Sentence examples for for any norm from inspiring English sources

Our result holds for a general definition of survivability and for any norm whose ball is specified by a piecewise algebraic curve of bounded degree and with a bounded number of pieces.

It is well known that for any norm on we have.

The second part of Property (i) follows for any norm on from the property of equivalence of norms.

Also, and for any norm defined on the smooth Banach space and there exists a nonempty bounded compact convex set such that the solution of (4.2) is permanent in, for all and some sufficiently large finite with.

Since is an infinitesimal generator of the -semigroup of the infinitesimal generator there exist real constants (which is norm dependent) and satisfying since is a stability matrix, such that for any matrix norm Then, one gets from (2.4 - 2.5 2.4 - 2.5 supremum methat, induced by the supremum normetricthen the supremum norm (2.6).

When the training data is non-separable, we show that the degree of non-separability naturally enters the analysis and informs the properties and convergence guarantees of two standard first-order methods: steepest descent (for any given norm) and stochastic gradient descent.

Notice that for any matrix norm (see, e.g., [1, page 336]).

It is not difficult to see that the results are also valid for any triangular norm satisfying (Delta ( a,a ) ge a).

Then T D is a t-norm on L. Since it holds that T D ≤ T for any t-norm T on L, T D is the smallest t-norm on L. The largest t-norm on a bounded lattice ( L, ≤, 0, 1 ) is given by T ∧ ( x, y ) = x ∧ y.

Thus, T D is T-distributive for any t-norm T on L. □.

For any t-norm T on L, T D is T-distributive.