Results 271 to 280 of about 556,704 (329)
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2000
There are many mathematical problems for which the solution is a function of some kind, and it is often whole real line has the useful property that sums and constant multiples of functions in the set are also in the s both possible and convenient to specify in advance the set of functions within which the solution is to be sought.
M. Carter, B. van Brunt
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There are many mathematical problems for which the solution is a function of some kind, and it is often whole real line has the useful property that sums and constant multiples of functions in the set are also in the s both possible and convenient to specify in advance the set of functions within which the solution is to be sought.
M. Carter, B. van Brunt
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International Mathematics Research Notices, 2010
A representation theorem is established for continuous valuations on L p -spaces whose underlying measure is non-atomic. As a consequence, a complete classification is obtained of continuous translation invariant valuations on and of continuous rotation invariant valuations on L p (S n−1 ).2000 AMS subject classification: 46E30 (52B45)
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A representation theorem is established for continuous valuations on L p -spaces whose underlying measure is non-atomic. As a consequence, a complete classification is obtained of continuous translation invariant valuations on and of continuous rotation invariant valuations on L p (S n−1 ).2000 AMS subject classification: 46E30 (52B45)
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Totally probabilistic Lp spaces
2013In this paper, we introduce the notion of probabilistic valued measures as a generalization of non-negative measures and construct the corresponding Lp spaces, for distributions p > "0. It is alsoshown that if the distribution p satises p "1 then, as in the classical case, these spaces are completeprobabilistic normed spaces.
Bahrami, F., Mohammadbaghban, M.
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1998
The L p -spaces of functions the pth power of whose absolute value is integrable are introduced. Minkowski’s and Holder’s inequality are shown, and the L p -spaces are seen to be Banach spaces. Also, the approximation of Lp-functions by smooth ones is discussed. These mollifications are also used to show the existence of partitions of unity.
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The L p -spaces of functions the pth power of whose absolute value is integrable are introduced. Minkowski’s and Holder’s inequality are shown, and the L p -spaces are seen to be Banach spaces. Also, the approximation of Lp-functions by smooth ones is discussed. These mollifications are also used to show the existence of partitions of unity.
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Space scannable LP-DOAS system
SPIE Proceedings, 2003The DOAS technique is currently the developing trend and the main technique of online monitoring of tropospheric air quality measurements. In order to enlarge the scope of monitoring with only one set of instrument, we recently developed an multi-path LP-DOAS system in which we put several sets of retroreflectors at their own appointed remote places ...
Zhenbi Li +4 more
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2002
Let { X,A,μ} be a measure space and let E be a measurable subset of X. A measurable function \(f:E \to {{\mathbb{R}}^{*}}\) is said to be in L P (E) for P≥1 if is integrable on E, i.e., if $$ \left\| f \right\|_p \mathop = \limits^{def} \left( {\smallint _E \left| f \right|^p d\mu } \right)^{1/p} < \infty $$ (1.1 ...
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Let { X,A,μ} be a measure space and let E be a measurable subset of X. A measurable function \(f:E \to {{\mathbb{R}}^{*}}\) is said to be in L P (E) for P≥1 if is integrable on E, i.e., if $$ \left\| f \right\|_p \mathop = \limits^{def} \left( {\smallint _E \left| f \right|^p d\mu } \right)^{1/p} < \infty $$ (1.1 ...
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1989
Before discussing an important special class of measurable functions we prove a fundamental inequality, known as Holder’s inequality. There are two variants, one for sums and one for integrals. The original variant for integrals of continuous functions or Riemann integrable functions was extended to measurable functions without additional difficulties.
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Before discussing an important special class of measurable functions we prove a fundamental inequality, known as Holder’s inequality. There are two variants, one for sums and one for integrals. The original variant for integrals of continuous functions or Riemann integrable functions was extended to measurable functions without additional difficulties.
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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