2n = 16 + X, n = 8+ X and 8. Tetanorhynchus mendesi - 2n = 16 + X, n = 8+X and 8. Gryliidae: Gryllus assimilis - 2n = 28 + X, n = 14+X and 14. Gryllodes sp. - 2n = 20 + X, n = 10- + and 10. Phalangopsitidae: Endecous cavernicola - 2n = 18 +X, n = 94-X and 9. It was pointed out by the present writer that in the Orthoptera similarly to what he observed in the Hemiptera the heterochromosome in the heterocinetic division shows in the same individual indifferently precession, synchronism or succession. This lack of specificity is therefore pointed here as constituting the rule and not the exception as formerly beleaved by the students of this problem, since it occurs in all the species referred to in the present paper and probably also m those hitherto investigated. The variability in the behavior of the heterochromosome which can have any position with regard to the autosomes even in the same follicle is attributed to the fact that being rather a stationary body it retains in anaphase the place it had in metaphase. When this place is in the equator of the cell the heterochromosome will be left behind as soon as anaphase begins (succession). When, on the contrary, laying out of this plane as generally happens (precession) it will sooner be reached (synchronism) or passed by the autosomes (succession). Due to the less kinetic activity of the heterochromosome it does not orient itself at metaphase remaining where it stands with the kinetochore looking indifferently to any direction. At the end of anaphase and sometimes earlier the heterochromosome begins to show mitotic activities revealed by the division of its body. Then, responding to the influence of the nearer pole it moves to it being enclosed with the autosomes in the nucleus formed there. The position of the heterochromosome in the cell is explained in the following manner: It is well known that the heterochromosome of the Orthoptera is always at the periphery of the nucleus, just beneath the nuclear membrane. This position may be any in regard of the axis of the dividing cell, so that if one of the poles of the spindle comes to coincide with it, the heterochromosome will appear at this pole in the metaphasic figures. If, on the other hand, the angle formed by the axis of the spindle with the ray reaching the heterochromosome increases the latter will appear in planes farther and farther apart from the nearer pole until it finishes by being in the equatorial plane. In this way it is not difficult to understand precession, synchronism or succession. In the species in which the heterochromosome is very large as it generally happens in the Phaneropteridae, the positions corresponding to precession are much more frequent. This is due to the fact that the probabilities for the heterochromosome taking an intermediary position between the equator and the poles at the time the spindle is set up are much greater than otherwise. Moreover, standing always outside the spindle area it searches for a place exactly where this area is larger, that is, in the vicinity of the poles. If it comes to enter the spindle area, what has very little probability, it would be, in virtue of its size, propelled toward the pole by the nearing anaphasic plate. The cases of succession are justly those in which the heterochromosome taking a position parallelly to the spindle axis it can adjust its large body also in the equator or in its proximity. In the species provided with small heterochromosome (Gryllidae, Conocephalidae, Acrididae) succession is found much more frequently because here as in the Hemiptera (PIZA 1945) the heterochromosome can equally take equatorial or subequatorial positions, and, furthermore, when in the spindle area it does offer no sereous obstacle to the passage of the autosomes. The position of the heterochromosome at the periphery of the nucleus at different stages may be as I suppose, at least in part a question of density. The less colourability and the surface irregularities characteristic of this element may well correspond to a less degree of condensation which may influence passive movements. In one of the species studied here (Anaulacomera sp.- 1) included in the Phaneropteridae it was observed that the plasmosome is left motionless in the spindle as the autosomes move toward the poles. It passes to one of the secondary spermatocytes being not included in its nucleus. In the second division it again passes to one of the cells being cast off when the spermatid is being transformed into spermatozoon. Thus it is regularly found among the tails of the spermatozoa in different stages of development. In the opinion of the present writer, at least in some cases, corpuscles described as Golgi body's remanents are nothing more than discarded plasmosomes.

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”.

Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

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.

On Hyperbolic once-punctured-torus bundles II. Fractal tessellations of the plane

We describe fractal tessellations of the complex plane that arise naturally from Cannon-Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations.

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.