On the Multimomentum Bundles and the Legendre Maps in Field Theories

We study the geometrical background of the Hamiltonian formalism of first-order Classical Field Theories. In particular, different proposals of multimomentum bundles existing in the usual literature (including their canonical structures) are analyzed and compared. The corresponding Legendre maps are introduced. As a consequence, the definition of regular and almost-regular Lagrangian systems is reviewed and extended from different but equivalent ways.Comment: LaTeX file, 19 pages. Replaced with the published version. Minor mistakes are correcte

Symplectic Cuts and Projection Quantization

The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several cases. This may be inferred from exact results established within symplectic cutting.Comment: 12 pages, v2: additional examples and a new reference to related wor

Stabilizing s-hole dimethyl interactions

Methyl groups bound to electronegative atoms, such as N or O, are recognized to participate in tetrel bonding as Lewis acids. On the other hand, the capability of methyl groups bound to electropositive atoms, such as B or Al, to act as Lewis bases has been recently reported. Herein, we analyze the combination of these two behaviors to establish attractive methyl···methyl interactions. We have explored the Cambridge Structural Database to find experimental examples of these dimethyl-bound systems, finding a significant degree of directionality in the relative disposition of the two methyl groups. Moreover, we have carried out a comprehensive computational analysis at the DFT level of the dimethyl interactions, including the natural bond orbital, energy decomposition analysis, and topological analysis of the electron density (QTAIM and NCI). The dimethyl interaction is characterized as weak yet attractive and based on electrostatics, with a non-negligible contribution from orbital charge transfer and polarization

On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories

The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between k-symplectic field theories and the so-called autonomous k-cosymplectic field theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric character of the solutions to the Hamilton-de Donder-Weyl and the Euler-Lagrange equations in these formalisms. Second, we study the equivalence between k-cosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangian field theories (those where the configuration bundle of the theory is trivial).Comment: 25 page

Geometric reduction in optimal control theory with symmetries

A general study of symmetries in optimal control theory is given, starting from the presymplectic description of this kind of system. Then, Noether's theorem, as well as the corresponding reduction procedure (based on the application of the Marsden-Weinstein theorem adapted to the presymplectic case) are stated both in the regular and singular cases, which are previously described.Comment: 24 pages. LaTeX file. The paper has been reorganized. Additional comments have been included in Section 3. The example in Section 5.2 has been revisited. Some references have been adde

Invariant Forms and Automorphisms of Locally Homogeneous Multisymplectic Manifolds

It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field) is characterized by their automorphisms. Thus, locally homogeneous multisymplectic manifolds extend the family of classical geometries possessing a similar property: symplectic, volume and contact. The proof of the first result relies on the characterization of invariant differential forms with respect to the graded Lie algebra of infinitesimal automorphisms, and on the study of the local properties of Hamiltonian vector fields on locally multisymplectic manifolds. In particular it is proved that the group of multisymplectic diffeomorphisms acts (strongly locally) transitively on the manifold. It is also shown that the graded Lie algebra of infinitesimal automorphisms of a locally homogeneous multisymplectic manifold characterizes their multisymplectic diffeomorphisms.Comment: 25 p.; LaTeX file. The paper has been partially rewritten. Some terminology has been changed. The proof of some theorems and lemmas have been revised. The title and the abstract are slightly modified. An appendix is added. The bibliography is update

Pathogenicity of Entomopathogenic Fungi on the Weevil of the Andes (Premnotrypes vorax Hustache) of the Potato (Solanum tuberosum L.) in Chimborazo Province, Ecuador

From thirty native isolates of entomopathogenic fungi, which were obtained from corpses of larvae and adults of Andean weevil (Premnotrypes vorax Hustache); two fungi with entomopathogenic characteristics were selected through laboratory tests, which will be used in a program of integrated management of this pest in the Ecuadorian inter-Andean region. The pathogenicity of the 30 isolates was determined by the mortality that they caused in larvae and adults and it was expressed in percentage; for this, a complete randomized design (CRD) was used. The LC50 and TL50 were determined by Probit analysis. The two selected isolates corresponded to: Metarhizium anisopliae (Metschnikoff 1879) Sorokin 1883 (A13) and  Beauveria bassiana (Bals.-Criv.) Vuill. 1912 (A21), which proved to be the best, because they caused the highest mortality in larvae of the fourth instar and adults of P. vorax. The Probit analysis showed that LC50 for A21 isolate (B. bassiana) in fourth instar larvae was obtained with a concentration of 1,75x109 spores/ml and 1,08x109 spores/ml for adults. Instead for A13 isolate (M. anisopliae), the LC50 was obtained with a concentration of 1,65x109 spores/ml for larvae and 2,42x109 spores/ml for adults. The LT50 for the selected isolates at the indicated concentrations, was 4,84 and 4,32 days for larvae with A13 and A21 isolates respectively, while, for adults, the shortest time was obtained with A21 isolate in 4.36 days, compared with A13 isolate, that delayed 20,70 days. The larval stage of P. vorax was the most susceptible to A13 isolate, on the other hand, larvae and adults were equally susceptible to A21 isolate at the indicated concentrations. According to the results obtained, the two selected isolates can be used as an alternative to the use of conventional agrochemicals, which will contribute to a more ecological production