# Integral Solutions of xï¿½ + yï¿½ = wï¿½ + Dzï¿½

## Related Articles

- Integral Solutions of kxy - w(x + y) = zï¿½. Gopalan, M. A.; Vidhyalakshmi, S. // Advances in Theoretical & Applied Mathematics;2006, Vol. 1 Issue 2, p167
We search for non-zero integer quadruples (x, y, z, w) satisfying the quadratic equation kxy - w(x + y) = zï¿½. The recurrence relations for the solutions are presented. Given a solution, a general formula for the generation of solutions is also obtained.

- On Bivariate Quadratic Equation kxy + 2m(x + y) = xï¿½ - yï¿½. Gopalan, M. A.; Vidhyalakshmi, S. // Advances in Theoretical & Applied Mathematics;2006, Vol. 1 Issue 2, p163
Non-trivial integral solutions of the bivariate quadratic equation kxy + 2m(x + y) = xï¿½-yï¿½, (k, m ? 0) are obtained. Recurrence relations for x,y are given. Interesting results among the solutions are presented.

- ANALYTICAL EXPLICIT FORMULA FOR PERFORMANCE OF CUMULATIVE SUM PROCEDURE FOR EXPONENTIAL DISTRIBUTION. Areepong, Yupaporn; Sukparungsee, Saowanit // Far East Journal of Mathematical Sciences;Nov2013, Vol. 82 Issue 1, p119
The main goal of this paper is to derive explicit formulas of Average Run Length (ARL) by using integral equation technique for detecting changes in process mean. We find explicit formulas of ARL for Cumulative Sum chart when observations are independent and identically distributed (i.i.d.)...

- Approximate solution of the two-dimensional singular integral equation. Ashyralyyev, Charyyar; Cakir, Zafer // AIP Conference Proceedings;2014, Vol. 1611, p73
Approximate quadrature formulas for the numerical calculation of the two-dimensional Vekua potential and singular integrals are obtained. The mechanical quadrature method for the two-dimensional quasilinear singular integral equation with Vekua operators is described. The numerical results are...

- Integral Solutions of Ternary Quadratic Equation. Gopalan, M. A.; Vidhayalakshmi, S.; Devibala, S. // Advances in Theoretical & Applied Mathematics;2007, Vol. 2 Issue 2, p145
Different patterns of non-zero integral solutions for the ternary quadratic diophantine equation xÂ² = yÂ² - xz - 2yz - 2zÂ² = 0 are obtained. A few interesting properties satisfied by the solutions are presented. Knowing a solution, a method of generating sequence of solutions is illustrated.

- Difference Equations and Pieri Formulas for G 2 Type Macdonald Polynomials and Integrability. Van Diejen, Jan Felipe; Ito, Masahiko // Letters in Mathematical Physics;Nov2008, Vol. 86 Issue 2/3, p229
We present a second explicit difference equation andâ€”by duality symmetryâ€”a second explicit Pieri formula for the Macdonald polynomials associated with the exceptional root system of type G 2, complementing the celebrated difference equation and Pieri formula due to Macdonald. As...

- Averaging of the magnetic properties of fibrous ferromagnetic composites. Fil'shtyns'kyi, L.; Shramko, Yu.; Kovalenko, D. // Materials Science;Sep2011, Vol. 46 Issue 6, p808
Within the framework of the model of regular structures, we average the magnetic properties of fibrous ferromagnetic composites with biperiodic structure. For the general case of packing of the fibers in any cross section, the problem is reduced to finding certain functionals determined from the...

- New Formulas for the Eigenfunctions of the Two-Particle Difference Calogeroâ€“Moser System. Gaillard, Pierre; Matveev, Vladimir // Letters in Mathematical Physics;Jul2009, Vol. 89 Issue 1, p1
We present a new proof of the integrability of the DDPT-I equation. The DDPT-I equation represents a functional-difference deformation of the well-known Darbouxâ€“PÃ¶schlâ€“Teller equation. The proof is based on some formula for special Casorati determinants established in the paper....

- Note on a q-Contour Integral Formula of Gasper-Rahman. Jian-Ping Fang // Abstract & Applied Analysis;2013, p1
We use the q-Chu-Vandermonde formula and transformation technique to derive a more general q-integral equation given by Gasper and Rahman, which involves the Cauchy polynomial. In addition, some applications of the general formula are presented in this paper.