Synonyymit & Tietoja | englanti sana BOUNDEDNESS

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Esimerkkejä BOUNDEDNESS käyttämisestä lauseessa

• In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem or Urysohn-Brouwer lemma) states that any real-valued, continuous function on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness if necessary.
• In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm.
• In the Hopf–Rinow theorem, the first characterization of completeness deals purely with the topology of the manifold and the boundedness of various sets; the second deals with the existence of minimizers to a certain problem in the calculus of variations (namely minimization of the length functional); the third deals with the nature of solutions to a certain system of ordinary differential equations.
• It led to what is now known as the "Calderón program", with major parts: Calderón's study of the Cauchy integral on Lipschitz curves, and his proof of the boundedness of the "first commutator".
• Chan and Tong (1986) rigorously proved that the family of STAR models includes the SETAR model as a limiting case by showing the uniform boundedness and equicontinuity with respect to the switching parameter.
• Informally, the martingale convergence theorem typically refers to the result that any supermartingale satisfying a certain boundedness condition must converge.
• Totemic and fragmented in form, De Staebler's figurative sculptures call forth the many contingencies of the human condition, such as resiliency and fragility, growth and decay, earthly boundedness and the possibility for spiritual transcendence.
• The problem of deciding whether for a given Datalog program there is an equivalent nonrecursive program (corresponding to a positive relational algebra query, or, equivalently, a formula of positive existential first-order logic, or, as a special case, a conjunctive query) is known as the Datalog boundedness problem and is undecidable.
• Ross and his coworkers showed that the Legendre and Chebyshev pseudospectral discretizations converge to an optimal solution of a problem under the mild condition of boundedness of variations.
• Topics include Lyapunov stability theory, partial stability, Lagrange stability, boundedness, ultimate boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets, stability of periodic orbits, and stability theorems via vector Lyapunov functions.
• Later, it has been further proved that when only one finite state machine communicates with single type of message while the communication of its partner is unconstrained, we can still decide and identify boundedness, deadlocks, and unspecified reception state.
• Based on the special properties of augmented marked graphs, the properties of the modelled systems, such as liveness, boundedness and reversibility, can be effectively analyzed.
• In 2020, she won a Whitehead Prize of the London Mathematical Society "for her deep contributions to arithmetic dynamics, to equidistribution, to bifurcation loci in families of rational maps, and her recent proof (with DeMarco and Ye) of uniform boundedness results for numbers of torsion points on families of bielliptic genus two curves in their Jacobians".
• Shortly thereafter, Keelin developed the family of metalog distributions, another instance of the QPD class, which is more shape-flexible than the Pearson and Johnson families, offers a choice of boundedness, has closed-form equations that can be fit to data with linear least squares, and has closed-form quantile functions, which facilitate Monte Carlo simulation.
• In order to state the hypergraph regularity and counting lemmas formally, we need to define several rather technical terms to formalize appropriate notions of pseudo-randomness (random-likeness) and boundedness, as well as to describe the random-like blocks and partitions.

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