Special Class Research Articles

Properties of a Linear Operator Involving Lambert Series and Rabotnov Function

This work is an attempt to apply Lambert series in the theory of univalent functions. We first consider the Hadamard product of Rabotnov function and Lambert series with coefficients derived from the arithmetic function σn to introduce a normalized linear operator JRα,βz. We then acquire sufficient conditions for JRα,βz to be univalent, starlike and convex, respectively. Furthermore, we discuss the inclusion results in some special classes, namely, spiral-like and convex spiral-like subclasses. In addition, we extend the findings by incorporating two Robin’s inequalities, one of which is analogous to the Riemann hypothesis.

Virtue ethics embedded: Aristotelianism in the post-war Japanese moral education

ABSTRACT For almost 80 years, post-war Japanese moral education has adopted a dual-process structure, which states morality is taught through two processes: one through all aspects of school education and the other through a special moral education class. The necessity and effectiveness of this structure were theorised by Eijiro Inatomi. However, it has been almost neglected that his theory is largely based on Aristotle’s theory of virtue. This paper examines Inatomi’s Aristotle-inspired theory and its significance. After reviewing the social and historical background of his theory, I argue that Inatomi successfully adopted Aristotle’s theory of virtue in three respects: human definition, intellectual virtue, and ethical virtue. Finally, I suggest that post-war Japanese moral education can be understood as a nationwide social implementation experiment on the efficacy of Aristotelian virtue ethics and that Inatomi’s notion of cosmos can serve as a conceptual device to enhance the social feasibility of Aristotle’s virtue ethics.

Minimal size balanced sets mod [formula omitted]

A nonempty set S of residues modulo N is said to be balanced if for each x∈S, there is a d with 0<d≤N/2 such that x±dmodN both lie in S. We denote the minimum cardinality of a balanced set modulo N by α(N). Minimal size balanced sets are needed for a winning strategy in the Vector game which was introduced together with balanced sets.In this paper, we describe a polynomial algorithm for constructing a minimal size balanced set modulo p, when p is from two special classes of primes called lucky primes. We prove that lucky primes are all primes among the sequence cn=2n+3+(−1)n3. Then we prove that the numbers cn=2n+3+(−1)n3 are never prime when n is odd and n>1. Thus, the sequence simplifies to cm=2m+13 with m odd. Finally, we prove that if 2p+13 is prime, then p must be a prime.

Structure Effects of Ligands in Gold-Ligand Complexes for Controlled Formation of Gold Nanoclusters.

Metal nanoclusters (NCs) are a special class of nanoparticles composed of a precise number of metal atoms and ligands. Because the proportion of ligands to metal atoms is high in metal NCs, the ligand type determines the physical properties of metal NCs. Furthermore, ligands presumably govern the entire formation process of the metal NCs. However, their roles in the synthesis, especially as factors in the uniformity of metal NCs, are not understood. It is because the synthetic procedure of metal NCs is highly convoluted. The synthesis is initiated by the formation of various metal-ligand complexes, which have different numbers of atoms and ligands, resulting in different coordinations of metal. Moreover, these complexes, as actual precursors to metal NCs, undergo sequential transformations into a series of intermediate NCs before the formation of the desired NCs. Thus, to resolve the complicated synthesis of metal NCs and achieve their uniformity, it is important to investigate the reactivity of the complexes. Herein, we utilize a combination of mass spectrometry, density functional theory, and electrochemical measurements to understand the ligand effects on the reactivity of AuI-thiolate complexes toward the reductive formation of Au NCs. We discover that the stability of the complexes can be increased by either van der Waals interactions induced by the long carbon chain of ligands or by non-thiol functional groups in the ligands, which additionally coordinate with AuI in the complexes. Such structural effects of thiol ligands determine the reduction reactivity of the complexes and the amount of NaBH4 required for the controlled synthesis of the Au NCs.

