Relevant bibliographies by topics / Alternative extension of the real numbers set

Contents

  1. Journal articles
  2. Book chapters
  3. Conference papers
  4. Reports

Academic literature on the topic 'Alternative extension of the real numbers set'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Alternative extension of the real numbers set.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Alternative extension of the real numbers set"

1

Sukhotin, A., and M. Zvyagin. "Alternative analysis: the prime numbers theory and an extension of the real numbers set." Bulletin of Science and Practice 398, no. 10(11) (2016): 10–14. https://doi.org/10.5281/zenodo.160909.

Full text
Abstract:
Here we consider the theory of prime numbers at a new methodology. The theory of prime numbers is one of the most ancient mathematical branches. We found an estimate of the all prime numbers sum using the notions of infinite lager numbers and infinitely small numbers, farther we estimated the value of the maximal prime number. We proved that Hardy–Littlewood Hypothesis has the positive decision too. The infinite small numbers define a new methodology of the well–known function o(x) application. We use the sets of the theory of prime numbers and infinitely small numbers with a linear function t
APA, Harvard, Vancouver, ISO, and other styles
2

Sukhotin, A. "Alternative analysis: some new methodology and extension of the real numbers set." Bulletin of Science and Practice, no. 11 (November 13, 2017): 16–20. https://doi.org/10.5281/zenodo.1048277.

Full text
Abstract:
Positive definitions made it possible to prove new theorems on well-known objects of analysis: numerical sequences and series. The estimates of the quantity of all primes and the largest of them are obtained. With linear function at, we define an Alternative extension of the real numbers set.
APA, Harvard, Vancouver, ISO, and other styles
3

Panev, A., and A. Sukhotin. "The limiting values of smoothly–convex monotonic functions and properties of infinity." Bulletin of Science and Practice, no. 3 (March 15, 2017): 8–13. https://doi.org/10.5281/zenodo.399057.

Full text
Abstract:
An introduction contains the short methodological agreement on symbols and on terms, on concepts and on mathematical texts. Then we have find the border between a finite and an infinite subset of the linearly ordered set. By definition each subset of the final set (except trivial) has two boundary points. The set is called as an infinite set if there [{exits}] its subset, which has less two boundary points. Further we have established some facts of the theory of smoothly convex monotonous functions. In particular, smoothly convex monotonous functions have the nonnegative first derivative and t
APA, Harvard, Vancouver, ISO, and other styles
4

Sen, Dilip Kumar, Saurav Datta, and Siba Sankar Mahapatra. "Extension of TODIM combined with grey numbers: an integrated decision making module." Grey Systems: Theory and Application 5, no. 3 (2015): 367–91. http://dx.doi.org/10.1108/gs-05-2015-0029.

Full text
Abstract:
Purpose – Decision making is the task of selecting the most appropriate alternative among a finite set of possible alternatives with respect to some attributes. The attributes may be subjective or objective (or combination of both), depending upon the situation; requirements may also be conflicting. In practice, most of the real-world decision-making problems are based on subjective evaluation criteria which are basically ill-defined and vague. Since subjective human judgment bears ambiguity and vagueness in the decision making; application of grey numbers set theory may be proved fruitful in
APA, Harvard, Vancouver, ISO, and other styles
5

Remad, Fedia Daami, and Hela Moalla Frikha. "The multicriteria group decision making FlowSort method under uncertainty." Multiple Criteria Decision Making 16 (2021): 122–39. http://dx.doi.org/10.22367/mcdm.2021.16.07.

