in this paper we introduce and study an algebraic structure, namely grouplike. a grouplike is something between semigroup and group and its axioms are generalizations of the four group axioms. every grouplike is a semigroup containing the minimum ideal that is also a maximal subgroup (but the converse is not valid). the first idea of grouplikes comes from b-parts and $b$-addition of real number...

The persistence diagram is the fundamental object in topological data analysis. It inherits the stochastic variability of the data we use as input. As such we need to understand how to perform statistics on the space of persistence diagrams. This paper looks at the space of persistence diagrams under a variety of different metrics which are analogous to L metrics on the space of functions. Usin...

In this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical propositions and show that they are closed under the syllogistic criterion of inference which is the deletion of middle term. Therefore, it is implemented to let the formali...

We study Vassiliev invariants of links in a 3-manifold M by using chord diagrams labeled by elements of the fundamental group of M . We construct universal Vassiliev invariants of links in M , where M = P 2×[0, 1] is a cylinder over the real projective plane P 2, M = Σ× [0, 1] is a cylinder over a surface Σ with boundary, and M = S1 × S2. A finite covering p : N −→ M induces a map π1(p) ∗ betwe...

One of the open questions in the geometry of line arrangements is to what extent does the incidence lattice of an arrangement determine its fundamental group. Line arrangements of up to 6 lines were recently classified by K.M. Fan [Fa2], and it turns out that the incidence lattice of such arrangements determines the projective fundamental group. We use actions on the set of wiring diagrams, int...

Since the major revision 2 of the Unified Modeling Language (UML), activity diagrams have acquired many new features, e.g. hierarchy, data flow and signals. Thus, UML 2 activity diagrams are one of the most versatile formalisms, and can be applied in different domains. Activity diagrams are supported by a number of tools enabling for instance the execution of activity models. Based on the domai...

The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, ...

Spatial diagrams of politics could and should be iconic for political science in much the same way as supply-and-demand curves are in economics. Many fundamental problems of political science can be connected with them, and many different concepts—such as ideological constraint, cross-pressures, framing, agenda-setting, political competition, voting systems, and party systems, to name just a fe...

The unsteady increase in using pharmaceutical opioids is a phenomenon that has existed in human societies for a long time. Furthermore, the ever-growing trend of addiction to opioids affects communities in various economic, social, and cultural aspects. Since abusing pharmaceutical opioids is a complex dynamic problem, it is extremely difficult to recognize the factors influencing this abuse. T...