Restrained Global Defensive Alliances on Some Special Classes of Graphs

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High-performance bipolar membrane for CO2 electro-reduction to CO in organic electrolyte with NaOH and Cl2 produced as byproducts

Bipolar membranes (BPM) are a special class of ion-exchange membranes constituted by a cation- and an anion-exchange layer, allowing the generation of protons and hydroxide ions via water dissociation. This unique feature makes them useful in a wide range of application. In this work, we have fabricated a novel BPM, with SnO2 hollow spheres used as water dissociation catalyst. Such fabricated BPM has been served as a diaphragm to construct a three-chamber electrolyzer for CO2 electro-reduction to CO in organic electrolyte. During the long-term electrolysis process, the cathodic current density has reached to ∼96.5 mA cm−2, with the Faraday efficiency of CO stabled at ∼92.6 %. Compared with widely used commercial BPM, as-prepared BPM exhibited many advantages, such as lower hydrolysis over-potential, high catalytic efficiency and low total resistance. This technology extends the prospect of BPM application in the field of CO2 reduction.

Causal Unit Selection using Tractable Arithmetic Circuits

The unit selection problem aims to find objects, called units, that optimize a causal objective function which describes the objects' behavior in a causal context (e.g., selecting customers who are about to churn but would most likely change their mind if encouraged). While early studies focused mainly on bounding a specific class of counterfactual objective functions using data, more recent work allows one to find optimal units exactly by reducing the causal objective to a classical objective on a meta-model, and then applying a variant of the classical Variable Elimination (VE) algorithm to the meta-model---assuming a fully specified causal model is available. In practice, however, finding optimal units using this approach can be very expensive because the used VE algorithm must be exponential in the constrained treewidth of the meta-model, which is larger and denser than the original model. We address this computational challenge by introducing a new approach for unit selection that is not necessarily limited by the constrained treewidth. This is done through compiling the meta-model into a special class of tractable arithmetic circuits that allows the computation of optimal units in time linear in the circuit size. We finally present empirical results on random causal models that show order-of-magnitude speedups based on the proposed method for solving unit selection.

Generation of genetic codes with 2-adic codon algebra and adaptive dynamics

This is a brief review on modeling genetic codes with the aid of 2-adic dynamical systems. In this model amino acids are encoded by the attractors of such dynamical systems. Each genetic code is coupled to the special class of 2-adic dynamics. We consider the discrete dynamical systems, These are the iterations of a function F:Z2→Z2, where Z2 is the ring of 2-adic numbers (2-adic tree). A genetic code is characterized by the set of attractors of a function belonging to the code generating functional class. The main mathematical problem is to reduce degeneration of dynamic representation and select the optimal generating function. Here optimality can be treated in many ways. One possibility is to consider the Lipschitz functions playing the crucial role in general theory of iterations. Then we minimize the Lip-constant. The main issue is to find the proper biological interpretation of code-functions. One can speculate that the evolution of the genetic codes can be described in information space of the nucleotide-strings endowed with ultrametric (treelike) geometry. A code-function is a fitness function; the solutions of the genetic code optimization problem are attractors of the code-function. We illustrate this approach by generation of the standard nuclear and (vertebrate) mitochondrial genetics codes.

Actinobacteria: Smart Micro-Factories for The Health Sector.

Antibiotics are considered "wonder drugs" due to the fact that they are the most extensively utilised medication in the world. They are used to cure a broad spectrum of diseases and lethal infections. A variety of bacteria and fungi produce antibiotics as a result of secondary metabolism; however, their production is dominated by a special class of bacteria, namely Actinobacteria. Actinobacteria are gram-positive bacteria with high G+C content and unparalleled antibiotic-producing ability. They produce numerous polyenes, tetracyclines, β-lactams, macrolides, and peptides. Actinobacteria are ubiquitous in nature and are isolated from various sources, such as marine and terrestrial endophytes of plants and air. They are studied for their relative antibiotic-producing ability along with the mechanism that the antibiotics follow to annihilate the pathogenic agents that include bacteria, fungi, protozoans, helminths, etc. Actinobacteria isolated from endophytes of medicinal plants have amassed significant attention as they interfere with the metabolism of medicinal plants and acquire enormous benefits from it in the form of conspicuous novel antibiotic-producing ability. Actinobacteria is not only an antibiotic but also a rich source of anticancer compounds that are widely used owing to its remarkable tumorigenic potential. Today, amongst Actinobacteria, class Streptomyces subjugates the area of antibiotic production, producing 70% of all known antibiotics. The uniqueness of bioactive Actinobacteria has turned the attention of scientists worldwide in order to explore its potentiality as effective "micronanofactories". This study provides a brief overview of the production of antibiotics from Actinobacteria inhabiting diverse environments and the methods involved in the screening of antibiotics.

