Special Class Research Articles

Generalized Padovan Sequences and Figurate Numbers

Generalized Padovan Sequences are more general class of sequences which are viewed as general form of the classical Padovan sequences named after English mathematician Richard Padovan. Figurate numbers are special class of numbers which occur in various problems in number theory. In this paper, we discuss the limiting ratio of the recurrence relation formed by generalizing Padovan sequence and considering Figurate numbers as coefficients in two possible cases. We find very interesting numbers turning out to be limiting ratios under our assumptions.

Catalysis in action via elementary thermal operations

We investigate catalysis in the framework of elementary thermal operations (ETOs), leveraging the distinct features of such operations to illuminate catalytic dynamics. As groundwork, we establish new technical tools that enhance the computability of state transition rules for ETOs. Specifically, we provide a complete characterisation of state transitions for a qutrit system and special classes of initial states of arbitrary dimension. By employing these tools in conjunction with numerical methods, we find that by adopting a small catalyst, including just a qubit catalyst, one can significantly enlarge the set of state transitions for a qutrit system. This advancement notably narrows the gap of reachable states between ETOs and generic thermal operations. Furthermore, we decompose catalytic transitions into time-resolved evolution, which critically enables the tracking of nonequilibrium free energy exchanges between the system and bath. Our results provide evidence for the existence of simple and practicable catalytic advantage in thermodynamics while offering insight into analysing the mechanism of catalytic processes.

Younger age is associated with better outcomes in autism severity, language, and adaptive skills after one school year in autism special education classes

A well-accepted hypothesis in the field of autism spectrum disorder (ASD) is that early intervention is crucial for better outcomes. However, research has noted significant variability in early intervention outcomes. This study examined the role of age in relation to outcomes in comprehensive developmental domains following one year of school in community special education classes for ASD. We compared two groups: a younger group (n = 35) aged 34–59 months and an older group (n = 38) aged 60–91 months. The groups did not differ in cognitive ability, autism severity or adaptive behavioral skills at the start of the school year. After one year, the entire study population showed significant progress in all developmental domains. However, changes in effect size were much more robust in the younger ASD group. Only younger children showed a significant decrease in the severity of communication, awareness and restricted interests and repetitive behavior subdomains and a significant increase in motor adaptive skills. Younger children also showed more remarkable improvement in the naming and expressive subdomains. Respectively, older age predicted more severe ASD symptoms at the end of the educational year.Corresponding to brain plasticity theories, our findings point to an association between age and outcomes. The findings should serve as a benchmark for policymakers regarding early intervention in young children with autism.

KMS Dirichlet forms, coercivity and superbounded Markovian semigroups on von Neumann algebras

We introduce a construction of Dirichlet forms on von Neumann algebras M associated to any eigenvalue of the Araki modular Hamiltonian of a faithful normal non-tracial state, providing also conditions by which the associated Markovian semigroups are GNS symmetric. The structure of these Dirichlet forms is described in terms of spatial derivations. Coercivity bounds are proved and the spectral growth is derived. We introduce a regularizing property of positivity preserving semigroups (superboundedness) stronger than hypercontractivity, in terms of the symmetric embedding of M into its standard space L2(M)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2(M)$$\\end{document} and the associated noncommutative Lp(M)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p(M)$$\\end{document} spaces. We prove superboundedness for a special class of positivity preserving semigroups and that some of them are dominated by the Markovian semigroups associated to the Dirichlet forms introduced above, for type I factors M. These tools are applied to a general construction of the quantum Ornstein–Uhlembeck semigroups of the Canonical Commutation Relations CCR and some of their non-perturbative deformations.

