We’re excited to celebrate International Women’s Day on March 8, as well as Women’s History Month, by spotlighting the Journal of Middle East Women’s Studies (JMEWS) throughout March. JMEWS is the official journal of the Association for Middle East Women’s Studies. This interdisciplinary journal advances the fields of Middle East gender, sexuality, and women’s studies through the contributions of academics, artists, and activists from around the globe working in the interpretive social sciences and humanities.
Interested in reading more? Here are the top ten most frequently read articles from JMEWS from the past year:

 “The Active Social Life of “Muslim Women’s Rights”: A Plea for Ethnography, Not Polemic, with Cases from Egypt and Palestine”
Lila AbuLughod
Volume 6, Issue 1
March 2010  “Everyday Intimacies of the Middle East”
Asli Zengin
Volume 12, Issue 2
July 2016  “Making Gender Dynamics Visible in the 2016 Coup Attempt in Turkey”
Banu Gökariksel
Volume 13, Issue 1
March 2017  “Muslim Diaspora: Gender, Culture and Identity by Haideh Moghissi”
Reviewed by Karen Leonard
Volume 4, Issue 2
Spring 2008  “Depicting Victims, Heroines, and Pawns in the Syrian Uprising”
Edith Szanto
Volume 12, Issue 3
November 2016  “Sawt Al Niswa”
Edith Szanto
Volume 11, Number 3
November 2015  “Saudi Arabian Women and Group Activism”
Edith Szanto
Volume 11, Issue 2
July 2015  “Middle East Masculinity Studies: Discourses of “Men in Crisis,” Industries of Gender in Revolution”
Paul Amar
Volume 7, Issue 3
Fall 2011  “Men’s Coups, Women’s Troubles”
Yeşim Arat
Volume 13, Issue 1
March 2017  “Castration, Sexual Violence, and Feminist Politics in PostCoup Attempt Turkey”
Zeynep Kurtuluş Korkman
Volume 13, Issue 1
March 2017
 “The Active Social Life of “Muslim Women’s Rights”: A Plea for Ethnography, Not Polemic, with Cases from Egypt and Palestine”
here we see as most read articles as say prof dr mircea orasanu and prof horia orasanu as followed
SOME ASPECTS OF GEOMETRIC TRANSFORMS AND MEAN VALUE OF INTEGRAL
ABSTRACT
these implies on the oscillatory and asymptotic behavior on the bounded solutions of differential forms
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here we mention as say prof dr mircea orasanu the following
DARBOUX THEOREM AND FERMAT THEOREM
ABSTRACT
In mathematics, Darboux’s theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that every function that results from the differentiation of other functions has the intermediate value property: the image of an interval is also an interval.
When ƒ is continuously differentiable (ƒ in C1([a,b])), this is a consequence of the intermediate value theore
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here we can see that appear some as say prof dr mircea orasanu and prof horia orasanu as followed with
HISTORY AND LAGRANGIAN FORMS
ABSTRACT The aim of this journal is to foster awareness of philosophical aspects of mathematics education and mathematics, understood broadly to include most kinds of theoretical reflection; to freely disseminate new thinking in these areas to interested persons; to encourage informal communication, dialogue and international cooperation between teachers, scholars and others engaged in such research and reflections.In keeping with the aims of the journal the editorial hand is used very lightly. This is an international unrefereed journal which aims to stimulate the sharing of ideas for no other reason than an interest in the ideas and love of discussion among its contributors and readers. If a contribution has some relevance to the broad areas of interest concerned, and contains some features of value it will be included; and these criteria are used very liberally.
Please send any items for inclusion to the editor including an electronic copy on disc or Email. Word for Windows versions 6 and 7 preferred, but most word processing formats can be accommodated. Most items are welcome include papers, short contributions, letters, discussions, provocations, reactions, halfbaked ideas, notices of relevant research groups, conferences or publications, reviews of books and papers, or even books or papers for review. Diagrams, figures and other inserted items are not always easy to accommodate and can use up a great deal of web space, so please use these economically in submissions
1 . INTRODUCTION
Surfaces do not need to be in R3; replacing R3 with a general space X yields a valid definition. In fact, some of the surfaces we will examine cannot be placed in R3.
For a sphere of radius r centered at the origin, a coordinate patch is x(u, v) = (rcos(u)cos(v), rsin(u)cos(v), rsin(v)), for – < u < , and – < v True].
Lastly, the two plots are shown together: Show[g1,g2,Lighting> True,ViewPoint>{x,y,z}]. Finding the proper viewpoint depends on the geodesic, and often requires trial and error. Now, we give specific examples of
this procedure by finding and plotting geodesics on several surfaces.
The Sphere
For the patch for the sphere, we see that G = xu ● xu = r2, and E = xv ● xv = r2cos2u, so the patch for the sphere is a vClairaut patch. So, using a unit sphere for simplicity, and . So . This implies
, and so
(13)
Note that the components of the patch for the sphere are here in this last equation. Setting x = cosu cosv, y= sinu cosv, z = sinv, we see that equation (13) implies that the points all lie on the same plane. So a geodesic on a sphere is the intersection of the sphere and a plane.
