270 research outputs found
On the Hecke Eigenvalues of Maass Forms
Let denote a primitive Hecke-Maass cusp form for with
the Laplacian eigenvalue . In this work we show
that there exists a prime such that , , and , where are the
Satake parameters of at , and is an absolute constant with
. In fact, can be taken as . In addition, we prove that the
natural density of such primes ( and ) is at least .Comment: Version 2: typos corrected and a new section on natural density adde
Impact of Parasitic and Load Current on the Attenuation of Motor Terminal Overvoltage in SiC-Based Drives
In SiC-based adjustable speed drives, the high
voltage slew rate (/) of the switching transitions results in
excessive overvoltage at the motor terminals due to the reflected
voltages across the drive power cables. Besides the cable length,
the switching rise/fall times of the voltage pulses are a key
parameter to quantify the motor overvoltage in PWM inverter-fed
drives. These times are varying depending on the load current and
parasitic elements of SiC MOSFETs, that is, a standard two-level
converter typically results in a non-uniform overvoltage envelop
at the motor terminals. This article analyses the switching
mechanism of the two-level converter considering the impact of
SiC parasitic elements and load current showing how they affect
the motor overvoltage in cable-fed drives. The analysis is then
extended to the mitigation of the motor overvoltage using quasithree-level (Q3L) modulation as a candidate filter-less approach
with a T-type converter. The theoretical analysis is validated
through experimental tests by using the Q3L T-type converter.
The analysis and results show that the instantaneous load current
value critically determines the peak motor overvoltage, while it
allows either a full or partial overvoltage mitigation when the Q3L
modulation is adopted
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