Twisted spatiotemporal optical vortex beams in dispersive media

We derive a closed-form expression for the mutual coherence function (MCF) of a twisted spatiotemporal optical vortex (STOV) beam after propagating a distance z in a linear dispersive medium. A twisted STOV beam is a partially coherent optical field that possesses a coherent STOV and a stochastic twist coupling its space and time dimensions. These beams belong to a special class of space–time-coupled light fields that carry transverse (to the direction of propagation) orbital angular momentum, making them potentially useful in numerous applications including quantum optics, optical manipulation, and optical communications. After presenting the derivation, we validate our new general MCF by showing that it simplifies to the MCFs for two example beams from the literature. Lastly, we present and analyze space–time beam profiles and complex arguments (phases) of the MCF at multiple z and differing amounts of material dispersion, field correlation or coherence, and beam twist to gain insight into how twisted STOV beams evolve in dispersive media. We conclude with a brief summary.

On the unicyclic graphs having vertices that belong to all their (strong) metric bases

A metric basis in a graph G is a smallest possible set S of vertices of G, with the property that any two vertices of G are uniquely recognized by using a vector of distances to the vertices in S. A strong metric basis is a variant of metric basis that represents a smallest possible set S′ of vertices of G such that any two vertices x,y of G are uniquely recognized by a vertex v∈S′ by using either a shortest x−v path that contains y, or a shortest y−v path that contains x. Given a graph G, there exist sometimes some vertices of G such that they forcedly belong to every metric basis or to every strong metric basis of G. Such vertices are called (resp. strong) basis forced vertices in G. It is natural to consider finding them, in order to find a (strong) metric basis in a graph. However, deciding about the existence of these vertices in arbitrary graphs is in general an NP-hard problem, which makes desirable the problem of searching for (strong) basis forced vertices in special graph classes. This article centres the attention in the class of unicyclic graphs. It is known that a unicyclic graph can have at most two basis forced vertices. In this sense, several results aimed to classify the unicyclic graphs according to the number of basis forced vertices they have are given in this work. On the other hand, with respect to the strong metric bases, it is proved in this work that unicyclic graphs can have as many strong basis forced vertices as we would require. Moreover, some characterizations of the unicyclic graphs concerning the existence or not of such vertices are given in the exposition as well.

Recent advances in employing the Laplace homotopy analysis method to nonlinear fractional models for evolution equations and heat-typed problems

This study stems from the growing need for effective mathematical tools to tackle nonlinear fractional evolution equations, which find wide applications in physics and engineering. Traditional methods often struggle to provide exact closed-form solutions for such equations, leading to the development of novel approaches. In this context, the combination of the homotopy analysis method with the Laplace transform presents a promising avenue for obtaining exact solutions to these complex equations. By exploring this hybrid approach, the study aims to address the existing challenges in solving nonlinear fractional models and provide a reliable method for obtaining closed-form solutions. In this way, this study focuses on rendering the coupling between the homotopy analysis approach and the Laplace transform in the search for exact closed-form solutions for the class of fractional evolution and heat-typed equations. In fact, this class of equations features some interesting nonlinear Caputo fractional partial differential equations that model dissimilar physical processes in physics and engineering. A generalized recurrent scheme is derived, which is applicable to all the members of the governing class, and further analyzed the application of this very scheme on some test fractional initial-value problems of much concern. Eventually, the method has been found to be advantageous, with various advantages, including convergence to available exact solutions. Thus, of the advantage of the current study is innovative combination of mathematical methods, the applicability of these methods to a special class of fractional equations, the development of a generalized scheme, the successful solution of prototype problems, and the practical advantages of the method.

