Lie algebroid structures on a class of affine bundles

We introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibred over the real numbers. It is argued that this is the framework which one needs for coming to a time-dependent generalization of the theory of Lagrangian systems on Lie algebroids. An extensive discussion is given of a way one can think of forms acting on sections of the affine bundle. It is further shown that the affine Lie algebroid structure gives rise to a coboundary operator on such forms. The concept of admissible curves and dynamical systems whose integral curves are admissible, brings an associated affine bundle into the picture, on which one can define in a natural way a prolongation of the original affine Lie algebroid structure.Comment: 28 page

The Structure of Conserved Charges in Open Spin Chains

We study the local conserved charges in integrable spin chains of the XYZ type with nontrivial boundary conditions. The general structure of these charges consists of a bulk part, whose density is identical to that of a periodic chain, and a boundary part. In contrast with the periodic case, only charges corresponding to interactions of even number of spins exist for the open chain. Hence, there are half as many charges in the open case as in the closed case. For the open spin-1/2 XY chain, we derive the explicit expressions of all the charges. For the open spin-1/2 XXX chain, several lowest order charges are presented and a general method of obtaining the boundary terms is indicated. In contrast with the closed case, the XXX charges cannot be described in terms of a Catalan tree pattern.Comment: 22 pages, harvmac.tex (minor clarifications and reference corrections added

THE TECHNICAL EFFICIENCY OF ILLINOIS GRAIN FARMS: AN APPLICATION OF A RAY-HOMOTHETIC PRODUCTION FUNCTION

The purpose of this paper is to measure the extent of technical inefficiency among a sample of Illinois grain farms using the corrected ordinary least squares method. Instead of assuming a Cobb-Douglas production function, a linear form of the ray-homothetic is used. The results show a significant amount of technical inefficiency among all the farms in the sample, but with large farms being less technically inefficient than small farms.Crop Production/Industries,

Poisson-Jacobi reduction of homogeneous tensors

The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold $M$, homogeneous with respect to a vector field $\Delta$ on $M$, and first-order polydifferential operators on a closed submanifold $N$ of codimension 1 such that $\Delta$ is transversal to $N$. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on $M$ to the Schouten-Jacobi bracket of first-order polydifferential operators on $N$ and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can be also understood as a sort of reduction; in the standard case -- a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between $\Delta$-homogeneous symplectic structures on $M$ and contact structures on $N$.Comment: 19 pages, minor corrections, final version to appear in J. Phys. A: Math. Ge

Clinical implications of cephalic vein morphometry in routine cardiac implantable electronic device insertion

Background: Morphometric parameters of the venous vasculature constitute an important aspect in successful cardiac implantable electronic device (CIED) insertion. The purpose of this study was to present morpho-anatomical variations of the cephalic vein (CV) and their effect on the course of CIED implantation procedures, based on the patients from our centre. Materials and methods: We analysed contrast venography results obtained during first-time lead placement. Venography was indicated in the cases of problematic lead introduction with either the CV cutdown or axillary/subclavian vein puncture techniques. The 214 cases of venography (15%) performed out of 1425 first-time lead placement in the period 2011–2013 were divided into 9 subgroups according to the most commonly observed CV variations of similar morpho-anatomical features that limited the use of the CV cutdown technique for lead insertion. Results: The following CV morphometric parameters were found to be unfavo­urable in terms of lead placement: CV diameter of ≤ 1 mm (18%), sharp curva­ture of the terminal CV segment as it joined the axillary vein (14%), terminal CV bifurcation (9%), additional CV branches (7%) or tributaries (7%), stenoses (5%), sharply winding course (5%), single CV with a supraclavicular course (4%). Conclusions: The radiographic records obtained during the procedures allowed us to assess the prevalence of those atypical CV variations in our study group, with graphic presentation of characteristic types and sporadically reported CV variations

Selected clinical challenges of a supraclavicular cephalic vein in cardiac implantable electronic device implantation

Background: Supraclavicular variations of the cephalic vein (CV) are detected sporadically. A somewhat more common finding is a CV variation with the typical course of the main vessel but with an additional supraclavicular branch, called the jugulocephalic vein (JCV). The aim of the study was to detect supraclavicular CVs or JCVs via intra-operative venography as well as assess their effects on primary and later revision cardiac implantable electronic device (CIED) procedures in our patients. Materials and methods: We analysed venographic images obtained during CIED procedures at our centre between 2011 and 2015. Out of the 324 venographies conducted during first-time CIED implantation, we identified 14 showing either a supraclavicular course of the CV itself or a persistent JCV. Among revision procedure venographies, we identified 1 case of pertinent CV variations. These vessels had been morphometrically altered by previous medical interventions. Results: Based on topography and morphometric parameters, we identified three anatomical variations of supraclavicular vessels: 2 cases of a supraclavicular CV and 12 cases of an infraclavicular CV accompanied by a persistent supraclavicular JCV (with the diameter larger than that of the main CV in 5 cases and smaller in 7 cases). In 2 cases the enlarged diameter of the JCV was probably due to increased collateral venous flow resulting from thrombotic lesions in the subclavian vein. Conclusions: Supraclavicular CV variations are rare. Nonetheless, they may significantly affect both first-time and later revision CIED procedures. The presence of a supraclavicular vein is an indication for diagnostic venography in the area of the clavipectoral triangle before the CIED procedure

Thermodyamic bounds on Drude weights in terms of almost-conserved quantities

We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions. Namely, the commutator between the Hamiltonian and the conservation law of a finite chain may result in boundary terms only. No reference to techniques used in Suzuki's proof of Mazur bound is made (which strictly applies only to finite-size systems with exact conservation laws), but Lieb-Robinson bounds and exponential clustering theorems of quasi-local C^* quantum spin algebras are invoked instead. Our result has an important application in the transport theory of quantum spin chains, in particular it provides rigorous non-trivial examples of positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ spin 1/2 chain [Phys. Rev. Lett. 106, 217206 (2011)].Comment: version as accepted by Communications in Mathematical Physics (22 pages with 2 pdf-figures

Interplane magnetic coupling effects in the multilattice compound Y_2Ba_4Cu_7O_{15}

We investigate the interplane magnetic coupling of the multilattice compound Y_2Ba_4Cu_7O_{15} by means of a bilayer Hubbard model with inequivalent planes. We evaluate the spin response, effective interaction and the intra- and interplane spin-spin relaxation times within the fluctuation exchange approximation. We show that strong in-plane antiferromagnetic fluctuations are responsible for a magnetic coupling between the planes, which in turns leads to a tendency of the fluctuation in the two planes to equalize. This equalization effect grows whit increasing in-plane antiferromagnetic fluctuations, i. e., with decreasing temperature and decreasing doping, while it is completely absent when the in-layer correlation length becomes of the order of one lattice spacing. Our results provide a good qualitative description of NMR and NQR experiments in Y_2Ba_4Cu_7O_{15}.Comment: Final version, to appear. in Phys. Rev. B (Rapid Communications), sched. Jan. 9

Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds

A description of time-dependent Mechanics in terms of Lagrangian submanifolds of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is presented. Two new Tulczyjew triples are discussed. The first one is adapted to the restricted Hamiltonian formalism and the second one is adapted to the extended Hamiltonian formalism