In this paper, we define the $M_\alpha $-integral of real-valued functions defined on an interval $[a,b]$ and investigate important properties of the $M_{\alpha }$-integral. In particular, we show that a function $f\colon [a,b]\rightarrow R$ is $M_{\alpha }$-integrable on $[a,b]$ if and only if there exists an $ACG_{\alpha }$ function $F$ such that $F'=f$ almost everywhere on $[a,b]$. It can be seen easily that every McShane integrable function on $[a,b]$ is $M_{\alpha }$-integrable and every $M_{\alpha }$-integrable function on $[a,b]$ is Henstock integrable. In addition, we show that the $M_{\alpha }$-integral is equivalent to the $C$-integral.
The objective of this paper is to give two descriptions of the $\scr A r$-free products of archimedean $\ell $-groups and to establish some properties for the $\scr A r$-free products. Specifically, it is proved that $\scr A r$-free products satisfy the weak subalgebra property.
The aim of this paper is to propose two arguments. First, since an insufficient historical perspective tends to be a characteristic feature of many studies about contemporary Islamic charitable organizations, the paper presents a view on some of the key aspects that have been linked to the granting of charity throughout history. In so doing, it reveals not only how the charitable institutions were supposed to work in theory, but how they actually functioned in reality. Furthermore, the paper explores the objectives of many of the charitable organizations from the inception. Already, by early medieval times, Islamic charitable work had shifted its focus from the individual to the welfare of the Muslim community as a whole and the category of “need” and “poverty” grew to encompass wider segments of society. Second, in modern times negative aspects have come to be associated, in particular, with those Islamic charitable organizations whose activities relate to the notions of jihad and da‘wa, or which strive to promote Islam. On the ideological level this is mainly represented by means of two lines of fundamentalist Sunni Islam: the Muslim Brotherhood and Salafism.
In this paper, the effects on the signless Laplacian spectral radius of a graph are studied when some operations, such as edge moving, edge subdividing, are applied to the graph. Moreover, the largest signless Laplacian spectral radius among the all unicyclic graphs with $n$ vertices and $k$ pendant vertices is identified. Furthermore, we determine the graphs with the largest Laplacian spectral radii among the all unicyclic graphs and bicyclic graphs with $n$ vertices and $k$ pendant vertices, respectively.
This article was created to the occasion of Czech presidential election in 2018. In light of the 100th anniversary of Austria and Czechoslovakia the article offers a comparison of Austrian and Czech presidential powers. With regard to common history of both countries it reflects the development from monarchy to a republican system in Austria. The role of president as a representative of statehood is treated with regard to major state functions: legislation, judiciary and administration., Herbert Schambeck., and Obsahuje bibliografické odkazy