Philosophers have always sought general theories.’ We have sought general theories of truth, knowledge, justice, and beauty, to mention just a few. In The Principles of Morals and Legislation, for example, Bentham says that ‘By the principle of utility is meant that principle which approves or disapproves of every action whatsoever, according to the tendency which it appears to have to augment ...

Albert algebras, a specific kind of Jordan algebra, are naturally distinguished objects among commutative non-associative algebras and also arise in the context simple affine group schemes type $F_4$, $E_6$, or $E_7$. We study these over an arbitrary base ring $R$, with particular attention to case integers. prove this generality results previously literature special where $R$ is field characte...

Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond to systems involving partly smooth operators, and particular variational inequalities over sets. As classical nonlinear programming, such active‐set structure underlies the design of accelerated local Newton type. We formalize this idea b...

The West, Brown and Enquist (WBE) theory has attracted great interest because it makes general predictions about scaling of ecological processes with body size. Recent research by Muller-Landau and co-workers challenges the generality of this theory by showing that demographic processes in natural forests do not scale in the way that the theory predicts. For WBE theory to be relevant to plant c...

The discussion in Janet, LeCons sur les Systames d 'Aquations aux Dirivkes Partielles, Paris 1929, pp. 74-75, is particularly relevant. The other references are: C. Riquier, Les Systames d'Aquations aux Derivees Partielles, Paris, 1910, and J. M. Thomas, Differential Systems, New York, 1937. 8 See the author's paper "The General Geometry of Paths," Ann. Math., 29, 143-168 (1928). 9 For the defi...

Qualitative physics has achieved considerable success in small and moderate scale problems but methods for managing the scope and depth of knowledge used by human problem solvers remain elusive. We argue that generality in a modelling approach is essential for extending qualitative physics to complex systems. A novel new model architecture is proposed which combines qualitative and quantitative...

The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation if and only if they must remain occurrences of the same variable in every generalization of the derivation. The variables in question are propositional or of another type. A generalization of the deriv...

Multipoint Padé interpolation methods have shown to be very efficient for model reduction of large-scale dynamical systems. The objective of this paper is to analyze the generality of this approach. We mainly focus our attention on the Single Input Single Output case. The generalization of this approach for MIMO model reduction is briefly introduced.

The Dirac quantization ‘procedure’ for constrained systems is well known to have many subtleties and ambiguities. Within this ill-defined framework, we explore the generality of a particular interpretation of the Dirac procedure known as refined algebraic quantization. We find technical conditions under which refined algebraic quantization can reproduce the general implementation of the Dirac s...