Evaluating the functions of the teacher-producer for preparing prospective economists in the modern context of education system digitalization

Introduction. The authors explore the problem of enhancing the communication culture of prospective economists in the context of digital transformation and interaction with artificial intelligence systems. The purpose of the article is to identify the role of the teacher-producer in organizing teacher-student interaction in the system of economic education (secondary school-university), as well as to evaluate the functions of pedagogical production necessary to improve the communicative culture of future economists in the era of digitalization. Materials and Methods. The Pareto principle is used as the methodological basis of the study, according to which 20% of teaching resources provide 80% of the obtained educational result. The sociological survey was conducted among students and academic staff of economic faculties at the Financial University under the Government of the Russian Federation, Astrakhan State University, State Social and Humanitarian University (Kolomna) and schoolchildren of specialized classes (gymnasium 19, Omsk). Results. The analysis of empirical data demonstrates the relevance of the role of the teacher-producer in the economic education system in the era of digitalization, as well as the positive attitude of the younger generation towards the prospects for the introduction of artificial intelligence. The functions of pedagogical production are highlighted, taking into account the digital specifics of modern economic education. Using the Pareto principle confirms that mastery of the functions of pedagogical production (information, communication, organizational) in the system of economic education, constituting about 20% of the component composition of pedagogical functions, determine 80% of the educational result in terms of increasing the level of communicative culture of future economists. Conclusions. The authors revealed and described the functions of pedagogical production are highlighted, taking into account the digital specifics of modern economic education.

Transiting from Units to Inclusive Education: Implication on Intellectual Disability Pupils’ Skills Development; Case Study at Dodoma City

The study explored of the transiting the pupils with intellectual disability from units to inclusive education in Dodoma city council, Tanzania. A field study research design was used to achieve the study objective. The sample of this study was purposively selected from thirty-six (36) primary schools. Created eight (8) participants which involved six (6) participants were special teachers in two units’ class means three 3 in Chinangali unit and others Mlezi unit, and two (2) participant were school heads in Chinangali and Mlezi an inclusive school. The study adopted a descriptive survey design where by qualitative approach used. Interview and observation were used to collect data. The findings revealed that high enrollment rate of children with intellectual disability in units, the teachers-pupil’s ratio insufficient, inadequate teaching and learning materials, and learning environment is not conducive. Therefore, it is recommended that special teachers, curriculum develop and addition building classes.

Effective numerical simulations of synchronous generator system

Synchronous generator system is a complicated dynamic system for energy transmission, which plays an important role in modern industrial production. In this article, we propose some predictor-corrector methods and structure-preserving methods for a generator system based on the first benchmark model of subsynchronous resonance, among which the structure-preserving methods preserve a Dirac structure associated with the so-called port-Hamiltonian descriptor systems. To illustrate this, the simplified generator system in the form of index-1 differential-algebraic equations has been derived. Our analyses provide the global error estimates for a special class of structure-preserving methods called Gauss methods, which guarantee their superior performance over the PSCAD/EMTDC and the predictor-corrector methods in terms of computational stability. Numerical simulations are implemented to verify the effectiveness and advantages of our methods.

Congruence filter pairs, equational filter pairs and adjoints

Abstract Filter pairs are a tool for creating and analyzing logics. A filter pair can be seen as a presentation of a logic, given by presenting its lattice of theories as the image of a lattice homomorphism, with certain properties ensuring that the resulting logic is substitution invariant. Every substitution invariant logic arises from a filter pair. Particular classes of logics can be characterized as arising from special classes of filter pairs. We consider so-called congruence filter pairs, i.e. filter pairs for which the domain of the lattice homomorphism is a lattice of congruences for some quasivariety. We show that the class of logics admitting a presentation by such a filter pair is exactly the class of logics having an algebraic semantics. We study the properties of a certain Galois connection coming with such filter pairs. We give criteria for a congruence filter pair to present a logic in some classes of the Leibniz hierarchy by means of this Galois connection, and its interplay with the Leibniz operator.

