This paper considers the problem of estimating the population mean Ybar of the study variate Y using information on different parameters such as population mean $(bar{X})$, coefficient of variation $(C_x)$, kurtosis  $beta_{2(x)}$, standard deviation $(S_x)$ of the auxiliary variate x and on the correlation coefficient, $rho$, between the study variate $Y$ and the auxiliary variate $...

1. PROLOGUE. Late in the last millennium, the second author ran a seminar course for undergraduates that was intended to introduce them to problem-solving and question-asking in the context of mathematical research. He led them through the classic " difficult " equation x y = y x (x, y > 0), (1) whose solution is much easier than one would think at first glance. Solutions were sought, first ove...

(1) The term α A Z,ξ0,η0 r(x, y) represents scene information that is of interest. Its magnitude spectrum peaks as DC, since it is a real-positive signal. Following modulation, the DC component of the scene information shifts to the carrier frequency (μμhξ0, μμvη0). We exploit this fact to identify the carrier frequency as the abscissa & ordinate of the largest value in the magnitude spectrum o...

Let $mathcal{A}$ be a $C^*$-algebra and $Z(mathcal{A})$ the‎ ‎center of $mathcal{A}$‎. ‎A sequence ${L_{n}}_{n=0}^{infty}$ of‎ ‎linear mappings on $mathcal{A}$ with $L_{0}=I$‎, ‎where $I$ is the‎ ‎identity mapping‎ ‎on $mathcal{A}$‎, ‎is called a Lie higher derivation if‎ ‎$L_{n}[x,y]=sum_{i+j=n} [L_{i}x,L_{j}y]$ for all $x,y in  ‎mathcal{A}$ and all $ngeqslant0$‎. ‎We show that‎ ‎${L_{n}}_{n...

The ρ-calculus, also called the rewriting calculus, originally emerged from di erent motivations and from a di erent community than the λ-calculus. It was introduced to make explicit all the ingredients of rewriting such as rule application and result [CK01]. In ne the ρ-calculus provides an extension of the λ-calculus with additional concepts originating from rewriting and functional programin...