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An intermediate value theorem . . .
, 2005
"... We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages {¯xn}n≥1 of sequences with terms in a given finite set {a1,..., ar}. For every such set we completely characterize the numbers Π (”intermediate values”) with the property that the consecutive average ..."
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We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages {¯xn}n≥1 of sequences with terms in a given finite set {a1,..., ar}. For every such set we completely characterize the numbers Π (”intermediate values”) with the property that the consecutive
THE AFTERMATH OF THE INTERMEDIATE VALUE THEOREM
, 2004
"... The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000–300 B.C.E.). However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to ..."
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to the time of Bolzano’s era (1781–1848). Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work. 1.
The Cantor intermediate value property
 Top. Proc
"... J. Stallings [9] asked the question: "If one considers 2I = [0,1] embedded in I x I 1 as I x 0, can a connectivity function I ~ X be extended to a connectivity function 21 ~ X? " J. L. Corne'tte [3] and J. H. Roberts [8] gave negative answers to this question. A natural question 2 a ..."
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Cited by 1 (1 self)
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arises: "In order for the extension 1 ~ I of a connectivity function I ~ I to be a connectivity function, what is both necessary and sufficient? " Toward this end we defined the Cantor Intermediate Value Property (CIVP) which is given in definition 2. The relationship between the Cantor
Hereditary Indecomposability And The Intermediate Value Theorem
, 2001
"... We show that hereditarily indecomposable spaces can be characterized by a special instance of the Intermediate Value Theorem in their ring of continuous functions. ..."
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We show that hereditarily indecomposable spaces can be characterized by a special instance of the Intermediate Value Theorem in their ring of continuous functions.
An Intermediate Value Theorem for the Arboricities
"... Let G be a graph. The vertex edge arboricity of G denoted by a G a 1 G is the minimum number of subsets into which the vertex edge set of G can be partitioned so that each subset induces an acyclic subgraph. Let d be a graphical sequence and let R d be the class of realizations of d. We prove that ..."
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Let G be a graph. The vertex edge arboricity of G denoted by a G a 1 G is the minimum number of subsets into which the vertex edge set of G can be partitioned so that each subset induces an acyclic subgraph. Let d be a graphical sequence and let R d be the class of realizations of d. We prove that if π ∈ {a, a 1 }, then there exist integers x π and y π such that d has a realization G with π G z if and only if z is an integer satisfying x π ≤ z ≤ y π . Thus, for an arbitrary graphical sequence d and π ∈ {a, a 1 }, the two invariants x π min π, d : We write d r n : r, r, . . . , r for the degree sequence of an rregular graph of order n. We prove that a 1 r n { r 1 /2 }. We consider the corresponding extremal problem on vertex arboricity and obtain min a, r n in all situations and max a, r n for all n ≥ 2r 2.
INTERMEDIATE VALUES AND INVERSE FUNCTIONS ON Nonarchimedean Fields
"... Continuity or even differentiability of a function on a closed interval of a nonArchimedean field are not sufficient for the function to assume all the intermediate values, a maximum, a minimum or a unique primitive function on the interval. These problems are due to the total disconnectedness of ..."
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Cited by 8 (8 self)
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Continuity or even differentiability of a function on a closed interval of a nonArchimedean field are not sufficient for the function to assume all the intermediate values, a maximum, a minimum or a unique primitive function on the interval. These problems are due to the total disconnectedness
A differential intermediate value theorem
, 2000
"... Let T be the field of gridbased transseries or the field of transseries with finite logarithmic depths. In our PhD. we announced that given a differential polynomial P with coefficients in T and transseries ' ! with P (') ! 0 and P () ? 0, there exists an f 2 (';), such that P (f) ..."
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Cited by 3 (0 self)
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Let T be the field of gridbased transseries or the field of transseries with finite logarithmic depths. In our PhD. we announced that given a differential polynomial P with coefficients in T and transseries ' ! with P (') ! 0 and P () ? 0, there exists an f 2 (';), such that P (f) = 0. In this note, we will prove this theorem.
Perhaps the Intermediate Value Theorem 1
"... Abstract: In the context of intuitionistic real analysis, we introduce the set F consisting of all continuous functions φ from [0, 1] to R such that φ(0) = 0 and φ(1) = 1. We let I0 be the set of all φ in F for which we may find x in [0, 1] such that φ(x) = 1 2.It is wellknown that there are fun ..."
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Abstract: In the context of intuitionistic real analysis, we introduce the set F consisting of all continuous functions φ from [0, 1] to R such that φ(0) = 0 and φ(1) = 1. We let I0 be the set of all φ in F for which we may find x in [0, 1] such that φ(x) = 1 2.It is wellknown that there are functions in F that we can not prove to belong to I0, and that, with the help of Brouwer’s Continuity Principle one may derive a contradiction from the assumption that I0 coincides with F. We show that Brouwer’s Continuity Principle also enables us to define uncountably many subsets G of F with the property
© Hindawi Publishing Corp. INTERMEDIATE VALUES AND INVERSE FUNCTIONS
, 2001
"... Continuity or even differentiability of a function on a closed interval of a nonArchimedean field are not sufficient for the function to assume all the intermediate values, a maximum, a minimum, or a unique primitive function on the interval. These problems are due to the total disconnectedness of ..."
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Continuity or even differentiability of a function on a closed interval of a nonArchimedean field are not sufficient for the function to assume all the intermediate values, a maximum, a minimum, or a unique primitive function on the interval. These problems are due to the total disconnectedness
The Varieties of Reference
, 1982
"... Tracing the development of concepts of affect and emotion in mathematics education (ME) research is informative for research on teaching statistics. In both areas, early research focused on more stable aspects of affect beliefs, values and attitudes using surveys to study dimensionality, and corre ..."
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Cited by 544 (2 self)
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Tracing the development of concepts of affect and emotion in mathematics education (ME) research is informative for research on teaching statistics. In both areas, early research focused on more stable aspects of affect beliefs, values and attitudes using surveys to study dimensionality
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