scholarly journals An Application of le-semigroup Techniques to Semigroups, Γ-semigroups and to Hypersemigroups

2019 ◽  
Vol 12 (1) ◽  
pp. 208-225
Author(s):  
Niovi Kehayopulu
Keyword(s):  
Prime Ideal ◽  
Ordered Set ◽  
Main Idea ◽  
Upper Semilattice

An $le$-semigroup, is a semigroup $S$ at the same time a lattice with a greatest element $e$ ($e\ge a$ for every $a\in S$) such that $a(b\vee c)=ab\vee ac$ and $(a\vee b)c=ac\vee bc$ for all $a,b,c\in S$. If $S$ is not a lattice but only an upper semilattice ($\vee$-semilattice), then is called $\vee e$-semigroup. A $poe$-semigroup is a semigroup $S$ at the same time an ordered set with a greatest element $e$ such that $a\le b$ implies $ac\le bc$ and $ca\le cb$ for all $c\in S$. Every $\vee e$-semigroup is a $poe$-semigroup. If $S$ is a semigroup or a $\Gamma$-semigroup, then the set ${\cal P}(S)$ of all subsets of $S$ is an $le$-semigroup. If $S$ is an hypersemigroup, then the set ${\cal P^*}(S)$ of all nonempty subsets of $S$ is an $le$-semigroup. So all the results of $le$-semigroups, $\vee e$-semigroups and $poe$-semigroups based on ideal elements, automatically hold for semigroups, $\Gamma$-semigroups and hypersemigroups. This is not the case for  ordered $\Gamma$-semigroups or ordered hypersemigroups; however the main idea, even in these cases, comes from the $le$ ($\vee e$)-semigroups. As an example, we study the weakly prime ideal elements of a $\vee e$-semigroup and their role to the different type of semigroups mentioned above.

ON THE SET-THEORETIC STRENGTH OF ELLIS’ THEOREM AND THE EXISTENCE OF FREE IDEMPOTENT ULTRAFILTERS ON ω

2018 ◽  
Vol 83 (2) ◽  
pp. 551-571
Author(s):  
ELEFTHERIOS TACHTSIS
Keyword(s):  
Prime Ideal ◽  
Ordered Set ◽  
Idempotent Element ◽  
Abelian Semigroup ◽  
Free Ultrafilter ◽  
Image Position ◽  
Idempotent Ultrafilter ◽  
Right Topological Semigroup ◽  
Linearly Ordered Set ◽  
Prime Ideal Theorem

AbstractEllis’ Theorem (i.e., “every compact Hausdorff right topological semigroup has an idempotent element”) is known to be proved only under the assumption of the full Axiom of Choice (AC); AC is used in the proof in the disguise of Zorn’s Lemma.In this article, we prove that in ZF, Ellis’ Theorem follows from the Boolean Prime Ideal Theorem (BPI), and hence is strictly weaker than AC in ZF. In fact, we establish that BPI implies the formally stronger (than Ellis’ Theorem) statement “for every family ${\cal A} = \{ ({S_i},{ \cdot _i},{{\cal T}_i}):i \in I\}$ of nontrivial compact Hausdorff right topological semigroups, there exists a function f with domain I such that $f\left( i \right)$ is an idempotent of ${S_i}$, for all $i \in I$”, which in turn implies ACfin (i.e., AC for sets of nonempty finite sets).Furthermore, we prove that in ZFA, the Axiom of Multiple Choice (MC) implies Ellis’ Theorem for abelian semigroups (i.e., “every compact Hausdorff right topological abelian semigroup has an idempotent element”) and that the strictly weaker than MC (in ZFA) principle LW (i.e., “every linearly ordered set can be well-ordered”) implies Ellis’ Theorem for linearly orderable semigroups (i.e., “every compact Hausdorff right topological linearly orderable semigroup has an idempotent element”); thus the latter formally weaker versions of Ellis’ Theorem are strictly weaker than BPI in ZFA. Yet, it is shown that no choice is required in order to prove Ellis’ Theorem for well-orderable semigroups.We also show that each one of the (strictly weaker than AC) statements “the Tychonoff product $2^{\Cal R} $ is compact and Loeb” and $BPI_{\Cal R}$ (BPI for filters on ${\Cal R}$) implies “there exists a free idempotent ultrafilter on ω” (which in turn is not provable in ZF). Moreover, we prove that the latter statement does not imply $BP{I_\omega }$ (BPI for filters on ω) in ZF, hence it does not imply any of $AC_{\Cal R} $ (AC for sets of nonempty sets of reals) and $BPI_{\Cal R} $ in ZF, either.In addition, we prove that the statements “there exists a free ultrafilter on ω”, “there exists a free ultrafilter on ω which is not idempotent”, and “for every IP set $A \subseteq \omega$, there exists a free ultrafilter ${\cal F}$ on ω such that $A \in {\cal F}$” are pairwise equivalent in ZF.

