Search

The notion of prime ideals is introduced in transitive BE-algebras. Prime ideals are characterized with the help of principal ideals. Prime ideal theorem is stated and derived for BE-algebras. The concept of minimal prime ideals is introduced in transitive BE-algebras. A decomposition theorem of proper ideals into minimal prime ideals is derived.

The concept of O-filters is introduced in commutative BE-algebras. An equivalent condition is derived for every strong regular filter of a BE-algebra to become an O-filter. The concept of quasi-complemented BE-algebras is introduced and also characterized these classes of BE-algebras in terms of dual annihilators. The concept of strong regular filter is introduced and then quasi-complemented BE-algebras and strong BE-algebras are characterized in terms of strong regular filters and O-filters.

In this paper, a Covid-19 pandemic model with five compartments is presented. Model assumptions, flowchart and the system of model equations are included. It is found that the solutions for the model equations exist and they are unique, positive and bounded. Hence, the present model is termed as mathematically well-posed and biologically meaningful. Mathematical analysis, sensitivity analysis are conducted in order to draw meaningful conclusions. Sensitivity analysis on the model equations reveal that the immunity loss has a positive impact while vaccination and treatment have negative impact on the effective reproduction number. The research results assert that the pandemic can be kept under control by enhancing vaccination and treatment facilities and similarly by implementing suitable methods to reduce loss of immunity. Outcomes of both qualitative and quantitative analyses are included and described elaborately. Disease free equilibrium point is identified and it's local and global stability analyses are conducted using powerful techniques like Routh-Hurwitz criteria and Lyapunov function method. Detailed description of the model is presented in the text of the paper lucidly. [ABSTRACT FROM AUTHOR]

BackgroundThe increasing usage of statins (the 3-hydroxy-3-methylglutaryl-coenzyme A reductase inhibitors) has revealed a number of unexpected beneficial effects, including a reduction in cancer risk.MethodsWe investigated the direct anticancer effects of different statins approved for clinical use on human breast and brain cancer cells. We also explored the effects of statins on cancer cells using in silico simulations.ResultsIn vitro studies showed that cerivastatin, pitavastatin, and fluvastatin were the most potent anti-proliferative, autophagy inducing agents in human cancer cells including stem cell-like primary glioblastoma cell lines. Consistently, pitavastatin was more effective than fluvastatin in inhibiting U87 tumour growth in vivo. Intraperitoneal injection was much better than oral administration in delaying glioblastoma growth. Following statin treatment, tumour cells were rescued by adding mevalonate and geranylgeranyl pyrophosphate. Knockdown of geranylgeranyl pyrophosphate synthetase-1 also induced strong cell autophagy and cell death in vitro and reduced U87 tumour growth in vivo. These data demonstrate that statins main effect is via targeting the mevalonate synthesis pathway in tumour cells.ConclusionsOur study demonstrates the potent anticancer effects of statins. These safe and well-tolerated drugs need to be further investigated as cancer chemotherapeutics in comprehensive clinical studies.

In this paper, we investigate the anisotropic and spatially homogeneous Bianchi type-I universe with Kaniadakis holographic dark energy in Saez–Ballester [Phys. Lett. A 113, 467 (1986)] theory of gravitation. We determine Kaniadakis holographic dark energy model by assuming a correlation between the metric potentials to solve the field equations of the model. This results in a dynamical deceleration parameter which demonstrates an accelerating expansion of the universe. Our model's equation of state parameter ω khde close to − 1 (Λ CDM model) at late-times and is in agreement with the most recent observations. Next, we obtained the squared sound speed ( v s 2 ) and found that it is positive, implying stability against perturbations. The ω khde − ω khde ′ plane is constructed to investigate the evolution of the models' EoS parameter turned out to be in a freezing zone. As should be the case in an expanding universe, the strong energy conditions of the model are violated. Statefinders (r , s) , and r − q planes were also examined. Our model includes the Chaplygin gas, Λ CDM limit, and is inclined towards the steady-state model. [ABSTRACT FROM AUTHOR]

The notion of divisibility is introduced in commutative BE-algebras. Some properties of the filters of multipliers are investigated in commutative BE-algebras. The concepts of prime elements and irreducible elements of commutative BE-algebras are introduced in terms of dual annihilators of BE-algebras. Finally, these elements are characterized in terms of prime filters and maximal filters respectively. [ABSTRACT FROM AUTHOR]

Effective deduction of air heating load and drag is a critical issue in hypersonic vehicle engineering applications. In this research, seven various geometrical models have been proposed to study and compare the effect of each configuration on the flow field, drag, and aerodynamic heating deduction under the same flow conditions. The presented configurations in this study: (a) bluntbody geometry as a reference of comparison, (b) blunt-body geometry with a spike, (c) blunt-body geometry with an counter flow jet, (d) blunt-body geometry with a spike and counter flow jet, (e) blunt-body geometry with a spike and aerodisk, (f) blunt-body geometry with a spike, aerodisk, and root counter flow jet, (g) blunt-body geometry with a spike, four aerodisks and root counter flow jet. The Reynolds-Averaged equations have been solved using the Finite Volume Method (FVM) along with the shear stress turbulence model (k-Ï SST). The flow is assumed compressible, steady-state, and axisymmetric with a free stream Mach number of 6. According to the study of each configuration's performance related to the parameters of drag, maximum pressure, and maximum heat flux factors on the blunt-body walls, (g) configuration with a drag factor of 0.2699, maximum pressure factor of 209.8, and maximum heat flux factor of 25.1, has the most deduction on the blunt-body walls among the seven configurations. The deduction percentage of drag, maximum pressure, and maximum heat flux factors of (g) configuration to (a) configuration are %72.1, %94.5, and %79.9, respectively, which significantly diminished drag and heat flux. Also, the best configuration scenarios for drag and aerodynamic heating deduction are geometrical models of g, f, d, e, c, b, and a, respectively. [ABSTRACT FROM AUTHOR]

