Abstract This paper studies a controlled backward-forward linear-quadratic-Gaussian (LQG) large population system in Stackelberg games. The leader agent is of backward state and follower agents are forward state. dominating as its enters those agents. On the other hand, state-average all affects cost functional agent. In reality, followers may represent two typical types participants involved m...

Separatrix cycles for a planar quadratic vector field are studied. The results obtained are used to show that in any bounded region of the plane a quadratic vector field has at most a finite number of limit cycles.

~ ABSTRACT. Let L/K be a right quadratic (skew) field extension and let P be a 3-dimensional projective space over K which is embedded in a 3dimensional projective space P over L. Moreover let I be a line of P which ~ carries no point of P. The main result is that even when L or K is a skew ~ field the following holds true: A desarguesian spread of P is given by the ~ ~ set of all lines of P wh...

We describe implementations for solving the discrete logarithm problem in the class group of an imaginary quadratic field and in the infrastructure of a real quadratic field. The algorithms used incorporate improvements over previously-used algorithms, and extensive numerical results are presented demonstrating their efficiency. This data is used as the basis for extrapolations, used to provide...

We investigate the number of limit cycles of a planar quadratic vector field with a perturbed center-like singular point. An upper bound is obtained on the number of δ-good limit cycles of such a vector field (Theorem 1). Here δ is a parameter characterizing the limit cycles: it shows how far those cycles are from the singular points of the vector field and from the infinite points. The bound a...

Starting from the analytic class number formula involving its Lfunction, we first give an expression for the class number of an imaginary quadratic field which, in the case of large discriminants, provides us with a much more powerful numerical technique than that of counting the number of reduced definite positive binary quadratic forms, as has been used by Buell in order to compute his class ...

Let −D be the field discriminant of an imaginary quadratic field. We construct a class of elliptic functions associated naturally with the quadratic field Q( √ −D) which, combined with the general theory of elliptic functions, allows us to provide a unified theory for two fundamental results (one classical and one due to Ramanujan) about the elliptic functions. §

In [Huang-Raskind 2009], the authors proved that the discrete logarithm problem in a prime finite field is random polynomial time equivalent to computing the ramification signature of a real quadratic field. In this paper, we do this for a quadratic extension of a prime field.

We analyze the influence of an external electric field on the ns and np Rydberg states. The impact of an electric field leads to a significant modification of the decay rate. Namely, the additional (linear and quadratic in the field) terms arise in the differential transition probabilities. In contrast to the quadratic term, the linear summand leads to a difference of the hydrogen (H) and antih...