Full text
Abstract:
Crisp values are insufficient to model real-life situations and imprecise ideas are frequently represented in multicriteria decision aid analysis. In fact, it is difficult to treat the evaluation criteria precisely and to fix exact preferences rating. The triangular intuitionistic fuzzy numbers succeeded to treat this kind of ambiguity in a great deal of research than other forms of fuzzy representation functions. The field of sorting issues is an active research topic in the multiple criteria decision aid (MCDA). This study extended one of the sorting methods, FLOWSORT, for solving multiple c
APA, Harvard, Vancouver, ISO, and other styles
6

Lev, Raskin, and Sira Oksana. "Development of methods for extension of the conceptual and analytical framework of the fuzzy set theory." Eastern-European Journal of Enterprise Technologies 6, no. 4(108) (2020): 14–21. https://doi.org/10.15587/1729-4061.2020.217630.

Full text
Abstract:
Fuzzy set theory is an effective alternative to probability theory in solving many problems of studying processes and systems under conditions of uncertainty. The application of this theory is especially in demand in situations where the system under study operates under conditions of rapidly changing influencing parameters or characteristics of the environment. In these cases, the use of solutions obtained by standard methods of the probability theory is not quite correct. At the same time, the conceptual, methodological and hardware base of the alternative fuzzy set theory is not sufficientl
APA, Harvard, Vancouver, ISO, and other styles
7

Riaz, Muhammad, Wojciech Sałabun, Hafiz Muhammad Athar Farid, Nawazish Ali, and Jarosław Wątróbski. "A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management." Energies 13, no. 9 (2020): 2155. http://dx.doi.org/10.3390/en13092155.

Full text
Abstract:
A q-rung orthopair fuzzy set (q-ROFS), an extension of the Pythagorean fuzzy set (PFS) and intuitionistic fuzzy set (IFS), is very helpful in representing vague information that occurs in real-world circumstances. The intention of this article is to introduce several aggregation operators in the framework of q-rung orthopair fuzzy numbers (q-ROFNs). The key feature of q-ROFNs is to deal with the situation when the sum of the qth powers of membership and non-membership grades of each alternative in the universe is less than one. The Einstein operators with their operational laws have excellent
APA, Harvard, Vancouver, ISO, and other styles
8

Fedia, Remadi Daami, and Frikha Moalla Hela. "The Intuitionistic Fuzzy FlowSort Method for Multicriteria Group Decision Making." International Journal of Fuzzy System Applications 11, no. 1 (2022): 1–21. http://dx.doi.org/10.4018/ijfsa.285554.

Full text
Abstract:
The real life problems are multidimensional in nature and may involve some ambiguity when it comes to decision making. It is, therefore, difficult to design the evaluation criteria precisely and determine the exact value of the attributes in the multicriteria analysis. The intuitionistic fuzzy set (IFS) achieved great success in treating this kind of ambiguity in a great deal of research. The study of sorting problems is an active research issue in the multiple criteria decision aid (MCDA) area. This paper investigated one of the sorting methods, FLOWSORT, and extended it to the multicriteria
APA, Harvard, Vancouver, ISO, and other styles
9

Solatikia, Farnaz, Erdem Kiliç, and Gerhard Wilhelm Weber. "Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces." Organizacija 47, no. 2 (2014): 90–97. http://dx.doi.org/10.2478/orga-2014-0010.

Full text
Abstract:
Abstract Background: This paper generalizes the results of Embedding problem of Fuzzy Number Space and its extension into a Fuzzy Banach Space C(Ω) × C(Ω), where C(Ω) is the set of all real-valued continuous functions on an open set Ω. Objectives: The main idea behind our approach consists of taking advantage of interplays between fuzzy normed spaces and normed spaces in a way to get an equivalent stochastic program. This helps avoiding pitfalls due to severe oversimplification of the reality. Method: The embedding theorem shows that the set of all fuzzy numbers can be embedded into a Fuzzy Ba
APA, Harvard, Vancouver, ISO, and other styles
10

Hashim, Hazwani, Noor Azzah Awang, and Lazim Abdullah. "A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making." International Journal of Neutrosophic Science 22, no. 1 (2023): 86–103. http://dx.doi.org/10.54216/ijns.220107.

