Przeprowadzono dowód ortogonalności funkcji Macdonalda z urojonym indeksem. Zastosowana metoda jest znacznie prostsza od innych prezentowanych do tej pory w literaturze.

Psoriasis is a multifactorial disease in which genetic, environmental and epigenetic factors regulating gene expression play a key role. In the “genomic era”, genome-wide association studies together with target genotyping platforms performed in different ethnic populations have found more than 50 genetic susceptible markers associated with the risk of psoriasis which have been identified so far. Up till now, the strongest association...

Orthogonality relations for the associated Legendre functions of imaginary order are derived. They are expressed in terms of the Dirac delta function. The method is based on some known properties of the associated Legendre functions and the Dirac delta distribution. A special case of one of the relations has appeared in some recent applications.

Przeprowadzono dowód ortogonalności funkcji Whittakera drugiego rodzaju rzędu urojonego. Użyto metody analogicznej do tej, którą zaprezentowano we wcześniejszej pracy tych samych autorów [J. Math. Anal. Appl. 365 (2010) 195-197], poświęconej funkcjom Macdonalda rzędu urojonego.

The classification of EEG signals provides an important element of brain-computer interface (BCI) applications, underlying an efficient interaction between a human and a computer application. The BCI applications can be especially useful for people with disabilities. Numerous experiments aim at recognition of motion intent of left or right hand being useful for locked-in-state or paralyzed subjects in controlling computer applications....