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

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

Upfront docetaxel with androgen deprivation therapy in the elderly patient with metastatic hormone-naïve prostate cancer: Single institution experience

Upfront docetaxel with androgen deprivation therapy in the elderly patient with metastatic hormone-naïve prostate cancer: Single institution experienc

Zawartość miedzi, cynku, ołowiu i kadmu w roślinach uprawnych w rejonie składowiska odpadów po flotacji rud miedzi Żelazny Most

Regular monitoring of soil and plants in the surroundings of Żelazny Most tailings impoundment has been held since 1996. The results presented in this paper refer to potatoes and grains of cereals such as wheat, barley, triticale and oats, which are the most popular crops planted in that area in 2004-2006. The average content of heavy metals in 2006 in cereals and potatoes was approximately: Cu – 3.7 and 1.3 mg kg-1 of fresh mass; Zn – 20.6 and 3.5 mg kg-1; Pb – 0.14 and 0.04 mg kg-1; Cd – 0.055 and 0.011 mg kg-1, respectively. All those concentrations are well below threshold limit values accepted in Poland. No significant differences in Cu, Pb and Cd concentrations between the tested cereals were found. Zinc concentration in wheat and oat was significantly lower than in barley and triticale. The copper ore tailings impoundment in Żelazny Most, although very large, at present has no negative impact on the quality of crops and species of cereals and pasture plants cropped in its surroundings.W celu oceny ryzyka związanego z uprawą roślin konsumpcyjnych i paszowych na terenach znajdujących się pod wpływem składowiska odpadów po flotacji rud miedzi Żelazny Most, od 1996 r. prowadzony jest regularny monitoring jakości gleb i roślin uprawnych. W pracy przedstawiono zawartości Cu, Zn, Pb i Cd w ziarnie zbóż (pszenicy ozimej, jęczmienia ozimego, pszenżyta i owsa) i w bulwach ziemniaka, w latach 2004-2006. Stwierdzono następujące średnie zawartości metali (odpowiednio w ziarnie zbóż i w bulwach): Cu – 3,7 i 1,3 mg⋅kg-1 św. m., Zn – 20,6 i 3,5 mg⋅kg-1 św. m., Pb – 0,14 i 0,04 mg⋅kg-1 św. m. oraz Cd – 0,055 i 0,011 mg⋅kg-1 św. m. Nie stwierdzono istotnych różnic w zawartości Cu, Pb i Cd w ziarnie różnych gatunków zbóż. Zawartość Zn była istotnie niższa w pszenicy i owsie w porównaniu z pszenżytem i jęczmieniem. Nie stwierdzono przekroczenia dopuszczalnych zawartości pierwiastków śladowych, co świadczy o dużej skuteczności działań ograniczających negatywny wpływ składowiska na środowisko otaczających obszarów i warunki produkcji rolniczej

Venous spread of renal cell carcinoma: MDCT

BACKGROUND: The purpose of our study was to present multidetector computed tomography (MDCT) findings in venous spread of renal cell carcinoma (RCC), to determine the superior extent of tumor thrombus and to compare MDCT findings with surgical report. ----- METHODS: The prospective MDCT study was performed on 31 patients diagnosed with RCC with venous spread (19 males and 12 females; age range 39-80 years; mean age 62.6 years). CT scans were obtained by MDCT scanner, in triphasic scanning protocol. All postprocessing techniques were performed by two independent radiologists, and the findings were reported in their consensus. MDCT diagnosis was compared with surgical and pathohistological findings. ----- RESULTS: Tumor thrombus extension into renal vein only (T3b stage) was found in 13/31 (42%) patients. Involvement of infradiaphragmatic level of inferior vena cava (IVC) (T3c stage) was found in 14/31 (45%) patients and supradiaphragmatic level of IVC (T4b stage) in 4/31 (13%) patients. In 27/31 (87%) patients surgery was performed, while 4/31 (13%) could not undergo surgery. In comparison with surgical report, in 25/27 (93%) operated patients the upper extent of the tumor thrombus was correctly diagnosed by MDCT, and 2/27 (7%) patients were falsely diagnosed. ----- CONCLUSION: MDCT represents a fast, relatively inexpensive, and reliable diagnostic method for evaluating the venous spread of RCC as well as the level of its upper extent. Triphasic MDCT is often the only diagnostic method necessary for planning the surgical procedure. Surgery should be performed as soon as possible for MDCT findings to be valid