Solid solution strengtheningIn metallurgy, solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element (the alloying element) to the crystalline lattice of another element (the base metal), forming a solid solution. The local nonuniformity in the lattice due to the alloying element makes plastic deformation more difficult by impeding dislocation motion through stress fields. In contrast, alloying beyond the solubility limit can form a second phase, leading to strengthening via other mechanisms (e.
ExistenceExistence is the ability of an entity to interact with reality. In philosophy, it refers to the ontological property of being. The term existence comes from Old French existence, from Medieval Latin existentia/exsistentia, from Latin existere, to come forth, be manifest, ex + sistere, to stand. Materialism holds that the only things that exist are matter and energy, that all things are composed of material, that all actions require energy, and that all phenomena (including consciousness) are the result of the interaction of matter.
Existence of GodThe existence of God (or more generally, the existence of deities) is a subject of debate in theology, philosophy of religion and popular culture. A wide variety of arguments for and against the existence of God or deities can be categorized as logical, empirical, metaphysical, subjective or scientific. In philosophical terms, the question of the existence of God or deities involves the disciplines of epistemology (the nature and scope of knowledge) and ontology (study of the nature of being or existence) and the theory of value (since some definitions of God include "perfection").
Bounded operatorIn functional analysis and operator theory, a bounded linear operator is a linear transformation between topological vector spaces (TVSs) and that maps bounded subsets of to bounded subsets of If and are normed vector spaces (a special type of TVS), then is bounded if and only if there exists some such that for all The smallest such is called the operator norm of and denoted by A bounded operator between normed spaces is continuous and vice versa. The concept of a bounded linear operator has been extended from normed spaces to all topological vector spaces.
Linear formIn mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers). If V is a vector space over a field k, the set of all linear functionals from V to k is itself a vector space over k with addition and scalar multiplication defined pointwise. This space is called the dual space of V, or sometimes the algebraic dual space, when a topological dual space is also considered.
