By means of the Ehrhart theory of inside-out polytopes we establish a general counting theory for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen, on a polygonal convex board. The number of ways to place q identical nonattacking pieces on a board of variable size n but fixed shape is (up to a normalization) given by a quasipolynomial function of n, ...

In response to the rapid spread of coronavirus epidemic, state authorities in Poland—as other countries—decided introduce various restrictions on rights and freedoms, including freedom practise religion. The purpose this study is analyse evaluate position taken by ministers Catholic Church Poland her faithful towards these during first wave pandemic. An analysis source material, documents publi...

This chapter examines De episcopis Salisburgensibus, a late 12th-century collection of texts concerning the bishops and history Salzburg that was seemingly compiled by monks belonging to Benedictine monastery Admont in Styria, Austria. It discusses structure, sources, manuscript tradition reception this little-known collection, which focuses primarily on ›glorious‹ early centuries archiepis...

Abstract Bishop Independence concerns determining the maximum number of bishops that can be placed on a board such no bishop attack any other bishop. This paper presents solution to independence problem, number, for all sizes boards surface square prism.

This article portrays how the Catholic Church in Indonesia 1980s faced some legal civil decrees that were contrary to beliefs, but they nonetheless responded a wise manner. Since Second Vatican Council, has had new outlook on relationship between and State. As stated canon 22 of 1983 Code Canon Law, is willing accept observe law, as long it “not divine law unless provides otherwise”. There thre...

The article describes the present situation in Church Czech Republic relation to topic of sexual abuse minors terms extension cases, education topic, church documents and measures adopted prayer initiatives. It also discusses specific factors that make it difficult accept reality existence by clerics Catholic territory Bishops Conference.

Parts I–III showed that the number of ways to place q nonattacking queens or similar chess pieces on an n × n chessboard is a quasipolynomial function of n whose coefficients are essentially polynomials in q and, for pieces with some of the queen’s moves, proved formulas for these counting quasipolynomials for small numbers of pieces and highorder coefficients of the general counting quasipolyn...

Social Network Analysis (SNA) has shed light on cultures where the influence of patronage, preferment, and reciprocal obligations are traditionally important. We argue here that episcopal appointments, culture, governance within Catholic Church ideal topics for SNA interrogation. This paper presents preliminary findings, using original network data Bishops’ Conference England Wales United State...