The dense linear ordering principle

1997 ◽  
Vol 62 (2) ◽  
pp. 438-456 ◽  
Author(s):  
David Pincus
Keyword(s):  
Prime Ideal ◽  
Set Theory ◽  
Ordered Set ◽  
Axiom Of Choice ◽  
Linear Ordering ◽  
Independence Result ◽  
The Axiom Of Choice ◽  
Infinite Set ◽  
Prime Ideal Theorem ◽  
The Way

AbstractLet DO denote the principle: Every infinite set has a dense linear ordering. DO is compared to other ordering principles such as O, the Linear Ordering principle, KW, the Kinna-Wagner Principle, and PI, the Prime Ideal Theorem, in ZF, Zermelo-Fraenkel set theory without AC, the Axiom of Choice.The main result is:Theorem. AC ⇒ KW ⇒ DO ⇒ O, and none of the implications is reversible in ZF + PI.The first and third implications and their irreversibilities were known. The middle one is new. Along the way other results of interest are established. O, while not quite implying DO, does imply that every set differs finitely from a densely ordered set. The independence result for ZF is reduced to one for Fraenkel-Mostowski models by showing that DO falls into two of the known classes of statements automatically transferable from Fraenkel-Mostowski to ZF models. Finally, the proof of PI in the Fraenkel-Mostowski model leads naturally to versions of the Ramsey and Ehrenfeucht-Mostowski theorems involving sets that are both ordered and colored.

ALGEBRA OF PREDICATES AND RELATED GEOMETRIC MODELS CREATION IN REGARDS OF UNIFIED STATE EXAM IN INFORMATICS (RUSSIAN EGE)

2019 ◽  
pp. 40-47
Author(s):  
E. A. Mironchik
Keyword(s):  
Geometric Model ◽  
Main Idea ◽  
Formal Logic ◽  
High Complexity ◽  
Geometric Models ◽  
Complexity Problem ◽  
Logical Expression ◽  
State Examination

The article discusses the method of solving the task 18 on the Unified State Examination in Informatics (Russian EGE). The main idea of the method is to write the conditions of the problem utilizing the language of formal logic, using elementary predicates. According to the laws of logic the resulting complex logical expression would be transformed into an expression, according to which a geometric model is supposed to be constructed which allows to obtain an answer. The described algorithm does allow high complexity problem to be converted into a simple one.

From Freezing to Investing: New Approaches to Monetary and Currency Policies

2008 ◽  
pp. 47-55
Author(s):  
A. Nekipelov ◽  
Yu. Goland
Keyword(s):  
Economic Policy ◽  
Property Rights ◽  
Main Idea ◽  
State Intervention ◽  
Economic Thought ◽  
Human Potential ◽  
Knowledge Based ◽  
Russian Economy ◽  
Knowledge Based Economy

The appeals to minimize state intervention in the Russian economy are counterproductive. However the excessive involvement of the state is fraught with the threat of building nomenclature capitalism. That is the main idea of the series of articles by prominent representatives of Russian economic thought who formulate their position on key elements of the long-term strategy of Russia’s development. The articles deal with such important issues as Russia’s economic policy, transition to knowledge-based economy, basic directions of monetary and structural policies, strengthening of property rights, development of human potential, foreign economic priorities of our state.