Role of Dilations in Reversing Physical Processes: Tabletop Reversibility and Generalized Thermal Operations

Irreversibility, crucial in both thermodynamics and information theory, is naturally studied by comparing the evolution—the (forward) channel—with an associated reverse—the reverse channel. There are two natural ways to define this reverse channel. Using logical inference, the reverse channel is the Bayesian retrodiction (the Petz recovery map in the quantum formalism) of the original one. Alternatively, we know from physics that every irreversible process can be modeled as an open system: one can then define the corresponding closed system by adding a bath (“dilation”), trivially reverse the global reversible process, and finally remove the bath again. We prove that the two recipes are strictly identical, both in the classical and in the quantum formalism, once one accounts for correlations formed between system and the bath. Having established this, we define and study special classes of maps: (including ), for which no such system-bath correlations are formed for some states; and , when the reverse channel can be implemented with the same devices as the original one. We establish several general results connecting these classes, and a very detailed characterization when both the system and the bath are one qubit. In particular, we show that, when reverse channels are well defined, product preservation is a sufficient but not necessary condition for tabletop reversibility; and that the preservation of local energy spectra is a necessary and sufficient condition to generalized thermal operations. Published by the American Physical Society 2024

Ramsey Numbers and Graph Parameters

According to Ramsey’s Theorem, for any natural p and q there is a minimum number R(p, q) such that every graph with at least R(p, q) vertices has either a clique of size p or an independent set of size q. In the present paper, we study Ramsey numbers R(p, q) for graphs in special classes. It is known that for graphs of bounded co-chromatic number Ramsey numbers are upper-bounded by a linear function of p and q. However, the exact values of R(p, q) are known only for classes of graphs of co-chromatic number at most 2. In this paper, we determine the exact values of Ramsey numbers for classes of graphs of co-chromatic number at most 3. It is also known that for classes of graphs of unbounded splitness the value of R(p, q) is lower-bounded by (p-1)(q-1)+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(p-1)(q-1)+1$$\\end{document}. This lower bound coincides with the upper bound for perfect graphs and for all their subclasses of unbounded splitness. We call a class Ramsey-perfect if there is a constant c such that R(p,q)=(p-1)(q-1)+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R(p,q)=(p-1)(q-1)+1$$\\end{document} for all p,q≥c\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p,q\\ge c$$\\end{document} in this class. In the present paper, we identify a number of Ramsey-perfect classes which are not subclasses of perfect graphs.

Cultural and Historical Considerations of Traditional Eco-Friendly Persimmon Juice Dyeing in Korea and Japan

By reviewing the cultural and historical literature on persimmon juice dyeing and Galot in Korea and Japan, this study aims to show the similarities and differences between the traditional and eco-friendly persimmon juice dyeing practices of these two countries and suggest a direction for the development of modern Galot. The root of persimmon dyeing in Korea is presumed to have begun around the 13<sup>th</sup> or 14<sup>th</sup> century; however, no documents or records have been found to support this notion. Meanwhile, there are records of persimmon dyeing in Japan that date back to around the 10th century, but that fact is rarely mentioned. The historical and folk cultural significance of traditional persimmon dyeing in Japan and Korea was different in terms of the use of persimmon dye and the wearing of Galot. In other words, in Korea, Galot was mainly used as work clothes for farmers and fishermen, who took advantage of the garment's functional strength, while kaki-tannin in Japan was applied to fishing tools and industrial materials. Furthermore, Japanese traditional Galot (Kakigoromo) was worn by monks. This was a remarkable difference in that the garments were used as clothing by a special class within society. There were also differences between the two countries in terms of their use of modern persimmon juice dye and Galot. Korea is currently developing and releasing a variety of modern Galots. Meanwhile, Japan is attempting to develop a feeling of relaxation by using the natural colors of Kakisibu dyeing and applying sophisticated traditional pattern printing techniques to modern Galot.

