The condition (C4) is used to obtain the second solution, by a nice homotopy argument, which is a technical hypothesis.
The boundedness of the functions (rho_{x}) and (zeta_{x}) is a technical hypothesis which simplifies the analysis but can be relaxed, provided that the above models have solutions which do not explode in finite time.
Our truthful mechanisms minimize any cost function that is monotone nondecreasing in agentsʼ costs under the technical hypothesis that the possible declarations of the selfish agents belong to a finite set.
Alif [5] studied Π p D ( a, b ) and Π p N ( a, b ) by means of 'zero functions', where the weights a and b were assumed to be sign-changing (i.e., a ± ≢ 0 and b ± ≢ 0 ) continuous functions without 'singular points' (which is a technical hypothesis).
It contained his trace class result with some additional technical hypotheses; a Dec. 1955 Berkeley technical report had the result as eventually published without the extra technical assumption.
The construction of Ultimate-$L$ is still incomplete, and it is not clear yet that it will succeed, for it rests upon some technical hypotheses that need to be confirmed.
It may be represented by the differential inclusion, for a real-valued function u x,t),∂∂t∂uΨ(x/ε,x,u)−∇x⋅∇ηψ(x/ε,x,t,u,∇u)∋f(x/ε,x,t,u), on a bounded domain Ω⊆Rn, t∈ 0,T), together with initial boundary conditions, where Ψ z,x,⋅) is strictly convex and ψ z,x,t,u,⋅) is a C1 convex function, both with quadratic growth, satisfying some additional technical hypotheses.
A direct demonstration of this hypothesis will await the technical possibility to sort out live pSTAT-5+ cells.
But before successful use of hazard information can occur, the scientists' first and main role is to make technical data, hypotheses, and uncertainties understandable to non-technical users of hazard information.
In geeky technical terms, my hypothesis is that conservation will achieve greater conservation gains if it supports plans and actions that optimize meeting multiple objectives (food security, energy, jobs, etc) as opposed to single mindedly pursuing only conservation goals.
As for Aβ oligomers however, while many reports identifying Aβ oligomers as triggers of synaptic degeneration support the amyloid hypothesis, technical restrictions limit interpretations of these results, and their relevance to the human disease is unclear, as we discuss below.
