A tree of linearisable second-order evolution equations by generalised hodograph transformations

We present a list of (1+1)-dimensional second-order evolution equations all connected via a proposed generalised hodograph transformation, resulting in a tree of equations transformable to the linear second-order autonomous evolution equation. The list includes autonomous and nonautonomous equations.Comment: arXiv version is already officia

On integration of the Kowalevski gyrostat and the Clebsch problems

For the Kowalevski gyrostat change of variables similar to that of the Kowalevski top is done. We establish one to one correspondence between the Kowalevski gyrostat and the Clebsch system and demonstrate that Kowalevski variables for the gyrostat practically coincide with elliptic coordinates on sphere for the Clebsch case. Equivalence of considered integrable systems allows to construct two Lax matrices for the gyrostat using known rational and elliptic Lax matrices for the Clebsch model. Associated with these matrices solutions of the Clebsch system and, therefore, of the Kowalevski gyrostat problem are discussed. The Kotter solution of the Clebsch system in modern notation is presented in detail.Comment: LaTeX, 24 page

Effective action for Einstein-Maxwell theory at order RF**4

We use a recently derived integral representation of the one-loop effective action in Einstein-Maxwell theory for an explicit calculation of the part of the effective action containing the information on the low energy limit of the five-point amplitudes involving one graviton, four photons and either a scalar or spinor loop. All available identities are used to get the result into a relatively compact form.Comment: 13 pages, no figure

Über die Temperaturempfindlichkeit des rohrzuckerspaltenden Enzyms des menschlichen Jejunums.

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On nonlocal symmetries, nonlocal conservation laws and nonlocal transformations of evolution equations

We discuss nonlocal symmetries and nonlocal conservation laws that follow from the systematic potentialisation of evolution equations. Those are the Lie point symmetries of the auxiliary systems, also known as potential symmetries. We define higher-degree potential symmetries which then lead to nonlocal conservation laws and nonlocal transformations for the equations. We demonstrate our approach by the Burgers' hierarchy and the Calogero-Degasperis-Ibragimov-Shabat hierarchy

Mechanism of Deep-focus Earthquakes Anomalous Statistics

Analyzing the NEIC-data we have shown that the spatial deep-focus earthquake distribution in the Earth interior over the 1993-2006 is characterized by the clearly defined periodical fine discrete structure with period L=50 km, which is solely generated by earthquakes with magnitude M 3.9 to 5.3 and only on the convergent boundary of plates. To describe the formation of this structure we used the model of complex systems by A. Volynskii and S. Bazhenov. The key property of this model consists in the presence of a rigid coating on a soft substratum. It is shown that in subduction processes the role of a rigid coating plays the slab substance (lithosphere) and the upper mantle acts as a soft substratum. Within the framework of this model we have obtained the estimation of average values of stress in the upper mantle and Young's modulus for the oceanic slab (lithosphere) and upper mantle.Comment: 9 pages, 7 figure

Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields

Using the Pauli-Villars regularization and arguments from convex analysis, we construct solutions to the classical time-independent Maxwell equations in Dirac's vacuum, in the presence of small external electromagnetic sources. The vacuum is not an empty space, but rather a quantum fluctuating medium which behaves as a nonlinear polarizable material. Its behavior is described by a Dirac equation involving infinitely many particles. The quantum corrections to the usual Maxwell equations are nonlinear and nonlocal. Even if photons are described by a purely classical electromagnetic field, the resulting vacuum polarization coincides to first order with that of full Quantum Electrodynamics.Comment: Final version to appear in Arch. Rat. Mech. Analysi

Chiral perturbation theory

The main elements and methods of chiral perturbation theory, the effective field theory of the Standard Model below the scale of spontaneous chiral symmetry breaking, are summarized. Applications to the interactions of mesons and baryons at low energies are reviewed, with special emphasis on developments of the last three years. Among the topics covered are the strong, electromagnetic and semileptonic weak interactions of mesons at and beyond next--to--leading order in the chiral expansion, nonleptonic weak interactions of mesons, virtual photon corrections and the meson--baryon system. The discussion is limited to processes at zero temperature, for infinite volume and with at most one baryon.Comment: 84 pages, Latex, 11 PostScript figures (in separate file) embedded with epsfig.sty, complete ps file (compressed, uuencoded, 0.6 MB) available via email on request; to appear in Progr. Part. Nucl. Phys., vol. 3

Quantum effects in the evolution of vortices in the electromagnetic field

We analyze the influence of electron-positron pairs creation on the motion of vortex lines in electromagnetic field. In our approach the electric and magnetic fields satisfy nonlinear equations derived from the Euler-Heisenberg effective Lagrangian. We show that these nonlinearities may change the evolution of vortices.Comment: REVTEX4 and 5 EPS figure

Espécies florestais nativas prioritárias para produção de sementes e mudas no estado do Amapá.

O Brasil assumiu compromisso internacional de restaurar e reflorestar 12 milhões de hectares de florestas até 2030, nas suas Contribuições Nacionalmente Determinadas firmadas no Acordo de Paris. Embora o desmatamento ainda não seja um grande problema para o Amapá, sementes e mudas de espécies nativas possuem grande potencial como produto regional capaz de contribuir para geração de renda complementar das comunidades e agricultores que detém florestas e utilizam esses recursos como meio de vida. Por isso é necessário conhecer a importância ecológica e comercial de espécies nativas, para auxiliar a cadeia de produção de sementes e mudas na região. O objetivo do estudo foi realizar um levantamento de espécies nativas prioritárias no estado do Amapá, avaliando o grau de importância econômica e ambiental dessas espécies