In this paper, the interplay between non-orthogonal multiple access (NOMA), device-to-device (D2D) communication, full-duplex (FD) technology, and cooperation networks is proposed, and a resource allocation problem is investigated. Specifically, a downlink FD cooperative NOMA-based cellular system with underlaying D2D communications is proposed, where, in each NOMA group, the strong user assists the weak user as an FD relay with imperfect self interference (SI) cancellation. In terms of reaping spectral efficiency benefits, the system sum rate is to be maximized by optimizing channel allocation. This optimization is based on quality of service (QoS) constraints of D2D pairs and cellular users (CUs), power budget of base station and strong user (cooperative phase), and successive interference cancellation (SIC) constraints. Since the maximization formulated problem is computationally challenging to be addressed, a two-sided stable many-to-one matching algorithm, based on Pareto improvement, performs sub-channel assignment. Extensive simulations are implemented to demonstrate the system performance indicated by different metrics.

The variational Monte Carlo method is used to evaluate the ground-state energy of the confined hydrogen molecule, . Accordingly, we considered the case of hydrogen molecule confined by a hard prolate spheroidal cavity when the nuclear positions are clamped at the foci (on-focus case). Also, the case of off-focus nuclei in which the two nuclei are not clamped to the foci is studied. This case provides flexibility for the treatment of the molecular properties by selecting an arbitrary size and shape of the confining spheroidal box. An accurate trial wave function depending on many variational parameters is used for this purpose. The obtained results are in good agreement with the most recent results.

AbsractBy Using the variational Monte Carlo (VMC) method, we calculate the 1 state energies, the dissociation energies and the binding energies of the hydrogen molecule and its molecular ion in the presence of an aligned magnetic field regime between 0 . . and 10 . . The present calculations are based on using two types of compact and accurate trial wave functions, which are put forward for consideration in calculating energies in the absence of magnetic field. The obtained results are compared with the most recent accurate values. We conclude that the applications of VMC method can be extended successfully to cover the case of molecules under the effect of the magnetic field.

Background: Cancer is a genetic disease caused by the accumulation of gene mutations. It is important to derive the number of driver mutations that are needed for the development of human breast cancer, which may provide insights into the tumor diagnosis and therapy. Objective: This work is designed to investigate whether there is any difference for the mutation mechanism of breast cancer between the patients in the USA and those in China. We study the mechanisms of breast cancer development in China, and then compare these mechanisms with those in the USA. Methods: This work designed a multistage model including both gene mutation and clonal expansion of intermediate cells to fit the dataset of breast cancer in China from 2004 to 2009. Results: Our simulation results show that the maximum number of driver mutations for breast epithelium stem cells of females in China is 13 which is less than the 14 driver mutations of females in the USA. In addition, the two-hit model is the optimal one for the tumorigenesis of females in China, which is also different from the three-hit model that was predicted as the optimal model for the tumorigenesis of females in the USA. Conclusion: The differences of the mutation mechanisms between China and the USA reflect a variety of lifestyle, genetic influences, environmental exposure, and the availability of mammography screening.

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