Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories

The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of mechanics. It will be shown that this relationship also stands in the presymplectic case. In a natural way, one can mimick the presymplectic constraint algorithm to obtain a constraint algorithm that can be applied to $k$-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations of field theories defined by a singular Lagrangian, as well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk formalism) for k-presymplectic field theory. Two examples of application of the algorithm are also analyzed.Comment: 22 p

Pre-multisymplectic constraint algorithm for field theories

We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of all the constraint submanifolds. The field equations are stated geometrically, either representing their solutions by integrable connections or, what is equivalent, by certain kinds of integrable m-vector fields. First, we consider the problem of finding connections or multivector fields solutions to the field equations in a general framework: a pre-multisymplectic fibre bundle (which will be identified with the first-order jet bundle and the multimomentum bundle when Lagrangian and Hamiltonian field theories are considered). Then, the problem is stated and solved in a linear context, and a pointwise application of the results leads to the algorithm for the general case. In a second step, the integrability of the solutions is also studied. Finally, the method is applied to Lagrangian and Hamiltonian field theories and, for the former, the problem of finding holonomic solutions is also analized.Comment: 30 pp. Presented in the International Workshop on Geometric Methods in Modern Physics (Firenze, April 2005

Lead Speciation in the Dusts Emitted from Non-Ferrous Metallurgy Processes

The paper presents results for the speciation analysis of lead in dusts derived from dedusting of technological gasses from metallurgical processes of non-ferrous metals with different elementary content, made in accordance with two equal sequential extractions. Analytical procedure A provided possibilities for determination of fraction of Pb2+, metallic lead and fraction containing mainly lead sulfides. The second procedure (procedure B) was sequential extraction in accordance with Tessier. The results obtained in accordance with procedure A indicate that, regardless of the dust origin, the dominant group of Pb compounds is composed of lead salts which are soluble under alkaline conditions or lead compounds that form plumbites in the reaction with NaOH

Formy żelaza i pierwiastków śladowych w silnie kwaśnych glebach bielicowych Gór Izerskich

Forms of Fe, Pb, Zn and Cu were determined by the means of sequential extraction in podzol profiles developed from granitogneiss in the Izerskie Mountains. Seven metal fractions were separated. Organic matter supply to soil profile was found to be a crucial factor determining the total concentration of lead in soil horizons. The main forms of copper and zinc were the ones occluded in Fe oxides and their total concentration increased with the depth within the soils profiles, which proved the considerable mobility of these elements. The results obtained from the study show that the total amount of trace elements in soil genetic horizons depends on the weathering process of primary and secondary soil minerals, organic matter input as well as the airborne contaminants, and their distribution in soil profile is modified by strongly acidic soil reaction

Total Contents and soluble forms of trace elements in serpentinite wastes of the Naslawice quarry

W trakcie mielenia skał serpentynitowych w celu uzyskania kruszywa o odpowiedniej granulacji powstają znaczne ilości drobnoziarnistych odpadów, zwałowanych w sąsiedztwie kamieniołomu i zakładu przeróbczego. Materiał zwałowany ma z reguły charakter utworu gliniasto lub piaszczysto-szkieletowego, o wysokim pH oraz bardzo niskiej zawartości przyswajalnego fosforu i potasu, a bardzo wysokiej magnezu. Całkowita zawartość Pb, Zn i Cu jest zbliżona do występującej w glebach wytworzonych z różnych skał macierzystych. Chrom występuje w ilości od 415 do 760 mg·kg⁻¹, natomiast nikiel nawet do 4100 mg·kg⁻¹, tj. w koncentracjach znacznie przewyższających normalnie występujące w glebach. Pojedyncza ekstrakcja z użyciem 0,1 mol(HCl) uwalniała 7,5-22 mg Cr·kg⁻¹ oraz 60-307 mg Ni·kg⁻¹, tj. odpowiednio do 5 i do 7,5% całkowitej zawartości tych pierwiastków. Ekstrakcja z użyciem 1 mol(NH₄NO₃)·dm⁻³ uwalniała do 2 mg Cr·kg⁻¹ i do 10,2 mg Ni·kg⁻¹ tj. odpowiednio do 0,34% i do 1,9% całkowitej zawartości Cr oraz Ni. Wydaje się, że znaczne ilości ekstrahowanych form rozpuszczalnych chromu oraz niklu, mimo niewielkiego ich udziału w całkowitej zawartości tych pierwiastków, mogą niekorzystnie (lub nawet toksycznie) oddziaływać na roślinność wprowadzaną na zwałowiska w trakcie ich rekultywacji.Large amounts of rock wastes produced during milling of the alkaline serpentinite rock are stored in piles formed closely to the quarry. In present study, the total content and soluble forms of selected heavy metals were analysed in the context of soil reclamation on waste piles in the Nasławice quarry. Strongly gravely, loamy or sandy material showed high pH value and soluble magnesium content, while very low contents of soluble potassium and phosphorus. Total contents of Pb, Zn and Cu were similar to the amount occurring in other rocks and are typical for „normal” soils in Poland. Cr and Ni contents were at least 100 fold higher than in unpolluted agricultural soils in Poland. Single extractions of soluble Ni and Cr release relatively high amounts of these metals, what may be harmful or toxic for plants

Straty prażenia jako podstawa wyliczania całkowitej zawartości węgla organicznego w glebach górskich

Due to the ease and low cost of implementation, a commonly used method of determining the humus content in soils is the loss-on-ignition (LOI) method. Several regression equations and transformation factors are reported for LOI conversion to soil organic matter (SOM) or total organic carbon (TOC) content. The vast majority of the conversion factors have been developed for surface horizons of lowland soils, while there are only few findings from the mountainous areas. 476 mineral and 79 organic (forest litter) samples from 31 soil profiles located in different altitude zones of the Karkonosze Mountains and under different vegetation were used for analysis. LOI was determined by the drying-weighing method and TOC by the dry combustion method with CO₂ absorption. The average LOI/TOC ratio was about 2, but varied in accordance to LOI value. At the LOI value above 8–10%, the LOI/TOC is maintained at a constant level of 2.0, but with a decreasing LOI it may significantly extend, up to 20 at LOI 8%, respectively) or when using separate regression equations for LOI of 8%. Because of huge TOC overestimation by LOI method at LOI values lower than 8–10%, the conversion LOI to TOC is not recommended, unless the direct measurement of TOC content is currently unavailable (e.g. in archival databases).