A numerical approach for solving weakly singular partial integro‐differential equations via two‐dimensional‐orthonormal Bernstein polynomials with the convergence analysis

In this paper, we develop an efficient matrix method based on two‐dimensional orthonormal Bernstein polynomials (2D‐OBPs) to provide approximate solution of linear and nonlinear weakly singular partial integro‐differential equations (PIDEs). First, we approximate all functions involved in the considerable problem via 2D‐OBPs. Then, by using the operational matrices of integration, differentiation, and product, the solution of Volterra singular PIDEs is transformed to the solution of a linear or nonlinear system of algebraic equations which can be solved via some suitable numerical methods. With a small number of bases, we can find a reasonable approximate solution. Moreover, we establish some useful theorems for discussing convergence analysis and obtaining an error estimate associated with the proposed method. Finally, we solve some illustrative examples by employing the presented method to show the validity, efficiency, high accuracy, and applicability of the proposed technique.     

Simple and efficient one-pot synthesis of N-phenyl-3,5-difunctionalized pyrazoles

A facile one-pot synthesis of N-phenyl-3,5-difunctionalized pyrazoles is described. The dialkyl 2-[(Z)-phenylhydrazono]succinate intermediate, which is prepared in situ from the mixture of phenylhydrazine and dialkyl acetylenedicarboxylate reacts with aroyl chloride or fumaryl chloride to afford the title compounds. Different types of compounds containing COCl functional group were used to investigate the scope and limitation of the reaction. Two -CO₂R and -O₂C groups at 3- and 5-position are potentially capable to convert to other functional groups. The reaction conditions are relatively mild and the yields are good.     

Normal subgroup based power graph of finite groups

Ricerche di Matematica - Let G be a finite group and $$N \unlhd G$$ . The normal subgroup based power graph of G, $$\Gamma _N(G)$$ , is an undirected graph with vertex set $$(G{\setminus }N) \cup...     

On the solution of constrained hartree-fock-bogolyubov equations

A method is described to solve constrained HFB-equations without introduction of a Lagrangian multiplier. To demonstrate the versatility of the method rotational bands in¹⁶⁴Er and¹⁶⁸Yb are calculated.     

Topology control in the mobile ad hoc networks in order to intensify energy conservation

Although studied for years, due to their dynamic nature, research in the field of mobile ad hoc networks (MANETs) has remained a vast area of interest. Since once distributed, there will be less to no plausibility of recharge, energy conservation has become one of the pressing concerns regarding this particular type of network. In fact, one of the main obligations of designers is to make efficient use of these scarce resources. There has been tremendous work done in different layers of protocol stack in order to intensify energy conservation. To date, numerous topology control algorithms have been proposed, however, only a few have used meta-heuristics such as genetic algorithms, neural networks and/or learning automata to overcome this issue. On the other hand, since nodes are mobile and thus in a different spatial position, as time varies, we can expect that by regulating time intervals between topology controls, one may prolong the network’s lifetime. The main initiative of this paper is to intensify energy conservation in a mobile ad hoc network by using weighted and learning automata based algorithms. The learning automata, regulates time intervals between which the topology controls are done. The represented learning automata based algorithm uses its learning ability to find appropriate time-intervals so that the nodes would regulate the energy needed in order to exchange the information to their neighbors, accordingly. Moreover, at first we have represented two weighted based algorithms which extend two prominent protocols, namely K-Neigh and LMST. Then these algorithms are combined with a learning based algorithm which regulates time intervals between which the topology controls are done. In comparison with approaches that are based on periodic topology controls, proposed approach shows enhanced results. On the other hand, considering the learning ability of the learning automata based algorithms, composition of the aforementioned algorithms has been proven to be enhanced, in the respect of energy consumed per data transmitted, over those compared with.     

Design and tailoring of one-dimensional ZnO nanomaterials for photocatalytic degradation of organic dyes: a review

Research on Chemical Intermediates - Photocatalysis using semiconductors has emerged as a promising wastewater treatment process to overcome the major challenges faced by conventional technologies....     

Graphene Quantum Dots Incorporated into β-cyclodextrin: a Novel Polymeric Nanocomposite for Non-Enzymatic Sensing of L-Tyrosine at Physiological pH

Graphene quantum dot-β-cyclodextrin modified glassy carbon electrode was used as a new nanosensor for determination of L-tyrosine (L-Tyr). It was found that graphene quantum dot-β-cyclodextrin has been stably electrodeposited on glassy carbon electrode modified by simple technique. The cyclic voltammograms of the modified electrode in an aqueous solution displayed a pair of well-defined, stable and irreversible reductive/oxidation redox systems. The apparent electron transfer rate constant (k_s) and transfer coefficient (α) determined by cyclic voltammetry were approximately equal to 8.0 s^–1 and 0.7, respectively. The modified electrode showed excellent catalytic activity towards the oxidation of L-Tyr at positive potential in buffer solution. The nanosensor also displayed fast response time, high sensitivity, low detection limit and a remarkably positive potential oxidation of L-Tyr that decreased the effect of interferences in analysis.