Assuming Jensen's diamond principle (⋄) we construct for every natural number n>0 a compact Hausdorff space K such that whenever the Banach spaces C(K) and C(L) are isomorphic some L, then covering dimension of L is equal to n. The constructed separable connected, has few operators i.e. bounded linear operator T:C(K)→C(K) form T(f)=fg+S(f), where g∈C(K) S weakly compact.

Uncertainty principles generated by Lie-groups Abstract: For unbounded operators A, B and C in general, the commutation relation [A, B] = C does not lead to the uncertainty relation ‖Au‖‖Bu‖ ≥ 1 2 |〈Cu, u〉|. If A, B and C are part of the generators of a unitary representation of a Lie group then the uncertainty principle above holds.

This work is concerned with a Freidlin--Wentzell type large deviation principle for family of multiscale quasilinear and semilinear stochastic partial differential equations. Employing the weak c...

An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C∗-embedded subspaces of ω∗, showing that there can be such sets of cardinality c and that it is consistent that ω∗ \ {p} is C∗-embedded for some but not all p ∈ ω∗.

Two ways to deduce the equivalence of field equations general relativity and principle maximum force $c^4/4G$ - or equivalent power $c^5/4G$ are presented. A simple deduction inverse square gravity directly from arises. Recent apparent counterarguments refuted. New tests in astronomy, cosmology, electrodynamics, numerical gravitation quantum proposed.

We show that the semi-linear ordering principle for continuous functions implies the determinacy of all Wadge and Lipschitz games. c © 2006 Elsevier B.V. All rights reserved.

Variational principle for probabilistic learning Yet another justification More simplification of updates for mean-field family Examples Dirichlet Process Mixture On minimization of divergence measures Energy minimization justifications Variational learning with exponential family Mean parametrization and marginal polytopes Convex dualities The log-partition function and conjugate duality Belie...

BACKGROUND Dealing with errors in psychotherapy is challenging, both ethically and practically. There is almost no empirical research on this topic. We aimed (1) to explore psychotherapists' self-reported ways of dealing with an error made by themselves or by colleagues, and (2) to reconstruct their reasoning according to the two principle-based ethical approaches that are dominant in the ethic...

Let HC ′ denote the set of sets of hereditary cardinality less than 2ω. We consider reflection principles for HC ′ in analogy with the Levy reflection principle for HC. Let B be a class of complete Boolean algebras. The principle Max(B) says: If R(x1, . . . , xn) is a property which is provably persistent in extensions by elements of B, then R(a1, . . . , an) holds whenever a1, . . . , an ∈ HC ...