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Capital budgeting problems with fuzzy cash flows.

Christer Carlsson, Robert Fuller (1999)

Mathware and Soft Computing

We consider the internal rate of return (IRR) decision rule in capital budgeting problems with fuzzy cash flows. The possibility distribution of the IRR at any r ≥ 0, is defined to be the degree of possibility that the (fuzzy) net present value of the project with discount factor r equals to zero. Generalizing our earlier results on fuzzy capital budegeting problems [Car99] we show that the possibility distribution of the {IRR} is a highly nonlinear function which is getting more and more unbalanced...

Cardinal and ordinal arithmetics of n -ary relational systems and n -ary ordered sets

Jiří Karásek (1998)

Mathematica Bohemica

The aim of this paper is to define and study cardinal (direct) and ordinal operations of addition, multiplication, and exponentiation for n -ary relational systems. n -ary ordered sets are defined as special n -ary relational systems by means of properties that seem to suitably generalize reflexivity, antisymmetry, and transitivity from the case of n = 2 or 3. The class of n -ary ordered sets is then closed under the cardinal and ordinal operations.

Cardinal characteristics of the ideal of Haar null sets

Taras O. Banakh (2004)

Commentationes Mathematicae Universitatis Carolinae

We calculate the cardinal characteristics of the σ -ideal 𝒩 ( G ) of Haar null subsets of a Polish non-locally compact group G with invariant metric and show that cov ( 𝒩 ( G ) ) 𝔟 max { 𝔡 , non ( 𝒩 ) } non ( 𝒩 ( G ) ) cof ( 𝒩 ( G ) ) > min { 𝔡 , non ( 𝒩 ) } . If G = n 0 G n is the product of abelian locally compact groups G n , then add ( 𝒩 ( G ) ) = add ( 𝒩 ) , cov ( 𝒩 ( G ) ) = min { 𝔟 , cov ( 𝒩 ) } , non ( 𝒩 ( G ) ) = max { 𝔡 , non ( 𝒩 ) } and cof ( 𝒩 ( G ) ) cof ( 𝒩 ) , where 𝒩 is the ideal of Lebesgue null subsets on the real line. Martin Axiom implies that cof ( 𝒩 ( G ) ) > 2 0 and hence G contains a Haar null subset that cannot be enlarged to a Borel or projective Haar null subset of G . This gives a negative (consistent) answer to a question of...

Cardinal invariants of the lattice of partitions

Barbara Majcher-Iwanow (2000)

Commentationes Mathematicae Universitatis Carolinae

We study cardinal coefficients related to combinatorial properties of partitions of ω with respect to the order of almost containedness.

Cardinal invariants of ultraproducts of Boolean algebras

Andrzej Rosłanowski, Saharon Shelah (1998)

Fundamenta Mathematicae

We deal with some problems posed by Monk [Mo 1], [Mo 3] and related to cardinal invariants of ultraproducts of Boolean algebras. We also introduce and investigate several new cardinal invariants.

Cardinal sequences and Cohen real extensions

István Juhász, Saharon Shelah, Lajos Soukup, Zoltán Szentmiklóssy (2004)

Fundamenta Mathematicae

We show that if we add any number of Cohen reals to the ground model then, in the generic extension, a locally compact scattered space has at most ( 2 ) V levels of size ω. We also give a complete ZFC characterization of the cardinal sequences of regular scattered spaces. Although the classes of regular and of 0-dimensional scattered spaces are different, we prove that they have the same cardinal sequences.

Cardinal sequences of length < ω₂ under GCH

István Juhász, Lajos Soukup, William Weiss (2006)

Fundamenta Mathematicae

Let (α) denote the class of all cardinal sequences of length α associated with compact scattered spaces (or equivalently, superatomic Boolean algebras). Also put λ ( α ) = s ( α ) : s ( 0 ) = λ = m i n [ s ( β ) : β < α ] . We show that f ∈ (α) iff for some natural number n there are infinite cardinals λ i > λ > . . . > λ n - 1 and ordinals α , . . . , α n - 1 such that α = α + + α n - 1 and f = f f . . . f n - 1 where each f i λ i ( α i ) . Under GCH we prove that if α < ω₂ then (i) ω ( α ) = s α ω , ω : s ( 0 ) = ω ; (ii) if λ > cf(λ) = ω, λ ( α ) = s α λ , λ : s ( 0 ) = λ , s - 1 λ i s ω - c l o s e d i n α ; (iii) if cf(λ) = ω₁, λ ( α ) = s α λ , λ : s ( 0 ) = λ , s - 1 λ i s ω - c l o s e d a n d s u c c e s s o r - c l o s e d i n α ; (iv) if cf(λ) > ω₁, λ ( α ) = α λ . This yields a complete characterization of the classes (α) for all α < ω₂,...

Categorical Pullbacks

Marco Riccardi (2015)

Formalized Mathematics

The main purpose of this article is to introduce the categorical concept of pullback in Mizar. In the first part of this article we redefine homsets, monomorphisms, epimorpshisms and isomorphisms [7] within a free-object category [1] and it is shown there that ordinal numbers can be considered as categories. Then the pullback is introduced in terms of its universal property and the Pullback Lemma is formalized [15]. In the last part of the article we formalize the pullback of functors [14] and it...

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