Sharp oscillation and nonoscillation tests for delay dynamic equations

In this paper, we give new sufficient conditions for both oscillation and nonoscillation of the delay dynamic equation where and satisfy τ(t) ≤ σ(t) for all large t and . As an important corollary, we obtain the time scale invariant integral condition for nonoscillation: for all large t. Also, with some examples, we show that newly presented results are sharp.     

Cost Optimization Technique for Quantum Circuits

In this paper, an attempt is made to present a method of quantum cost minimization or optimization technique for quantum reversible circuits using proposed merger rules in Exclusive Sum of Product (ESOP) method. These modified ESOP methods are used to minimize the quantum circuits. We found that the quantum cost is drastically decreased than the previous ESOP method. It will be easy to find the quantum cost and quantum gate optimized quantum circuits implementation. It will also reduce quantum error while the quantum circuit is executed in real quantum processor.

     

Garratt–Braverman cyclization on basic alumina: a green protocol with improved selectivity

A green protocol (compared to the existing methodology) for carrying out Garratt–Braverman cyclization has been developed. The method involves stirring a pre-absorbed bispropargyl sulfone/ether/sulfonamide over basic alumina. The reaction with sulfones was over within 10–15 min at room temperature whereas for the ether/sulfonamide the reaction took 6–8 h at 130 °C. The products, aryl naphthalene derivatives, are obtained by simple filtration through Celite, in excellent yields.