The term isomorphism literally means equality or sameness (iso) of form (morphism). In mathematics an isomorphism between two systems requires a one-toone correspondence between their elements (that is, each element of one system corresponds to one and only one element of the other system, and conversely), which also preserves structures. Referring to isomorphism as one of the most important an...

Prior work has shown that extremely small code patterns, such as the conditional operator and implicit type conversion, can cause considerable misunderstanding in programmers. Until now, the real world impact of these patterns ś known as ‘atoms of confusion’ ś was only speculative. This work uses a corpus of 14 of the most popular and inluential open source C and C++ projects to measure the pre...

Let ∅≠Ŕ,Ś be subsets of a partial metric space (Ω,ϑ) and Ψ:Ŕ→Ś mapping. If Ŕ∩Ś=∅, it cannot have solution equation Ψς=ς for some ς∈Ŕ. Hence, is sensible to investigate if there point ἣ satisfying ϑ(ἣ,Ψἣ)=ϑ(Ŕ,Ś) which called best proximity point. In this paper, we first introduce concept Hausdorff cyclic mapping pair. Then, revise the definition 0-boundedly compact on spaces. After that, give re...

ŚŒredniowieczna architektura kolegiaty w Sandomierzu, drugiej pod względem godnośœci śœwiątyni diecezji krakowskiej, nie została jak dotąd satysfakcjonująco opracowana. Artykuł stanowi więc próbę nowego przedstawienia architektury kośœcioła genetycznym kontekśœcie czternastowiecznego budownictwa Europy ŚŒrodkowo-Wschodniej. Przeprowadzone ostatnio prace konserwatorskie pozwalają na zrewidowanie...

One of the most frequently used methods in the speech disfluence therapy is the one based on the acoustical echo. A patient, who is a subject to therapy, hears his own voice with some delay and, thanks to that, his speech fluency increases. As it turned out a therapeutic effect can also be achieved by feedback of the speech with other human senses, such as touch or sight. The article presents a...

Ways to reduce nitrogen oxide emissions One of MTU ś aims for its engines is to reduce the emission of soot particles and nitrogen oxides in order to achieve compliance with increasingly strict emissions regulations around the world. The main approach pursued by MTU is low-emission combustion, in other words an internal engine solution. However, this means taking into account a basic principle ...

This paper presents PROVERB a text planner for argumentative texts. PROVERB ś main feature is that it combines global hierarchical planning and unplanned organization of text with respect to local derivation relations in a complementary way. The former splits the task of presenting a particular proof into subtasks of presenting subproofs. The latter simulates how the next intermediate conclusio...