Special Class Research Articles

A direct approach for solving the cubic Szegö equation

AbstractWe study the cubic Szegö equation which is an integrable nonlinear nondispersive and nonlocal evolution equation. In particular, we present a direct approach for obtaining the multiphase and multisoliton solutions as well as a special class of periodic solutions. Our method is substantially different from the existing one which relies mainly on the spectral analysis of the Hankel operator. We show that the cubic Szegö equation can be bilinearized through appropriate dependent variable transformations and then the solutions satisfy a set of bilinear equations. The proof is carried out within the framework of an elementary theory of determinants. Furthermore, we demonstrate that the eigenfunctions associated with the multiphase solutions satisfy the Lax pair for the cubic Szegö equation, providing an alternative proof of the solutions. Last, the eigenvalue problem for a periodic solution is solved exactly to obtain the analytical expressions of the eigenvalues.

Current issues of conducting classes on fire training of police officers under martial law

The article addresses pertinent issues related to conducting firearms training sessions for police officers in conditions of a state of war. The authors analyze significant aspects of this activity, including teaching methods and techniques, personnel training specifics, as well as challenges and threats that may arise during armed conflicts. The main focus is on practical recommendations aimed at enhancing the effectiveness of police training for operating in conditions of a state of war. The article analyzes changes and modifications in the methodology of teaching and studying fire training in institutions of higher education with specific conditions of study, subordinated to the Ministry of Internal Affairs of Ukraine under martial law, which would take into account all aspects of the application and use of firearms and ensure high- quality training of students of higher education for actions in stressful and dangerous situations. The authors explore the practical-tactical possibilities of conducting firearms training sessions, comparing them with regulated and recommended regulatory acts. It is established that existing methods do not correspond to the real conditions of firearms application. Special attention is given to the issues of modern methods of firearms usage and changes in teaching methodology to increase proficiency. Features and methods of teaching fire training in higher education institutions with specific training conditions of the Ministry of Internal Affairs of Ukraine are outlined, as well as innovations in this field of training are indicated. A separate view is focused on the need for modern material and technical support, since the solution to the problem of police training requires a comprehensive approach, which includes the provision of the necessary resources for conducting specialized classes, both in closed rooms and on appropriately equipped modern training grounds, and support in the development of professional skills. Also, the authors emphasize the need to improve the legal training of personnel to provide them with a clear understanding of the laws and regulations related to the use of weapons.

Damage sensing in multi-functional nanocomposite polymer bonded energetics with embedded multi-walled carbon nanotube sensing networks

Abstract This experimental investigation evaluates the strain and damage sensing abilities of multi-walled carbon nanotube (MWCNT) networks embedded in the binder phase of polymer-bonded energetics (PBEs). PBEs are a special class of particulate composite materials that consist of energetic crystals bound by a polymer matrix, wherein the polymer matrix serves to maintain the composite’s shape and form. The structural health monitoring (SHM) approach presented in this work exploits the piezoresistive properties of the distributed MWCNT networks. Major challenges faced during such implementation include the low binder concentrations of PBEs, the presence of conductive/non-conductive particulate phases, the high degree of heterogeneity in the PBE microstructure, and achieving the optimal MWCNT dispersion. In this study, ammonium perchlorate (AP) crystals as the oxidizer, Aluminum grains as the metallic fuel, and Polydimethylsiloxane (PDMS) as the binder are used as the constituents for fabricating PBEs. To study the effect of each constituent on the MWCNT network’s SHM abilities, various materials systems are comprehensively studied: MWCNT/PDMS materials are first evaluated to study the binder’s electromechanical response, followed by AP/MWCNT/PDMS to assess the impact of AP addition, and finally, AP/AL/MWCNT/PDMS to evaluate the impact of adding conductive aluminum grains. Compression samples (ASTM D695) were fabricated and subjected to monotonic compression. Electrical resistance is recorded in conjunction with the mechanical test via an LCR meter. Gauge factors relating to the change in normalized resistance to applied strain are calculated to quantify the electromechanical response. MWCNT dispersions and mechanical failure modes are analyzed via scanning electron microscopy imaging of the fracture surfaces. Correlations between the electrical behavior in response to the mechanical behavior are presented, and possible mechanisms that influence the electromechanical behavior are discussed. The results presented herein demonstrate the successful ability of MWCNT networks as SHM sensors capable of real-time strain and damage assessment of PBEs.

