Various broadband multi-resonator gap-coupled configurations of equilateral triangular microstrip antenna and its compact variation, half equilateral triangular microstrip antenna, are proposed. The broadband proximity fed equilateral triangular microstrip antenna yields bandwidth of more than 650 MHz (~44%), whereas equivalent proximity fed gap-coupled half equilateral triangular microstrip an...

Block lower triangular and block upper triangular matrices are popular preconditioners for nonsymmetric saddle point matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned systems are related. Nonsingular saddle point matrices of the form

Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related.

Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related.

In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...

ultraviolet waves, because of their short wavelength, have a high energy and considerable damaging effects on surfaces. protection against ultraviolet radiations is one of the finishing treatments done on surfaces exposed to sunlight. the importance of this issue in relation to human health, due to complications such as skin burns and cancer, is doubled. up to now, different materials such as z...