We consider the numerical simulation of Hamiltonian systems of ordinary differential equations. Two features of Hamiltonian systems are that energy is conserved along trajectories and phase space volume is preserved by the flow. We want to determine if there are integration schemes that preserve these two properties for all Hamiltonian systems, or at least for all systems in a wide class. This ...

In this letter we establish the impossibility of existence of self replicating machine in the quantum world. We established this result by three different but consistent ways of linearity of quantum mechanics, no signalling criterion and conservation of entanglement under LOCC.

Opening Paragraph: Where do risk preferences come from? How do we decide if it is safe to eat unpasteurized cheese, whether to take up paragliding or mini-golf as a new hobby, whether to save in government bonds or place our money in a new technology hedge fund? Asking about the origin of risk preference in this general form requires two presuppositions, both of which may be challenged. The fir...

In 1950, P. R. Halmos, motivated in part by the successful development of the theory of normal operators, introduced the notions of subnormality and hyponormality for (bounded) Hilbert space operators. An operator T is subnormal if it is the restriction of a normal operator to an invariant subspace; T is hyponormal if T*T > TT*. It is a simple matrix calculation to verify that subnormality impl...

We prove the existence of pairs of models of the same cardinality λ which are very equivalent according to EF games, but not isomorphic. We continue the paper [4], but we don’t rely on it.

Let X be a compact, or path-connected, metric space whose topological dimension is at least 2. We show that there does not exist a continuous choice function (i.e., single-valued choice correspondence) defined on the collection of all finite feasible sets in X. Not to be void of content, therefore, a revealed preference theory in the context of most infinite consumption spaces must either relin...

For the connections model of strategic network formation, with two-way flow of information and without information decay, specific parameter configurations are given for which Nash networks do not exist. Moreover, existence and the scope of Nash network architectures are briefly discussed. JEL Classification Numbers C72 · D85

A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if X is a Banach space such that X ∗ has a SRBF, then X has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space X has an approximative Schauder frame, then X ∗ has a SRBF. Finally, the existence of a non-lin...

This note reports the result of a computer search which shows that no 19-point connguration can be extended to a complete nite projective plane of order 10. Previous work has shown that such a plane, if it exists, must contain 24,675 19-point conngurations. Together, these results imply the non-existence of a projective plane of order 10. This note presents a brief summary of the previous work ...