On application of Gaussian kernels and Laplace functions combined with Kolmogorov's theorem for approximation of functions of several variables

A special class of approximations of measurable functions of several variables on the unit coordinate cube is investigated. The class is constructed on the base of Kolmogorov's theorem (in version by Sprecher–Golubkov) stating that a continuous function $f$ of several variables can be represented as a finite superposition of continuous single-variable functions — so called outer functions (which depend of $f$) and inner one $\Psi$ (which is independent of $f$ and is monotone). In the case of continuous functions $f$ the class under study is obtained with outer functions approximated by linear combinations of quadratic exponentials (also known as Gaussian functions or Gaussian kernels) and with the inner function $\Psi$ approximated by Laplace functions. As is known, a measurable function $f$ can be approximated by a continuous one (up to a set of small measure) with the help of classical Luzin's theorem. The effectiveness of such approach is based on assertions that, firstly, the Mexican hat mother wavelet on any fixed bounded interval can be approximated as accurately as desired by a linear combination of two Gaussian functions, and, secondly, that a continuous monotone function on such an interval can be approximated as accurately as desired by a linear combination of translations and dilations of the Laplace integral (in other words, Laplace functions). It is proved that the class of approximations under study is dense everywhere in the class of continuous multivariable functions on the coordinate cube. For the case of continuous and piecewise continuous functions of two variables, numerical results are presented that confirm the effectiveness of approximations of the studied class.

Multivortex traveling waves for the Schrödinger map equation

We construct traveling wave solutions for the Schrödinger map equation in R2. These solutions have n(n + 1)/2 pairs of degree ±1 vortices. The locations of those vortices are symmetric in the plane and determined by the roots of a special class of Adler–Moser polynomials. With a few modifications, a similar construction allows for the creation of traveling wave solutions of the Schrödinger map equation in R3. These solutions have the shape of 2n + 1 vortex rings, whose locations are given by a sequence of polynomials with rational coefficients and are far away from each other.

Pore structure characteristics of coral reef limestone: a combined polarizing microscope and CT scanning study

Coral reef limestone is a special class of geological medium formed through long-term deposition following the death of reef-building coral groups. Because it retains the skeletal structure of marine organisms during its formation, its pore structure is hyper-developed and complex. Deciphering the pore structure of the coral reef limestone is important because it is closely related to its macroscopic physical and mechanical properties. This study conducted a comprehensive analysis of the pore structure features of two types of coral reef limestone collected from the construction site of a nuclear power station located in the South China Sea using a combination of polarizing microscopy and CT scanning technologies. The fractal dimension of the pore structure of the treated reef limestone image was calculated, and the pore structure characteristics were statistically analyzed by considering several parameters including porosity, pore size, pore equivalent radius, shape factor, etc. In addition, the directional feature of the pore structure was explored. The results show that the improved watershed segmentation algorithm can accurately segment the pore structure of reef limestone images; both coral reef limestone specimens are loose of high porosity; the fractal dimension of pore structure lay between 1.58∼1.75, indicative of a high self-similarity; the pore size of the two coral reef limestone specimens is quite different, and the distribution of equivalent pore radius conforms to the normal distribution law; the pore structure of the two samples had obvious directionality, which can be quantified using a directional tensor. This study sheds light on future investigations linking the microscopic structure and macroscopic properties of coral reef limestones.

Credal identification of damage patterns in ultra-thin-ply composite bonded/bolted interference-fit joints

Investigating the mechanical behavior and damage patterns of ultra-thin-ply composite joints is essential for ensuring their widespread application in the aerospace field. It is currently an advanced method of exploring the damage patterns of composite joint structures via a combination of acoustic emission and machine learning algorithms. However, the existing research lacks the evaluation indexes for the determination of the number of damage categories, and on the other hand, the overlapping area and noise of the monitored damage data cannot be accurately identified. In this paper, load-bearing performance of ultra-thin-ply composite hybrid bonded/bolted interference-fit joints is studied, then the SDI(Structural Damage Index) evaluation index is proposed to quantitatively analyze the number of damage categories of the complex joints, and finally the adaptive optimization algorithm based on the credal partition for the complex joints of composite is studied. The experimental results demonstrate the accuracy and generalization of the SDI formulae, and the introduction of the credal partition that submits data where overlapping regions cannot be accurately identified to ensembles of special single classes (meta-clusters) obtains deeper insights into the damage data and improves identification and isolation of noise.