PENGARUH MODEL PEMBELAJARAN COOPERATIVE INTEGRATED READING AND COMPOSITION (CIRC) TERHADAP KEMAMPUAN MENENTUKAN IDE POKOK PARAGRAF SISWA KELAS V SD NEGERI 003 PULAU KOPUNG KECAMATAN SENTAJO RAYA KABUPATEN KUANTAN SINGINGI

2019 ◽  
Vol 3 (2) ◽  
Author(s):  
Yuwanda Megri Santika ◽  
Otang Kurniaman ◽  
Zariul Antosa
Keyword(s):  
Main Idea ◽  
Learning Model ◽  
Communication Process ◽  
Fifth Grade ◽  
Control Group ◽  
Control Group Design ◽  
Group Design ◽  
Fifth Grade Students ◽  
Quasi Experimental ◽  
Main Ideas

Reading is one of the important aspects in the communication process. Reading can make someone better understand the contents of the reading. In learning to make it easier for students to understand the contents of the reading it will be easier if it begins with the ability to determine the main ideas of the paragraph. Based on this, the researcher conducted a study by applying the Cooperative Integrated Reading and Composition (CIRC) learning model to the ability to determine the main idea of the paragraph at the fifth grade students of SD 003 Pulau Kopung. This study aims to determine the effect of the CIRC learning model on the ability to determine the main ideas of paragraphs of fifth grade students of SD Negeri 003 Pulau Kopung. This research method is a quasi- experimental Nonequivalent Control Group Design. This research was conducted in two classes, the VA class as the control class and VB class as the experimental class with 22 students in each class. The results of the study showed that the CIRC learning model influenced the ability to determine paragraph main ideas with the results of calculations derived from the gain index, the experimental class using the CIRC learning model got an increase in gain of 0.59 with the middle class and the control class with the normal learning model got an increase of 0.31 with medium class.

New Feature Vectors using GFCC for Speaker Identification

2018 ◽  
Vol 6 (8) ◽  
pp. 243
Author(s):  
A. Nagesh
Keyword(s):  
Speaker Recognition ◽  
Speaker Identification ◽  
Signal To Noise Ratio ◽  
Main Idea ◽  
Extraction Methods ◽  
Identification System ◽  
Identification Performance ◽  
Feature Vectors ◽  
Overall Performance ◽  
New Feature

The feature vectors of speaker identification system plays a crucial role in the overall performance of the system. There are many new feature vectors extraction methods based on MFCC, but ultimately we want to maximize the performance of SID system.  The objective of this paper to derive Gammatone Frequency Cepstral Coefficients (GFCC) based a new set of feature vectors using Gaussian Mixer model (GMM) for speaker identification. The MFCC are the default feature vectors for speaker recognition, but they are not very robust at the presence of additive noise. The GFCC features in recent studies have shown very good robustness against noise and acoustic change. The main idea is  GFCC features based on GMM feature extraction is to improve the overall speaker identification performance in low signal to noise ratio (SNR) conditions.

REVIVING ECONOMIC THOUGHT BY MANNAN PERPECTIVE

2020 ◽  
Vol 15 (2) ◽  
pp. 353-378
Author(s):  
Muhammad Majdy Amiruddin ◽  
Muhammad Ismail ◽  
Hasanuddin Hasim
Keyword(s):  
Adam Smith ◽  
Main Idea ◽  
Scientific Work ◽  
Economic Thought ◽  
Small Contribution ◽  
Literature Study ◽  
Goods And Services ◽  
Study Techniques ◽  
Islamic Economic ◽  
Modern Era

