Sentence examples for under certain hypotheses from inspiring English sources

Under certain hypotheses on the initial data and parameters, we prove that non-simultaneous blow-up is possible.

Under certain hypotheses, we can construct a scattering operator for the Boussinesq equation which carries a neighborhood of 0 in the energy spaceXintoX.

Under certain hypotheses, we approximate solutions in the sense of distributions to problem by a sequence of weak solutions to weak problems.

Under certain hypotheses on the initial data, we get the sufficient and necessary conditions, on which there exist initial data such that non-simultaneous blow-up occurs.

This approximation exploits the fact that (under certain hypotheses) neurons become independent in the thermodynamic limit when the number of neurons N in the network goes to infinity.

A notable approach to the problem is to encode it as a combinatorial problem (under certain hypotheses, such as the pure parsimony criterion) and to solve it using off-the-shelf combinatorial optimization techniques.

We show under certain hypothesis that the neighborhood of the origin is stable in probability.

When E is of index-finite type we show that there exists a conditional expectation G from the crossed-product to A which is unique under certain hypothesis.

Essentially, the SSA shows that under certain hypothesis the time to the next occurrence of a biochemical reaction is a random variable following a negative exponential distribution.

We prove Sobolev inequalities for singular and fractional Radon transforms which are defined as in a paper of Phong and Stein under certain hypothesis on the corresponding Lagrangian ((N*C ′) which does not necessarily have to be a canonical graph.

It is shown that, under certain hypothesis, these methods are able to correct the lack of synopticity in hydrographic data sets, and improve the diagnosis of vertical velocities computed from the Omega equation.