In the present paper we introduce a q-analogue of the Baskakov-Kantorovich operators and investigate their weighted statistical approximation properties. By using a weighted modulus of smoothness, we give some direct estimations for error in case 0 < q < 1.

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Depression remains an underdiagnosed comorbidity which significantly decreases the quality of life in amyotrophic lateral sclerosis (ALS) patients. We aimed to investigate the prevalence of depression in a cohort of ALS patients with more than one year of disease evolution. A total of 50 ALS patients were evaluated with the Beck Depression Inventory II (BDI-II) and cognition, using the Mini-Cog Standardized Instrument (MCSI). The clinical disability was evaluated using the ALS Functional Rating Scale (ALSFRS). The prevalence of depression was 42.8%. A lower BDI-II score was significantly correlated with a higher education level, the spouse as a caregiver, spiritual devotion, and employment status (p < 0.05). A multiple linear regression analysis between the BDI-II score as the dependent variable and various independent variables such as spirituality, caregiver status, educational level, and occupational status revealed that only the type of caregiver (spouse or parent/child) significantly affected the BDI-II total score (p = 0.006). The functional disability significantly correlated with loss of appetite and loss of libido (p < 0.001). A high education, spiritual devotion, high ALSFRS, and the presence of the spouse as the caregiver were associated with the absence of depression.

Assimilating the solid-liquid interface to a binary domain described by a set of coupled equations, one studies the solidification process. The numerical solutions of the thermal breather, the thermal breather pair and the thermal cluster type are associated to a virtual crystallization germ, a stable crystallization germ and a crystalline grain, respectively. The fractal characteristics of the solidification process are analyzed by means of fractal dimension dynamics.