We study shift spaces over a finite alphabet that can be approximated by mixing shifts of finite type in the sense of (pseudo)metrics connected to Ornstein’s $\bar {d}$ metric ($\bar {d}$-approachable shift spaces). The class of $\bar {d}$-approachable shifts can be considered as a topological analog of measure-theoretical Bernoulli systems. The notion of $\bar {d}$-approachability, together with a closely connected notion of $\bar {d}$-shadowing, was introduced by Konieczny, Kupsa, and Kwietniak [Ergod. Th. & Dynam. Sys. 43(3) (2023), 943–970]. These notions were developed with the aim of significantly generalizing specification properties. Indeed, many popular variants of the specification property, including the classic one and the almost/weak specification property, ensure $\bar {d}$-approachability and $\bar {d}$-shadowing. Here, we study further properties and connections between $\bar {d}$-shadowing and $\bar {d}$-approachability. We prove that $\bar {d}$-shadowing implies $\bar {d}$-stability (a notion recently introduced by Tim Austin). We show that for surjective shift spaces with the $\bar {d}$-shadowing property the Hausdorff pseudodistance ${\bar d}^{\mathrm {H}}$ between shift spaces induced by $\bar {d}$ is the same as the Hausdorff distance between their simplices of invariant measures with respect to the Hausdorff distance induced by Ornstein’s metric $\bar {d}$ between measures. We prove that without $\bar {d}$-shadowing this need not to be true (it is known that the former distance always bounds the latter). We provide examples illustrating these results, including minimal examples and proximal examples of shift spaces with the $\bar {d}$-shadowing property. The existence of such shift spaces was announced in the earlier paper mentioned above. It shows that $\bar {d}$-shadowing indeed generalizes the specification property.

Because of the interfacial interactions between mineral soil particles and soil organic matter (SOM), SOM occurs in various forms in the soil, and the mineral-associated and particulate forms are fundamental. Many recent studies have concentrated on the effects of SOM content and type on the geotechnical behavior of soil. However, the influence of SOM occurrence forms is not well understood, nor is there a scientific classification standard for SOM in geotechnical engineering. The main objectives of this study were to explore the effects of SOM occurrence forms on a few physical properties of clays to develop an engineering classification standard of SOM. First, this paper reviews the interfacial interaction mechanism, factors that influence the relation between mineral soil particles and SOM, and the classification method of SOM in soil science. Three predominant clays (montmorillonite, illite, and kaolinite) were then used as the matrix, and three groups of artificial soil samples with different SOM contents (wu ranging from 0 to 50% by weight) were prepared by adding peat. A chemical extraction method was used to determine the amount of different forms of SOM. Moreover, the Atterberg limits wL (wp) and thermal conductivity λ of artificial soil samples were tested. Based on the experimental results, the relationship between the form of SOM and these physical parameters was established. The experimental results show that the wL (wp) vs wu, and λ vs wu fitted curves were not monotonic but piecewise linear and could be divided into two straight lines with different slopes; wu corresponded to the inflection point of wL (wp) vs wu, and λ vs wu curves were closer to the threshold value wu,2. Finally, a simple engineering classification method of SOM is proposed.

Under certain conditions, we construct a countable Markov partition for pointwise hyperbolic diffeomorphism $f:M\rightarrow M$ on an open invariant subset $O\subset M$, which allows the Lyapunov exponents to be zero. From this partition, we define a symbolic extension that is finite-to-one and onto a subset of O that carries the same finite f-invariant measures as O. Our method relies upon shadowing theory of a recurrent-pointwise-pseudo-orbit that we introduce. As a canonical application, we estimate the number of closed orbits for f.

Some theories of goodness are descriptively rich: they have much to say about what makes things good. Neo-Aristotelian accounts, for instance, detail the various features that make a human being, a dog, a bee good relative to facts about those forms of life. Famously, such theories of relative goodness tend to be comparatively poor: they have little or nothing to say about what makes one kind of being better than another kind. Other theories of goodness – those that take there to be absolute goodness – are comparatively rich: they offer grounds for judging some types of things better than others because they have more absolute goodness. Moorean accounts, for example, can tell us that humans and human experiences are superior to bees and blades of grass. But such theories tend to be descriptively poor: they struggle to tell us in virtue of what this is so. In this article we motivate and flesh out a view that splits the difference between accounts of goodness as relative and accounts of goodness as absolute. Such a view holds promise only if the mechanics of this kind of metaphysics of goodness can be worked out. Here we present a view on which the paradigm for absolute goodness is God and the paradigm for each kind of relative goodness is a divine idea.

This article critically analyses the substantial inadequacies of the current Customer Due Diligence (CDD) framework in safeguarding marginalised communities from financial exclusion in Malaysia. It highlights that for vulnerable groups such as rural inhabitants, undocumented migrants, and refugees, the CDD, as currently framed and applied, only impedes access to formal financial services. While Malaysia's implementation of a risk-based approach in CDD policies complies with global standards of CDD, this article argues that these standards fall far short of effectively helping marginalised communities. In addition, there is evidence that banks are exhibiting over-cautious compliance behaviour, which resulted in banks hesitating to implement some of the CDD flexibilities introduced by the regulators. In order to address these problems and overcome the barriers, proposals for the development of new CDD strategies are analysed. These include reducing documentation requirements, widening the list of acceptable documents, and introducing entry-level accounts. The aim is to address banking access issues for marginalised communities without compromising the regulatory objectives of CDD. The article recommends that CDD regulations can better assist financial inclusion if they are tailored to the specific needs of the excluded communities by using a risk-based approach.

We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers p and q in base $pq$ to higher dimensional multiplication tessellation systems. We develop the theory of these systems and link different multiplication tessellation systems with each other via macrotile operations that glue cubes in one tessellation system into larger cubes of another tessellation system. The macrotile operations yield topological conjugacies and factor maps between cellular automata performing multiplication by positive numbers in various bases.

Given a two-sided shift space on a finite alphabet and a continuous potential function, we give conditions under which an equilibrium measure can be described using a construction analogous to Hausdorff measure that goes back to the work of Bowen. This construction was previously applied to smooth uniformly and partially hyperbolic systems by the first author, Pesin, and Zelerowicz. Our results here apply to all subshifts of finite type and Hölder continuous potentials, but extend beyond this setting, and we also apply them to shift spaces with synchronizing words.

The recent rise of active shootings calls for adequate preparation. Currently, the “Run, Hide, Fight” concept is widely accepted and adopted by many hospitals nationwide. Unfortunately, the appropriateness of this concept in hospitals is uncertain due to lack of data. To understand the “Run, Hide, Fight” concept application in hospitals, a review of currently available data is needed. A systematic review was done focusing on the “Run, Hide, Fight” concept using multiple databases from the past 12 years. The PRISMA flow diagram was used to systematically select the articles based on specific inclusion and exclusion criteria. The measurements were subjective evaluations and survival probabilities post-concept. One agent-based modeling study suggested a high survival probability in non-medical settings. However, there is a paucity of data supporting its effectiveness and applicability in hospitals. Literature suggests a better suitable concept, the “Secure, Preserve, Fight” concept, as a response protocol to active shootings in hospitals. The effectiveness of the “Run, Hide, Fight” concept in hospitals is questionable. The “Secure, Preserve, Fight” concept was found to be designed more specifically for hospitals and closes the gaps on the flaws in the “Run, Hide, Fight” concept.