Full text
Abstract:
Decision-making problems involve uncertain and incomplete information, which can be well represented by the Neutrosophic set (NS). Various extensions of NS are available in the literature for solving such problems. However, the published extensions of NS have some restrictions such as single based membership degree. Neutrosophic vague set (NVS) is a newly developed theory to address the shortcomings of previous set theory. NVS is structured based on interval membership in the context of dependent membership functions. Beside uncertainty information, aggregation operators (AOs) are critical com
APA, Harvard, Vancouver, ISO, and other styles
More sources

Book chapters on the topic "Alternative extension of the real numbers set"

1

Mak, Carol, C. H. Luke Ong, Hugo Paquet, and Dominik Wagner. "Densities of Almost Surely Terminating Probabilistic Programs are Differentiable Almost Everywhere." In Programming Languages and Systems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72019-3_16.

Full text
Abstract:
AbstractWe study the differential properties of higher-order statistical probabilistic programs with recursion and conditioning. Our starting point is an open problem posed by Hongseok Yang: what class of statistical probabilistic programs have densities that are differentiable almost everywhere? To formalise the problem, we consider Statistical PCF (SPCF), an extension of call-by-value PCF with real numbers, and constructs for sampling and conditioning. We give SPCF a sampling-style operational semantics à la Borgström et al., and study the associated weight (commonly referred to as the densi
APA, Harvard, Vancouver, ISO, and other styles
2

Mamouras, Konstantinos, Agnishom Chattopadhyay, and Zhifu Wang. "Algebraic Quantitative Semantics for Efficient Online Temporal Monitoring." In Tools and Algorithms for the Construction and Analysis of Systems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72016-2_18.

Full text
Abstract:
AbstractWe investigate efficient algorithms for the online monitoring of properties written in metric temporal logic (MTL). We employ an abstract algebraic semantics based on semirings. It encompasses the Boolean semantics and a quantitative semantics capturing the robustness of satisfaction, which is based on the max-min semiring over the extended real numbers. We provide a precise equational characterization of the class of semirings for which our semantics can be viewed as an approximation to an alternative semantics that quantifies the distance of a system trace from the set of all traces
APA, Harvard, Vancouver, ISO, and other styles
3

Barthe, Gilles, Raphaëlle Crubillé, Ugo Dal Lago, and Francesco Gavazzo. "On the Versatility of Open Logical Relations." In Programming Languages and Systems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44914-8_3.

Full text
Abstract:
AbstractLogical relations are one among the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be immediately proved by means of logical relations, for instance program continuity and differentiability in higher-order languages extended with real-valued functions. Informally, the problem stems from the fact that these properties are naturally expressed on terms of non-ground type (or, equivalently, on open terms of base type), and there is no appar
APA, Harvard, Vancouver, ISO, and other styles
4

"Extension of results to arbitrary formalisms of predicate logic, and applications to the formalization of the arithmetics of natural and real numbers." In A Formalization of Set Theory without Variables. American Mathematical Society, 1987. http://dx.doi.org/10.1090/coll/041/07.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Schumer, Peter D. "Geometric Series, Powers of Three." In Fractions. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/9780198916567.003.0002.

Full text
Abstract:
Abstract Geometric series are introduced and developed, a concept dating back at least to Zeno of Elea in the fifth century bce. We then relate geometric series to finding the fractional equivalent of a repeating decimal expansion. Of particular interest are fractions with powers of 3 in the denominator such as 1/81 and 1/243. Next, we discuss the Cantor set, a topic usually covered only in an advanced real analysis course. However, here it fits in naturally within our discussion of thirds. The Cantor set is the set of real numbers between 0 and 1 that do not require the digit 1 in their terna
APA, Harvard, Vancouver, ISO, and other styles
6

Balderas Cepeda, Marco-Antonio. "Mining Hidden Association Rules from Real-Life Data." In Rare Association Rule Mining and Knowledge Discovery. IGI Global, 2010. http://dx.doi.org/10.4018/978-1-60566-754-6.ch011.

