Exact solutions and critical behaviour for a linear growth-diffusion equation on a time-dependent domain

A linear growth-diffusion equation is studied in a time-dependent interval whose location and length both vary. We prove conditions on the boundary motion for which the solution can be found in exact form and derive the explicit expression in each case. Next, we prove the precise behaviour near the boundary in a ‘critical’ case: when the endpoints of the interval move in such a way that near the boundary there is neither exponential growth nor decay, but the solution behaves like a power law with respect to time. The proof uses a subsolution based on the Airy function with argument depending on both space and time. Interesting links are observed between this result and Bramson's logarithmic term in the nonlinear FKPP equation on the real line. Each of the main theorems is extended to higher dimensions, with a corresponding result on a ball with a time-dependent radius.

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.

Analysis of COVID-19 data using neutrosophic Kruskal Wallis H test

Background Kruskal-Wallis H test from the bank of classical statistics tests is a well-known nonparametric alternative to a one-way analysis of variance. The test is extensively used in decision-making problems where one has to compare the equality of several means when the observations are in exact form. The test is helpless when the data is in an interval form and has some indeterminacy. Methods The interval-valued data often contain uncertainty and imprecision and often arise from situations that contain vagueness and ambiguity. In this research, a modified form of the Kruskal-Wallis H test has been proposed for indeterminacy data. A comprehensive theoretical methodology with an application and implementation of the test has been proposed in the research. Results The proposed test is applied on a Covid-19 data set for application purposes. The study results suggested that the proposed modified Kruskal-Wallis H test is more suitable in interval-valued data situations. The application of this new neutrosophic Kruskal-Wallis test on the Covid-19 data set showed that the proposed test provides more relevant and adequate results. The data representing the daily ICU occupancy by the Covid-19 patients were recorded for both determinate and indeterminate parts. The existing nonparametric Kruskal-Wallis H test under Classical Statistics would have given misleading results. The proposed test showed that at a 1% level of significance, there is a statistically significant difference among the average daily ICU occupancy by corona-positive patients of different age groups. Conclusions The findings of the results suggested that our proposed modified form of the Kruskal-Wallis is appropriate in place of the classical form of the test in the presence of the neutrosophic environment.

What is a Conspiracy Theory?

In much of the current academic and public discussion, conspiracy theories are portrayed as a negative phenomenon, linked to misinformation, mistrust in experts and institutions, and political propaganda. Rather surprisingly, however, philosophers working on this topic have been reluctant to incorporate a negatively evaluative aspect when either analyzing or engineering the concept conspiracy theory. In this paper, we present empirical data on the nature of the concept conspiracy theory from five studies designed to test the existence, prevalence and exact form of an evaluative dimension to the ordinary concept conspiracy theory. These results reveal that, while there is a descriptive concept of conspiracy theory, the predominant use of conspiracy theory is deeply evaluative, encoding information about epistemic deficiency and often also derogatory and disparaging information. On the basis of these results, we present a new strategy for engineering conspiracy theory to promote theoretical investigations and institutional discussions of this phenomenon. We argue for engineering conspiracy theory to encode an epistemic evaluation, and to introduce a descriptive expression—such as ‘conspiratorial explanation’—to refer to the purely descriptive concept conspiracy theory.

Self-similar cosmological solutions in f(R,T) gravity theory

We study the [Formula: see text] cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the field equations (FE) admit exact self-similar (SS) solutions through the matter collineation approach. We study two models: the case[Formula: see text] and the case [Formula: see text]. In each case, we state general theorems which determine completely the form of the unknown functions [Formula: see text] such that the FE admit SS solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous SS metric[Formula: see text] In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.

Can Menzerath’s law be a criterion of complexity in communication?

