On the Birkhoff factorization problem for the Heisenberg magnet and nonlinear Schroedinger equations

A geometrical description of the Heisenberg magnet (HM) equation with classical spins is given in terms of flows on the quotient space $G/H_+$ where $G$ is an infinite dimensional Lie group and $H_+$ is a subgroup of $G$. It is shown that the HM flows are induced by an action of $\mathbb{R}^2$ on $G/H_+$, and that the HM equation can be integrated by solving a Birkhoff factorization problem for $G$. For the HM flows which are Laurent polynomials in the spectral variable we derive an algebraic transformation between solutions of the nonlinear Schroedinger (NLS) and Heisenberg magnet equations. The Birkhoff factorization for $G$ is treated in terms of the geometry of the Segal-Wilson Grassmannian $Gr(H)$. The solution of the problem is given in terms of a pair of Baker functions for special subspaces of $Gr(H)$. The Baker functions are constructed explicitly for subspaces which yield multisoliton solutions of NLS and HM equations.Comment: To appear in Journal of Mathematical Physic

INFLUENCE OF FINISHING DIET ON FATTY ACID PROFILE OF LONGISSIMUS MUSCLE OF BLACK SLAVONIAN PIGS

Regarding nutritional recommendations for humans, pork in general has too high ratio of n-6 and n-3 polyunsaturated fatty acids. The n-6/n-3 index is particularly high if animals were intensively fed concentrate feeds, because the cereals like corn are rich in linoleic acid (C18:2 n-6). Traditional Black Slavonian pig production is an outdoor grazing system, which includes utilization of the natural resources of pasture and oak woodland with supplement of small amounts of corn or some other grains. However, fattening with corn-based concentrate mixtures before slaughter is common. In this study, the influence of finishing diet of acorn or corn-based mixture on fatty acid profile of longissimus muscle of Black Slavonian pigs was investigated. The indication of beneficial effects of acorn was found when Black Slavonian pigs were fed acorn instead of concentrate feed during pre-slaughter fattening. Feeding acorn ad libitum for a period of three weeks prior slaughter significantly increased the content of alpha linolenic acid (C18:3 n-3) in the longissimus muscle in comparison to concentrate fed pigs (0.37 vs. 0.12, respectively; expressed as % of total fatty acid methyl esters, P ≤ 0.01). As a consequence, the n-6/n-3 ratio in the muscle of acorn finishing pigs was nearly threefold lower than in concentrate finishing pigs (24.1 vs. 69.3, P ≤ 0.01)

CHARACTERISTICS OF FEMUR AND HUMERUS IN TUROPOLJE PIG – AN AUTOCHTHONOUS CROATIAN BREED

Since 1996, Turopolje pig breed–autochthonous Croatian breed has been in the state of renewal and protection. The size of breeding population was 137 sows and 13 boars in 2006. The aim of this study was to present some bones characteristics of femur and humerus (weight, length, circumference, diameters of diaphysis and epiphysis proximalis and distalis) of the hogs of Turopolje pig breed (T) in comparison to selected pigs, Swedish Landrace breed (SL) and Hypor (Hy) pigs. The hogs T (n=19, live weight 100.3±4.9 kg) were produced by traditional Croatian technologies of low feed input in outdoor system. The selected hogs (SL and Hy, n=62 and 53, live weight 103.3±5.3 and 104±5.8 kg) were produced by conventional technologies of fattening in large farm. Characteristics of femur and humerus at hogs T were as follows: weights 271.4 and 256.6 g, length 202.0 and 194.9 mm, diameters of epiphysis proximalis 58.3 and 67.9 mm, and epiphysis distalis 49.0 and 42.0 mm, the minimum and maximum diameters of diaphysis 19.0 and 18.9 mm and 23.0 and 25.8 mm and circumference of diaphysis 78.1 and 77.0 mm. Significantly higher values for all traits of femur and humerus except for length and circumference of diaphysis were found in hogs SL and Hy. The length of both femur and humerus were significantly higher in T than in SL and Hy pigs. The results should be the contribution to explanation of carcass composition and distribution of tissues in the carcass of Turopolje pig breed

Numerical Analysis of Power System Electromechanical and Electromagnetic Transients based on the Finite Element Technique

This paper presents a novel technique for numerical analysis of electromagnetic transients and electromechanical oscillations in a power system. The proposed method is based on the finite element method (FEM). The finite element technique so far used for numerical analysis of continuum field problems here has been adopted to analyse electromagnetic and electromechanical transients in a power system. According to the finite element technique in the field problem, where the region of interest is divided into finite elements, in the proposed method power system is also divided into electric power system (finite) elements. Each finite element (generator, transformer, transmission line, load etc.) is characterized by a system of governing differential equations. Using generalized trapezoidal rule, also known as thetamethod for time integration, the system of differential equations of each electric power system (finite) element can be transformed to the system of algebraic equations for every time step. Once when a system of algebraic equations of each electric power system element is obtained, assembly procedure has to be done. The main contribution of the proposed approach is in an assembly procedure. With the proposed approach, in case of any disturbances in power system or in a part of power system, nodal voltage and branch currents will be obtained, as well as all other interesting variables. The proposed method will be tested on the example of the single-phase short circuit in the power system