The Hopf Monoid of Hypergraphs and its Sub-Monoids: Basic Invariant and Reciprocity Theorem

In arXiv:1709.07504 Aguiar and Ardila give a Hopf monoid structure on hypergraphs as well as a general construction of polynomial invariants on Hopf monoids. Using these results, we define in this paper a new polynomial invariant on hypergraphs. We give a combinatorial interpretation of this invariant on negative integers which leads to a reciprocity theorem on hypergraphs. Finally, we use this invariant to recover well-known invariants on other combinatorial objects (graphs, simplicial complexes, building sets, etc) as well as the associated reciprocity theorems.

Mapping of Substrate Categories Changes in Exposure to Coral Reefs Using Alos Avnir-2 and Spot 7 Images in The South Area of Kotabaru District

The South of Pulau Laut is an area in the which is included in the Coral Triangle and Aquatic Conservation Areas. The purpose of this study was to map changes in the extent of coral reefs based on the class of substrate categories and objects on exposure to coral reefs in the southern waters of Sea Island within 6 years from 2011- 2017 using SPOT 7 satellite imagery in 2017 and AVNIR ALOS-2 in 2011. Using the method of Lyzenga Dept Index for basic invariant detection of waters. Based on the results of substrate-based classification using both satellite images overlaye, there has been a decline for the coral category as much as -19.21 ha, seagrass and algae as much as -3.57 ha. On the Contrary, the category of open substrate has Increased by 22.77 ha. Object-based classification results using the Object Based Image Analysis (OBIA) method have a reduction in area for the hard coral category (HC) of -1.66 ha, hard sand mixed with sand (HC S) of -15.99 ha, dead coral overgrown with algae and sand (DCA S) of -0.39 ha, algae and seagrass (FS) covering an area of ​​-1.65 ha, sand-mixed coral fragments (RS) of 4:45 ha. On the other hand, there was an increase of in the area.

MODELLING OF SOCIO-HUMANITARIAN EDUCATION PLATFORM FOR TRANS-PROFESSIONALISM DEVELOPMENT OF PROFESSIONALS INVOLVED IN MULTI-DISCIPLINARY PROJECTS

Introduction. Dynamic changes of the labour market and blurring of the boundaries of professional functions of a modern expert dictate the need for trans-professionalism development. Trans-professionalism development involves such meta qualities as social and professional mobility, communicativeness, developed emotional intelligence, innovation, tolerance for uncertainty, etc. All members of multi-disciplinary projects have to possess the listed above characteristics. Joint activity of several professional groups requires the participants of the project to possess the following skills and abilities: search for the consistent principles of work; “common language”; coherence of various abilities, caused by specifics of their occupation, to differentiate duties and to work harmoniously in neutral spheres; mastering of new roles in the cooperation process.The aimof the publication is to present a product of structural-functional modelling which is the socio-humanitarian educational platform of trans-professionalism development of professionals involved in multi-disciplinary projects (hereinafter the “Platform”).Methodology and research methods. The authors used a comparative analysis and generalization of the models of the multi-professional relations offered by foreign and Russian authors. The methodological framework of the research was based on the following approaches to the design of the Platform: multidimensional, trans-disciplinary, network, design, nonlinear synergetic, and transpective competency-based.Results and scientific novelty.The structural and functional model of the Platform has been developed and described. The Platform model has a block-modular organization. It consists of three blocks: basic (invariant), poly professional and functional. The technological basis of the Platform is social and humanitarian educational technologies.The authors highlighted the principles of the Platform. In the present study, the authors substantiated the importance of the development of the structural and functional model of the Platform in terms of additional education. The presented model of the Platform accumulates the results of theoretical and applied research in the field of vocational education. For the first time, different models of multi-professional relations (from inter-professional to trans-professional) have been used in a single course of additional education. The development of adjacent areas of activity is a stage for the development of distant, non-contiguous areas. Interactive development of these spheres is facilitated by immersion of listeners in the poly professional communicative environments. The result of the implementation of the Platform is a trans-professional project of the full life cycle.Practical significance. The results of the study can be partially or fully applied in the system of additional education.