Data‐Driven Screening of Pivotal Subunits in Edge‐Anchored Single Atom Catalysts for Oxygen Reactions

AbstractOxygen reduction reaction (ORR) and the oxygen evolution reaction (OER) are key reactions in diverse energy conversion devices, highlighting the importance of efficient catalysts. Edge‐anchored single atom catalysts (E‐SACs) emerge as a special class of atomic structure, but the detailed configuration and its correlation with catalytic activity remain little explored. Herein, a total of 78 E‐SACs (E‐TM‐Nx‐C) have been constructed based on 26 transition metal (TM) species with three coordination patterns. Using structural stability and ORR/OER catalytic activity as the evaluation criteria, a few catalytic structures comparable to Pt (111) for ORR and IrO2 (110) for OER are screened based on high‐throughput calculations. The screening results unveil that the E‐Rh‐N4‐C configuration exhibits most efficient bifunctional activity for both ORR and OER with an overpotential of 0.38 and 0.61 V, respectively. Electronic structure analysis confirms the distinctive edge effects on the electronic properties of TM and N species, and the feature importance derived from machine learning illustrates the efficacy of E‐TM‐Nx subunit configuration in determining the catalytic activity of E‐SACs. Finally, the trained Gradient Boosting Regression (GBR) model exhibits acceptable accuracy in predicting the OH intermediates adsorption strength for E‐SACs, thereby paving the way for expanding catalytic structures based on E‐SACs.

Not All Probability Density Functions Are Tomograms.

This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true pdfs, are used to completely describe the states of quantum systems. Unlike quasi-pdfs, like the Wigner function, tomograms can be analysed using all the tools of classical probability theory for pdf estimation, which can allow a better quality of state reconstruction. This is particularly useful when dealing with non-Gaussian states where the pdfs are multi-mode. The knowledge of the family of distributions plays an important role in the application of both parametric and nonparametric density estimation methods. We show that not all pdfs can play the role of tomograms of quantum states and introduce the conditions that must be fulfilled by pdfs to be "quantum".

The Cossacks of Southern Russia in 21st-Century Memory Politics

In modern Russia, the memory of the Cossacks is perpetuated in monuments and museum exhibitions; their culture and history are described in school textbooks, including specialized ones; some regions open special Cossack classes; and hundreds of social media groups discuss the history of the Cossacks. Central and regional authorities as well as Cossack organizations, both official and unofficial, take an active part in the politics of remembering the Cossacks. However, there are practically no specialized studies exploring memory politics regarding the Cossacks. Nevertheless, this topic deserves attention and careful analysis not only because a variety of intensive processes are taking place in this area, but also because this case has a number of specific features and allows one to take a fresh look at some dichotomies widely used in memory studies such as victim and heroic narratives, official and unofficial memory, and local and national memory politics.

Open-loop and closed-loop local and remote stochastic nonzero-sum game with inconsistent information structure

In this paper, the open-loop and closed-loop local and remote stochastic nonzero-sum game (LRSNG) problem is investigated. Different from previous works, the stochastic nonzero-sum game problem under consideration is essentially a special class of two-person nonzero-sum game problem, in which the information sets accessed by the two players are inconsistent. More specifically, both the local player and the remote player are involved in the system dynamics, and the information sets obtained by the two players are different, and each player is designed to minimise its own cost function. For the considered LRSNG problem, both the open-loop and closed-loop Nash equilibrium are derived. The contributions of this paper are given as follows. Firstly, the open-loop optimal Nash equilibrium is derived, which is determined in terms of the solution to the forward and backward stochastic difference equations (FBSDEs). Furthermore, by using the orthogonal decomposition method and the completing square method, the feedback representation of the optimal Nash equilibrium is derived for the first time. Finally, the effectiveness of our results is verified by a numerical example.

