Complex linear Diophantine fuzzy sets and their cosine similarity measures with applications

In this paper, the concept of complex linear Diophantine fuzzy set (CLDFS), which is obtained by integrating the phase term into the structure of the linear Diophantine fuzzy set (LDFS) and thus is an extension of LDFS, is introduced. In other words, the ranges of grades of membership, non-membership, and reference parameters in the structure of LDFS are extended from the interval [0, 1] to unit circle in the complex plane. Besides, this set approach is proposed to remove the conditions associated with the grades of complex-valued membership and complex-valued non-membership in the framework of complex intuitionistic fuzzy set (CIFS), complex Pythagorean fuzzy set (CPyFS), and complex q-rung orthopair fuzzy set (Cq-ROFS). It is proved that each of CIFS, CPyFS, and Cq-ROFS is a CLDFS, but not vice versa. In addition, some operations and relations on CLDFSs are derived and their fundamental properties are investigated. The intuitive definitions of cosine similarity measure (CSM) and cosine distance measure (CDM) between two CLDFSs are introduced and their characteristic principles are examined. An approach based on CSM is proposed to tackle medical diagnosis issues and its performance is tested by dealing with numerical examples. Finally, a comparative study of the proposed approach with several existing approaches is created and its advantages are discussed.

Implications of Glycosaminoglycans on Viral Zoonotic Diseases

Zoonotic diseases are infectious diseases that pass from animals to humans. These include diseases caused by viruses, bacteria, fungi, and parasites and can be transmitted through close contact or through an intermediate insect vector. Many of the world’s most problematic zoonotic diseases are viral diseases originating from animal spillovers. The Spanish influenza pandemic, Ebola outbreaks in Africa, and the current SARS-CoV-2 pandemic are thought to have started with humans interacting closely with infected animals. As the human population grows and encroaches on more and more natural habitats, these incidents will only increase in frequency. Because of this trend, new treatments and prevention strategies are being explored. Glycosaminoglycans (GAGs) are complex linear polysaccharides that are ubiquitously present on the surfaces of most human and animal cells. In many infectious diseases, the interactions between GAGs and zoonotic pathogens correspond to the first contact that results in the infection of host cells. In recent years, researchers have made progress in understanding the extraordinary roles of GAGs in the pathogenesis of zoonotic diseases, suggesting potential therapeutic avenues for using GAGs in the treatment of these diseases. This review examines the role of GAGs in the progression, prevention, and treatment of different zoonotic diseases caused by viruses.

Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making

In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their uncertain linguistic terms to handle problematic and challenging data in factual life impasses. By using the elaborated CLDULSs, some operational laws are also settled. Furthermore, by using the power Einstein (PE) aggregation operators based on CLDULS: the complex linear Diophantine uncertain linguistic PE averaging (CLDULPEA), complex linear Diophantine uncertain linguistic PE weighted averaging (CLDULPEWA), complex linear Diophantine uncertain linguistic PE Geometric (CLDULPEG), and complex linear Diophantine uncertain linguistic PE weighted geometric (CLDULPEWG) operators, and their useful results are elaborated with the help of some remarkable cases. Additionally, by utilizing the expounded works dependent on CLDULS, I propose a multi-attribute decision-making (MADM) issue. To decide the quality of the expounded works, some mathematical models are outlined. Finally, the incomparability and relative examination of the expounded approaches with the assistance of graphical articulations are evolved.

Ultralong π-Conjugated Bis(terpyridine)metal Polymer Wires Covalently Bound to a Carbon Electrode: Fast Redox Conduction and Redox Diode Characteristics

We developed an efficient and convenient electrochemical method to synthesize π-conjugated redox metal-complex linear polymer wires composed of azobenzene-bridged bis(terpyridine)metal (2-M, M = Fe, Ru) units covalently immobilized on glassy carbon (GC). Polymerization proceeds by electrochemical oxidation of bis(4′-(4-anilino)-2,2′:6′,2″-terpyridine)metal (1-M) in a water–acetonitrile–HClO4 solution, affording ultralong wires up to 7400 mers (corresponding to ca. 15 μm). Both 2-Fe and 2-Ru undergo reversible redox reactions, and their redox behaviors indicate remarkably fast redox conduction. Anisotropic hetero-metal-complex polymer wires with Fe and Ru centers are constructed via stepwise electropolymerization. The cyclic voltammograms of two hetero-metal-complex polymer wires, GC/[2-Fe]–[2-Ru] (3) and GC/[2-Ru]–[2-Fe] (4), show irreversible redox reactions with opposite electron transfer characteristics, indicating redox diodelike behavior. In short, the present electrochemical method is useful to synthesize polymer wire arrays and to integrate functional molecules on carbon.

ON AN INTEGRAL OF -BESSEL FUNCTIONS AND ITS APPLICATION TO MAHLER MEASURE

Cogdell et al. [‘Evaluating the Mahler measure of linear forms via Kronecker limit formulas on complex projective space’, Trans. Amer. Math. Soc. (2021), to appear] developed infinite series representations for the logarithmic Mahler measure of a complex linear form with four or more variables. We establish the case of three variables by bounding an integral with integrand involving the random walk probability density $a\int _0^\infty tJ_0(at) \prod _{m=0}^2 J_0(r_m t)\,dt$ , where $J_0$ is the order-zero Bessel function of the first kind and a and $r_m$ are positive real numbers. To facilitate our proof we develop an alternative description of the integral’s asymptotic behaviour at its known points of divergence. As a computational aid for numerical experiments, an algorithm to calculate these series is presented in the appendix.

On Stability of a General Bilinear Functional Equation

We prove the Hyers–Ulam stability of the functional equation $$\begin{aligned}&f(a_1x_1+a_2x_2,b_1y_1+b_2y_2)=C_{1}f(x_1,y_1)\nonumber \\ \nonumber \\&\quad +C_{2}f(x_1,y_2)+C_{3}f(x_2,y_1)+C_{4}f(x_2,y_2) \end{aligned}$$ f ( a 1 x 1 + a 2 x 2 , b 1 y 1 + b 2 y 2 ) = C 1 f ( x 1 , y 1 ) + C 2 f ( x 1 , y 2 ) + C 3 f ( x 2 , y 1 ) + C 4 f ( x 2 , y 2 ) in the class of functions from a real or complex linear space into a Banach space over the same field. We also study, using the fixed point method, the generalized stability of $$(*)$$ ( ∗ ) in the same class of functions. Our results generalize some known outcomes.

Dual exponential polynomials and a problem of Ozawa

Complex linear differential equations with entire coefficients are studied in the situation where one of the coefficients is an exponential polynomial and dominates the growth of all the other coefficients. If such an equation has an exponential polynomial solution $f$ , then the order of $f$ and of the dominant coefficient are equal, and the two functions possess a certain duality property. The results presented in this paper improve earlier results by some of the present authors, and the paper adjoins with two open problems.