Presentations and Low-dimensional Homology

This chapter presents explicit computations of the first and second homology groups of the mapping class group. It begins with a simple proof, due to Harer, of the theorem of Mumford, Birman, and Powell; the proof includes the lantern relation, a relation in Mod(S) between seven Dehn twists. It then applies a method from geometric group theory to prove the theorem that Mod(Sɡ) is finitely presentable. It also provides explicit presentations of Mod(Sɡ), including the Wajnryb presentation and the Gervais presentation, and gives a detailed construction of the Euler class, the most basic invariant for surface bundles, as a 2-cocycle for the mapping class group of a punctured surface. The chapter concludes by explaining the Meyer signature cocycle and the important connection of this circle of ideas with the theory of Sɡ-bundles.

FUNCTIONAL FEATURES OF PERSONAL-PRONOMINAL WORDS OF SPANISH DISCOURSE IN THE COGNITIVE ASPECT ON THE EXAMPLE OF CONSTRUCTION YO CREO

The article deals with the semantic-grammatical construction (Yo) creo, I think, which is used to form the context of evidence and reliability under a certain assumption. The use of the subject, personal-pronominal word of the first person уo, is associated with the contexts of argumentation and the desire to express one's own opinion, and that is why this option focuses on the presence of the speaker, and also concentrates discourse on the personal sphere. On the other hand, the omission of the subject in such a context is more often encountered in cases of the lack of confidence, formulating a hypothesis with assumptions which are usually found in the field of the generalized. But precisely this sociolinguistic variability can also depend on certain cognitive factors. From the cognitive point of view, the verb form сreo has a basic invariant content, although, depending on the context, it can acquire a variety of shades and interpretations. In all studied cases of use the investigated form is characterized by a certain conceptual content: the speaker expresses a part of his knowledge of reality or what is his assumption of reality beyond his knowledge. And vice versa, should be emphasized that there are significant differences at the semantic level between the constructions creo / yo creo. The use or omission of the subject in the investigated statements is not casual, because it correlates with the semantics of the discoursecognitive nature and can be an important stylistic resource of communication. These semantics can be positioned in an abstract form between the subjectivity and the objectivity of the linguistic statement.

The Many Facets of Chaos

There are many ways that a person can encounter chaos, such as through a time series from a lab experiment, a basin of attraction with fractal boundaries, a map with a crossing of stable and unstable manifolds, a fractal attractor, or in a system for which uncertainty doubles after some time period. These encounters appear so diverse, but the chaos is the same in all of the underlying systems; it is just observed in different ways. We describe these different types of chaos. We then give two conjectures about the types of dynamical behavior that is observable if one randomly picks out a dynamical system without searching for a specific property. In particular, we conjecture that from picking a system at random, one observes (1) only three types of basic invariant sets: periodic orbits, quasiperiodic orbits, and chaotic sets; and (2) that all the definitions of chaos are in agreement.

Invariant subspaces and Jordan form

This chapter starts by introducing the notion of root subspaces for quaternion matrices. These are basic invariant subspaces, and the chapter proves in particular that they enjoy the Lipschitz property with respect to perturbations of the matrix. Another important class of invariant subspaces are the one-dimensional ones, i.e., generated by eigenvectors. Existence of quaternion eigenvalues and eigenvectors is proved, which leads to the Schur triangularization theorem (in the context of quaternion matrices) and its many consequences familiar for real and complex matrices. Jordan canonical form for quaternion matrices is stated and proved (both the existence and uniqueness parts) in full detail. The chapter also discusses various concepts of determinants for square-size quaternion matrices. Several applications of the Jordan form are given, including functions of matrices and boundedness properties of systems of differential and difference equations with constant quaternion coefficients.

A Computation of the Basic Invariant J+ for Closed 2-Vertex Curves

In this paper, we will give an explicit and simple formula for J+-invariant of closed 2-vertex curves. As an application, we give an affirmative answer to a problem conjectured by Arnold [A2], related to Legendrian knots in R2 × S1.

Optical propagation in a nonhomogeneous medium and squeezed states

In this paper, using the concept of the basic invariant, we study optical propagation in a nonhomogeneous medium and obtain the squeezed states for the system. These should be of importance for the discussion of the propagation of waves with finite width.