On the ubiquity of trivial torsion on elliptic curves

The purpose of this paper is to give a "down--to--earth" proof of the well--known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion

Biogeography and ecology of geographically distant populations of sibling Cryptocephalus leaf beetles

Different populations of two closely related species, Cryptocephalusflavipes and C. bameuli, from western (Alps, Apennines and Pyrenees) and central Europe (Poland, Ukraine and Pannonia) were analysed. On the basis of DNA sequences from two genes, cox1 and ef1-alpha, distinctiveness of both species was confirmed. Nevertheless, possible hybrids were identified in Carpathian mountains. We found a significant genetic differentiation among populations of C. flavipes and C. bameuli from distant regions but a high genetic similarity between populations of C. bameuli from north and south of the Carpathians. Demographic estimates suggest a past population expansion in the case of C. bameuli and a recent one for C. flavipes, possibly occurred during Pleistocene and Holocene, respectively. Distribution modelling showed that C. flavipes is typically present in the mountain systems, whereas C. bameuli is associated with hilly areas of central and eastern Europe. Based on the present data, Last Glacial Maximum refugia of both species were located in the Alpine region and Black Sea coasts, but on different elevations. The characterization of the insect diet, through a DNA metabarcoding approach targeting the trnL plant intron, demonstrated a significant differentiation of food preferences between the two species, as well as between geographic populations within the species

Stationary Einstein-Maxwell fields in arbitrary dimensions

The Einstein-Maxwell equations in D-dimensions admitting (D-3) commuting Killing vector fields have been investigated. The existence of the electric, magnetic and twist potentials have been proved. The system is formulated as the harmonic map coupled to gravity on three-dimensional base space generalizing the Ernst system in the four-dimensional stationary Einstein-Maxwell theory. Some classes of the new exact solutions have been provided, which include the electro-magnetic generalization of the Myers-Perry solution, which describes the rotating black hole immersed in a magnetic universe, and the static charged black ring solution.Comment: 26 page

Gravity and Geometric Phases

The behavior of a quantum test particle satisfying the Klein-Gordon equation in a certain class of 4 dimensional stationary space-times is examined. In a space-time of a spinning cosmic string, the wave function of a particle in a box is shown to acquire a geometric phase when the box is transported around a closed path surrounding the string. When interpreted as an Aharonov-Anandan geometric phase, the effect is shown to be related to the Aharonov-Bohm effect.Comment: 11 pages, latex fil

Chiral doublers of heavy-light baryons

We discuss the consequences of the chiral doubling scenario for baryons built of heavy and light quarks. In particular, we use the soliton description for baryons, demonstrating why each heavy-light baryon should be accompanied by the opposite parity partner. Our argumentation holds both for ordinary baryons and for exotic heavy pentaquarks which are required by the symmetries of QCD to appear in parity doublets, seperated by the mass shift of the chiral origin. Interpreting the recently observed by BaBaR, CLEO and Belle charmed mesons with assignment $(0^+,1^+)$ as the chiral partners of known $D$ and $D^*$ mesons, allows us to estimate the parameters of the mesonic effective lagrangian, and in consequence, estimate the masses of ground states and excited states of both parities. In particular, we interpret the state recently reported by the H1 experiment at HERA as a chiral partner $\tilde{\Theta}_c^0(3099)$ of yet undiscovered ground state pentaquark $\Theta_c^0(2700)$.Comment: 10 pages, in v2 some typos corrected, references adde

Interior of a Schwarzschild black hole revisited

The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one still encounters the existence of misconceptions and a certain ambiguity inherent in the Schwarzschild solution in the literature. By taking into account the point of view of an observer in the interior of the event horizon, one verifies that new conceptual difficulties arise. In this work, besides providing a very brief pedagogical review, we further analyze the interior Schwarzschild black hole solution. Firstly, by deducing the interior metric by considering time-dependent metric coefficients, the interior region is analyzed without the prejudices inherited from the exterior geometry. We also pay close attention to several respective cosmological interpretations, and briefly address some of the difficulties associated to spacetime singularities. Secondly, we deduce the conserved quantities of null and timelike geodesics, and discuss several particular cases in some detail. Thirdly, we examine the Eddington-Finkelstein and Kruskal coordinates directly from the interior solution. In concluding, it is important to emphasize that the interior structure of realistic black holes has not been satisfactorily determined, and is still open to considerable debate.Comment: 15 pages, 7 figures, Revtex4. V2: Version to appear in Foundations of Physic

Adsorption of mono- and multivalent cat- and anions on DNA molecules

Adsorption of monovalent and multivalent cat- and anions on a deoxyribose nucleic acid (DNA) molecule from a salt solution is investigated by computer simulation. The ions are modelled as charged hard spheres, the DNA molecule as a point charge pattern following the double-helical phosphate strands. The geometrical shape of the DNA molecules is modelled on different levels ranging from a simple cylindrical shape to structured models which include the major and minor grooves between the phosphate strands. The densities of the ions adsorbed on the phosphate strands, in the major and in the minor grooves are calculated. First, we find that the adsorption pattern on the DNA surface depends strongly on its geometrical shape: counterions adsorb preferentially along the phosphate strands for a cylindrical model shape, but in the minor groove for a geometrically structured model. Second, we find that an addition of monovalent salt ions results in an increase of the charge density in the minor groove while the total charge density of ions adsorbed in the major groove stays unchanged. The adsorbed ion densities are highly structured along the minor groove while they are almost smeared along the major groove. Furthermore, for a fixed amount of added salt, the major groove cationic charge is independent on the counterion valency. For increasing salt concentration the major groove is neutralized while the total charge adsorbed in the minor groove is constant. DNA overcharging is detected for multivalent salt. Simulations for a larger ion radii, which mimic the effect of the ion hydration, indicate an increased adsorbtion of cations in the major groove.Comment: 34 pages with 14 figure

Effective interaction between helical bio-molecules

The effective interaction between two parallel strands of helical bio-molecules, such as deoxyribose nucleic acids (DNA), is calculated using computer simulations of the "primitive" model of electrolytes. In particular we study a simple model for B-DNA incorporating explicitly its charge pattern as a double-helix structure. The effective force and the effective torque exerted onto the molecules depend on the central distance and on the relative orientation. The contributions of nonlinear screening by monovalent counterions to these forces and torques are analyzed and calculated for different salt concentrations. As a result, we find that the sign of the force depends sensitively on the relative orientation. For intermolecular distances smaller than $6\AA$ it can be both attractive and repulsive. Furthermore we report a nonmonotonic behaviour of the effective force for increasing salt concentration. Both features cannot be described within linear screening theories. For large distances, on the other hand, the results agree with linear screening theories provided the charge of the bio-molecules is suitably renormalized.Comment: 18 pages, 18 figures included in text, 100 bibliog

Categorizing Different Approaches to the Cosmological Constant Problem

We have found that proposals addressing the old cosmological constant problem come in various categories. The aim of this paper is to identify as many different, credible mechanisms as possible and to provide them with a code for future reference. We find that they all can be classified into five different schemes of which we indicate the advantages and drawbacks. Besides, we add a new approach based on a symmetry principle mapping real to imaginary spacetime.Comment: updated version, accepted for publicatio