Memes, Meme Viruses: Their Essence and Distribution in the Infosphere and Media Space

The article is dedicated to memes, their genesis, essence and typology. The purpose of the research was to analyze the current state of infosphere from memetics perspective. The meth­odology is based on the extrapolation principle of conceptual construct of evolutionary biol­ogy to understanding of the essence of culture and its development. The final conclusion of this research was an assumption that biological evolution continues in cultural. Cultures, which are evaluated as highly developed, spread their values in form of memes: any culture carries out semantic expansion and is aimed at their “advance”. Memes of life-affirming or rational values contribute to preservation and development of culture, and memes of life-rejecting or irrational values lead culture to the dead-end by causing intellectual stagnation in society. The latter could be interpreted as viruses. The environment for appearance and replication of meme-viruses is mass media and mediasphere in general. Based on the findings there are two main theses: there is a need to deal with meme-viruses, which requires improving skills/tech- niques of effective confrontation; it is necessary to develop intellectual immunity, providing a professional handicap to its carrier.

Introducing Roots and Extrema in Calculus

Use cubic polynomial functions before increasing the difficulty with irrational values.

Rationality of dynamical canonical height

We present a dynamical proof of the well-known fact that the Néron–Tate canonical height (and its local counterpart) takes rational values at points of an elliptic curve over a function field $k=\mathbb{C}(X)$, where $X$ is a curve. More generally, we investigate the mechanism by which the local canonical height for a map $f:\mathbb{P}^{1}\rightarrow \mathbb{P}^{1}$ defined over a function field $k$ can take irrational values (at points in a local completion of $k$), providing examples in all degrees $\deg f\geq 2$. Building on Kiwi’s classification of non-archimedean Julia sets for quadratic maps [Puiseux series dynamics of quadratic rational maps. Israel J. Math.201 (2014), 631–700], we give a complete answer in degree 2 characterizing the existence of points with irrational local canonical heights. As an application we prove that if the heights $\widehat{h}_{f}(a),\widehat{h}_{g}(b)$ are rational and positive, for maps $f$ and $g$ of multiplicatively independent degrees and points $a,b\in \mathbb{P}^{1}(\bar{k})$, then the orbits $\{f^{n}(a)\}_{n\geq 0}$ and $\{g^{m}(b)\}_{m\geq 0}$ intersect in at most finitely many points, complementing the results of Ghioca et al [Intersections of polynomials orbits, and a dynamical Mordell–Lang conjecture. Invent. Math.171 (2) (2008), 463–483].

On the Identical Simulation of the Entire Universe

A time ago, I published an article about deceleration of the universe. It was especially based on uncertainty, and it explains how does matter work. In this work, it was performed some analysis of the some specific subjects as an approach such as deceleration, uncertainty, possible particle formation, black hole, gravitation, energy, mass and light speed as the elements for identical simulation computations of the entire universe as the most sensitive as possible being related that article. There are some information about escaping from black holes, event horizon lengths, viscosity of free space, re-derivation of Planck constants and infrastructure of some basic laws of existence mathematically as matter is directly dependent of geometric rules. Also, some elements were given for the readers to solve some required constants as the most sensitive manner. As the constants are not enough in the name of engineering, also finally I found a working algorithm out which reduces process number of the power series to process number of the quadratic equations like calculating a root of an integer as an irrational number by solving equation; so also it can be used to calculate trigonometric values in the best manner for simulations of the entire universe besides physical constants as irrational values.

Trust, culture, and territorial development

Some researchers think that economic life is inseparable from culture, i.e., the "irrational" values associated with moral, public spirit, family, and religion, thus the latter manifests itself in neo-liberal economics that predominantly relies on interests and making rational choices only to a limited extent. Therefore, modern societies see preservation or creation of high-level social trust and social capital as their major task, since its lack is capable of hindering economic growth in a way similar to that of a deficit in physical capital. The above considerations provide a ground for explaining the success of certain settlements and the failure of others to succeed.

Strongly Maximal Matchings in Infinite Graphs

Given an assignment of weights $w$ to the edges of an infinite graph $G$, a matching $M$ in $G$ is called strongly $w$-maximal if for any matching $N$ there holds $\sum\{w(e) \mid e \in N \setminus M\} \le \sum\{w(e) \mid e \in M \setminus N\}$. We prove that if $w$ assumes only finitely many values all of which are rational then $G$ has a strongly $w$-maximal matching. This result is best possible in the sense that if we allow irrational values or infinitely many values then there need not be a strongly $w$-maximal matching.

A Quantum-Geometrical Description of Fracton Statistics

We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1 < h < 2, a fractal distribution function associated with a fractal von Newmann entropy. Fractons are charge-flux systems defined in two-dimensional multiply connected space and they carry rational or irrational values of spin. This formulation can be considered in the context of the fractional quantum Hall effect-FQHE and number theory.