Full text
Abstract:
Association rule mining has been a highly active research field over the past decade. Extraction of frequency-related patterns has been applied to several domains. However, the way association rules are defined has limited people’s ability to obtain all the patterns of interest. In this chapter, the authors present an alternative approach that allows us to obtain new kinds of association rules that represent deviations from common behaviors. These new rules are called anomalous rules. To obtain such rules requires that we extract all the most frequent patterns together with certain extension p
APA, Harvard, Vancouver, ISO, and other styles
7

Madhura K, Dr, and Dr Manjula H M. "QUERY EXPANSION USING WORD EMBEDDING, ONTOLOGY, AND NATURAL LANGUAGE PROCESSING." In Futuristic Trends in Computing Technologies and Data Sciences Volume 3 Book 3. Iterative International Publisher, Selfypage Developers Pvt Ltd, 2024. http://dx.doi.org/10.58532/v3bfct3p3ch3.

Full text
Abstract:
Query Expansion (QE) is the art of reconstructing specific queries to expand validation presentation, especially in the data mining process in a requirements-understanding environment. Expanding requirements is one of the techniques involved in finding information. In the search engine environment, the query extension includes the evaluation of the value of the construction and the extension of search queries to match new documents. In natural language processing (NLP), word embedding is a term used in textbook parsing, usually as a real-valued vector that encodes the meaning of adjacent words
APA, Harvard, Vancouver, ISO, and other styles
8

Robins, James M., and Thomas S. Richardson. "Alternative Graphical Causal Models and the Identification of Direct Effects." In Causality and Psychopathology. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780199754649.003.0011.

Full text
Abstract:
The subject-specific data from either an observational or experimental study consist of a string of numbers. These numbers represent a series of empirical measurements. Calculations are performed on these strings and causal inferences are drawn. For example, an investigator might conclude that the analysis provides strong evidence for ‘‘both an indirect effect of cigarette smoking on coronary artery disease through its effect on blood pressure and a direct effect not mediated by blood pressure.’’ The nature of the relationship between the sentence expressing these causal conclusions and the st
APA, Harvard, Vancouver, ISO, and other styles
9

Valente, Marco. "Innovations and Organizational Structures." In Relational Methodologies and Epistemology in Economics and Management Sciences. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9770-6.ch010.

Full text
Abstract:
This chapter presents a novel model to represent the relative results that different innovation strategies can be expected to attain in respect of technological spaces defined by different complexity levels. The model representing complexity is based on Kauffman's fitness landscape (known, also, as NK fitness landscape). However, contrary to the original proposal, we used a functional and deterministic representation of complexity defined over a real-valued space, replacing a stochastic and statistical-based definition of complexity in binary-valued spaces. The search strategies proposed are i
APA, Harvard, Vancouver, ISO, and other styles
10

Campbell, Donna M. "Yours for the (Marriage) Revolution." In American Literary History and the Turn toward Modernity. University Press of Florida, 2018. http://dx.doi.org/10.5744/florida/9780813056043.003.0009.

Full text
Abstract:
In 1915, Mary Austin (1868-1934) wrote to her old friend and fellow writer Jack London (1876-1916) to upbraid him for failing to write a novel that truthfully depicted the life of a modern woman, and by extension, companionate marriage. Companionate marriage was a rational system based in idealism, tailor-made for the Progressive Era and for revolutionists such as Austin and London in Greenwich Village, who shared their era’s enthusiasm for scientific systems. Austin and London protested conventional forms of marriage both from the sociological standpoint of its unnecessary conventions and fro
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Alternative extension of the real numbers set"

1

Coles, James K., Richard H. Crawford, and Kristin L. Wood. "Form Feature Recognition Using Base Volume Decomposition." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0069.

