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It is shown how one can get upper bounds for ju ? vj when u and v are the (viscosity) solutions of ut ? (Dxu))xu = 0 and vt ? (Dxv))xv = 0; respectively, in (0;1) with Dirichlet boundary conditions. Similar results are obtained for some other parabolic equations as well, including certain equations in divergence form. 1. Introduction In this paper we study… (More)
To demonstrate the presence or absence of antibodies, results derived from a single serum dilution in an ELISA are sufficient. However, qualitative differences in antibodies are reflected by the shape of dose-response curves. A method based on approximating the absorbance value by a polynomial p(x) = a1x + a2x2, where 1/x is the dilution factor, was used to… (More)
Sufficient conditions are given for a generalized viscosity solution of an elliptic boundary value problem to satisfy the boundary values in the strong sense.
A total of 218 samples obtained during a follow-up study of 36 patients with systemic lupus erythematosus (SLE) were tested for the presence of cryoglobulins. Cold-insoluble precipitates were found in 81% for the patients (29 patients, 114 samples). The protein concentration of the cryoglobulins correlated significantly with the disease activity.… (More)
The equation () where D t and D x are fractional derivatives of order and is studied. It is shown that if f = f(t; x), h 1 = h 1 (x), and h 2 = h 2 (t) are HH older-continuous and f(0; 0) = 0, then there is a solution such that D t u and D x u are HH older-continuous as well. This is proved by rst considering an abstract fractional evolution equation and… (More)
Antibodies against single-stranded DNA (ssDNA) were followed by enzyme-linked immunosorbent assay in weekly serum samples of 39 patients with acute myeloid leukaemia (AML), 11 with acute lymphatic leukaemia (ALL) and 26 with other haematological malignancies. Their frequency and mean level during the entire follow-up were higher than in sera of healthy… (More)
The problem of the existence of a stationary distribution and the convergence towards it in a certain semistochastic model for the growth of a population is considered. It is assumed that the population grows according to a deterministic equation, but at certain times there are catastrophes, which lead to a decrease in the population level. The hazard… (More)
The existence of periodic solutions of the equation (see formula in text) is established. This equation arises in the study of the spread of a disease which does not induce permanent immunity.