Ternary Weighted Function and Beurling Ternary Banach Algebra l

Let S be a ternary semigroup. In this paper, we introduce our notation and prove some elementary properties of a ternary weight function ω on S. Also, we make ternary weighted algebra l1ω(S) and show that l1ω(S) is a ternary Banach algebra

Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem

In this paper, we introduce the concept of ternary antiderivation on ternary Banach algebras and investigate the stability of ternary antiderivation in ternary Banach algebras, associated to the $(\alpha,\beta)$-functional inequality: \begin{align*} &\Vert \mathcal{F}(x+y+z)-\mathcal{F}(x+z)-\mathcal{F}(y-x+z)-\mathcal{F}(x-z)\Vert \nonumber\\ &\leq \Vert \alpha (\mathcal{F}(x+y-z)+\mathcal{F}(x-z)-\mathcal{F}(y))\Vert + \Vert \beta (\mathcal{F}(x-z)\\ &+\mathcal{F}(x)-\mathcal{F}(z))\Vert \end{align*} where $\alpha$ and $\beta$ are fixed nonzero complex numbers with $\vert\alpha \vert +\vert \beta \vert<2$ by using the fixed point method

A system of additive functional equations in complex Banach algebras

In this article, we solve the system of additive functional equations: fx y gx gy gx y f y x fx 2 , 2 4 ⎧ ⎨ ⎩ ( ) () () ( ) ( ) () +− = +− −= and prove the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of f -hom-ders in Banach algebras

A Pexider system of additive functional equations in Banach algebras

Abstract In this paper, we solve the system of functional equations { f ( x + y ) + g ( y − x ) = 2 f ( x ) , g ( x + y ) − f ( y − x ) = 2 g ( y ) $$\begin{aligned} \textstyle\begin{cases} f(x+y)+g(y-x)=2f(x), \\ g(x+y)-f(y-x)=2g(y) \end{cases}\displaystyle \end{aligned}$$ and we investigate the stability of g-derivations in Banach algebras

A practical approach for distribution network load balancing by optimal re‐phasing of single phase customers using discrete genetic algorithm

Voltage and current imbalance have adverse impacts on power systems such as power loss increase, communication interference, and component lifetime reduction. This paper attempts to look at unbalance impacts from distribution system operator's (DSO) viewpoint in order to understand them and then mitigate the impacts. Since solving the unbalance conditions is influenced by the way the imbalance is defined, standard unbalance indexes are studied, and new indexes are proposed in this paper. Re-phasing of the customers is selected to reduce the level of unbalance in distribution feeders. Due to the huge number of customers, a wide variety of choices can be selected for re-phasing of customers, which makes the solution questionable. Therefore, discrete genetic algorithm (DGA) as a metaheuristic method has been utilized in order to distribute customers among the network phases optimally considering the fact that DSO has a limitation for the re-phasing practice. The aim is to reduce the unbalance indexes and power losses throughout the network. Simulations have been carried out on a real test case network, which shows the importance of load balancing and its effects on the power losses, voltage profile, and current flow in that network. The effectiveness of the proposed indexes has also been demonstrated for the four-wire multigrounded distribution system. Since re-phasing of the majority of customers in distribution networks seems impractical, a re-phasing limitation is also investigated in this paper, and some practical suggestions of optimal load balancing in a real-world low-voltage distribution system have been presented here. Results show the importance of load balancing in power loss reduction and voltage unbalance improvement in the low-voltage four-wire multigrounded distribution system. They also illustrate that by changing phases of a few customers, power losses and unbalance indexes will be improved significantly.acceptedVersionPeer reviewe

Stability Results for Some Classes of Cubic Functional Equations

Applications involving functional equations (FUEQs) are commonplace. They are essential to various applications, such as fog computing. Ulam’s notion of stability is highly helpful since it provides a range of estimates between exact and approximate solutions. Using Brzdȩk’s fixed point technique (FPT), we establish the stability of the following cubic type functional equations (CFUEQs): Fξ13+ξ233+Fξ13−ξ233=2F(ξ1)+2F(ξ2),2Fξ13+ξ2323=F(ξ1)+F(ξ2) for all ξ1,ξ2∈R

Delayed Esophageal Pseudodiverticulum after Anterior Cervical Spine Fixation: Report of 2 Cases

Introduction: Although perforation of the esophagus, in the anterior cervical spine fixation, is well established, cases with delayed onset, especially cases that present pseudodiverticulum, are not common. In addition, management of the perforation in this situation is debated.  Case Report:   Delayed esophageal pseudodiverticulum was managed in two patients with a history of anterior spine fixation. Patients were operated on, the loose plate and screws were extracted, the wall of the diverticulum was excised, the perforation on the nasogastric tube was suboptimally repaired, and a closed suction drain was placed there. The NGT was removed on the 7th day and barium swallow demonstrated no leakage at the operation site; therefore, oral feeding was started without any problem.  Conclusion:  In cases with delayed perforation, fistula, or diverticulum removal of anterior fixation instruments, gentle repair of the esophageal wall without persistence on definitive and optimal perforation closure, wide local drainage, early enteral nutrition via NGT, and antibiotic prescription is suggested

Guest Editorial: Energy storage for green transition of electrical grids

Energy storage systems (ESSs) are needed in the smart grids both at the generation, transmission, and distribution levels, and different types of ESSs have widely different characteristics and are suitable for different tasks and situations. In recent years, the smart grid concept has been dramatically developed in different applications, such as islands, shipboards, aircraft, microgrids and grid integration of renewables. With the wide application of ESS in smart grids, significant technical challenges remain along with the enhancement of smart grid operations and services. These challenges can be categorised as control of ESS, optimal operation, and energy management systems, optimal design of hybrid ESS, protection of ESS, and power electronics for ESS connections. This necessitates suitable design and control of the interfaces between ESSs in smart grids, as well as consideration of different applications of smart grid systems. This special issue of IET smart grid is focused on research ideas, articles, and experimental studies related to ‘Energy Storage for Green Transition of Electrical Grids’ from contributors in universities, industries, and research laboratories to develop and propose novel solutions on applications of ESS in smart grids

Decentralized Multi-Objective Energy Management With Dynamic Power Electronic Converters and Demand Response Constraints

Energy management plays a pivotal role in enhancing the economic efficiency of power systems. However, it is noteworthy that a substantial number of microgrids (MGs) exhibit inherent unbalances that impose a range of critical issues, including voltage instability, elevated losses, power quality violations, safety concerns, and inefficiencies in energy management. Fast-acting power electronic converters present a relevant and efficacious solution for balancing such complex networks. This paper investigates the application of such converters within the realm of 3-phase unbalanced networks, wherein the proposed algorithm not only ameliorates network imbalances but also yields substantial reductions in operational costs, power losses, voltage deviations, and emissions. Demand response (DR) program has been applied to the model to enhance the system efficiency. The uncertainty about electric demand and renewable energy sources is considered in the simulation model for precise results. By implementing DR programs and penetrating distributed generators (DGs), the proposed model has been shown to reduce network losses and operation costs by 23&#x0025; and 80&#x0025;, respectively. Also, the total up-to-down voltage deviation of the voltage profile has been significantly reduced by 400&#x0025;

In- vitro corrosion behavior of the cast and extruded biodegradable Mg-Zn-Cu alloys in simulated body fluid (SBF)

In the present study, a new biodegradable Mg-Zn-Cu magnesium alloy was introduced for biological applications. The microstructural analysis showed the formation of MgZnCu intermetallics for the Mg-2Zn-0.1Cu alloy and also the Mg(Zn,Cu)2 compounds for the Mg-2 Zn alloys with higher Cu contents. Moreover, the hot extrusion was applied for the grain refinement and changing the distribution of intermetallics. In vitro immersion tests, electrochemical and corroded surface analyses represented the enhancement of corrosion resistance with 0.1 wt.% Cu addition. Furthermore, the extruded alloys demonstrated more corrosion resistance behavior than that of the cast alloys. By considering the improved tensile properties of Mg-2Zn-0.1Cu alloy, this alloy was regarded as the potential candidate for use as the biodegradable magnesium implant