Consider combining several elementary detectors by the extreme decision rule of responding "no" only when all elementary detectors respond "no" and "yes" otherwise. The question raised is: Which psychometric functions for the detectors have the property that the resulting psychometric function is simply the original function displaced in the logarithm of the physical scale? The answer is p(I) =...

vspace{0.2cm} Let $G$ be a graph and $f:V(G)rightarrow {1,2,3,.....left|V(G)right|}$ be a bijection. Let $p_{uv}=f(u)f(v)$ and\ $ d_{uv}= begin{cases} left[frac{f(u)}{f(v)}right] ~~if~~ f(u) geq f(v)\ \ left[frac{f(v)}{f(u)}right] ~~if~~ f(v) geq f(u)\ end{cases} $\ for all edge $uv in E(G)$. For each edge $uv$ assign the label $1$ if $gcd (p_{u...

Page 182 in Ramanujan’s lost notebook corresponds to page 5 of an otherwise lost manuscript of Ramanujan closely related to his paper providing elementary proofs of his partition congruences p(5n + 4) ≡ 0 (mod 5) and p(7n+ 5) ≡ 0 (mod 7). The claims on page 182 are proved and discussed, and further results depending on Ramanujan’s ideas are established.

Brain drain BD, human capital h, and inequality's institutional impact is examined in a model where rent-seeking elite taxes residents voicing affects the likelihood of regime change. We find that BD h's on quality (Q) are as follows: i) Q U-shaped function with maximum (minimum) at = 0 (0 ) BD1, maximized 0; vi) increases high (low) country under host country's immigration promotion (restricti...

Theorem 2: Let H be as in Theorem 1 of Ref. [2]. Then H is pseudo-Hermitian if and only if it is Hermitian with respect to an inner product 〈〈 , 〉〉 that supports a positivesemidefinite basis [3] including the eigenvectors of H . In particular, for every eigenvector ψ of H , 〈〈ψ|ψ〉〉 ≥ 0; if the corresponding eigenvalue is real and nondefective (algebraic and geometric multiplicities are equal), ...