In the present paper we deal with a generalization of the classical Wilson's equation for mappings defined on a locally compact abelian group and taking their values in the field of complex numbers.

In a recent paper we introduced sine functions on commutative hypergroups. These functions are natural generalizations of those functions on groups which are products of additive and multiplicative homomorphisms. In this paper we describe sine functions on different types of hypergroups, including polynomial hypergroups, Sturm-Liouville hypergroups, etc. A non-commutative hypergroup is also considered.

The COVID-19 pandemic is related to changes in rates of suicide and suicide attempts in many countries, and some differences have been observed regarding the prevalence of suicidal behaviours in different age and gender groups. The aim of this study is to analyse the number of suicides and suicide attempts per 100,000 people between 2019 and 2021 in Poland. Using police and government data on suicide and suicide attempts in Poland, three age categories were investigated: 13–24 years old, 25–65 years old, and above 65 years old, and the analysis encompassed the whole population and the populations of men and women separately. Study results indicated an increase in suicide attempts in the two younger age categories (aged 7–24 years and 25–65 years) between 2021 and 2019–2020. There was an increase in suicide among women in all age categories during the study period, whilst no increase was observed in suicide in men in any age group. The differences in the prevalence of suicide and attempted suicide in Poland during the COVID-19 pandemic in different age and gender groups indicate the need for tailored suicide prevention activities.

In the present paper we deal with the following generalization of the sine-cosine equation ż f 1 px`y´tq`f 2 px´y`tqdµptq " gpxqhpyq for complex valued functions f 1 , f 2 , g and h defined on a commutative topological group G, where µ is a complex measure defined on G.