Results 301 to 310 of about 6,264,556 (344)

Matrix inequalities for the difference between arithmetic mean and harmonic mean

Annals of Functional Analysis, 2015
Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between arithmetic mean and ...
Wenshi Liao, Junliang Wu
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On Means That are Both Quasi-Arithmetic and Conjugate Arithmetic

Acta Mathematica Hungarica, 2001
The authors determine all means of two variables that are simultaneously of the form \[ \psi^{-1}\biggl({\psi(x)+\psi(y)\over 2}\biggr)\quad\text{and}\quad \varphi^{-1}(\varphi(x)+\varphi(y)-\varphi\Bigl({x+y\over 2}\Bigl)). \] The functions \(\psi\) and \(\varphi\) are strictly monotonic, continuous, defined on an open real interval, and one of them ...
Daróczy, Z., Páles, Zs.
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“Meaning” in Arithmetic

The Arithmetic Teacher, 1957
There are so many meanings in arithmetic that the only difficulty in writing on this subject is one of selection. The following ideas are miscellaneous rather than organized.
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Arithmetic Facts without Meaning

Cortex, 1997
The paper presents a single-case study of patient J.G. showing severe calculation problems (and also agraphia, finger agnosia, right-left disorientation and apraxia) after the surgery of a left parietal tumor. Although the patient completely lost conceptual knowledge of arithmetic, she preserved part of memorised fact knowledge (multiplications and ...
M, Delazer, T, Benke
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Arithmetic mean as a linear combination of two quasi-arithmetic means

Publicationes Mathematicae Debrecen, 2002
Under twice continuous differentiability assumptions on the generator functions \(f\) and \(g\), the authors determine all two variable quasi-arithmetic means \(M^{[f]}\), \(M^{[g]}\) and all real numbers \(\lambda\) and \(\mu\) such that \[ \lambda M^{[f]}+\mu M^{[g]}=A, \] where \(A\) denotes the two variable arithmetic mean.
Głazowska, Dorota, Jarczyk, Witold, Matkowski, Janusz   +2 more
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Meanings of savarṇana in Indian Arithmetic*

Ganita Bharati, 2023
Summary: In Indian mathematical texts the term savarṇana ``reduction to the same color'' is usually found in the context of calculation for fractions. A number of explanations for the term have been offered in previous studies, but they slightly differ from each other. The Triśatī{b}hāṣya is an anonymous commentary on Śrīdhara's Triśatī. In the present
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THE MEAN-VALUES OF ARITHMETICAL FUNCTIONS

The Quarterly Journal of Mathematics, 1949
Es wird zunächst folgender Satz bewiesen: Es seien \(\{a_n\}\), \(\{A_n\}\) zwei Folgen, verknüpft durch \[ A_n = \sum_{m\mid n} a_m,\quad a_n = \sum_{m\mid n} \mu(n) A_m, \] dann gilt \[ \lim_{N\to\infty} N^{-1} \sum_{n=1}^N A_n \rightarrow \lim_{N\to\infty} N^{-1} \sum_{n=1}^N a_nn^{-1}, \qquad (N\to\infty), \] wenn es eine positive nichtabnehmende ...
Atkinson, F. V., Lord Cherwell
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Iterative Truncated Arithmetic Mean Filter and Its Properties

IEEE Transactions on Image Processing, 2012
Xudong Jiang
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The Arithmetic-Geometric Mean of Gauss

1997
This paper is an expository account of the arithmetic-geometric mean M(a,b) of two numbers a,b. For \(a,b>0\) define \(a_ 0=a\), \(b_ 0=b\) and \(a_{n+1}=(a_ n+b_ n)/2,\quad b_{n+1}=(a_ nb_ n)^{1/2},\quad n=0,1,2,\ldots.\) It follows by elementary methods that the two sequences \(a_ n\), \(b_ n\) have a common limit M(a,b).
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An Analysis of Meaning in Arithmetic. II

The Elementary School Journal, 1949
Thinking educators recognize that children of all ages need to have arithmetic related to their own experiences. Such a relation not only enriches living but lays an essential background for understanding arithmetic. It is only in this way that children may acquire the necessary understandings for arithmetical processes in a social background.12 ...
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