Correlation between hydration status and VO2max in Pencak Silat athletes

Maintaining proper hydration conditions is important to support athlete performance. The study aimed to determine the relationship between hydration status and the VO2max capacity of martial arts athletes. The research was conducted using a correlational method. The subjects of the study were 14 Pencak Silat Athletes Special Class for Sports at State Junior High School (JHS) 1 Surakarta. Self-Urine Check (SUC) test data collection to test hydration status and Bleep Test to measure athletes' VO2max capacity. Data analysis techniques with product-moment correlation tests. The results obtained the relationship coefficient between hydration status and VO2max capacity was r = -0.844; p = 0.001. Therefore, there was a significant negative relationship between these two variables. This study concludes that there was a negative correlation between hydration status and VO2max capacity in JHS Special Sports Class athletes. The novelty of this study lies in the observation of stable hydration levels among Pencak Silat athletes in the Special Sports Class of SMPN 1 Surakarta. The results of this study can be used as a reference for athletes to maintain adequate hydration during activities, and for coaches to ensure that all athletes are in a well-hydrated state to avoid dehydration.

Unit Groups of a Finite Extension of Galois Rings

Let $R_{o}$ be a Galois ring. It is well known that every element of $R_{o}$ is either a zero divisor or a unit. Galois rings are building blocks of completely primary finite rings which have yielded interesting results towards classification of finite rings. Recent studies have revealed that every finite commutative ring is a direct sum of completely primary finite rings. In fact, extensive account of finite rings have been given in the recent past. However, the classification of finite rings into well known structures still remains an open problem. For instance, the structure of the group of units of $R_{o}$ is known and some results have been obtained on the structure of its zero divisor graphs. In this paper, we construct a finite extension of $R_{o}$ (a special class of completely primary finite rings) and classify its group of units for all the characteristics.

Unit Groups of a Finite Extension of Galois Rings

Let $R_{o}$ be a Galois ring. It is well known that every element of $R_{o}$ is either a zero divisor or a unit. Galois rings are building blocks of completely primary finite rings which have yielded interesting results towards classification of finite rings. Recent studies have revealed that every finite commutative ring is a direct sum of completely primary finite rings. In fact, extensive account of finite rings have been given in the recent past. However, the classification of finite rings into well known structures still remains an open problem. For instance, the structure of the group of units of $R_{o}$ is known and some results have been obtained on the structure of its zero divisor graphs. In this paper, we construct a finite extension of $R_{o}$ (a special class of completely primary finite rings) and classify its group of units for all the characteristics.

Comment on “A Special Topic Class in Chemistry on Feminism and Science as a Tool to Disrupt the Dysconcious Racism in STEM”

Comment on “A Special Topic Class in Chemistry on Feminism and Science as a Tool to Disrupt the Dysconcious Racism in STEM”

On Bäcklund transformations to stationary equations in hierarchy of the second Painlevé equation

The analytical properties of solutions to stationary equations of the second and fourth orders in the hierarchy of the second Painlevé equation are considered. For the second-order equation, it is shown that the Bäcklund transformation in the general case determines the formula of the addition theorem for the Weierstrass elliptic function. For the fourth and sixth-order equations, Bäcklund transformations and special classes of solutions are constructed. It has been established that, for a certain relationship between the parameters, the set of solutions to the first term of the stationary hierarchy is a subset of solutions to the second term and the set of solutions to the second term of the hierarchy is a subset of solutions of the six-order equation of the stationary hierarchy of the second Painlevé equation.

