Orthogonal rational bases are generalized to expand linear time-varying systems.
The obtained results are generalized to elaborate guidelines for industrial users for selecting suitable signal reconstruction algorithms based on their specific requirements and boundary conditions.
As is well known, NLSDP (1.1) is an extension of nonlinear programming, some efficient numerical methods for the latter are generalized to solve NLSDP.
The methods are generalized to hyperbolic systems that are not in conservation form and to problems that include a "capacity function".
In actual proof-theoretic practice, as well as explicitly in (Hilbert and Bernays, 1934; Bernays, 1930), these basic operations are generalized to operations defined by recursion, paradigmatically, primitive recursion, e.g., multiplication and exponentiation (see Parsons 1998 for a discussion of philosophical difficulties in relation to exponentiation).
But research in textual entailment seems to be moving towards a similar conception, as exemplified in the work of Dagan et al. (2008), where statistical entailment relations are based on syntactic trees, and these are generalized to templates that may replace subtrees by typed variables.
The deriving Hermite-Hadamard type inequalities for certain classes of abstract convex functions are considered totally, the inequalities derived for some of these classes before are summarized, new inequalities for others are obtained, and for one class of these functions the results on are generalized to.
In the middle block the intervals are generalized to fuzzy sets using fuzzification procedure.
The alternative breeder's equation is derived in the third subsection, and all the results are generalized to selection on multiple traits in the fourth subsection.
Both the H2 and H∞ ARE based methods are generalized to consider systems where all input channels are not necessarily subject to saturation, and explicit design methods are developed.
First we consider a one-dimensional LDS with nearest neighborhood to interpret the idea of our methodology, then the derived results are generalized to general cases in the rest of this section.
