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Search Results: 1 - 10 of 318 matches for " Saburou Saitoh "
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Generalized Inversions of Hadamard and Tensor Products for Matrices  [PDF]
Saburou Saitoh
Advances in Linear Algebra & Matrix Theory (ALAMT) , 2014, DOI: 10.4236/alamt.2014.42006
Abstract:
We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
Matrices and Division by Zero z/0 = 0  [PDF]
Tsutomu Matsuura, Saburou Saitoh
Advances in Linear Algebra & Matrix Theory (ALAMT) , 2016, DOI: 10.4236/alamt.2016.62007
Abstract: In this paper, a new viewpoint of the division by zero z/0 = 0 in matrices is introduced and the results will show that the division by zero is our elementary and fundamental mathematics. New and practical meanings for many mathematical and physical formulas for the denominator zero cases may be given. Furthermore, a new space idea for the point at infinity for the Eucleadian plane is also introduced.
Some isometrical identities in the wave equation
Saburou Saitoh
International Journal of Mathematics and Mathematical Sciences , 1984, DOI: 10.1155/s0161171284000132
Abstract: We consider the usual wave equation utt(x,t)=c2uxx(x,t) on the real line with some typical initial and boundary conditions. In each case, we establish a natural isometrical identity and inverse formula between the sourse function and the response function.
Stability of Lipschitz type in determination of initial heat distribution
Saburou Saitoh,Masahiro Yamamoto
Journal of Inequalities and Applications , 1997, DOI: 10.1155/s1025583497000052
Abstract: For the solution u(x,t)=u(f)(x,t) of the equations {u ¢ € 2(x,t)= ”u(x,t),u(x,0)=f(x),u(x,t)=0, ¢ € x ¢ ,t>0x ¢ x ¢ ¢ ,t>0} where ¢ ¢ r,2 ¢ ‰ ¤r ¢ ‰ ¤3 is a bounded domain with C2-boundary and for an appropriate subboundary “ of we prove a Lipschitz estimate of ¢ € –f ¢ € –L2( ) : For ¢ (1,54) and for a positive constant CC ¢ ’1 ¢ € –f ¢ € –L2( ) ¢ ‰ ¤ ¢ € – ¢ u(f) ¢ v ¢ € –B ( “ —(0, ¢ )) ¢ ‰ ¢ “{ ¢ ‘n=0 ¢ 1n! “(n+2 +1) ¢ 0 ¢ |(p ¢ pn+1+n ¢ pn)p ¢ ’32 ¢ u(f) ¢ v(x,14p)|2p2n+2 ¢ ’1dp}ds. The norm ¢ € – ¢ … ¢ € –B ( “ —(0, ¢ )) is involved and strong, but it is a natural one in our situation relating to a typical and simple norm for analytic functions. Furthermore, it is acceptable in the sense that ¢ € – ¢ u(f) ¢ v ¢ € –B ( “ —(0, ¢ )) ¢ ‰ ¤C ¢ € –f ¢ € –H2( ) holds.
Stability of Lipschitz type in determination of initial heat distribution
Saitoh Saburou,Yamamoto Masahiro
Journal of Inequalities and Applications , 1997,
Abstract: For the solution of the equations where , is a bounded domain with -boundary and for an appropriate subboundary of we prove a Lipschitz estimate of : For and for a positive constant The norm is involved and strong, but it is a natural one in our situation relating to a typical and simple norm for analytic functions. Furthermore, it is acceptable in the sense that holds.
A Matrix Inequality for the Inversions of the Restrictions of a Positive Definite Hermitian Matrix  [PDF]
Weixiong Mai, Mo Yan, Tao Qian, Matteo Dalla Riva, Saburou Saitoh
Advances in Linear Algebra & Matrix Theory (ALAMT) , 2013, DOI: 10.4236/alamt.2013.34011
Abstract: We exploit the theory of reproducing kernels to deduce a matrix inequality for the inverse of the restriction of a positive definite Hermitian matrix.
A ball rolling down a rotating board
Akio Saitoh
Latin-American Journal of Physics Education , 2010,
Abstract: This article describes an easily constructed apparatus for an experiment on a rolling ball a rotating board.From the experimental and theoretical results, we can find that the ball leaves the board at the instant boththe ball and the board are released from hand. Then, the ball can’t roll down the board until the balltouches the board again.
New apparatus for “Monkey and Hunter” demonstration
Akio Saitoh
Latin-American Journal of Physics Education , 2011,
Abstract: We present an apparatus for “Monkey and Hunter” demonstration in the student lab. We can easily construct it at a low cost and the blow gun has a high hit rate.
Winding motion in a spiral-like trajectory
Akio Saitoh
Latin-American Journal of Physics Education , 2011,
Abstract: In this article I shall describe an easily constructed apparatus for an experiment on winding motion in a spiral-liketrajectory in three dimensions. The experimental results show how the total time of the process depends on the initialspeed, and the total time has its maximum value of 16.3s for a speed of 2.67m/s. The experimental results were ingood agreement with the theoretical predictions. The analytical solution of the problem is original
Folding three-dimensional model of equipotential surfaces
Akio Saitoh
Latin-American Journal of Physics Education , 2011,
Abstract: We present a new model of equipotential surfaces. We can easily construct it at a low cost. Using the model, students come to realize that the gradient of the electric potential is directly proportional to the density of lines of force, and hence the electric field intensity.
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