The related inequality (1.1) was obtained by Maher [3, Theorem 3.2] who showed that, if A is normal and AT = TA, where T ∈ Cp , then ‖T − (AX −XA)‖p ≥ ‖T‖p for all X ∈ ( ), where Cp is the von Neumann-Schatten class, 1≤ p <∞, and ‖·‖p its norm. Here we show that Maher’s result is also true in the case where Cp is replaced by ( ), the ideal of all compact operators with ‖·‖∞ its norm.Which allow...

The readers of this article should be familiar with modular arithmetic, and may also recall Sophie Germain's identity. This article deals with an application of the identity in solving the equation 3 + 4 = 5. A word about the identity As the name says, Sophie Germain's identity was rst discovered by Sophie Germain. It reads a 4 + 4b = a + 4ab + 4b 4ab = (a + 2b) 4ab = (a + 2ab+ 2b)(a 2ab+ 2b) ....

We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums ∑n k=1 ∏r j=1Hk({1} ) when ∑r j=1 λj ≤ 5. We apply these identities to the study of two congruences modulo a power of a prime.

We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewedaffine and similarity Lie groups, and explain the procedure for a generic Lie group. The time complexity of our algorithms is linear in the number of vertices and they are noise resi...

We utilise a non-local gauge transform which renders the entire action of SUSY QED invariant and respects the SUSY algebra modulo the gauge-fixing condition, to derive twoand three-point ghost-free SUSY Ward identities in SUSY QED. We use the cluster decomposition principle to find the Green’s function Ward identities and then takes linear combinations of the latter to derive identities for the...

The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.