Decidability in Orthomodular Lattices

We discuss the possibility of automatic simplification of formulas in orthomodular lattices. We describe the principles of a program which decides the validity of equalities and inequalities, as well as implications between them and other important relations significant in quantum mechanics. PACS: 02.10.-v, 02.10.Ab, 02.10.De, 03.65.Fd. AMS Subject classification: 06C15, 03G12, 06B10, 06B25, 81P10.     

Associativity of operations on orthomodular lattices

It is known that orthomodular lattices admit 96 binary operations, out of which 16 are commutative. We clarify which of them are associative.     

About two characteristic points concerning two circles and their use in study of bicentric polygons

The article primarily deals with the connection between Fuss’ relation for bicentric n-gons where conics are two nested circles and Fuss’ relation for bicentric n-gons where conics are two separated circles. It is proved that one of them is quite determined by other. Also, the article deals with solutions of some old and difficult problems where characteristic points of two corresponding circles are defined and often used. Several interesting properties are established and some difficult problems are solved.     

One-dimensional stock cutting: optimization of usable leftovers in consecutive orders

Central European Journal of Operations Research - This paper deals with usable leftovers (UL) in one-dimensional stock cutting in consecutive orders. UL are leftovers longer than a certain...     

Different approaches to obtain functionalized alumina as additive in polymer electrolyte membranes

Journal of Solid State Electrochemistry - A series of sulfated aluminum oxides (S-Al2O3), investigated as an electrolyte additive in Nafion membranes, was synthesized via three different methods:...     

Concentrated monotone measures with non-unique tangential behavior in ?3

We show that for every ɛ > 0 there is a set A ⊂ ℝ³ such that H ¹ ⌞A is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and H ¹ ⌞A has the 1-dimensional density between 1 and 2+ɛ everywhere in the support.