A Study on Developmental Strategies for Improving the Quality of Secondary Special Education for Students with Disabilities

In the era of the fourth industrial revolution, addressing the multifaceted learning needs of students with special needs has become increasingly pivotal. This study aims to explore and enhance the quality of secondary special education, adapting to new educational methodologies in tandem with technological advancements while fostering the development of teachers and educational stakeholders. To identify the key areas necessitating development in secondary special education, interviews were conducted with special education teachers. These interviews informed the creation of a questionnaire, which was subsequently disseminated through a Google survey to special education teachers in various special schools and classes nationwide. The survey responses were analyzed using descriptive statistics to gain comprehensive insights. This study's findings integrate the perspectives from the interviews and survey data, leading to the formulation of strategies for the advancement of secondary special education. The analysis categorized the developmental needs into four primary domains: teacher development, curriculum enhancement, school infrastructure, and external factors related to the school environment. The paper concludes with a discussion that synthesizes these findings, offering a pathway for future improvements in the quality of secondary special education, and highlighting the importance of adapting to the changing educational landscape in the era of technological progress.

Standard translation twists and an operator-bounded energy inequality

Twist operators implement symmetries in bounded regions of the space. Standard twists are a special class of twists constructed using modular tools. The twists corresponding to translations have interesting special properties. They can move continuously an operator from a region to a disjoint one without ever passing through the gap separating the two. In addition, they have generators satisfying the spectrum condition. We compute explicitly these twists for the two-dimensional chiral fermion field. The twist generator gives place to a new type of energy inequality where the smeared energy density is bounded below by an operator. Published by the American Physical Society 2024

MOOD DISORDER IN STUDENTS WITH LEARNING DISABILITIES

The current research aims to identify the level of mood disorder among students with learning difficulties in special education classes and the level of mood disorder among students with learning difficulties according to the variable of the school stage (third grade, fourth grade). The research sample was selected randomly, consisting of (101) students of the third and fourth grades (special education) in government primary schools affiliated with the General Directorate of Education in Babylon governorate. To achieve the two objectives of the study, the researcher prepared a mood disorder scale and applied it to the students of the research sample. After confirming the indications of honesty and consistency, the data were collected and analyzed using (SPSS) The results of the current research indicated that there are significant differences between the arithmetic mean and the hypothetical average and in favor of the arithmetic mean of the recent research sample; which shows a clear correlation between mood disorders and learning difficulties among special education students in the third and fourth grades of primary (special education).

Objectionable Commemorations: Ethical and Political Issues

AbstractThe term, "objectionable commemorations”, refers to a broad category of public artefacts – such as, and especially, memorials, monuments and statues – that are regarded as morally problematic in virtue of what or whom they honour. In this regard, they are a special class of public artefacts that are subject to public contestation. In this paper, we survey the general ethical and political issues on this topic. First, we categorise the arguments on offer in the literature, concerning the objectionable nature of such commemorations. Second, we review common political responses to objectionable commemorations. Finally, we identify fruitful areas for further philosophical inquiry on this topic.

Did a Kilonova Set Off in Our Galactic Backyard 3.5 Myr ago?

The recent detection of the live isotopes 60Fe and 244Pu in deep ocean sediments dating back to the past 3–4 Myr poses a serious challenge to the identification of their production site(s). While 60Fe is usually attributed to standard core-collapse supernovae, actinides are r-process nucleosynthesis yields, which are believed to be synthesized in rare events, such as special classes of supernovae or binary mergers involving at least one neutron star. Previous works concluded that a single binary neutron star merger cannot explain the observed isotopic ratio. In this work, we consider a set of numerical simulations of binary neutron star mergers producing long-lived massive remnants expelling both dynamical and spiral-wave wind ejecta. The latter, due to a stronger neutrino irradiation, also produce iron-group elements. Assuming that large-scale mixing is inefficient before the fading of the kilonova remnant and that the spiral-wave wind is sustained over a 100–200 ms timescale, the ejecta emitted at mid-high latitudes provide a 244Pu over 60Fe ratio compatible with observations. The merger could have happened 80–150 pc away from the Earth and between 3.5 and 4.5 Myr ago. We also compute expected isotopic ratios for eight other live radioactive nuclides showing that the proposed binary neutron star merger scenario is distinguishable from other scenarios proposed in the literature.