The theory of rough sets has been classified into several directions where the information granules are generated using tolerances, pre-orders and binary relations. Maximal Compatibility Block (MCB) plays an important role in case of tolerance relations. In the present work, the lattice structure of rough sets generated by MCBs is explored. The concepts are applied to establish equivalence between the isomorphism of graphs with isomorphism of rough lattices constructed using MCBs. [ABSTRACT FROM AUTHOR]

The notion of skew-simple BE-algebras is introduced and derived an equivalent assertions for every skew-simple BE-algebra to become semi-simple. The concept of radical of filters is introduced in a BE-algebra and certain properties of these radicals are derived in terms of direct products and homomorphisms. The concept of semi-maximal filters is introduced in BE-algebras. Some equivalent assertions are derived for every semi-maximal filter to become a maximal filter. Properties of semi-maximal filters are derived in terms of homomorphisms and congruences. [ABSTRACT FROM AUTHOR]

Let's denote $\mathcal{S}^{\ast}(f_c)$ as a family of analytic functions $f(z)=z+a_2z^2+a_3z^3+\cdots$ in the open unit disk $\mathbb{D}$ that satisfy the following relation for $c\in (0,1)$:$$\frac{zf'(z)}{f(z)}\prec f_c(z)=\frac{1}{\sqrt{1-cz}}, \quad z\in\mathbb{D}.$$First, we introduce the analytic functions $f_c(z)$ and examine their starlike and positivity properties of the real part. Then, we obtain their images in the open unit disk $\mathbb{D}$, which are Cassini ovals. Cassini ovals, due to their properties, have applications in solving various problems in fields such as geometry, physics, and mathematics. These curves are used in studying the motion of waves and electromagnetic waves in interstellar spaces, as well as in the design of engineering structures such as telescopes. In this article, with the help of integrals, we investigate the structure of mappings in this family and some properties including maximum and minimum moduli, bounds of the real part of these functions. Moreover, we obtain the relationships between the defined geometric ranks with this family, including the order of starlikeness and order of strong starlikeness.1. IntroductionLet $\mathcal{A}$ be a set of analytic functions of the form $f(z)=z+a2z^2+a3z^3+\cdots$ in the open unit disc $\mathbb{D}:=\left\{z\in\mathbb{C}\colon |z|\beta\right\},\quad \mathcal{K}(\beta):=\left\{f\in\mathcal{A}\colon zf'(z)\in\mathcal{S}^{\ast}(\beta)\right\}.\end{equation}Similarly, in [2], the class of functions called strongly starlike with order $0

Uterus transplantation (UTx) is fast evolving from an experimental to a clinical procedure, combining solid organ transplantation with assisted reproductive technology. The commencement of the first human uterus transplant trial in the United Kingdom leads us to examine and reflect upon the legal and regulatory aspects closely intertwined with UTx from the process of donation to potential implications for fertility treatment and the birth of the resultant child. As the world's first ephemeral transplant, the possibility of organ restitution requires consideration and is discussed herein. Uterine transplantation warrants a closer look at the legal frameworks on fertility treatment and transplantation in England. Uterine transplantation warrants a closer look at the legal frameworks on fertility treatment and transplantation in England. [ABSTRACT FROM AUTHOR]

Abstract: The notion of generalized lower sets is introduced in transitive BE-algebras. Some properties of generalized lower sets are investigated in transitive BE-algebras. Furthermore, a sufficient condition is derived for every generalized lower set BE-algebra to become an ideal. [ABSTRACT FROM AUTHOR]

A simulation on the overestimation or underestimation of multiregional input-output model confirms that the model overestimates interregional intermediate outputs (INOUs) and underestimates intraregional INOUs in cases where strong interconnectedness and general enhancement in final demands exist. Overestimation of sectorial outputs and INOUs of sectors whose products are not in demand was the tendency in instances of economies with weak spatial interconnection and mixed shift in the direction of final-demands shocks.

The concept of regular filters is introduced in commutative BE-algebras. The class of all regular filters of a commutative BE-algebra is characterized in terms of dual annihilators. Some equivalent conditions are derived for every filter of a commutative BE-algebra to become a regular filter. Some properties of prime regular filters of a commutative BE-algebra are investigated. [ABSTRACT FROM AUTHOR]

The notion of ideals is introduced in transitive BE-algebras. Some characterization theorems of ideals of transitive BE-algebras are derived. The notion of semi-ideals is introduced and studied a relationship between semi-ideals and ideals. Properties of ideals are studied with the help of homomorphisms and congruences. [ABSTRACT FROM AUTHOR]

The concept of radicals of ideals is introduced in BE-algebras and certain properties of these radicals are derived in terms of direct products and homomorphisms. The notion of semi-maximal ideals is introduced in BE-algebras through the radical of ideals and their significant properties are investigated. Some equivalent conditions are derived for every semi-maximal ideal to become a maximal ideal. [ABSTRACT FROM AUTHOR]

The notion of -filters is introduced on the lines of a dual annihilator of commutative BE-algebras. An equivalent condition is given for a proper ω-filter of a commutative BE-algebra to become a prime filter. A characterization theorem of ω-filters is established which in turn establishes some of equivalent conditions for a prime filter of a commutative BE-algebra to become an ω-filter. It is proved that every ω-filter is an intersection of all minimal prime filters. [ABSTRACT FROM AUTHOR]