scholarly journals The variance of the single point range of two dimensional recurrent random walk

1992 ◽  
Vol 68 (7) ◽  
pp. 195-197 ◽  
Author(s):  
Yuji Hamana
1988 ◽  
Vol 50 (3-4) ◽  
pp. 599-609
Author(s):  
A. Kr�mli ◽  
P. Luk�cs ◽  
D. Sz�sz
Keyword(s):  

2021 ◽  
Author(s):  
Laura Namisnak ◽  
Sepideh Khoshnevis ◽  
Kenneth R. Diller

Abstract Various medical procedures are accomplished by manipulating skin temperature in a nonuniform pattern. Skin temperature monitoring is essential to assess conformance to protocol specifications and to prevent thermal injury. Existing solutions for skin temperature monitoring include single point sensors, such as thermocouples, and two-dimensional methods of sensing surface temperature, such as infrared thermography, and wearable technology. Single point sensors cannot detect the average temperature and consequently their measurements cannot be representative of average surface temperature in a nonuniform temperature field. Infrared thermography requires optical access, and wearable sensors may require complex manufacturing processes and impede the heat exchange with a source by introducing a layer of insulation. Our solution is a two-dimensional resistance temperature detector (2D RTD) created by knitting copper magnet wire into custom shapes. The 2D RTDs were calibrated, compared to one-dimensional sensors and wearable sensors, and analyzed for hysteresis, repeatability, and surface area conformation. Resistance and temperature were correlated with an R2 of 0.99. The 2D RTD proved to be a superior device for measuring average skin temperature exposed to a nonuniform temperature boundary in the absence of optical access such as when a full body thermal control garment is worn.


2010 ◽  
Vol 20 (6) ◽  
pp. 1091-1098 ◽  
Author(s):  
NORIO KONNO

Pólya showed in his 1921 paper that the generating function of the return probability for a two-dimensional random walk can be written in terms of an elliptic integral. In this paper we present a similar expression for a one-dimensional quantum walk.


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