A few remarks on Pimsner–Popa bases and regular subfactors of depth 2

We prove that a finite index regular inclusion of $II_1$ -factors with commutative first relative commutant is always a crossed product subfactor with respect to a minimal action of a biconnected weak Kac algebra. Prior to this, we prove that every finite index inclusion of $II_1$ -factors which is of depth 2 and has simple first relative commutant (respectively, is regular and has commutative or simple first relative commutant) admits a two-sided Pimsner–Popa basis (respectively, a unitary orthonormal basis).

Splittings of right-angled Artin groups

We show that if a right-angled Artin group [Formula: see text] has a non-trivial, minimal action on a tree [Formula: see text] with more than two ends, then [Formula: see text] contains a separating subgraph [Formula: see text] such that [Formula: see text] stabilizes an edge in [Formula: see text].

I can tell you know a lot, although I'm not sure what: Modeling broad epistemic inference from minimal action

Inferences about other people's knowledge and beliefs are central to social interaction. In many situations, however, it's not possible to be sure what other people know because their behavior is consistent with a range of potential epistemic states. Nonetheless, this behavior can give us coarse intuitions about how much someone might know, even if we cannot pinpoint the exact nature of this knowledge. We present a computational model of this kind of broad epistemic-state inference, centered on the expectation that agents maximize epistemic utilities. We evaluate our model in a graded inference task where people had to infer how much an agent knew based on the actions they chose. Critically, the agent's behavior was always under-determined, but nonetheless contained information about how much knowledge they possessed. Our model captures nuanced patterns in participant judgments, revealing a quantitative capacity to infer amorphous knowledge from minimal behavioral evidence.

Entropy-Time Relationship in an Isochoric Adiabatic System

The fundamental equation that connects the magnitudes entropy and time has been found out by static thermodynamics for the first time: dS/S = dVI/V0 = kdτ, VI internal volume. Constant k also equals dT/Tdτ and is an individual characteristic for each isochoric adiabatic system in evolution. The constancy of k does not hold for a nonisochoric adiabatic system. In such manner time is introduced in the frame of thermodynamic variables as a genuine magnitude. The theoretically deduced entropy-time differential equation is empirically upheld by Newton cooling law. It was found in connection with an a priory, uncritical notion of thermodynamic equilibrium that irreversible heat capacity (CIR = TΔS/ΔT) drawing near to thermodynamic equilibrium is an indicator for the equilibrium. CIR is alike to statistical Boltzmann H in the approach to thermodynamic equilibrium, and the undisclosed connection of H with temperature is presented. The integrated entropy-time equation was modified by rotation of the coordinate axes to fulfill the necessary thermodynamic condition that pertinent irreversible heat (QIR = TΔS) is smaller than reversible heat (dQ = TdS), which is not embodied in the primitive S-τ differential equation. This thermodynamically indispensable rotation gives rise to an otherwise naive maximal entropy and an entropy-time maximum point. The transformation conveys a contraction of both entropy and time and is in agreement with the principle of minimal action.

Classical Mechanics According to Newton and Hamilton

This chapter introduces classical mechanics, starting with the familiar definitions of position, momentum, velocity, acceleration force, kinetic, potential, and total energy. It is shown how the Newton equation of motion is solved for the one-dimensional harmonic oscillator, which is a point mass oscillating around the position x = 0 driven by a force that is proportional to x (Hooke’s law). Next, the minimal action principle, the Lagrange equation of motion, and the classical Hamilton function (Hamiltonian) and conjugated variables are introduced. The chapter also discusses angular momentum and rotational motion.

KNOWLEDGE INFLATION IN THE CONDITIONS OF INFORMATIZATION AND SOCIO TECHNOLOGICAL CHANGES

A model of the dynamics of socio-technological evolution is developed, an analysis of the be- havior of the system at specific points in the phase space is carried out. The model describes the interaction of technological progress and the volume of knowledge of an individual. A dependence is established that demonstrates the presence of two conditional zones in the phase space, which describes the interaction for different initial conditions. The model also illustrates that under certain conditions (for example, with low skill) irreversible regression takes place. For the first time, the content of the scientific category “knowledge inflation” has been determined, which means a constant increase in the general level of information / knowledge about new technologies and means of production. Thus, the amount of knowledge obtained earli- er after some time loses its value due to a decrease in relevance / relevance to the changed social and tech- nological environment. This approach to understanding the concept of “inflation of knowledge” formalizes the process of loss of relevance, the aging of knowledge, and the like. It is noted that inflation of knowledge is a natural process that reflects the disequilibrium position of an individual in relation to technological evo- lution and, in turn, is an incentive for individual development. A mathematical model of knowledge inflation is proposed, which qualitatively describes the dependence of knowledge inflation on time. In particular, it has been shown that inflation of knowledge is exponential, which in turn actualizes the issue of searching for effective mechanisms for “modernizing” skills and knowledge. The results of the analysis of the problem of the adequacy of knowledge indicate that updating is always directed in accordance with the law of minimal action (minimization time, resources, etc.). The issues of the evolution of forms of actualization are dis- closed. It is noted that the evolution of actualization is a derivative of socio-technological development, that is, the forms of knowledge acquisition each time change as a result of socio-technological transformations.

