We give a sufficient condition in order that an ideal of a real quadratic field F capitulates in the cyclotomic Z3-extension of F by using a unit of an intermediate field. Moreover, we give new examples of F ’s for which Greenberg’s conjecture holds by calculating units of fields of degree 6, 18, 54

<p style='text-indent:20px;'>In this paper, we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in second unknown <inline-formula><tex-math id="M1">\begin{document}$ z $\end{document}</tex-math></inline-formula>. Using a linearization technique and BMO martingale theory, first apply fixed-point argument to...

high-precision three-axis attitude control scheme is vitally important to deal with the overactuated spacecraft, as long as the overall performance through rapid response can be in general acquired. due to the fact that the rigid-flexible spacecraft is somehow applicable, in so many academic and real environments, there is a consensus among experts of this field that the new insights in develop...

In this paper, we give several new results on solvability of a quadratic BSDE whose generator depends also the mean both variables. First, consider such using John-Nirenberg's inequality for BMO martingales to estimate its contribution evolution first unknown variable. Then having an additive expected value in addition usual one. In case, use deterministic shift tra...

has a solution in Fn. The representation problem of quadratic forms is to determine, in an effective manner, the set of elements of F that are represented by a particular quadratic form over F . We shall discuss the case when F is a field of arithmetic interest, for instance, the field of complex numbers C, the field of real numbers R, a finite field F, and the field of rational numbers Q. The ...

The quadratic assignment problem (QAP) is very challengeable and interesting problem that can model many real-life problems. In this paper, we will simply discuss the meaning of quadratic assignment problem, solving techniques and we will give a survey of some developments and researches.

Davenport and Heilbronn defined a bijection between classes of binary cubic forms and classes of cubic fields, which has been used to tabulate the latter. We give a simpler proof of their theorem then analyze and improve the table-building algorithm. It computes the multiplicities of the O(X) general cubic discriminants (real or imaginary) up to X in time O(X) and space O(X3/4), or more general...