Moreover, note that if a point (x, y, z) on the sphere satisfies (13) so too does (x, y, z). So if the plane in question includes (x, y, z), it includes (x, y, z). Hence it includes the line between them, and therefore the plane passes through the origin. So a geodesic on the sphere is the intersection of the sphere and a plane passing through the origin—a great circle! Choosing two points that are not antipodal—that is, not on opposite sides of the sphere—allows one to solve for a unique k and c.
Using the Mathematica procedure above verifies the fact that the geodesics on a sphere are great circles. Figure 4 shows a few geodesics on a sphere.
The opinions expressed in this work are those of the authors and do not necessarily reflect the official policy of the Council of Europe.
All correspondence concerning this publication or the reproduction or translation of all or part of the document should be addressed to the Director of School, Out of School and Higher Education of the Council of Europe (F67075 Strasbourg Cedex).
The reproduction of extracts is authorised, except for commercial purposes, on conditio
Language in Mathematics? A comparative study of four national curricula
Sigmund Ongstad 7
Language across the mathematics curriculum in England
Birgit Pepin 15
Language across the mathematics curriculum in Sweden
Brian Hudson and Peter Nyström 21
Language across the mathematics curriculum in Romania
Mihaela Singer 35
Language and communication in Norwegian curricula for mathematics
Sigmund Ongstad 51
Culture, language and mathematics education: aspects of language
in English, French and German mathematics education
Birgit Pepin 59
Language across the mathematics curriculum: some aspects related
to cognition
Florence Mihaela Singer 71
Language in Mathematics?
A comparative study of four national curricula
Sigmund Ongstad
Background
This short, somewhat summative study builds on four coordinated smallscale investigations of the explicit role of language and communication in mathematics curricula in England, Norway, Sweden and Romania. The study aims at addressing major, relevant key issues for an overall, international framework for language(s) of schooling. The background papers and texts hence consist of a study of each country’s curriculum (Pepin, 2007a, Hudson and Nyström, 2007, Singer, 2007a and Ongstad, 2007a). The Swedish and the Romanian studies both have an attachment. In the former, particular tasks for evaluating language in mathematics are discussed. The latter gives a rather detailed overview over how language and communication is discursively positioned within the national curriculum in mathematics in Romania.
Finally there are two other texts published separately, one by B. Pepin that compares mathematics education in United Kingdom, Germany and France (Pepin, 2007b), and one by F. M. Singer that discusses the role of cognition in relation to language (Singer, 2007b). A longer paper by S. Ongstad, published separately, will sum up how language and communication is positioned within mathematics education on the curricular level in more general terms (Ongstad, 2007b). This overarching text will even suggest
Figure 4
Returning to the example of a plane flying from New York City to Madrid,
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and here we see since as say prof dr mircea orasanu and prof horia orasanu as followed
THE MOST HISTORY IN SCIENCE
ABSTIn considering the aim of mathematics and its role in education, compulsory schooling has the task of:
…providing pupils with the knowledge in mathematics needed for them to be able to make wellfounded decisions when making different choices in everyday life, in order to be able to interpret and use the increasing flow of information and be able to follow and participate in decisionmaking processes in society. It is intended that the subject should provide a sound basis for studying other subjects, for further education and lifelong learning.
The importance of mathematics as part of the wider culture and education is stressed in terms of giving an insight into the subject’s historical development, its significance and role in society. A central aim of the subject is seen in terms of developing the pupil’s interest in mathematics and aspects of language and communication are highlighted
RACT
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we consider more aspects of sets and other situations as observed prof dr mircea orasanu and prof horia orasanu for followings
HISTORY OF DEDEKIND ,CANTOR RESULTS IN CASE OF LEBESGUE INTEGRATION
ABSTRACT
We need to restrict to subsets of the real line for which translation invariance and countable additivity holds; when we use Lebesgue outer measure on these sets we call it Lebesgue measure.
So, what we are going to show is this: if we restrict our sets to those sets for which:
(where is the set complement of ) for ALL subsets , then Lebesgue outer measure IS countably additive with respect to those subsets. Lebesgue outer measure applied to these sets is called Lebesgue measure.
Note: If is true we say that “ splits and sometimes refer to as a “test set”.
So, why is this condition the one that we want? Well, well prove the following results assuming that the given sets splits all test sets .
1. If and are measurable sets (e. g., splits all sets ) then is also measurable (splits all sets) and is also measurable.
Proof: first recall that by countable subadditivity of Lebesgue outer measure. We need to show the other inequality.
First recall that by DeMorgan’s laws. (the latter is supposed to be the compliment of the union of the set .
Now because is measurable, (1)
Now recall that, from basic set theory,
1 INTRODUCTION
So now attempt to compute: (3)
But is measurable and therefore splits and so the last two terms can be combined to so (3) becomes which is the right hand of inequality (2).
