We use difference sets to construct interesting sets of lines in complex space. Using (v, k, 1)-difference sets, we obtain k2−k+1 equiangular lines in Ck when k − 1 is a prime power. Using semiregular relative difference sets with parameters (k, n, k, λ) we construct sets of n + 1 mutually unbiased bases in Ck. We show how to construct these difference sets from commutative semifields and that ...

We use combinatorial and Fourier analytic arguments to prove various non-existence results on systems of real and complex unbiased Hadamard matrices. In particular, we prove that a complete system of complex mutually unbiased Hadamard matrices (MUHs) in any dimension cannot contain more than one real Hadamard matrix. We also give new proofs of several known structural results in low dimensions.

We show that non of the spaces ( ⊕∞ n=1 lp)lq , 1 ≤ p ̸= q < ∞ have a greedy basis. This solves a problem raised by Dilworth, Freeman, Odell and Schlumprect. Similarly, the spaces ( ⊕∞ n=1 lp)c0 , 1 ≤ p < ∞, and ( ⊕∞ n=1 co)lq , 1 ≤ q < ∞, do not have greedy bases. It follows from that and known results that a class of Besov spaces on Rn lack greedy bases as well.

We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions which are power of a prime is presented. It is also proved that in any dimension d ...

This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $bar{b} = 1-b$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed ...

Changes in the physicochemical conditions of process unit, even under control, may lead to what are generically referred to as faults. The cognition of causes is very important, because the system can be diagnosed and fault tolerated. In this article, we discuss and propose an artificial neural network that can detect the incipient and gradual faults either individually or mutually. The mai...

Banc assurance is a concept of "Rightpartnership" between bank and insurance company to work hand in be mutually benefitted by each other's expertise the existing market. It model, which partner companies try take leverage others competencies offer non banking products act as one stop shop. In India, after privatization lots private player have entered market hence competing find out new ways i...