Full text
Abstract:
Abstract A new feature recognition method is presented that generates volumetric feature representations from conventional boundary representations of mechanical parts. Recognition is accomplished by decomposing the known total feature volume of a part into a set of smaller volumes through analytic face extension. The decomposed volumes are combined to generate an initial set of features. Alternative sets of features are generated by maintaining and evaluating information on intersections of the initial feature set. The capabilities of the method are demonstrated through both a hypothetical an
APA, Harvard, Vancouver, ISO, and other styles
2

Boot, Peter. "The TEI Processing Model." In Declarative Amsterdam. John Benjamins, 2024. https://doi.org/10.1075/da.2024.boot.tei-processing-model.

Full text
Abstract:
The TEI Processing Model (PM) is a TEI (Text Encoding Initiative) facility that can be used to give a declarative description of the expected behaviour associated with TEI XML elements. The paper will introduce the model and its implementation in TEI Publisher. It will go on to discuss a number of real-life edition requirements that the current model cannot handle. It will propose extensions to the model to deal with those requirements. Among these are: (i) being able to associate multiple behaviours with an element, such as in the case of a page break rendered as an image that is also a link
APA, Harvard, Vancouver, ISO, and other styles
3

Bannikov, Denis, Maxim Voronin, Abdul Muqtadir Khan, and Murtaza Ziauddin. "Optimizing Corrosion Inhibitor Package to Mitigate Metal Corrosion and Formation Damage: A Machine-Learning Advisory Model." In SPE Oklahoma City Oil and Gas Symposium. SPE, 2025. https://doi.org/10.2118/224361-ms.

Full text
Abstract:
Abstract Acid fracturing and matrix acidizing are widely used techniques to stimulate productivity of hydrocarbon-producing wells in carbonate and sandstone reservoirs. While increased acid concentration benefits stimulation designs, it also introduces several challenges, including corrosion of the surface and downhole equipment and tubulars. We use a data science approach to predict the corrosion rate (CR) and pitting index (PI) of a metal surface in acid-containing fluid under arbitrary conditions without conducting physical experiments. We explored a database containing more than 10,000 exp
APA, Harvard, Vancouver, ISO, and other styles
4

Ugel, Diego, Sven Olmes, Claudio Cassinelli, et al. "Rotor Design of Heavy-Duty Gas Turbines for Power Generation: A Comparative Analysis for Transition to Net Zero Emission Target." In ASME Turbo Expo 2024: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/gt2024-128686.

Full text
Abstract:
Abstract Current scenarios towards net zero emission assume an increasing demand for peaking operation of installed and new heavy-duty gas turbines for power generation, resulting in raising targets for transient behaviors of gas turbine rotors. During the design development process cyclic damaging mechanisms related to centrifugal and thermal loads, as well as rotordynamic effects leading to high vibration and associated high-cycle fatigue mechanisms are mandatorily considered, accounting for potential aging effects taking place during the engine life. Additionally, rotor deformation due cent
APA, Harvard, Vancouver, ISO, and other styles

Reports on the topic "Alternative extension of the real numbers set"

1

Nolan, Brian, Brenda Gannon, Richard Layte, Dorothy Watson, Christopher T. Whelan, and James Williams. Monitoring Poverty Trends in Ireland: Results from the 2000 Living in Ireland survey. ESRI, 2002. http://dx.doi.org/10.26504/prs45.

Full text
Abstract:
This study is the latest in a series monitoring the evolution of poverty, based on data gathered by The ESRI in the Living in Ireland Surveys since 1994. These have allowed progress towards achieving the targets set out in the National Anti Poverty Strategy since 1997 to be assessed. The present study provides an updated picture using results from the 2000 round of the Living in Ireland survey. The numbers interviewed in the 2000 Living in Ireland survey were enhanced substantially, to compensate for attrition in the panel survey since it commenced in 1994. Individual interviews were conducted
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Alternative extension of the real numbers set' for particular source types:
Journal articles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography