Optimal planning of resources with daily/real time resource management is important for obtaining the most benefit from microgrids. There exist several mathematical models and heuristic rule based policies for microgrid resource management. Mathematical models provide optimal results, while heuristic policies are simple to implement but cannot guarantee optimality. Although both models are used in the literature, studies do not analyze the benefits of using mathematical models over heuristic rule based ones. This study proposes a mixed integer programming based mathematical model and a rule based model and compares their performances for a newly established microgrid at Turkey. Both models aim to minimize the daily cost of the microgrid by planning the use, sale, and storage of the energy obtained from the renewable resources. The results quantify the benefits of using the mathematical model over the rule based model for the case microgrid under different conditions. The analysis shows that the difference between the models' performances changes according to the energy pricing policy and seasons. Under certain conditions, the simple rule based policy can provide close to optimal results.

To determine the most suitable acquisition model, or to decide whether or not the model they have already chosen is functioning efficiently and economically, librarians must carry out relevant evaluations of their current or potential acquisition models. In this study, an evaluation of the Cambridge evidence-based acquisition (EBA), was carried out at Hacettepe University Libraries between December 16, 2019, and December 31, 2020. Within the scope of the EBA, the number of e-books opened for access was 35,624, the number of unique books used was 2,462 and the number of the books purchased at the end of the model was 168. In total, the books were used 36,934 times. Ninety-three percent of the books were never used during the EBA model implementation term. While 52 percent of the books opened for access consisted of “books for research,” 47 percent of the number of unique books used consisted of “coursebooks.” Usage cost per unit was calculated as 0.82 USD, and the average book cost was calculated at 180 USD. Purchasing the books based on their list price was a reason for the high average book cost; nevertheless, one should consider that the entire collection of books was open for access for a year-long period of evaluation. In addition, one should not forget that further usage of e-books from the entire collection would decrease the unit cost of the books in the final purchase. During the implementation term, we observed that the Cambridge EBA Model was a suitable option for Hacettepe University Libraries.

BCK/BCI-algebra is a class of logical algebras that was defined by K. Iseki and S. Tanaka. BCK-algebras have a lot of generalizations. One of them is d-algebras. Near set theory which is a generalization of rough set theory. This theory is based on the determination of universal sets according to the available information of the objects. Based on the image analysis, the near set theory was created. Oztu¨rk applied the¨ notion of near sets defined by J. F. Peters to the theory of d-algebras. In this paper we introduce upper-nearness d-ideal, upper-near (upper nearness) d # -ideal, upper-near (upper-nearness) d∗-ideal. We explored what conditions we should put on the ideal for quotient nearness d-algebra to become an nearness d-algebra again. Finally, we introduce quotient nearness d-algebras with the help of upper-nearness d∗-ideals of nearness d-algebras.MSC Classification: 03E75 , 03E99 , 03F55 , 06F35 , 06S40

In the paper we examined the some effects of derivation, trace of permuting tri-derivation and endomorphism on each other in prime and semiprime ring.Let $R$ be a $2,3$-torsion free prime ring and $F:R\times R\times R\rightarrow R$ be a permuting tri-derivation with trace $f$, $ d:R\rightarrow R$ be a derivation. In particular, the following assertions have been proved:1) if $[d(r),r]=f(r)$ for all $r\in R$, then $R$ is commutative or $d=0$ (Theorem 1);\ 2) if $g:R\rightarrow R$ is an endomorphism such that $F(d(r),r,r)=g(r)$ for all $r\in R$, then $F=0$ or $d=0$ (Theorem 2); 3) if $F(d(r),r,r)=f(r)$ for all $r\in R$, then $(i)$ $F=0$ or $d=0$, $(ii)$ $d(r)\circ f(r)=0$ for all $r\in R$ (Theorem 3). In the other hand, if there exist permuting tri-derivations $F_{1},F_{2}:R\times R\times R\rightarrow R$ such that $F_{1}(f_{2}(r),r,r)=f_{1}(r)$ for all $r\in R$, where $f_{1}$ and $%f_{2}$ are traces of $F_{1}$ and $F_{2}$, respectively, then $(i)$ $F_{1}=0$ or $F_{2}=0$, $(ii)$ $f_{1}(r)\circ f_{2}(r)=0$ for all $r\in R$ (Theorem 4).

An MV-algebra is an algebraic structure with a binary operation ⊕, a unary operation ′ and the constant 0 satisfying certain axioms. MV-algebras are the algebraic semantics of Lukasiewicz logic. This work includes a type of derivation research on MV-algebras. Our aim is to introduce the concept of permuting tri-derivation on MV-algebras and to discuss some results.