Solvability of the Matric Equation AX = B

Integer Solutions of the Equation y 2 = Ax 4 + B

Let A ∈ {k2(k2l2 + 1), 4k2(k2(2l − 1)2 + 1)}, where k and l are positive integers, and let B be a non-zero square-free integer such that |B| < √ A. In this paper we determine all the possible integer solutions of the equation y2 = Ax4 + B by using terms of Lucas sequences of the form mx2.

On the ⋆-Sylvester equation AX ± X⋆ B⋆ = C

We consider the solution of the ?-Sylvester equation AX±X?B? = C, for ? = T,H and A,B,∈ Cm×n, and some related linear matrix equations (AXB? ± X? = C, AXB? ± CX?D? = E, AX ± X?A? = C, AX ± Y B = C, AXB ± CY D = E, AXA? ± BY B? = C and AXB ± (AXB)? = C). Solvability conditions and stable numerical methods are considered, in terms of the (generalized and periodic) Schur, QR and (generalized) sing...

Exact soultion of full interval linear equation AX=B based on Kaucher arithmetic

A note on unique solvability of the absolute value equation

It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...

Wave equation and multiplier estimates on ax + b groups

Let L be the distinguished Laplacian on certain semidirect products of R by R which are of ax+ b type. We prove pointwise estimates for the convolution kernels of spectrally localized wave operators of the form e √ ψ( √ L/λ) for arbitrary time t and arbitrary λ > 0, where ψ is a smooth bump function supported in [−2, 2] if λ ≤ 1 and in [1, 2] if λ ≥ 1. As a corollary, we reprove a basic multipl...