So, it follows by a routine induction argument than a finite union of measurable sets is measurable.
Now, what about the intersection? If and are measurable, so are their complements (and vicaversa; the definition is symmetric). Now recall that = (note: the outer “ ” denotes set complement as I couldn’t get the LaTex command for the outer “tilde” to work) and the result follows.
2. Now we show finite additivity of disjoint measurable sets :
We need to show that
Clearly, the statement is true for . Assume that the statement is true for all integers up to .
Now by disjointness, and .
Now splits therefore
3. We now need to show that the countable union of measurable sets is measurable.
First note that if we can assume that the are disjoint. Here is why: Let , , and so on. Then and the are mutually disjoint. So we can assume with no loss of generality that the have this property.
Note: I am getting tired of the “tilde” notation and so will be using the notation to denote the set complement.
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here also we remember aspects as see prof dr mircea orasanu and prof horia orasanu and followed
LEBESGUE THEOREM AND INTEGRATION WITH FUBINI THEOREM
LAGRANGIAN AND FATOU
ABSTRACT
The advantage of the Fubini–Tonelli over Fubini’s theorem is that the repeated integrals of the absolute value of f may be easier to study than the double integral. As in Fubini’s theorem, the single integrals may fail to be defined on a measure 0 set.
For complete measures
The versions of Fubini’s and Tonelli’s theorems above do not apply to integration on the product of the real line R with itself with Lebesgue measure. The problem is that Lebesgue measure on R×R is not the product of Lebesgue measure on R with itself, but rather the completion of this: a product of two complete measure spaces X and Y is not in general complete. For this reason one sometimes uses versions of Fubini’s theorem for complete measures: roughly speaking one just replaces all measures by their completions. The various versions of Fubini’s theorem are similar to the versions above, with the following minor differences:
• Instead of taking a product X×Y of two measure spaces, one takes the completion of some product.
• If f is a measurable on the completion of X×Y then its restrictions to vertical or horizontal lines may be nonmeasurable for a measure zero subset of lines, so one has to allow for the possibility that the vertical or horizontal integrals are undefined on a set of measure 0 because they involve integrating nonmeasurable functions. This makes little difference, because they can already be undefined due to the functions not being integrable.
• One generally also assumes that the measures on X and Y are complete, otherwise the two partial integrals along vertical or horizontal lines may be welldefined but not measurable. For example, if f is the characteristic function of a product of a measurable set and a nonmeasurable set contained in a measure 0 set then its single integral is well defined everywhere but nonmeasurable.
1 . INTRODUCTION
The following examples show how Fubini’s theorem and Tonelli’s theorem can fail if any of their hypotheses are omitted.
Failure of Tonelli’s theorem for non σfinite spaces
Suppose that X is the unit interval with the Lebesgue measurable sets and Lebesgue measure, and Y is the unit interval with all subsets measurable and the counting measure, so that Y is not σfinite. If f is the characteristic function of the diagonal of X×Y, then integrating f along X gives the 0 function on Y, but integrating f along Y gives the function 1 on X. So the two iterated integrals are different. This shows that Tonelli’s theorem can fail for spaces that are not σfinite no matter what product measure is chosen. The measures are both decomposable, showing that Tonelli’s theorem fails for decomposable measures (which are slightly more general than σfinite measures).
Failure of Fubini’s theorem for nonmaximal product measures
Fubini’s theorem holds for spaces even if they are not assumed to be σfinite provided one uses the maximal product measure. In the example above, for the maximal product measure, the diagonal has infinite measure so the double integral of f is infinite, and Fubini’s theorem holds vacuously. However, if we give X×Y the product measure such that the measure of a set is the sum of the Lebesgue measures of its horizontal sections, then the double integral of f is zero, but the two iterated integrals still have different values. This gives an example of a product measure where Fubini’s theorem fails.
This gives
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in this case we consider some important aspects as look prof dr mircea prasanu and prof horia orasanu as followed
FUNDAMENTAL CONSIDERATIONS OF FERMAT THEORIES. LAGRANGIAN
ABSTRACT
which means it can’t be in ALL of them and therefore can’t be in the intersection.
What does this have to do with our measurable sets? We’ve just seen that the countable union of measurable sets is measurable and by symmetry, the complement of a measurable set is measurable. Hence the countable intersection of measurable sets is measurable.
Set algebras An algebra of sets is a collection of sets which is closed with respect to finite unions and complements; hence it is immediate that the set of measurable sets forms a set algebra.
Sigma algebras A set algebra is called a sigmaalgebra if it is closed with respect to countable unions as well (and by DeMorgan’s laws: closed with respect to countable intersections as well). So we’ve just shown that the collection of measurable sets forms a sigmaalgebra.
What we haven’t shown is a single measurable set as yet! THAT is what we are going to do next. and thus we conclude that AMS :: Quarterly of Applied Mathematics – American Mathematical has only false results as written in ..QUARTERLY OF APPLIED MATHEMATICS
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