Menzerath’s law is a quantitative linguistic law which states that, on average, the longer is a linguistic construct, the shorter are its constituents. In contrast, Menzerath-Altmann’s law (MAL) is a precise mathematical power-law-exponential formula which expresses the expected length of the linguistic construct conditioned on the number of its constituents. In this paper, we investigate the anatomy of MAL for constructs being word tokens and constituents being syllables, measuring its length in graphemes. First, we derive the exact form of MAL for texts generated by the memoryless source with three emitted symbols, which can be interpreted as a monkey typing model or a null model. We show that this null model complies with Menzerath’s law, revealing that Menzerath’s law itself can hardly be a criterion of complexity in communication. This observation does not apply to the more precise Menzerath-Altmann’s law, which predicts an inverted regime for sufficiently range constructs, i.e., the longer is a word, the longer are its syllables. To support this claim, we analyze MAL on data from 21 languages, consisting of texts from the Standardized Project Gutenberg. We show the presence of the inverted regime, not exhibited by the null model, and we demonstrate robustness of our results. We also report the complicated distribution of syllable sizes with respect to their position in the word, which might be related with the emerging MAL. Altogether, our results indicate that Menzerath’s law—in terms of correlations—is a spurious observation, while complex patterns and efficiency dynamics should be rather attributed to specific forms of Menzerath-Altmann’s law.

A new neutrosophic sign test: An application to COVID-19 data

The Sign test is a famous nonparametric test from classical statistics used to assess the one or two sample averages. The test is practical when the sample size is small, or the distributional assumption under a parametric test does not satisfy. One of the limitations of the Sign test is the exact form of the data, and the existing methodology of the test does not cover the interval-valued data. The interval-valued data often comes from the fuzzy logic where the experiment’s information is not sure and possesses some kind of vagueness, uncertainty or indeterminacy. This research proposed a modified version of the Sign test by considering the indeterminate state and the exact form of the data—the newly proposed sign test methodology is designed for both one-sample and two-sample hypothesis testing problems. The performance of the proposed modified versions of the Sign test is evaluated through two real-life data examples comprised of covid-19 reproduction rate and covid-positive daily occupancy in ICU in Pakistan. The findings of the study suggested that our proposed methodologies are suitable in nonparametric decision-making problems with an interval–valued data. Therefore, applying the new neutrosophic sign test is explicitly recommended in biomedical sciences, engineering, and other statistical fields under an indeterminate environment.

Authenticity Paradox: an Examination on Local Gastronomy

Local gastronomy offers authenticity, an important element of tourist experience. However, some tourists cannot experience gastronomic products in their exact authentic forms. This issue causes from tourists' typology, importance level of gastronomy, and quest for authenticity. For serving widely variated tourists, producers of the local gastronomic products make changes in the essence of products. Current study aims to investigate changing process of gastronomic products’ authenticity which are served in the context of tourism, and to develop an understanding on causes and costs of deterioration. Methodologically, existing literature had evaluated with conceptual inferences. As the findings propose, the changes start with touristic exploration which is followed by tourism-related deterioration. After deterioration, if process of recovery conducted, turning back to the exact form of authenticity does not seem possible. The alternative forms of authenticity are most likely to occur. Additionally, mistaken perspectives like considering recovery preventions as short-term actions can lead the deterioration again, like a loop. Raising awareness for prevent this loop is this study's critical proposition to destinations. Opening new horizons for the phenomenon of authenticity and overthrowing the idea that see tourists as the sole reason for deterioration are the contributions to the literature. The changes that lead deterioration are responsibility of locals, too.

Transition to a Sustainable Bioeconomy

Exceeding planetary boundaries, and especially climate change, requires economies worldwide to decarbonize and to incorporate principles of sustainable development. Transforming a traditional economy into a sustainable bioeconomy by replacing fossil resources through renewable biogenic resources offers a solution to this end. However, seemingly opposing transition perspectives (i.e., technology-based vs. socio-ecological) lead to fragmented efforts, and the exact form of the transition pathway to the goal of a bioeconomy remains unclear. We examine the issue by involving an international expert sample in a Delphi survey and subsequent cross-impact analysis. Based on the experts’ views, we present a list of events necessary to achieve the transformation ranked by the experts to reflect their urgency. The cross-impact analysis facilitates combining the eight most urgent events to create an integrated model of the transition to a sustainable bioeconomy. Our findings suggest that, rather than bioeconomy strategies, investment in the relevant sectors currently constitutes the main bottleneck hindering such a transition.