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In-memory computing is an emerging technique to fulfill the fast growing demand for high-performance data processing. This technique provides fast processing and high throughput by accessing data stored in the memory array rather than dealing with complicated operation and data movement on hard drive. For data processing, the most important computation is dot product, which is also the core computation for applications such as deep learning neuron networks, machine learning, etc. As multiplication is the key function in dot product, it is critical to improve its performance and achieve faster memory processing. In this paper, we present a design with the ability to perform in-memory multi-bit multiplications. The proposed design is implemented by using quantum-dot transistors, which enable multi-bit computations in the memory cell. Experimental results demonstrate that the proposed design provides reliable in-memory multi-bit multiplications with high density and high energy efficiency. Statistical analysis is performed using Monte Carlo simulations to investigate the process variations and error effects.

This paper studies the Nevanlinna type classes and operators such as multipliers, nontangential maximal function operator and area operator. These operators are useful in complex and harmonic analysis.