Sentence examples for rigorous meaning from inspiring English sources

We demonstrate that although these heuristic integral expressions look rather singular it is possible to give a rigorous meaning to them by combining constructions from White noise analysis with certain regularization techniques like "loop smearing" and "framing".

In order to give a rigorous meaning to ℓ T, we approximate the Dirac delta function by the heat kernel p ε ( x ) = ( 2 π ε ) - d 2 e - | x | 2 2 ε, x ∈ ℝ d.

This is achieved whenever there is a positive self-adjoint reference operator C that behaves well with respect to the Fβα, allowing us to prove that Dom C1/2 is left invariant by the operators Ut, thereby giving rigorous meaning to the formal expression above.

It is indeed abstract since it does not have any rigorous mathematical meaning but it is only used to visually and conceptually illustrate the dependencies of the CR decision making engine to the "design dimensions": environment, parameters (usually referred to as knobs) and objectives (or criteria defined from the user's expectations).

The rigorous measurement of meaning in life is essential for the study of this key aspect of well-being and quality of life.

"C" is a rigorous inquiry into the meaning of meaning: our need to find it in the world around us and communicate it to one another; our methods for doing so; the hubs and networks and skeins of interaction that result.

Despite the failure of these attempts to provide a rigorous empiricist criterion of meaning, Ayer continued to hold that there was a close connection between evidence and meaning, maintaining that a satisfactory account of confirmation was needed before a fool-proof criterion of empirical meaning could be supplied.

For example, in the "language" L ω,ω1), formulas will have only finitely many free variables, while there will be a host of "useless" quantifiers able to bind infinitely many free variables.[2] These informal definitions need to be tightened up in a rigorous development, but their meaning should be clear to the reader.

For a period immediately following the revelation, a certain amount of wild rage and sanctimony is permissible, but after that the rigorous work of exploring the meaning and motives of an affair must begin.

The judiciary committee's opinion, which Mr. Del Vecchio himself requested after learning how rigorous the rules were, was advisory, meaning that in theory, he could have ignored it and remained on the bench.

Besides the description of the modeling, the discussion includes a mathematically rigorous validation with respect to the meaning of the model as well as a presentation of some numerical results.