123081155
On the transformation group for diabolic magic squares of order four
A superposed wafer is separated to a processing target wafer and a supporting wafer while being heated. Then, an adhesive on a joint surface of the processing target wafer is removed by supplying an organic solvent onto the joint surface of the processing target wafer. Then, an oxide film formed on the predetermined pattern on the joint surface of the processing target wafer is removed by supplying acetic acid to the joint surface of the processing target wafer. Then, the joint surface of the processing target wafer is inspected. Then, based on an inspection result, the adhesive on the joint surface of the processing target wafer is removed and the oxide film formed on the predetermined pattern on the joint surface of the processing target wafer is removed.
122658305
The algebraic theory of diabolic magic squares
121846133
Almost periodic factorization of block triangular matrix functions revisited
Abstract Let G be an n×n almost periodic ( AP ) matrix function defined on the real line R . By the AP factorization of G we understand its representation in the form G = G + ΛG − , where G + ±1 ( G − ±1 ) is an AP matrix function with all Fourier exponents of its entries being non-negative (respectively, non-positive) and Λ ( x )=diag[e i λ 1 x ,…,e i λ n x ], λ 1 ,…,λ n ∈ R . This factorization plays an important role in the consideration of systems of convolution type equations on unions of intervals. In particular, systems of m equations on one interval of length λ lead to AP factorization of matrices (0.1) G(x)= e i λx I m 0 f(x) e − i λx I m . We develop a factorization techniques for matrices of the form (0.1) under various additional conditions on the off-diagonal block f . The cases covered include f with the Fourier spectrum Ω(f) lying on a grid ( Ω(f)⊂−ν+h Z ) and the trinomial f (( Ω(f)={−ν,μ,α} ) with − ν μ α , α +| μ |+ ν ⩾ λ .