H ∞ bumpless transfer control for switched affine systems with its application to turbofan engine model

Switched affine systems (SASs) are a special class of switched systems. The existing works about SASs predominantly focuses on steady-state performance. There exist limited attention given to transient performance, particularly the transient performance induced by switchings. The inappropriate switchings can induce severe signal jumps, degrade the steady-state performance of the system, and even lead to instability. The bumpless transfer control (BTC) represents an effective strategy for mitigating signal jumps. However, the existing BTC methods are primarily designed for general switched systems, and these approaches are often not applicable to SASs. This article is focussed on the issue of H ∞ BTC for SASs under unmodeled disturbances. Firstly, an affine term (AT) related to H ∞ bumpless transfer (BT) performance definition is introduced for the SAS to characterise the alleviation level of the bumps in the control input signal at switching points. Secondly, a criterion is established to enable the solvability of the H ∞ BTC problem for the SAS. Thirdly, an H ∞ BT controller and a switching signal are co-designed to drive the SAS to satisfy the H ∞ BT performance which may not be shared by the subsystems. Finally, a turbofan engine model example is implemented to illustrate the availability and rationality of the suggested H ∞ BTC scheme.

Australia at an educational crossroads: special schools and inclusive education

The ongoing debate surrounding special schools and inclusive education in Australia has come to the forefront since the recommendations of the 2023 Royal Commission into Violence, Abuse, Neglect and Exploitation of People with Disability, where the Commissioners were split on the implementation of full educational inclusion and the elimination of special schools. The authors discuss the controversy surrounding segregated special education classes and schools, particularly considering the push for full inclusion. The concept of inclusion is examined through a brief review of national and international policies and academic and popular literature, including how the inclusion continuum is conceptualized by policymakers, academics, and families. Stakeholder perspectives on the complexities and challenges of implementing full inclusion in mainstream school settings offer differing experiences and opinions on what is possible. Lastly, by examining the nuances of the special school controversy, the authors provide recommendations on how best to meet the educational needs of all students, across the spectrum of abilities.

At the Speed of Light: Recent Advances on Photocatalyzed Generation and Applications of Iminyl Radicals Promoted by Visible-light

: Nitrogen-positioned radicals are chemical entities that have a lengthier history than carbon ones and their high reactivity makes them invaluable. But, despite its power, much of its chemistry is still uncharted. Currently, developed methodologies to access nitrogen-positioned radicals, such as transition metal catalysis or visible-light photoredox methods through a single-electron transfer process, avoiding the use of harmful or toxic reagents, excess raw materials, solvents as well as pre-functionalization steps or extensive synthetic routes are in continuous progress. This revision aims to depict the recent advances in the field of iminyl-radicals’ syntheses, a special class of radicals placed on nitrogen, catalyzed by transition metals or photoredox techniques for the construction of C-N bonds and their synthetic applications. This work serves as a comprehensive guide for the scope of synthetic applications that this kind of radicals could have.

CircTMTC1 Mediates Nucleo-cytoplasmic Translocation of DDX3X to Regulate Osteogenic Differentiation of Human Ligamentum Flavum Cells.

This study was aimed to investigate the potential roles of circTMTC1 in the underlying pathophysiological mechanisms of ossification of the ligamentum flavum (OLF). OLF is the primary contributor to thoracic spinal stenosis, which may cause severe neurological symptoms. There is a lack of effective medical therapy for OLF available so far because the exact underlying mechanism of OLF has not been fully elucidated. CircRNAs are a special class of non-coding RNAs and have attracted a growing interest of research in various human diseases recently. Therefore, we explored the potential roles of circRNAs in the underlying pathophysiological mechanisms of OLF. We performed RNA-seq analysis to investigate the differentially expression profile of circRNAs in osteogenic differentiation of human LF cells, and identified a key circular RNA circTMTC1 functioned in OLF. Subsequently, we performed a series of experiments to investigate the exact molecular and cellular mechanisms in osteogenic differentiation of human ligamentum flavum cells. CircTMTC1 is significantly up-regulated during osteogenic differentiation of human LF cells. Mechanistically, we found that circTMTC1 could interact with the RNA binding protein DDX3X and enhance its nucleo-cytoplasmic translocation. An increased cytoplasmic level of DDX3X activated the NLRP3 inflammasome pathway and thus promoted osteogenic differentiation of human ligamentum flavum cells. Our findings suggested the circTMTC1-DDX3X-NLRP3 inflammasome signaling plays a pivotal role in osteogenic differentiation of human ligamentum flavum cells, which may provide novel diagnostic and therapeutic strategies for OLF.

