Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...

Let Q be a positive definite integral quadratic form in ti variables, with the additional property that the adjoint form Q' is also integral. Using the functional equation of the Epstein zeta function, we obtain a symmetric functional equation of the ¿-function of Q with a primitive character to mod q (additive or multiplicative) defined by £io(2(x))C(x)-ï. Re(s) > nl2> where the summation exte...

background: background and objectives: the biological variation of body mass index (bmi) and waist circumference (wc) with age may vary by gender. the objective of this study was to investigate the functional relationship of anthropometric measures with age and sex.methods: the data were collected from a population-based cross-sectional study of 1800 men and 1800 women aged 20-70 years in north...