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1
Content available remote Several Differentiation Formulas of Special Functions. Part IV
100%
Li B. , Wang P.
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nr 3
109-114
EN
In this article, we give several differentiation formulas of special and composite functions including trigonometric function, polynomial function and logarithmic function.
2
Content available remote Generators for algebras dense in $L^{p}$-spaces
100%
Izzo A. , Li B.
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tom 217
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nr 3
243-263
EN
For various $L^{p}$-spaces (1 ≤ p < ∞) we investigate the minimum number of complex-valued functions needed to generate an algebra dense in the space. The results depend crucially on the regularity imposed on the generators. For μ a positive regular Borel measure on a compact metric space there always exists a single bounded measurable function that generates an algebra dense in $L^{p}(μ)$. For M a Riemannian manifold-with-boundary of finite volume there always exists a single continuous function that generates an algebra dense in $L^{p}(M)$. These results are in sharp contrast to the situation when the generators are required to be smooth. For smooth generators we prove a result similar to a known fact about algebras uniformly dense in continuous functions: for M a smooth manifold-with-boundary of dimension n, at least n smooth functions are required in order to generate an algebra dense in $L^{p}(M)$. We also show that on every smooth manifold-with-boundary there exists a bounded continuous real-valued function that is one-to-one on the complement of a set of measure zero.
3
Content available remote Basic Properties of Even and Odd Functions
100%
Li B. , Men Y.
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nr 2
187-192
EN
In this article we present definitions, basic properties and some examples of even and odd functions [6].
4
Content available remote Integrability Formulas. Part III
100%
Li B. , Ma N.
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tom 18
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nr 2
143-157
EN
In this article, we give several differentiation and integrability formulas of composite trigonometric function.
5
Content available remote Integrability Formulas. Part I
100%
Li B. , Ma N.
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tom 18
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nr 1
27-37
EN
In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, and the polynomial function.
6
Content available remote Several Differentiation Formulas of Special Functions. Part III
80%
Li B. , Zhang Y. , Liang X.
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nr 1
37-45
EN
In this article, we give several differentiation formulas of special and composite functions including trigonometric function, inverse trigonometric function, polynomial function and logarithmic function.
7
Content available remote Simple Continued Fractions and Their Convergents
80%
Li B. , Zhang Y. , Korniłowicz A.
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nr 3
71-78
EN
The article introduces simple continued fractions. They are defined as an infinite sequence of integers. The characterization of rational numbers in terms of simple continued fractions is shown. We also give definitions of convergents of continued fractions, and several important properties of simple continued fractions and their convergents.
8
Content available remote Difference and Difference Quotient
80%
Li B. , Zhang Y. , Liang X.
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nr 3
115-119
EN
In this article, we give the definitions of forward difference, backward difference, central difference and difference quotient, and some of their important properties.
9
Content available remote Difference and Difference Quotient. Part II
80%
Li B. , Zhuang Y. , Liang X.
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tom 16
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nr 1
45-49
EN
In this article, we give some important properties of forward difference, backward difference, central difference and difference quotient and forward difference, backward difference, central difference and difference quotient formulas of some special functions [11].MML identifier: DIFF 2, version: 7.8.09 4.97.1001
10
Content available remote Several Integrability Formulas of Special Functions. Part II
80%
Li B. , Zhuang Y. , Men Y. , Liang X.
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nr 1
23-35
EN
In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, the hyperbolic function and the polynomial function [3].MML identifier: INTEGR11, version: 7.11.01 4.117.1046
11
Content available remote Several Integrability Formulas of Some Functions, Orthogonal Polynomials and Norm Functions
80%
Li B. , Zhuang Y. , Xie B. , Wang P.
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nr 1
11-21
EN
In this article, we give several integrability formulas of some functions including the trigonometric function and the index function [3]. We also give the definitions of the orthogonal polynomial and norm function, and some of their important properties [19].MML identifier: INTEGRA9, version: 7.11.01 4.117.1046
12
Content available remote Some Operations on Quaternion Numbers
80%
Li B. , Liang X. , Wang P. , Zhuang Y.
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nr 2
61-65
EN
In this article, we give some equality and basic theorems about quaternion numbers, and some special operations.
13
Content available remote Basic Properties of Periodic Functions
80%
Li B. , Li D. , Men Y. , Liang X.
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nr 4
245-248
EN
In this article we present definitions, basic properties and some examples of periodic functions according to [5].
14
Content available remote Integrability Formulas. Part II
80%
Li B. , Ma N. , Liang X.
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tom 18
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nr 2
129-141
EN
In this article, we give several differentiation and integrability formulas of special and composite functions including trigonometric function, and polynomial function.
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