Reply to Comment on “A Special Topic Class in Chemistry on Feminism and Science as a Tool to Disrupt the Dysconcious Racism in STEM”

Reply to Comment on “A Special Topic Class in Chemistry on Feminism and Science as a Tool to Disrupt the Dysconcious Racism in STEM”

Planar decomposition of the HOMFLY polynomial for bipartite knots and links

AbstractThe theory of the Kauffman bracket, which describes the Jones polynomial as a sum over closed circles formed by the planar resolution of vertices in a knot diagram, can be straightforwardly lifted from $$\mathfrak {sl}(2)$$ sl ( 2 ) to $$\mathfrak {sl}(N)$$ sl ( N ) at arbitrary N – but for a special class of bipartite diagrams made entirely from the antiparallel lock tangle. Many amusing and important knots and links can be described in this way, from twist and double braid knots to the celebrated Kanenobu knots for even parameters – and for all of them the entire HOMFLY polynomials possess planar decomposition. This provides an approach to evaluation of HOMFLY polynomials, which is complementary to the arborescent calculus, and this opens a new direction to homological techniques, parallel to Khovanov–Rozansky generalizations of the Kauffman calculus. Moreover, this planar calculus is also applicable to other symmetric representations beyond the fundamental one, and to links which are not fully bipartite what is illustrated by examples of Kanenobu-like links.

Global dynamics of a special class of planar sector-wise linear systems

In this article, we study the global dynamics of a special class of planar sector-wise linear differential systems with two subsystems being the same except for their equilibriums. Taking the position of one equilibrium as the bifurcation parameter, we provide a complete analysis about sliding cycle bifurcation and sliding homoclinic bifurcation. Moreover, we obtain the existence of all important separatrix orbits and their dependence on the bifurcation parameter, including sliding heteroclinic orbit, heteroclinic cycle, limit cycle, sliding homoclinic cycle and sliding cycle. For more information see https://ejde.math.txstate.edu/Volumes/2024/57/abstr.html

The Changes in High School Special Class Student and Practical Knowledge of Special Education Teacher in the Action Process of Career Institution Exploration Program

The Changes in High School Special Class Student and Practical Knowledge of Special Education Teacher in the Action Process of Career Institution Exploration Program

NON-INVARIANT SUBMANIFOLDS OF ALMOST POLY-NORDEN RIEMANNIAN MANIFOLDS

In this paper, we study a special class of submanifolds of almost polyNorden manifolds in the Riemannian setting. We examine the sufficient conditions for such kind of submanifolds to be totally geodesic or minimal.

Outer Independent Double Roman Domination Stability in Graphs

An outer independent double Roman dominating function (OIDRDF) on a graph G is a function f : V ( G ) → { 0 , 1 , 2 , 3 } having the property that (i) if f ( v ) = 0 , then the vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f ( w ) = 3 , and if f ( v ) = 1 , then the vertex v must have at least one neighbor w with f ( w ) ≥ 2 and (ii) the subgraph induced by the vertices assigned 0 under f is edgeless. The weight of an OIDRDF is the sum of its function values over all vertices, and the outer independent double Roman domination number γ o i d R ( G ) is the minimum weight of an OIDRDF on G . The γ o i d R -stability ( γ − o i d R -stability, γ + o i d R -stability) of G , denoted by s t γ o i d R ( G ) ( s t − γ o i d R ( G ) , s t + γ o i d R ( G ) ), is defined as the minimum size of a set of vertices whose removal changes (decreases, increases) the outer independent double Roman domination number. In this paper, we determine the exact values on the γ o i d R -stability of some special classes of graphs, and present some bounds on s t γ o i d R ( G ) . In addition, for a tree T with maximum degree Δ , we show that s t γ o i d R ( T ) = 1 and s t − γ o i d R ( T ) ≤ Δ , and characterize the trees that achieve the upper bound.

