FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS

The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.

Anycast Transmission in Routing Modulation Level Spectrum Assignment (RMLSA) Problem on Space Division Multiplexing (SDM) Elastic Optical Networks (EON)

With the rise of cloud computing in recent years, a large number of streaming media has yielded an exponential growth in network traffic. With the now present 5G and future 6G, the development of the Internet of Things (IoT), social networks, video on demand, and mobile multimedia platforms, the backbone network is bound to bear more traffic. The transmission capacity of Single Core Fiber (SCFs) may be limited in the future and Spatial Division Multiplexing (SDM) leveraging multi-core fibers promises to be one of the solutions for the future. Currently, Elastic optical networks (EONs) with multi-core fibers (MCFs) are a kind of SDM-enabled EONs (SDM-EON) used to enhance the capacity of transmission. The resource assignment in MCFs, however, will be subject to Inter-Core Crosstalk (IC-XT), hence, reducing the effectiveness of transmission. This research highlights the routing, modulation level, and spectrum assignment (RMLSA) problems with anycast traffic mode in SDM-EON. A multipath routing scheme is used to reduce the blocking rate of anycast traffic in SDM-EON with the limit of inter-core crosstalk. Hence, an integer linear programming (ILP) problem is formulated and a heuristic algorithm is proposed. Two core-assignment strategies: First-Fit (FF) and Random-Fit (RF) are used and their performance is evaluated through simulations. The simulation results show that the multipath routing method is better than the single-path routing method in terms of blocking ratio and spectrum utilization ratio. Moreover, the FF is better than the RF in low traffic load in terms of blocking ratio (BR), and the opposite in high traffic load. The FF is better than the RF in terms of a spectrum utilization ratio. In an anycast protection problem, the proposed algorithm has a lower BR than previous works.

Architecture design for reliable and reconfigurable FPGA-based GNC computer for deep space exploration

SRAM(static random access memory)-based FPGA(field programmable gate array), owing to its large capacity, high performance, and dynamical reconfiguration, has become an attractive platform for So PC(system on programmable chip) development. However, as the configuration memory and logic memory of the SRAM-based FPGA are highly susceptible to SEUs(single-event upsets) in deep space, it is a challenge to design and implement a highly reliable FPGA-based system for spacecraft, and no practical architecture has been proposed. In this paper, a new architecture for a reliable and reconfigurable FPGAbased computer in a highly critical GNC(guidance navigation and control) system is proposed. To mitigate the effect of an SEU on the system, multi-layer reconfiguration and multi-layer TMR(triple module redundancy) techniques are proposed, with a reliable reconfigurable real-time operating system(Space OS) managing the system level fault tolerance of the computer in the architecture. The proposed architecture for the reconfigurable FPGA-based computer has been implemented with COTS(commercial off the shelf) FPGA and has firstly been applied to the GNC system of a circumlunar return and reentry flight vehicle. The in-orbit results show that the proposed architecture is capable of meeting the requirements of high reliability and high availability, and can provide the expressive varying functionality and runtime flexibility for an FPGA-based GNC computer in deep space.

Convergence of compressible Navier-Stokes-Maxwell equations to incompressible Navier-Stokes equations

The combined quasi-neutral and non-relativistic limit of compressible Navier-Stokes-Maxwell equations for plasmas is studied.For well-prepared initial data,it is shown that the smooth solution of compressible Navier-Stokes-Maxwell equations converges to the smooth solution of incompressible Navier-Stokes equations by introducing new modulated energy functional.

Toward a nonlinear control of an AC-DC-PWM converter dedicated to induction heating

In this paper, a applied to an AC-DC-pulse nonlinear control strategy width modulation （PWM） converter is developed and simulated. First a nonlinear system modeling is derived with state variables of the input current and the output voltage by using power balance of the input and output. The system is linearized and decoupled, and then a state feedback law is obtained. For robust control of parameter perturbation, integrators are added to the exact feedback control law. The simulation is provided to verify the validity of the control algorithm.

Extensions of Generalized Fitting Modules

In this paper, we study the closeness of strongly （∞）-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if M[X] is strongly hopfian （resp. strongly co-hopfian） in R[X]-Mod, then M is strongly hopfian （resp. strongly co-hopfian） in R-Mod.