Wireless Networks with Energy Harvesting and Power Transfer: Joint Power and Time Allocation

In this letter, we consider wireless powered communication networks which could operate perpetually, as the base station (BS) broadcasts energy to the multiple energy harvesting (EH) information transmitters. These employ “harvest then transmit” mechanism, as they spend all of their energy harvested during the previous BS energy broadcast to transmit the information towards the BS. Assuming time division multiple access (TDMA), we propose a novel transmission scheme for jointly optimal allocation of the BS broadcasting power and time sharing among the wireless nodes, which maximizes the overall network throughput, under the constraint of average transmit power and maximum transmit power at the BS. The proposed scheme significantly outperforms “state of the art” schemes that employ only the optimal time allocation. If a single EH transmitter is considered, we generalize the optimal solutions for the case of fixed circuit power consumption, which refers to a much more practical scenario.

Joint Information and Jamming Beamforming for Secrecy Rate Maximization in Cognitive Radio Networks

In this paper, we consider the secure beamforming design for an underlay cognitive radio multiple-input singleoutput broadcast channel in the presence of multiple passive eavesdroppers. Our goal is to design a jamming noise (JN) transmit strategy to maximize the secrecy rate of the secondary system. By utilizing the zero-forcing method to eliminate the interference caused by JN to the secondary user, we study the joint optimization of the information and JN beamforming for secrecy rate maximization of the secondary system while satisfying all the interference power constraints at the primary users, as well as the per-antenna power constraint at the secondary transmitter. For an optimal beamforming design, the original problem is a nonconvex program, which can be reformulated as a convex program by applying the rank relaxation method. To this end, we prove that the rank relaxation is tight and propose a barrier interior-point method to solve the resulting saddle point problem based on a duality result. To find the global optimal solution, we transform the considered problem into an unconstrained optimization problem. We then employ Broyden-Fletcher-Goldfarb-Shanno (BFGS) method to solve the resulting unconstrained problem which helps reduce the complexity significantly, compared to conventional methods. Simulation results show the fast convergence of the proposed algorithm and substantial performance improvements over existing approaches.

Isolation and structural determination of non-racemic tertiary cathinone derivatives

The racemic tertiary cathinones N,N-dimethylcathinone (1), N,N-diethylcathinone (2) and 2-(1-pyrrolidinyl)-propiophenone (3) have been prepared in reasonable yield and characterized using NMR and mass spectroscopy. HPLC indicates that these compounds are isolated as the anticipated racemic mixture. These can then be co-crystallized with (+)-O,O′-di-p-toluoyl-d-tartaric, (+)-O,O′-dibenzoyl-d-tartaric and (-)-O,O′-dibenzoyl-l-tartaric acids giving the single enantiomers S and R respectively of 1, 2 and 3, in the presence of sodium hydroxide through a dynamic kinetic resolution. X-ray structural determination confirmed the enantioselectivity. The free amines could be obtained following basification and extraction. In methanol these are reasonably stable for the period of several hours, and their identity was confirmed by HPLC and CD spectroscopy.

Three dimensional Sklyanin algebras and Gröbner bases

We consider Sklyanin algebras $S$ with 3 generators, which are quadratic algebras over a field $\K$ with $3$ generators $x,y,z$ given by $3$ relations $pxy+qyx+rzz=0$, $pyz+qzy+rxx=0$ and $pzx+qxz+ryy=0$, where $p,q,r\in\K$. this class of algebras has enjoyed much attention. In particular, using tools from algebraic geometry, Feigin, Odesskii \cite{odf}, and Artin, Tate and Van Den Bergh, showed that if at least two of the parameters $p$, $q$ and $r$ are non-zero and at least two of three numbers $p^3$, $q^3$ and $r^3$ are distinct, then $S$ is Artin--Schelter regular. More specifically, $S$ is Koszul and has the same Hilbert series as the algebra of commutative polynomials in 3 indeterminates (PHS). It has became commonly accepted that it is impossible to achieve the same objective by purely algebraic and combinatorial means like the Groebner basis technique. The main purpose of this paper is to trace the combinatorial meaning of the properties of Sklyanin algebras, such as Koszulity, PBW, PHS, Calabi-Yau, and to give a new constructive proof of the above facts due to Artin, Tate and Van Den Bergh. Further, we study a wider class of Sklyanin algebras, namelyr/>the situation when all parameters of relations could be different. We call them generalized Sklyanin algebras. We classify up to isomorphism all generalized Sklyanin algebras with the same Hilbert series as commutative polynomials onr/>3 variables. We show that generalized Sklyanin algebras in general position have a Golod–Shafarevich Hilbert series (with exception of the case of field with two elements).