In this paper, we study fuzzy calculus in two main branches differential and integral. Some rules for finding limit and gH -derivative of gH -difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating gH -derivative of a composite function. Two techniques namely, Leibniz’s rule and integration by parts are introduced for fuzzy integrals. Furthermore, we prove three essential theorems such as a fuzzy intermediate value theorem, fuzzy mean value theorem for integral and mean value theorem for gH -derivative. We derive a Bolzano’s theorem, Rolle’s theorem and some properties for gH -differentiable functions. To illustrate and explain these rules and theorems, we have provided several examples in details.

Developing hard items with complicate calculation algorithms cause to in appropriate trends such as teaching to the test and test preparation strategies in examinees. Having exact educational standards and applying taxonomy models, however, will help to obtain fine evaluation of educational programs, contents and students achievement. In this manuscript, a small sample of differential calculi multiple choice items test has been studied in behavioral objectives framework which is based on combining the Bloom and Web approaches; the goal was to illustration of capability-complexity approach in taxonomy of test items. Twenty items of a 30 items test battery which administered on a 3409 sample of students has been classified by capability-complexity approach. Outcomes of 3 items have been reported in this article. Results had shown all the test items measuring procedural knowledge at level three. 92% of items were abstract, and simultaneously recalling multiple calculation algorithms require for responding correctly to each item. Tasks with one calculation algorithm and lower complexity had better statistical parameters such as scalability and their item information functions yielded much more information about examinees capability.

Critical theory has always been unders tood by contemporary philosophy and sociology as something definite and “known” that finds its main roots in Hegelian-Marxis t negation. But less attention has been paid to the ques tion of whether other lineages and societies can be discovered or “invented” for it? Leibniz can be considered a philosopher who, through the lens of his differential philosophy, exerted a marginal but powerful influence on critical theory. Here it is shown how the three aes thetic concepts: Inequality, Autonomy and Harmony, are rooted in a kind of differential calculus and can be explained using concepts such as Identity, Monad and Com-Possibility. In addition to identifying the Leibnizian roots of negative aes thetics, the ques tion has also been raised as to how these concepts relate to differential concepts. Apart from the concept of Inequality in Adorno’s thought, which is somehow in antagonis tic relation to the Principle of Identity, the other two concepts can be considered as philosophical-aes thetic forms of mathematical-physical concepts,In a way, the Autonomic Art was shown to be a kind of monad, and Harmony was shown as a form of Continuity. The idea of ​​how a philosophical theory can be inspired by new mathematics or physics should be considered the mos t promising achievement of this research.

Introduction: In this paper, the solution of fuzzy differential inclusions (FDIs) with Lower-Upper Representation is established.Aim: Finding an approximate solution of fuzzy differential inclusions.Materials and Methods: Instead of a precise fuzzy number as an initial value, we have just some information in some a -cuts of it, which shows the value of initial value at the endpoints of a -cuts and also the slopes of the fuzzy number's membership function in the mentioned points.Results: Using the intervals formed with the a -cut of initial value we apply the Euler method and solve the FDIs to find the same information for the solution of the given problem.Also to determine the slopes of the estimated fuzzy solution again we use the Euler method and solve the fuzzy differential equations (FDEs). Finally with an specific interpolation polynomial we obtain the approximated solution.Conclusion: The method presented in this paper is based on the LU-representation of fuzzy numbers with N=1. We find the solution set just in two a -cuts and then the approximate solution will introduce via interpolation polynomials.

Introduction: The theory and application of linear and nonlinear delay differential equations is an important subject within physics and applied mathematics.There are several numerical approaches for solving linear and nonlinear delay differential equations.Aim: In this paper, differential transform method (DTM) is applied to numerical solution of linear and nonlinear delay differential equations.Materials and Methods: In this work, we presented simple proofs of the differential transform Theorems and then we applied them to solving linear and nonlinear delay differential equations.Results: Numerical results compared to exact solutions are reported and it is shown that DTM is a reliable tool for the solution of delay differential equations.Conclusion: The present method reduces the computational difficulties of the other traditional methods and all the calculations can be made simple manipulations. Several examples were tested by applying the DTM and the results have shown remarkable performance.

Can users decide on the status of the accounts he used in cyberspace to create, receive, send, transfer, store or display information, after their death, through a will? It seems that due to the financial value of the accounts and the information contained therein, as well as the rule of jurisprudence of dominance, users have the right to transfer the account and its content or leave their management to other in the form of a will for various purposes. However, many digital account service companies use existing legal loopholes to resist users 'wills under various pretexts, such as violating users' privacy or the non-transferability of the account and its contents. Considering the legal gap in Iranian legal system and many other countries in determining the fate of digital accounts after the death of users and also the insufficiency of the legal literature in this field, this study, attempts to examine the possibility and validity of a person's will to the digital account and information. Assessing the issue and applying legal rules leads us to the conclusion that users can make a will about the information contained in their account under particular circumstances, and such a will would be valid.