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 ...

In this paper a new family of methods free from second derivative is presented. This new family of methods is constructed such that convergence is of order three and requires two require two evaluations of the function and first derivative per iteration. To illustrate the efficiency and performance of the new family of methods, several numerical examples are presented. Further numerical compari...

Traditionally, syllogisms are arguments with two premises and one conclusion which are constructed by propositions of the form “All... are...” and “At least one... is...” and their respective negated versions. Unfortunately, the practical use of traditional syllogisms is quite restricted. On the one hand, the “All...” propositions are too strict, since a single counterexample suffices for falsi...

two modified methods for assaying sodium diclofenac were developed by gc and hplc. diclofenac was converted into methyl ester derivative by methyl iodide in acetone. the ester was extract and subjected to glc with flame ionization detector. %5 se-30/chrom w-hp (80-100 mesh) was used as a column in gc. for reversed phase hplc, the mobile phase was methanol and water (55-45). the separation was p...

In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools ...

Two simple and rapid spectrophotometric methods were developed for the determination of two binary mixtures: moxifloxacin hydrochloride (MFH) with ketorolac tromethamine (KTM) and ciprofloxacin hydrochloride (CFH) with dexamethasone sodium phosphate (DSP). The first method, zero-crossing derivative spectrophotometry, depends on measuring the second derivative peak and trough values at 304 nm an...

Abstract In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework is proposed to suitably handle those problems. First, scheme for bound combines dense seque...