1. The extremal formula of binary quadratic functions is studied by using method of undetermined coefficients, substitution method and method of completing the square.

2. The study of extremal surfaces is of substantial interest in mathematics, general relativity and string theory.

3. HCMU metric is a special kind of extremal metric on Riemannian surface with global rotational symmetric.

4. Extremal multi - function,[sentencedict.com/extremal.html] multi - function partial derivative method.

5. The representation theorem with order - extremal points is obtained for compact order - convex sets.

6. An extremal small ant, which looked like an old man, was wriggling on the table.

7. Finally, the Bahadur asymptotic efficient est imator is constructed through extremal statistic.

8. By using algebraic techniques, Some inequalities related to the degree sequence of a graph are established, and the corresponding extremal graphs are also determined.

9. The maximum of the total trapping population in a given system can be obtained by calculating the extremal solution of its analytic equations.

10. In this paper, inverse degree of unicyclic graphs and bicyclic graphs is discussed, and the extremal graphs that reach the upper and lower bounds are given.

11. According to physical signification, three metrical methods are introduced: optical communication stimulant method, extremal measure method and frequency doubling modulation method.

12. The monotone iterative techniques is used to investigate the existence of extremal solution of periodic boundary value problems (PBVP) for neutral delay differential equation.

13. The final optimal results show that the approach with the numerical technique are very effective in obtaining composite with extremal constitutive properties.