The reviving of modern economic theory is usually stated starting from the publication of Adam Smith's The Wealth of Natoins, in 1776, although other thinkers who first also gave no small contribution. The main idea put forward by Adam Smith is that competition between various suppliers of goods and buyers will produce the best possibilities in the distribution of goods and services because it will encourage everyoe to do the specialization and increase in capital so that it will produce more value with a permanent workforce. From the Islamic perspective, there are several names that commonly known such, Baqir, Umar Chapra, and Mannan. The purpose of this research is to explore the revival economic though by Abdul Mannan. This research adapts content analysis method, which is a researcher conducts a discussion of the contents of written or edition information in the mass media. The data analysis techniques of this scientific work use literature study techniques, comparative, induction, and deduction. The study began by collecting literature data from Muhammad Abdul Mannan's Concept of Thinking about the Development of Modern Era Islamic economics and Modern Era Islamic Economic concepts in general, (researchers only participated in the discussion). Then proceed with the interpretation that researchers try to understand Muhammad Abdul Mannan's thoughts about the Development of Islamic Economics in the Modern Era. The result of this reseacrh indicates that the revival of Islamic thought by determining basic economic functions that simply cover three functions, namely consumption, production and distribution. Those basics are rooted by Five basic principles rooted in Shariah for basic economic functions in the form of consumption functions are the principles of righteousness, cleanliness, moderation, benefit and morality

Near-Perfect Reconstruction Oversampled Nonuniform Cosine-Modulated Filter Banks Based on Frequency Warping and Subband Merging

2012 ◽  
Vol 58 (2) ◽  
pp. 177-192 ◽  
Author(s):  
Marek Parfieniuk ◽  
Alexander Petrovsky
Keyword(s):  
Group Delay ◽  
Filter Banks ◽  
Main Idea ◽  
Perceptual Processing ◽  
Perfect Reconstruction ◽  
Frequency Warping ◽  
Small Loss ◽  
Novel Method ◽  
The One ◽  
Near Perfect Reconstruction

Near-Perfect Reconstruction Oversampled Nonuniform Cosine-Modulated Filter Banks Based on Frequency Warping and Subband MergingA novel method for designing near-perfect reconstruction oversampled nonuniform cosine-modulated filter banks is proposed, which combines frequency warping and subband merging, and thus offers more flexibility than known techniques. On the one hand, desirable frequency partitionings can be better approximated. On the other hand, at the price of only a small loss in partitioning accuracy, both warping strength and number of channels before merging can be adjusted so as to minimize the computational complexity of a system. In particular, the coefficient of the function behind warping can be constrained to be a negative integer power of two, so that multiplications related to allpass filtering can be replaced with more efficient binary shifts. The main idea is accompanied by some contributions to the theory of warped filter banks. Namely, group delay equalization is thoroughly investigated, and it is shown how to avoid significant aliasing by channel oversampling. Our research revolves around filter banks for perceptual processing of sound, which are required to approximate the psychoacoustic scales well and need not guarantee perfect reconstruction.

Morrison's Beloved and its Two "Amadas": Postcolonial Signifying upon Translation within African-American Intertextualities

1969 ◽  
Author(s):  
José Endoença Martins
Keyword(s):  
African American ◽  
Main Idea ◽  
Black Nationalism ◽  
The Other ◽  
Source Text ◽  
Specific Source ◽  
Theoretical Foundations ◽  
Specific Concern

This article compares two different Brazilian translated versions of Toni Morrison's novel Beloved: the first published in 1994, the other in 2007, both as Amada. The analysis concentrates on the speech delivered by Baby Suggs, in which she exhorts her listeners to care for their bodies. The main idea behind this article is that Beloved and the Amadas converse or talk, thus performing signifyin(g), a concept which, in Henry Louis Gates's words, explains how intertextual conversation happens through “repetition and revision, or repetition with a signal of difference” (xxiv). Its general theoretical foundations include interconnections involving several instantiations of signifyin(g): between Black nationalism and negritude, postcolonialism and African Americanism. In its specific concern with translation, the conversation that the source keeps with the target texts involves two translation theories: fluency and resistance; two kinds of translating interventions: omission and addition; and three types of strategies: syntactic, semantic, and pragmatic. These distinct categories help readers grasp translation as a continuum by means of which a specific source text encounters its target equivalents and, then, returns to its origin. The original article is in English.

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