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In this paper we prove a sharp global existence theorem in all dimensions for nonlinear wave equations with power-type nonlinearities. The proof is based on a weighted Strichartz estimate involving powers of the Lorentz distance.

Objectives: The study was aimed to evaluate the oxidative/nitrosative stress status in prostate cancer (CaP) and benign prostatic hyperplasia (BPH). Design and methods: 312 men from two different populations were included: 163 men from Macedonia (73 CaP patients, 67 BPH patients and 23 control subjects) and 149 men from Turkey (34 prostate cancer patients, 100 BPH patients and 15 control subjects). We measured erythrocyte malondialdehyde (MDA) levels, erythrocyte activities of superoxide dismutase (CuZn-SOD), glutathione peroxidase (GPX) and catalase (CAT); plasma nitrite/nitrate (NO 2 − /NO 3 − ), cGMP and 8-hydroxy-2′-deoxyguanosine (8-OHdG) levels.Results: A similar pattern of alteration in the oxidative/nitrosative stress-related parameters was found in both, Macedonian and Turkish studied samples: higher MDA concentrations with lower GPX and CuZn-SOD activities in CaP patients versus controls and BPH groups. The CAT activity was decreased in the CaP patients versus controls in the Turkish studied sample. Furthermore, CaP patients had increased plasma NO 2 − /NO 3 − and cGMP levels versus controls and BPH groups in both studied samples.Conclusions: This study has confirmed an imbalance in the oxidative stress/antioxidant status and revealed an altered nitrosative status in prostate cancer patients.

The Maxwell-Dirac system describes the interaction of an electron with its own electromagnetic field. We prove the existence of soliton-like solutions of Maxwell-Dirac in (3+l)-Minkowski space-time. The solutions obtained are regular, stationary in time, and localized in space. They are found by a variational method, as critical points of an energy functional. This functional is strongly indefinite and presents a lack of compactness. We also find soliton-like solutions for the Klein-Gordon-Dirac system, arising in the Yukawa model.

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Glutathione peroxidase 1 (GPX1) is a ubiquitously expressed selenium-dependent enzyme that protects cells against oxidative damage by reducing hydrogen peroxide and a wide range of organic peroxides. Some epidemiological studies have correlated low GPX activity or particular GPX1 polymorphisms with enhanced risk of cancer, although these correlations have not been consistently observed in all populations. Therefore, we conducted the present study to evaluate the possible association of GPX1 Pro198Leu polymorphism and erythrocyte GPX activity with the risk of developing prostate cancer and to clarify whether erythrocyte GPX activity levels were correlated with the GPX1 Pro198Leu genotype in the Macedonian population. The GPX1 Pro198Leu genotype was determined in 82 prostate cancer cases and 123 control individuals. We found an overall protective effect of the variant Leu allele of the GPX1 polymorphism on the prostate cancer risk. Heterozygous carriers of the variant Leu allele had a significantly lower risk of prostate cancer compared with homozygous wild-type individuals (OR, 0.38; 95% CI, 0.20-0.75; P = 0.004). Erythrocyte GPX activity was analyzed in 73 cases and 91 controls. The erythrocyte GPX activity in the cancer group was lower than in the healthy controls. Additionally, we compared the erythrocyte GPX activity in the control group of 90 subjects and found no significant differences by genotype. These findings suggest that individual susceptibility of prostate cancer may be modulated by GPX1 polymorphism and that the combination of genetic factors involved in oxidative response with environmental carcinogens may play an important role in prostate carcinogenesis.

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