Page 343 - Electrical Engineering Dictionary

uniform strength or to measure the magnetic F m×n [z 1 ][z 2 ] if
moment of a magnet.
  
a 11 a 12 ... a 1n



  0 a 22 ... a 2n 

  

Helmholtz equation a partial differential   ... ... ... ... 

 


equation mathematically described by   0 0 ... a nn  if m>n

 


  0 0 ... 0 

  

  ... ... ... ... 



 0 0 ... 0

  

a 11 a 12 ... a 1n
2
∇ + k 2 φ = 3Df , A H (z 1 ,z 2 ) =  
 0 a 22 ... a 2n
  if m = n

  ... ... ... ... 



 0
 0 ... a nn
  


 a 11 a 12 ... a 1m ... a 1n

 

2
where ∇ is the Laplacian, k is the wavenum-  0 a 22 ... a 2m ... a 2n 


  ... ... ... ... ... ... 
ber, f is the forcing function, and φ is the 


 0 0 ... a mm ... a mn
equation’s solution. 


if m<n
where deg a ii > deg a ki for k 6= i (deg
HEMT See high electron mobility z 2 z 2 z 2
denotes the degree with respect to z 2 ). In a
transistor.
similar way, the Hirmite form of A(z 1 ,z 2 )
with respect to F [z 1 ][z 2 ] can be defined.
A(z 1 ,z 2 ) can be reduced to its Hermite form
Henry, Joseph Henry is best known as A H (z 1 ,z 2 ) by the use of elementary row
the first Director (1846) of the Smithsonian operations or equivalently by premultiplica-
Institution, and President of the National tion by suitable unimodular matrix U(z 1 ,z 2 )
Academy of the Sciences. Henry was largely
(det U(z 1 ,z 2 ) ∈ F(z 1 )), i.e., A H (z 1 ,z 2 ) =
self-taught, but his early experiments gar- U(z 1 ,z 2 )A(z 1 ,z 2 ). See for example, T.
nered him sufficient recognition to become a Kaczorek, Two-DimensionalLinearSystems,
Professor of Natural Philosophy at New Jer- Springer-Verlag, Berlin, 1985.
sey College (now Princeton). Henry’s early
experiments resulted in the development of a Hermite Gaussian beam electromag-
practical electric motor and a relay later quite netic beam solution of the paraxial wave
important in telegraphy. equation in which the field is a product of
a Hermite-polynomial and a Gaussian func-
tion of distance from the beam axis.
hermetic seal a seal that is such that the
object is gas-tight (usually a rate of less than Hermitian matrix a square matrix that
1 × 10 −6 cc/s of helium). equals its conjugate transpose.
hertz a measure of frequency in which
Hermite form of 2-D polynomial matrix the number of hertz measures the number of
denote by F m×n (z 1 ) [z 2 ] (F m×n [z 1 ][z 2 ]) occurrences (of whatever is being measured)
the set of m × n polynomial matrices in z 2 per second.
with coefficients in the field F(z 1 ) (poly-
nomial coefficients in z 1 ). 2-D polyno- Hertz dipole a straight, infinitesimally
mial matrix A(z 1 ,z 2 ) ∈ F m×n [z 1 ,z 2 ] of short and infinitesimally thin conducting fil-
full rank has Hermite form with respect to ament with uniform current distribution. The
c
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