A new type Co(II)-based photocatalyst for the nitrofurantoin antibiotic degradation

Coordination polymers (CPs) are a special class of multidimensional materials that can be employed for the photocatalytic degradation of antibiotics in wastewater. In this paper, a new Co(II)-based coordination polymer with the molecular formula {[Co(H2L)(dpa)(H2O)]·H2O}n (1), (H4L = 1,1′:2′,1″-triphenyltetracarboxylic acid, dpa = 1,2-di(pyridin-4-yl)diazene) was synthesized and characterized. Single-crystal x-ray diffraction results showed that 1 formed a 2D layered structure, which was stacked into a three-dimensional (3D) supramolecular structure through hydrogen-bonding interactions. In addition, the results of the photocatalytic experiments showed that 1 possesses good photocatalytic activity at nitrofurantoin (NFT). The photocatalytic mechanism has been discussed in detail.

Improved inequalities between Dirichlet and Neumann eigenvalues of the biharmonic operator

We prove that the ( k + d ) (k+d) -th Neumann eigenvalue of the biharmonic operator on a bounded connected d d -dimensional ( d ≥ 2 ) (d\ge 2) Lipschitz domain is not larger than its k k -th Dirichlet eigenvalue for all k ∈ N k\in \mathbb {N} . For a special class of domains with symmetries we obtain a stronger inequality. Namely, for this class of domains, we prove that the ( k + d + 1 ) (k+d+1) -th Neumann eigenvalue of the biharmonic operator does not exceed its k k -th Dirichlet eigenvalue for all k ∈ N k\in \mathbb {N} . In particular, in two dimensions, this special class consists of domains having an axis of symmetry.

Development of Cell and Gene Therapies for Clinical Use in the US and EU: Summary of Regulatory Guidelines.

Recent decades have seen advancements in the management and treatment of difficult-- to-treat diseases such as cancer. A special class of therapeutics called cell and gene therapy has been introduced in the past 10 years. Cell and gene therapy products have strengthened the treatment options for life-threatening diseases with unmet clinical needs and also provided the possibility of a potential cure for the disease in some of the patients. Cell and gene therapy products are gaining recognition, and the interest in clinical development of cell and gene therapy products is increasing. Moreover, as the class of cell and gene therapy products is relatively new, there is a limited regulatory experience in the development, and the developers of the cell and gene therapy products can often be puzzled with an array of questions on regulations. The current review intends to provide a basic understanding of regulatory guidelines from the FDA and EMA that are applicable to cell and gene therapy products. Essentials such as which office is responsible for the evaluation of applications, which regulatory class/pathway is appropriate for development, and what are the quality, nonclinical and clinical studies that are needed to support the application are discussed in the article. In addition, a summary of regulatory designations and the post-approval requirements, such as Risk Evaluation and Mitigation Strategies (REMS) and long-term follow- up, is included in the article. Developers (referred to as 'sponsors' in this article) of cell and gene therapies can use the respective guidance documents and other specific review articles cited in this review for detailed information on the topics.

The hsa_circ_0082152 maintains NF-κB mRNA stability by binding to MTDH to promote anti-tuberculosis drug-induced liver injury

Anti-tuberculosis drug-induced liver injury (ADLI) is a common adverse reaction during anti-tuberculosis treatment and often leads to treatment interruptions. Circular RNAs (circRNAs) have been identified as key modulators in liver diseases. CircRNAs is a special class of noncoding RNAs that have been found to have significant impacts on the progression of inflammation via various mechanisms. In the serum of ADLI patients, upregulation of the circular RNA hsa_circ_0082152 (derived from the host gene snd1) was observed, along with increased ALT and AST levels, as well as alterations in the levels of inflammation-related factors such as NF-κB, IL-1β and TNF-α. To elucidate the underlying mechanisms, we established an HL-7702-ADLI cell model and confirmed similar upregulation of hsa_circ_0082152. Downregulation of hsa_circ_0082152 significantly inhibited inflammatory injury in ADLI cells, while upregulation had the opposite effect. RNA immunoprecipitation showed that hsa_circ_0082152 functions by interacting with metadherin (MTDH). Our study further verified that the interaction of hsa_circ_0082152 with the MTDH protein binding to NF-κB mRNA to maintain NF-κB mRNA stability, which increases the expression of NF-κB and its targets IL-1β and TNF-α. Conversely, depletion of MTDH rescued the promotive effect of hsa_circ_0082152 overexpression on ADLI inflammation. Therefore, hsa_circ_0082152 overexpression promotes ADLI progression via the MTDH/NF-κB axis.