Which subnormal Toeplitz operators are either normal or analytic?

We study subnormal Toeplitz operators on the vector-valued Hardy space of the unit circle, along with an appropriate reformulation of P.R. Halmos's Problem 5: Which subnormal block Toeplitz operators are either normal or analytic? We extend and prove Abrahamse's Theorem to the case of matrix-valued symbols; that is, we show that every subnormal block Toeplitz operator with bounded type symbol (i.e., a quotient of two analytic functions), whose co-analytic part has a "coprime decomposition," is normal or analytic. We also prove that the coprime decomposition condition is essential. Finally, we examine a well known conjecture, of whether every submormal Toeplitz operator with finite rank self-commutator is normal or analytic.Comment: Final version, accepted for publication in Journal of Functional Analysi

Hyponormality and Subnormality of Block Toeplitz Operators

In this paper we are concerned with hyponormality and subnormality of block Toeplitz operators acting on the vector-valued Hardy space $H^2_{\mathbb{C}^n}$ of the unit circle. Firstly, we establish a tractable and explicit criterion on the hyponormality of block Toeplitz operators having bounded type symbols via the triangularization theorem for compressions of the shift operator. Secondly, we consider the gap between hyponormality and subnormality for block Toeplitz operators. This is closely related to Halmos's Problem 5: Is every subnormal Toeplitz operator either normal or analytic? We show that if $\Phi$ is a matrix-valued rational function whose co-analytic part has a coprime factorization then every hyponormal Toeplitz operator $T_{\Phi}$ whose square is also hyponormal must be either normal or analytic. Thirdly, using the subnormal theory of block Toeplitz operators, we give an answer to the following "Toeplitz completion" problem: Find the unspecified Toeplitz entries of the partial block Toeplitz matrix A:=[U^*& ? ?&U^*] so that $A$ becomes subnormal, where $U$ is the unilateral shift on $H^2$.Comment: Final version, accepted for publication in Advances in Mathematic

A gap between hyponormality and subnormality for block Toeplitz operators

AbstractThis paper concerns a gap between hyponormality and subnormality for block Toeplitz operators. We show that there is no gap between 2-hyponormality and subnormality for a certain class of trigonometric block Toeplitz operators (e.g., its co-analytic outer coefficient is invertible). In addition we consider the extremal cases for the hyponormality of trigonometric block Toeplitz operators: in this case, hyponormality and normality coincide

Organic core-sheath nanowire artificial synapses with femtojoule energy consumption

Emulation of biological synapses is an important step toward construction of large-scale brain-inspired electronics. Despite remarkable progress in emulating synaptic functions, current synaptic devices still consume energy that is orders of magnitude greater than do biological synapses (similar to 10 fJ per synaptic event). Reduction of energy consumption of artificial synapses remains a difficult challenge. We report organic nanowire (ONW) synaptic transistors (STs) that emulate the important working principles of a biological synapse. The ONWs emulate the morphology of nerve fibers. With a core-sheath-structured ONW active channel and a well-confined 300-nm channel length obtained using ONW lithography, similar to 1.23 fJ per synaptic event for individual ONW was attained, which rivals that of biological synapses. The ONW STs provide a significant step toward realizing low-energy-consuming artificial intelligent electronics and open new approaches to assembling soft neuromorphic systems with nanometer feature size.1161Yscopu

Development of Micro-Heaters with Optimized Temperature Compensation Design for Gas Sensors

One of the key components of a chemical gas sensor is a MEMS micro-heater. Micro-heaters are used in both semiconductor gas sensors and NDIR gas sensors; however they each require different heat dissipation characteristics. For the semiconductor gas sensors, a uniform temperature is required over a wide area of the heater. On the other hand, for the NDIR gas sensor, the micro-heater needs high levels of infrared radiation in order to increase sensitivity. In this study, a novel design of a poly-Si micro-heater is proposed to improve the uniformity of heat dissipation on the heating plate. Temperature uniformity of the micro-heater is achieved by compensating for the variation in power consumption around the perimeter of the heater. With the power compensated design, the uniform heating area is increased by 2.5 times and the average temperature goes up by 40 °C. Therefore, this power compensated micro-heater design is suitable for a semiconductor gas sensor. Meanwhile, the poly-Si micro-heater without compensation shows a higher level of infrared radiation under equal power consumption conditions. This indicates that the micro-heater without compensation is more suitable for a NDIR gas sensor. Furthermore, the micro-heater shows a short response time of less than 20ms, indicating a very high efficiency of pulse driving