Collineations of a symmetric 2-covariant tensor: Ricci collineations

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra, but in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra. As an application, we study the Ricci collineations of a type B warped spacetime

Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings

The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to geometrical integration of Hamiltonian systems are obtained.Comment: 33 page

The Electromagnetic Lorentz Condition Problem and Symplectic Properties of Maxwell and Yang-Mills Type Dynamical Systems

Symplectic structures associated to connection forms on certain types of principal fiber bundles are constructed via analysis of reduced geometric structures on fibered manifolds invariant under naturally related symmetry groups. This approach is then applied to nonstandard Hamiltonian analysis of of dynamical systems of Maxwell and Yang-Mills type. A symplectic reduction theory of the classical Maxwell equations is formulated so as to naturally include the Lorentz condition (ensuring the existence of electromagnetic waves), thereby solving the well known Dirac -Fock - Podolsky problem. Symplectically reduced Poissonian structures and the related classical minimal interaction principle for the Yang-Mills equations are also considered. 1

Lie algebroid foliations and E1(M){\cal E}^1(M)-Dirac structures

We prove some general results about the relation between the 1-cocycles of an arbitrary Lie algebroid $A$ over $M$ and the leaves of the Lie algebroid foliation on $M$ associated with $A$. Using these results, we show that a ${\cal E}^1(M)$-Dirac structure $L$ induces on every leaf $F$ of its characteristic foliation a ${\cal E}^1(F)$-Dirac structure $L_F$, which comes from a precontact structure or from a locally conformal presymplectic structure on $F$. In addition, we prove that a Dirac structure $\tilde{L}$ on $M\times \R$ can be obtained from $L$ and we discuss the relation between the leaves of the characteristic foliations of $L$ and $\tilde{L}$.Comment: 25 page

Expression and Purification of Recombinant Hemoglobin in Escherichia coli

Recombinant DNA technologies have played a pivotal role in the elucidation of structure-function relationships in hemoglobin (Hb) and other globin proteins. Here we describe the development of a plasmid expression system to synthesize recombinant Hbs in Escherichia coli, and we describe a protocol for expressing Hbs with low intrinsic solubilities. Since the α- and β-chain Hbs of different species span a broad range of solubilities, experimental protocols that have been optimized for expressing recombinant human HbA may often prove unsuitable for the recombinant expression of wildtype and mutant Hbs of other species.As a test case for our expression system, we produced recombinant Hbs of the deer mouse (Peromyscus maniculatus), a species that has been the subject of research on mechanisms of Hb adaptation to hypoxia. By experimentally assessing the combined effects of induction temperature, induction time and E. coli expression strain on the solubility of recombinant deer mouse Hbs, we identified combinations of expression conditions that greatly enhanced the yield of recombinant protein and which also increased the efficiency of post-translational modifications.Our protocol should prove useful for the experimental study of recombinant Hbs in many non-human animals. One of the chief advantages of our protocol is that we can express soluble recombinant Hb without co-expressing molecular chaperones, and without the need for additional reconstitution or heme-incorporation steps. Moreover, our plasmid construct contains a combination of unique restriction sites that allows us to produce recombinant Hbs with different α- and β-chain subunit combinations by means of cassette mutagenesis