An ideal-based cozero-divisor graph of a commutative ring

Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this article, we introduce the cozero-divisor graph $\acute{\Gamma}_I(R)$ of $R$ and explore some of its basic properties. This graph can be regarded as a dual notion of an ideal-based zero-divisor graph.

Reconstruction of the ZnAl Mixed Oxides Into the Layered Double Hydroxide Catalysts Active in the Aldol Condensation of Furfural: The Role of ZnO Particles

A memory effect is the ability to restore the original, lamellar layered double hydroxide structure. Herein, we have described 1) the changes in the structural and basic properties of ZnAl mixed oxides during their transformation into ZnAl-reconstructed LDHs (RE-LDHs); 2) the extraordinary properties of ZnAl RE-LDHs compared to the original ZnAl LDHs; and 3) the changes of basic properties during the interaction of ZnAl RE-LDHs with atmospheric CO2. Aldol condensation was selected as probe reaction to prove the catalytic potential of ZnAl RE-LDHs. We have described a target method for preparing ZnAl RE-LDHs with a large number of basic sites. ZnAl RE-LDHs possess significantly higher furfural conversion in the aldol condensation of furfural than MOs. The structural, textural, and basic properties of the studied materials were described by temperature-programmed analysis, X-ray diffraction, N2 adsorption, temperature-programmed desorption of CO2, and in-situ diffuse reflectance spectroscopy.

Some further studies on strong ℐλ-statistical convergence in probabilistic metric spaces

We prove some basic properties of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical convergence of sequences in probabilistic metric spaces and introduce the notion of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical cluster point. We also introduce the notion of strong ℐ λ {\mathcal{I}_{\lambda}} -statistical Cauchy sequences in probabilistic metric spaces. Further, we establish a connection between strong ℐ λ {\mathcal{I}_{\lambda}} -statistical convergence and strong ℐ λ {\mathcal{I}_{\lambda}} -statistical Cauchy sequences.

A New Model of Fuzzy Logic: Monadic Monoidal T-Norm Based Logic

In this article, we introduce the variety of monadic MTL-algebras as MTL-algebras equipped with two monadic operators. After a study of the basic properties of this variety, we define and investigate monadic filters in monadic MTL-algebras. By using the notion of monadic filters, we prove the subdirect representation theorem of monadic MTL-algebras and characterize simple and subdirectly irreducible monadic MTL-algebras. Moreover, present monadic monoidal t-norm based logic (MMT L), a system of many valued logic capturing the tautologies of monadic MTL-algebras and prove a completeness theorem.AMS Classification: 08A72, 03G25, 03B50, 03C05.

Synthesis of poly-tetrahydropyrimidine antibacterial polymers and research of their basic properties

Modern medicine has increasingly higher requirements for antibacterial materials. In order to overcome this challenge, we use alkynyl monomers, amino monomers, formaldehyde, and acetic acid as raw materials to synthesize...

Liquid metal biomaterials for biomedical imaging

Liquid metals (LMs) not only retain the basic properties of metallic biomaterials, such as high thermal conductivity, high electrical conductivity, but also possess flexibility, flowability, deformability, plasticity, good adhesion, and...

GENERALIZED MULTIVARIATE PRABHAKAR TYPE FRACTIONAL INTEGRALS AND INEQUALITIES

We introduce here the mixed generalized multivariate Prabhakar type left and right fractional integrals and study their basic properties, such as preservation of continuity and their boundedness as positive linear operators. Then we produce an interesting variety of related multivariate left and right fractional Hardy type inequalities under convexity. We introduce also other related multivariate fractional integrals

Post-Quantum Two-party Adaptor Signature Based on Coding Theory

An adaptor signature can be viewed as a signature concealed with a secret value and, by design, any two of the trio yield the other. In a multiparty setting, an initial adaptor signature allows each party create additional adaptor signatures without the original secret. Adaptor signatures help address scalability and interoperabity issues in blockchain. They can also bring some important advantages to cryptocurrencies, such as low on-chain cost, improved transaction fungibility, and less limitations of a blockchain’s scripting language. In this paper, we propose a new two-party adaptor signature scheme that relies on quantum-safe hard problems in coding theory. The proposed scheme uses a hash-and-sign code-based signature scheme introduced by Debris-Alazard et al. and a code-based hard relation defined from the well-known syndrome decoding problem. To achieve all the basic properties of adaptor signatures formalized by Aumayr et al., we introduce further modifications to the aforementioned signature scheme. We also give a security analysis of our scheme and its application to the atomic swap. After providing a set of parameters for our scheme, we show that it has the smallest pre-signature size compared to existing post-quantum adaptor signatures.

Perspectives of Electricity Storage in Polymer Capacitors

The price and environmental aspects of electricity storage significantly affect the application of green technologies. The electrochemical batteries are currently the best choice for storing electricity for most industrial needs and products. Polymer capacitors show very low energy density compared to conventional batteries and therefore cannot be widely used for electricity disposal. At the same time, all other features of polymer capacitors that characterize battery systems are ideal. After a brief comparison of the basic properties of electrochemical and physical batteries, this paper presents the influence of electron trapping on the energy density of a polyethylene capacitor. The presented results indicate that the phenomenon of electron trapping in polymers can increase the energy deposit of polymer capacitors.