Abstract We define generalised zeta functions associated with indefinite quadratic forms of signature $$(g-1,1)$$ (g-1,1) —and more generally, to complex symmetric matrices whose imaginary ...

Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a “definite totality” but rather is “indefinitely extensible”. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this pictur...

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon. The performance function is assumed to be indefinite and the underlying system affine. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium.

Our purpose is to find positive solutions u ∈ D(R ) of the semilinear elliptic problem −∆u = h(x)u for 2 < p. The function h may have an indefinite sign. Key ingredients are a h-dependent concentration-compactness Lemma and a characterization of compact embeddings of D(R ) into weighted Lebesgue spaces.

Sarnak gave an expressions of Selberg’s zeta function for the modular group in terms of the class numbers and the fundamental units of the indefinite binary quadratic forms. The main result of the present paper is the extension of his expression to the congruence subgroups of the modular groups in SL2(R) and SL2(C).

It is known that the Selberg zeta function for the modular group has an expression in terms of the class numbers and the fundamental units of the indefinite binary quadratic forms. In the present paper, we generalize such a expression to any congruence subgroup of the modular groups in SL2(R) and SL2(C).

In this paper the state-space solution to discretetime H optimization problem for linear timeinvariant infinite-horizon difference equations in Hilbert space and sign-indefinite cost function is proposed. The necessary and sufficient conditions as well as the parametrization of all admissible controllers are derived in terms of the stabilizing solution to the Riccati equation.

In this paper the solution to generalized H sampled-data control problem with sign-indefinite cost function for linear periodic systems is proposed. Using state space approach and following the main ideas of Doyle at al (1989) the necessary and sufficient condition in terms of the existence of stabilizing periodic solutions of DRE is obtained, with the set of all suboptimal controllers paramete...

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium.