We construct a specific feedback control scheme for a class of linear parabolic systems such that some nontrivial linear functionals of the state decay faster than the state, while the state is stabilized. In particular, we raise a new question of pole allocation which is subject to constraint, and derive the necessary and sufficient condition: an essential extension of the well known result by W. M. Wonham (1967).

Our aim in this note is to deal with Lindelöf theorems for monotone Sobolev functions with variable exponent.

In this paper we shall give an explicit formula for the coefficient of the expansion of a given generating function raised to an arbitrary power, when that function has an appropriate form. One of the many examples is the generalized Euler numbers and we shall clarify the situation surrounding the congruence $E_{\frac{p-1}{2}}\not\equiv 0 (\text{mod}\ p), p\equiv 1 (\text{mod}\ 4)$, a prime, and restore the priority. At the same time we shall state the true meaning of such a congruence.

In this note we will show that an injection of the hyperbolic plane is Möbius if and only if for some $0<\theta<\pi$, $f$ preserves triangles with an interior angle equal to $\theta$.