Legendre multiwavelet collocation method for solving the linear fractional time delay systems

In this article the Legendre multiwavelet basis with aid of collocation method has been applied to give approximate solution for fractional delay systems. The properties of Legendre multiwavelet are presented. These properties together with the collocation method are then utilized to reduce the problem to the solution of algebraic system. Numerical results and comparison with exact solutions in the cases when we have exact solution are given in test examples in order to demonstrate the applicability and efficiency of the method.     

The prenylated dioxopiperazine alkaloid Cristatin A has selective telomeric DNA G-quadruplex stabilising properties

Cristatin A (1a/b), a prenylated dioxopiperazine alkaloid, has been shown to bind selectively to telomeric quadruplex DNA using a FRET-based DNA melting assay. Crucially, the molecule is more drug-like than most previously identified quadruplex-binding agents, and provides a unique chemical scaffold for future chemical biology and drug discovery studies.     

In situ high pressure study of ZIF-8 by FTIR spectroscopy

ZIF-8 as a promising storage material was investigated at high pressures up to ~39 GPa by in situ FTIR spectroscopy for the first time. Structural modifications are found to be reversible in a low-pressure region but irreversible in a high-pressure region. Overall, the ZIF-8 framework exhibits an unusual chemical stability even under extreme compression.     

Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique

In this paper, the problem of finite-time chaos synchronization between two different chaotic systems with fully unknown parameters is investigated. First, a new nonsingular terminal sliding surface is introduced and its finite-time convergence to the zero equilibrium is proved. Then, appropriate adaptive laws are derived to tackle the unknown parameters of the systems. Afterwards, based on the adaptive laws and finite-time control idea, an adaptive sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time. It is mathematically proved that the introduced sliding mode technique has finite-time convergence and stability in both reaching and sliding mode phases. Finally, some numerical simulations are presented to demonstrate the applicability and effectiveness of the proposed technique.     

On measuring the neutron coherent scattering length with ultrahigh precision

We propose an order of magnitude improvement in the present five parts in 10⁵ precision of a nondispersive interferometric measurement of the neutron coherent scattering lengthb _c. For this purpose we make a judicious selection of the Bragg angle for the interferometer and the sample thickness. The precision is further improved by an optimal choice of the Bragg reflection (and a consequent neutron wavelength). By performing the experiment in vacuum, errors arising from possible variations in the pressure, composition or humidity of the ambient air can be eliminated. On attaining such precision, we ought to account for the neutron beam refraction at the sample-ambient interfaces, to infer the correctb _c from the observed phase. The formula for the phase used hitherto is approximate and would significantly overestimateb _c. The refractive index for neutrons can thus be determined to a phenomenal precision of a few parts in 10¹².     

Hydroxy-thioxanthones as suitable neutral ionophores for the preparation of PVC-membrane potentiometric sensors for Al(III) ion.

The complexation of five recently synthesized hydroxy-thioxanthone derivatives with Al3+ ion was studied in a methanol solution spectrophotometrically, and the stepwise formation constants of the resulting 1:1 and 2:1 (ligand-to-metal) complexes were evaluated. The suitability of the thioxanthone derivatives as neutral ionophores for the preparation of a new Al3+ ion-selective PVC-membrane electrode was investigated, and 1-hydroxy-3-methyl-thiocanthone was selected as the best compound for this purpose. The prepared electrode exhibits a Nernstian response for Al3+ ions over a wide concentration range (2.0 x 10(-2) to 2.0 x 10(-6) M), with a limit of detection of 1.0 x 10(-6) M. It has a very fast response time of about 5 s and can be used for at least 3 months without any considerable divergence in the potentials. The proposed membrane sensor revealed very good selectivities for Al3+ over a wide variety of other metal ions, and could be used at a working pH range of 3.4 - 5.0. It was used as an indicator electrode in potentiometric titration of aluminum ions with EDTA, and in the determination of Al3+ in different real samples.     

Three-Component Reaction of Triphenylphosphine,Acetylenic Esters,and 6-Aminouracil or 6-Amino-N,N′-dimethyluracil

Protonation of the reactive 1:1 intermediate produced in the reaction of acetylenic esters and triphenylphosphine by 6-aminouracil or 6-amino-N,N′-dimethyluracil leads to vinylphosphonium salts, which undergo Michael addition with the conjugate base of the NH acid to produce highly fanctionalized, salt-free phosphorus ylides in excellent yields.     

Towards classification of the bifurcation structure of a spherical cavitation bubble

We focus on a single cavitation bubble driven by ultrasound, a system which is a specimen of forced nonlinear oscillators and is characterized by its extreme sensitivity to the initial conditions. The driven radial oscillations of the bubble are considered to be implicated by the principles of chaos physics and owing to specific ranges of control parameters, can be periodic or chaotic. Despite the growing number of investigations on its dynamics, there is not yet an inclusive yardstick to sort the dynamical behavior of the bubble into classes; also, the response oscillations are so complex that long term prediction on the behavior becomes difficult to accomplish. In this study, the nonlinear dynamics of a bubble oscillator was treated numerically and the simulations were proceeded with bifurcation diagrams. The calculated bifurcation diagrams were compared in an attempt to classify the bubble dynamic characteristics when varying the control parameters. The comparison reveals distinctive bifurcation patterns as a consequence of driving the systems with unequal ratios of (where R₀ is the bubble initial radius and λ is the wavelength of the driving ultrasonic wave). Results indicated that systems having the equal ratio of , share remarkable similarities in their bifurcating behavior and can be classified under a unit category.     

On fuzzy linear projection equation and applications

This paper introduces the concept of fuzzy projection of a fuzzy number on a set of fuzzy numbers based on r-cut approach. It is proved that the projection of a fuzzy number on the set of all fuzzy numbers is itself and under a special metric, the proposed fuzzy projection is a non-expansive mapping. By using this definition, the concept of fuzzy linear projection equation is defined and to solve it, a numerical method is applied. Based on the proposed algorithm and as an important application, two different types of system of fuzzy linear equations with fuzzy variables are solved. Numerical results illustrate the applicabilities of proposed approach.