A novel nonlinear fractional order sliding mode controller is proposed to control the chaotic atomic force microscope system in presence of uncertainties and disturbances. In the design of the suggested fractional order controller, conformable fractional order derivative is applied. The stability of the scheme is proved by means of the Lyapunov theory based on conformable fractional order deriv...

a series of amino derivative of 1-indene and 9-fluorene have been synthesized from their corresponding iminium salt, generated in situ in the concentrated ethereal lithium perchlorate solution, and 1-indenyl or 9-fluorenyl anions. the yields of the reactions depend on the kind of anion. addition of 1-indeny anion to the iminium salt gives the amino derivative of 1-indene, while addition of fluo...

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...

The chemiluminescence (CL) arising from the reaction of bis(2,4,6-trichlorophenyl)oxalate (TCPO) with H2O2 in the presence of a novel blue fluorescer, furandicarboxylate derivative, has been studied. The relationship between the CL intensity and concentrations of peroxyoxalate, sodium salicylate, H2O2 and furandicarboxylate derivative as fluorescer has been investigated. Kinetic parameters for ...

The aim of this study was to synthesize a new oxetan-phenyltetrahydropyridazine-3,6-dione derivative (compound 6) using with different techniques. The first method was achieved by the preparation of a phenylhydrazine derivative (2) using three components system (3,17-aldol-estradiol, phenylhydrazine, 5-hexyn-3-ol) in presence of Copper(II). Then, 2 Was reacted with tert-butyldimethylsilyl chlor...

purpose: in this study, we have focused on antibacterial effect of newly synthesized thiazole, imidazole and tetrahydropyrimidine derivatives in iran on listeria monocytogenes. materials and methods: for evaluation of antibacterial effect, the disk diffusion method was applied to measure the growth inhibition zone diameter and broth micro dilution was performed to determine the minimum inhibito...

Previous work (Pradines, 1966, Aof and Brown, 1992) has given a setting for a holon-omy Lie groupoid of a locally Lie groupoid. Here we develop analogous 2-dimensional notions starting from a locally Lie crossed module of groupoids. This involves replacing the Ehresmann notion of a local smooth coadmissible section of a groupoid by a local smooth coadmissible homotopy (or free derivation) for t...

We propose a recipe to construct matrix representations of Nambu– Lie 3-algebras in terms of irreducible representations of underlying Lie algebra. The case of Euclidean four-dimensional 3-algebra is considered in details. We find that representations of this 3-algebra are not possible in terms of only Hermitian matrices in spite of its Euclidean nature.

Let g be a complex simple Lie algebra. Fix a Borel subalgebra b and a Cartan subalgebra t ⊂ b. The nilpotent radical of b is denoted by u. The corresponding set of positive (resp. simple) roots is ∆ (resp. Π). An ideal of b is called ad-nilpotent, if it is contained in [b, b]. The theory of ad-nilpotent ideals has attracted much recent attention in the work of Kostant, Cellini-Papi, Sommers, an...

Any Lie algebra equipped with a symplectic form can be equipped with an affine structure. On the other hand there exist (2p + 1)-dimensional Lie algebras with contact form and no affine structure. But each nilpotent contact Lie algebra is a one-dimensional central extension of a symplectic algebra. The aim of this work is to study how we can extend, under certain conditions, the symplectic stuc...