Lototsky-Schabl operators on the unit interval

1999 ◽  
Vol 48 (3) ◽  
pp. 517-536 ◽  
Author(s):  
José A. Adell ◽  
Jesús de la Cal ◽  
Ioan Rasa
Keyword(s):  
Unit Interval

scholarly journals A Lochs-Type Approach via Entropy in Comparing the Efficiency of Different Continued Fraction Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 255
Author(s):  
Dan Lascu ◽  
Gabriela Ileana Sebe
Keyword(s):  
Dynamical Systems ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Unit Interval ◽  
Probability Measures ◽  
Absolutely Continuous ◽  
Continued Fraction Expansions ◽  
Absolutely Continuous Invariant

We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aim to compare the efficiency by describing the rate at which the digits of one number-theoretic expansion determine those of another. We study Chan’s continued fractions, θ-expansions, N-continued fractions, and Rényi-type continued fractions. A central role in fulfilling our goal is played by the entropy of the absolutely continuous invariant probability measures of the associated dynamical systems.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

2021 ◽  
pp. 1-23
Author(s):  
Peide Liu ◽  
Tahir Mahmood ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Imaginary Part ◽  
Fuzzy Set ◽  
Score Function ◽  
Aggregation Operators ◽  
Unit Interval ◽  
Multi Criteria Decision Making ◽  
Accuracy Function ◽  
Special Cases

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

scholarly journals GENETICS OF ARGININE BIOSYNTHESIS IN NEUROSPORA CRASSA

Genetics ◽  
1979 ◽  
Vol 93 (3) ◽  
pp. 557-575
Author(s):  
Rowland H Davis
Keyword(s):  
Neurospora Crassa ◽  
Gene Product ◽  
Unit Interval ◽  
Starting Material ◽  
Limited Extent ◽  
Arginine Biosynthesis ◽  
Regulatory Mutants ◽  
Intragenic Complementation ◽  
Translocation Breakpoints ◽  
Bifunctional Gene

ABSTRACT A large number of arginine-requiring mutants of Neurospora was isolated, using a strain already partially impaired in an enzyme of the pathway. Among the mutants, all previously described loci, except one, were represented, and several new loci were defined and mapped. Four groups of mutants were of particular interest. First, thc large group of arg-6 mutants, when tested for intragenic complementation, suggested a bifunctional gene, possibly controlling two steps in ornithine synthesis. This is consistent with the limited enzymic information about this locus. Second, the arg-13 locus was represented by 14 new mutants. All five tested were quite leaky. suggesting that the function controlled by this gene can be rarried out to a limited extent spontaneously or by another gene product. Third, a new locus, arg-14, was defined. It controls a step in ornithine synthesis. It lies in a 1 to 2 map-unit interval between arg-2 and pyr-3 on LG IVR, as shown by mapping in relation tG translocation breakpoints. Fourth, a second new locus whose mutants render the partial mutation in starting material auxotrophic was defined and mapped near the centromere of LG VIL. These new mutants are unable to derepress enzymes of the pathway and may qualify as regulatory mutants.

A Partition of the Unit Interval

1984 ◽  
Vol 91 (9) ◽  
pp. 564 ◽  
Author(s):  
F. S. Cater
Keyword(s):  
Unit Interval

On the continuity of lattice isomorphisms on C(X, I)

2021 ◽  
Vol 71 (6) ◽  
pp. 1477-1486
Author(s):  
Vahid Ehsani ◽  
Fereshteh Sady
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Unit Interval ◽  
Lattice Isomorphism

Abstract We investigate topological conditions on a compact Hausdorff space Y, such that any lattice isomorphism φ : C(X, I) → C(Y, I), where X is a compact Hausdorff space and I is the unit interval [0, 1], is continuous. It is shown that in either of cases that the set of G δ points of Y has a dense pseudocompact subset or Y does not contain the Stone-Čech compactification of ℕ, such a lattice isomorphism is a homeomorphism.

scholarly journals Best Simultaneous Approximation in Orlicz Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-7 ◽  
Author(s):  
M. Khandaqji ◽  
Sh. Al-Sharif
Keyword(s):  
Banach Space ◽  
Simultaneous Approximation ◽  
Closed Subspace ◽  
Orlicz Spaces ◽  
Unit Interval ◽  
Luxemburg Norm ◽  
Integrable Functions ◽  
Best Simultaneous Approximation ◽  
Distance Formula

LetXbe a Banach space and letLΦ(I,X)denote the space of OrliczX-valued integrable functions on the unit intervalIequipped with the Luxemburg norm. In this paper, we present a distance formula dist(f1,f2,LΦ(I,G))Φ, whereGis a closed subspace ofX, andf1,f2∈LΦ(I,X). Moreover, some related results concerning best simultaneous approximation inLΦ(I,X)are presented.

A weak completeness theorem for infinite valued first-order logic

1963 ◽  
Vol 28 (1) ◽  
pp. 43-50 ◽  
Author(s):  
L. P. Belluce ◽  
C. C. Chang
Keyword(s):  
Completeness Theorem ◽  
Unit Interval ◽  
Order Logic ◽  
First Order Logic ◽  
Order System ◽  
First Order ◽  
Recursively Enumerable ◽  
Weak Completeness ◽  
Truth Value

This paper contains some results concerning the completeness of a first-order system of infinite valued logicThere are under consideration two distinct notions of completeness corresponding to the two notions of validity (see Definition 3) and strong validity (see Definition 4). Both notions of validity, whether based on the unit interval [0, 1] or based on linearly ordered MV-algebras, use the element 1 as the designated truth value. Originally, it was thought by many investigators in the field that one should be able to prove that the set of valid sentences is recursively enumerable. It was first proved by Rutledge in [9] that the set of valid sentences in the monadic first-order infinite valued logic is recursively enumerable.

The distribution of the sequence {nξ}(n = 0, 1, 2, …)

1965 ◽  
Vol 61 (3) ◽  
pp. 665-670 ◽  
Author(s):  
John H. Halton
Keyword(s):  
Unit Interval ◽  
Simple Generalization ◽  
Unit Hypercube

Introduction and statement of results. We shall describe how, for successive integers N, the points {nξ}, with n = 0, 1, …,N – 1, are distributed in the closed unit interval U = [0, 1]; by showing how successive points {Nξ,} modify the partition of U produced by the previous points. The simple generalization to the k-dimensional sequence {nξ} = ({nξ(1)},{nξ(2)}, …,{nξ(k)}), in the unit hypercube Uk, is also made.

A PRIMER ON SOLVING FUZZY RELATIONAL EQUATIONS ON THE UNIT INTERVAL

1994 ◽  
Vol 02 (02) ◽  
pp. 205-225 ◽  
Author(s):  
BERNARD DE BAETS ◽  
ETIENNE E. KERRE
Keyword(s):  
Unit Interval ◽  
Triangular Norm ◽  
Fuzzy Relational Equations ◽  
Number Of Publications

This paper has to be considered as a guide to solving fuzzy relational equations on the unit interval. Although the number of publications on this topic is quite impressive, there doesn't seem to exist a handy structured overview of all types of equations and their solution procedures. Our overview starts with a thorough treatment of [Formula: see text] equations and systems of [Formula: see text] equations, with [Formula: see text] a continuous triangular norm. It is shown that these are the basic problems: all other equations, image and composition equations, can be reduced to these problems. We do not only structure well-known results, we also present some new insights in the solution procedures of fuzzy relational equations.

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