Compositional and dramaturgical analysis of Mykola Lysenko’s Concert polonaises Op. 5 and Op. 7 and specificity of their performing interpretation

The relevance of the article. Mykola Lysenko’s creativity attracts the attention of the world music community. This is confirmed by the availability of CD albums with the composer’s music created by Ukrainian and foreign musicians. The composer’s piano opuses are of considerable interest, but among them there are pieces that, despite their artistic value, are performed relatively infrequent. The purpose of the article is to identify the compositional and dramaturgical features of two Concert polonaises Op. 5 and Op. 7 by M. Lysenko and analyze their performance versions. Taken in combination, this will allow us to better understand the specifics of the composer’s interpretation of the polonaise genre and identify approaches to the interpretation of these works that are common in contemporary piano performance practice. The methodology is based on an integrative approach, and involves the use of systematic, analytical, structural-functional, inductive and comparative methods. The results. In his two Concert polonaises, M. Lysenko presents different approaches to the understanding of the genre, which is manifested at the level of their composition, musical dramaturgy, and the embodiment of the virtuoso-concert principle. In addition, the study examines the performing versions of polonaises created by contemporary Ukrainian pianists, which helped to identify trends in their performing interpretation. Conclusions. The compositional structure of the first Concert polonaise is proportional, while in the second Concert polonaise the composer does not keep the symmetry of the form of the sections, expanding the middle section and shortening the reprise. The musical dramaturgy of the first Concert polonaise is marked by the contrast of musical images, while the second Concert polonaise is dominated by lyrical imagery. These pieces embody opposite aspects of virtuosity, which is manifested at the level of texture and dynamic palette. Interpreting these Concert polonaises by M. Lysenko, the pianists reveal different aspects of their musical and figurative sphere: lyricism or poetry, bright dancing or heroics. An interesting trend in the performing interpretation of the works is the reduction of the middle section (episode), which is possible due to the repetition of the thematic material. The practical significance. The material of the article can be used in the further study of the specifics of the performance interpretation of M. Lysenko’s music, as well as in the study of the artist’s work in a special piano class, courses “The analysis of musical forms”, “The history of music”.

Development of toxicity tests for Polyurethane foams

Polyurethanes (PUs) are a special class of polymeric materials that differ significantly from most other types of plastic in many aspects. They can be utilized in a wide range of products, including paints, coatings, elastomers, insulators, elastic fibers, and foams. PU foams are especially important as part of various convenience products. PU products often end up in landfills when they are no longer useful and can release toxic compounds when damaged by humans or microbes. Therefore, the ecotoxicological assessment of PU foams is essential. In this paper, five PU foam samples were prepared with different NCO indices (NCO-0.8, 0.9, 1.0, 1.1, and 1.2) and together with the Control sample (a previously tested non-toxic foam sample) were applied to develop toxicity tests procedure, while intentionally prepared Toxic foam has been used to verify the accuracy of the developed testing procedure. Two test organisms were successfully applied, Sinapis alba (white mustard) seeds and Escherichia coli (non-pathogenic) bacterial model organisms, and toxicity tests were adapted for the examination of PU-derived substances. Regarding Sinapis alba test, the highest NCO index (NCO-1.2) significantly reduced root length by 9.8 % compared to the Control sample. In the bacterial test, it was observed that the samples containing NCO-1.1 and NCO-1.2 had lower colony numbers (5.0 × 108 and 4.9 × 108 CFU/mL respectively) in comparison to the Control plate (9.6 × 108 CFU/mL). All in all, two toxicity tests were successfully adapted for PU foams, and both are applicable in their ecotoxicological assessment.