Iterated Differential Forms II: Riemannian Geometry Revisited

A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.Comment: 12 pages, extended version of the published note Dokl. Math. 73, n. 2 (2006) 18

Discretized rotation has infinitely many periodic orbits

For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.Comment: Revised after referee reports, and added a quantitative statemen

Sub-wavelength imaging: Resolution enhancement using metal wire gratings

An experimental evidence of subwavelength imaging with a "lens", which is a uniaxial negative permittivity wire medium slab, is reported. The slab is formed by gratings of long thin parallel conducting cylinders. Taking into account the anisotropy and spatial dispersion in the wire medium we theoretically show that there are no usual plasmons that could be exited on surfaces of such a slab, and there is no resonant enhancement of evanescent fields in the slab. The experimentally observed clear improvement of the resolution in the presence of the slab is explained as filtering out the harmonics with small wavenumbers. In other words, the wire gratings (the wire medium) suppress strong traveling-mode components increasing the role of evanescent waves in the image formation. This effect can be used in near-field imaging and detection applications.Comment: 12 pages, 6 figure

Electromagnetic wave refraction at an interface of a double wire medium

Plane-wave reflection and refraction at an interface with a double wire medium is considered. The problem of additional boundary conditions (ABC) in application to wire media is discussed and an ABC-free approach, known in the solid state physics, is used. Expressions for the fields and Poynting vectors of the refracted waves are derived. Directions and values of the power density flow of the refracted waves are found and the conservation of the power flow through the interface is checked. The difference between the results, given by the conventional model of wire media and the model, properly taking into account spatial dispersion, is discussed.Comment: 17 pages, 11 figure

Presymplectic current and the inverse problem of the calculus of variations

The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon and Lawson and generalizes an older result of Henneaux from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.Comment: v2: 17 pages, no figures, BibTeX; minor corrections, close to published versio

The graded Jacobi algebras and (co)homology

Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of describing such structures by classical Lie algebroids via certain gauging (in the spirit of E.Witten's gauging of exterior derivative) is developed. One constructs a corresponding Cartan differential calculus (graded commutative one) in a natural manner. This, in turn, gives canonical generating operators for triangular Jacobi algebroids. One gets, in particular, the Lichnerowicz-Jacobi homology operators associated with classical Jacobi structures. Courant-Jacobi brackets are obtained in a similar way and use to define an abstract notion of a Courant-Jacobi algebroid and Dirac-Jacobi structure. All this offers a new flavour in understanding the Batalin-Vilkovisky formalism.Comment: 20 pages, a few typos corrected; final version to be published in J. Phys. A: Math. Ge

Digital seed morphometry for genotype identification — case study of seeds of excavated (15th century Hungary) and current vinegrape (Vitis v. vinifera) varieties

Abstract Digital seed image analysis of seed remains of three ancient vinegrape samples excavated from 15th-century sites of Hungary was conducted and compared to those of ten currently grown old grapevine varieties. Digital seed images were analysed by Fovea Pro 4.0 computer program, with the final aim to identify the ancient grapevine cultivars with a final genotype reconstruction. Discriminant analysis, XY plot and histogram analyses revealed that seeds of two archaeological samples (11–13) show the closest similarity to the currently grown old vinegrape Vitis v. vinifera cv. ‘Mézesfehér’ (sample 6). Histogram analysis of seed parameter Equiv.Diam. (cm) of the archaeological seed sample ‘Budai vár’ (sample 11) showed diverse multimodal distribution compared to the unimodal distribution of cv. ‘Mézesfehér’ (sample 6), which results indicated that cv. ‘Mézesfehér’ went through a selection through the last five centuries, which narrowed the morphological diversity of this seed character

The Influence of Mineral Nutrition on the Productivity of Spring Rape

This article presents data on the influence of mineral nutrition on the productivity of spring bird rape varieties in the conditions of the non-chernozem zone of Russia. The experiments were carried out on agro-gray loamy soils of the experimental agrotechnological station of the Federal State Budgetary Educational Institution of Higher Education “Ryazan State Agrotechnological University” (FSBEI HE RSATU) in the Ryazan Region in 2016-2018. A level of mineral nutrition for spring bird rape was calculated asN180P100K100. Based on this, the options for mineral nutrition in research were established. According to the results of the experiments, the duration of the growing season of spring bird rape varieties was established: 73-91 days.An increase in nitrogen to 150 kg of the active substance turned out to be less effective, as the yield increased slightly or remained at the level of N90P50K50. The use of phosphoruspotassium fertilizers did not contribute to the creation of such a nutritional regime that would increase seed productivity. An increase in the nitrogen nutrition of the plants led to increased protein content anddecreased oil content in seeds. This trend was observed in all varieties of spring bird rape. The average oil content was 38.5-45.5% and the average protein contentwas 18.0-24.7%, depending on the variety and the level of mineral nutrition. On average, the highest oil content was shown by varieties Lipchanka (44.1%) and Kulta (42.6%). Keywords: agro-gray soil, level of mineral nutrition, oil content, productivity, spring bird rape, variet