Rationale for the parameters of steeply inclined ramps of kimberlite pits deep horizons exposing

Research aim is to substantiate optimal road grade when operating 4WD dump trucks and to develop analytical method of calculating the volume of additional spacing of non-mining slopes of an opencast from motor transport lanes placement when exposing deep kimberlite pits with spiral routes. Research relevance. Transition to steeply inclined ramps and 4WD dump trucks is a basic trend in improving the efficiency of deep kimberlite pits mining. In this regard, the issues of substantiating road grades and developing the method of calculating the volume of additional spacing of non-mining slopes of an opencast from motor transport lanes placement are becoming increasingly relevant. Research methodology. When substantiating road grade for 4WD dump trucks the physical principle of minimal action was used as well as dump trucks tractive and dynamic, braking and fuel conditions together with some experimental data. A new notion of “specific action” has been introduced. Optimal grade by the criterion of specific action complies with minimum energy for mined rock lifting under maximum hauling capacity. The elaborated analytical method of calculating the volume of additional spacing of non-mining slopes of an opencast is characterized by the integrated record of basic process parameters of uncovering. Graphical method of finding the angle of the non-mining slope has been proposed being a controlled parameter at uncovering with steeply pitching ramps. Results. It has been determined that optimal grade value by physical criterion of specific action are determined by the dependences between transmission efficiency, road speed and specific fuel consumption by 4WD dump trucks and the total traction resistance in slopes. For CAT-745С dump trucks optimal values slopes for macadamized roads within the range of 0.18–0.24. The patterns of basic mine engineering factors influence on the volume of additional spacing of slopes from motor transport lanes placement. Major effect on the volume of flattening is brought about by the depth of the pit, spiral ramps grade and ore body thickness. So, the introduction of steeply inclined uncovering is primarily recommended in kimberlite open pits when mining thin ore bodies. Scope of results. The obtained results may be applied in deep kimberlite open pits design and operation when introducing 4WD dump trucks. The results may also be applied in ore open pits when uncovering deep horizons by spiral ramps.

Big mapping class groups and rigidity of the simple circle

Let $\unicode[STIX]{x1D6E4}$ denote the mapping class group of the plane minus a Cantor set. We show that every action of $\unicode[STIX]{x1D6E4}$ on the circle is either trivial or semiconjugate to a unique minimal action on the so-called simple circle.

Discourses of climate delay

Non-technical summary ‘Discourses of climate delay’ pervade current debates on climate action. These discourses accept the existence of climate change, but justify inaction or inadequate efforts. In contemporary discussions on what actions should be taken, by whom and how fast, proponents of climate delay would argue for minimal action or action taken by others. They focus attention on the negative social effects of climate policies and raise doubt that mitigation is possible. Here, we outline the common features of climate delay discourses and provide a guide to identifying them.

Teoria kapitału ludzkiego a minimalne wynagrodzenia w wybranych krajach Trójmorza

The aim of the paper is to present a method for estimating the percentage compliance of statutory minimum wages in selected Trisea countries with minimum wages established on the basis of human capital theory. The first part of the study deals with the essence of capital, human capital and fair wage. Thermodynamic theory enables a deeper understanding of the nature of capital and perception the complementarity of capital and labor, from which follows a set of basic economic concepts. From this basis are developed the Human Capital Measurement Model and the Fair Pay Model. The models used to measure the value of human capital presented in the article help determine the minimal fair wages in Poland and selected Trisea countries. These models are based on fundamental laws of reality: the first and second laws of thermodynamics and the principle of minimal action. Especially the second law of thermodynamics in its basic formulation is indispensable in economic considerations, because the human body has the features of a heat engine and experiences spontaneous, random dispersions of energy. Fair wage means that the earnings of two working parents allow the two descendants to reach the level of human capital they achieve, i.e. this wage guarantees the preservation of human capital. The article ends with a comparison of the percentage compliance of statutory minimum wages in selected Trisea countries with minimum wages set on the basis of human capital theory. This percentage shows the similarities and differences between the economies of the countries surveyed in terms of costs of living and indicates the possibility of creating their own economic union.