scholarly journals THE GENERIC DEGREES OF DENSITY-1 SETS, AND A CHARACTERIZATION OF THE HYPERARITHMETIC REALS

2015 ◽  
Vol 80 (4) ◽  
pp. 1290-1314 ◽  
Author(s):  
GREGORY IGUSA
Keyword(s):  
Complexity Theory ◽  
Point Of View ◽  
Turing Degrees ◽  
Worst Case ◽  
Know How ◽  
Theoretic Point ◽  
Image Position ◽  
Generic Computation

AbstractA generic computation of a subsetAof ℕ is a computation which correctly computes most of the bits ofA, but which potentially does not halt on all inputs. The motivation for this concept is derived from complexity theory, where it has been noticed that frequently, it is more important to know how difficult a type of problem is in the general case than how difficult it is in the worst case. When we study this concept from a recursion theoretic point of view, to create a transitive relationship, we are forced to consider oracles that sometimes fail to give answers when asked questions. Unfortunately, this makes working in the generic degrees quite difficult. Indeed, we show that generic reduction is$\Pi _1^1$―complete. To help avoid this difficulty, we work with the generic degrees of density-1 reals. We demonstrate how an understanding of these degrees leads to a greater understanding of the overall structure of the generic degrees, and we also use these density-1 sets to provide a new a characterization of the hyperartithmetical Turing degrees.

K-Theory and Asymptotically Commuting Matrices

1988 ◽  
Vol 40 (1) ◽  
pp. 197-216 ◽  
Author(s):  
Terry A. Loring
Keyword(s):  
Original Problem ◽  
Unsolved Problem ◽  
Point Of View ◽  
Commuting Matrices ◽  
Theoretic Point ◽  
K Theory ◽  
Image Position ◽  
Shed Light

To shed light on the following unsolved problem, several authors have considered related problems. The problem is that of finding commuting approximants to pairs of asymptotically commuting self-adjoint matrices:Suppose that Hn and Kn are self-adjoint matrices of dimension m(n), with ║Hn║, ║Kn║ ≦ 1, which commute asymptotically in the sense thatMust there then exist commuting self-adjoint matrices H′n and K′n for whichOne may alter the conditions imposed on Hn and Kn, for example, by requiring Hn to be normal and Kn to be self-adjoint, and ask whether commuting approximants H′n and K′n can be found satisfying the same conditions. Some of these related problems have been solved. This paper will examine their solutions from a K-theoretic point of view, illustrating the difficulty inherent in modifying them to work for the original problem.

THE STRENGTH OF RAMSEY’S THEOREM FOR COLORING RELATIVELY LARGE SETS

2014 ◽  
Vol 79 (01) ◽  
pp. 89-102 ◽  
Author(s):  
LORENZO CARLUCCI ◽  
KONRAD ZDANOWSKI
Keyword(s):  
Current Knowledge ◽  
Type Theorem ◽  
Complete Characterization ◽  
Infinite Subset ◽  
Point Of View ◽  
Ramsey's Theorem ◽  
Ramsey’S Theorem ◽  
Arithmetical Truth ◽  
Image Position

Abstract We characterize the effective content and the proof-theoretic strength of a Ramsey-type theorem for bi-colorings of so-called exactly large sets. An exactly large set is a set $X \subset {\bf{N}}$ such that ${\rm{card}}\left( X \right) = {\rm{min}}\left( X \right) + 1$ . The theorem we analyze is as follows. For every infinite subset M of N, for every coloring C of the exactly large subsets of M in two colors, there exists and infinite subset L of M such that C is constant on all exactly large subsets of L. This theorem is essentially due to Pudlák and Rödl and independently to Farmaki. We prove that—over RCA0 —this theorem is equivalent to closure under the ωth Turing jump (i.e., under arithmetical truth). Natural combinatorial theorems at this level of complexity are rare. In terms of Reverse Mathematics we give the first Ramsey-theoretic characterization of ${\rm{ACA}}_0^ +$ . Our results give a complete characterization of the theorem from the point of view of Computability Theory and of the Proof Theory of Arithmetic. This nicely extends the current knowledge about the strength of Ramsey’s Theorem. We also show that analogous results hold for a related principle based on the Regressive Ramsey’s Theorem. We conjecture that analogous results hold for larger ordinals.

scholarly journals The Powerdomain of Indexed Valuations

2002 ◽  
Vol 9 (38) ◽  
Author(s):  
Daniele Varacca
Keyword(s):  
Denotational Semantics ◽  
Point Of View ◽  
Domain Theory ◽  
Theoretic Point ◽  
Equational Characterization ◽  
Imperative Language

This paper is about combining nondeterminism and probabilities. We study this phenomenon from a domain theoretic point of view. In domain theory, nondeterminism is modeled using the notion of powerdomain, while probability is modeled using the powerdomain of valuations. Those two functors do not combine well, as they are. We define the notion of powerdomain of indexed valuations, which can be combined nicely with the usual nondeterministic powerdomain. We show an equational characterization of our construction. Finally we discuss the computational meaning of indexed valuations, and we show how they can be used, by giving a denotational semantics of a simple imperative language.

HARMONIC TWO-SPHERES IN THE SYMPLECTIC GROUP Sp(n)

2006 ◽  
Vol 17 (03) ◽  
pp. 295-311 ◽  
Author(s):  
RUI PACHECO
Keyword(s):  
Projective Space ◽  
Symplectic Group ◽  
Harmonic Maps ◽  
Point Of View ◽  
Quaternionic Projective Space ◽  
Alternative Characterization ◽  
Theoretic Point

We shall exploit the Grassmannian theoretic point of view introduced by Segal in order to study harmonic maps from a two-sphere into the symplectic group Sp(n). By using this methodology, we shall be able to deduce an "uniton factorization" of such maps and an alternative characterization of harmonic two-spheres in the quaternionic projective space ℍPn.

The Analyses of Learning Strategies in English as a Second Language: Theoretical Classification and Measurement Test

2020 ◽  
Vol 4 (2) ◽  
pp. 118-129
Author(s):  
Asti Gumartifa ◽  
◽  
Indah Windra Dwie Agustiani
Keyword(s):  
Language Learning ◽  
Learning Outcomes ◽  
Learning Strategies ◽  
Learning Process ◽  
English Learners ◽  
English Language ◽  
Point Of View ◽  
Effective Learning ◽  
The Impact

Gaining English language learning effectively has been discussed all years long. Similarly, Learners have various troubles outcomes in the learning process. Creating a joyful and comfortable situation must be considered by learners. Thus, the implementation of effective learning strategies is certainly necessary for English learners. This descriptive study has two purposes: first, to introduce the classification and characterization of learning strategies such as; memory, cognitive, metacognitive, compensation, social, and affective strategies that are used by learners in the classroom and second, it provides some questionnaires item based on Strategy of Inventory for Language Learning (SILL) version 5.0 that can be used to examine the frequency of students’ learning strategies in the learning process. The summary of this study explains and discusses the researchers’ point of view on the impact of learning outcomes by learning strategies used. Finally, utilizing appropriate learning strategies are certainly beneficial for both teachers and learners to achieve the learning target effectively.

The Algorithm of Characterization of an Action as a Jointly Committed Crime

2018 ◽  
pp. 37-44
Keyword(s):  
Criminal Code ◽  
Point Of View

The article discusses a sequence of activities to identify a crime as jointly committed. The requirements to the algorithm of such activities are formulated. Programme-based and targeted methods applied by the authors allowed detecting a range of stages of the algorithm. The first four stages aim at defining mandatory elements of a crime allowing to characterize it as a jointly committed action. The rest of the stages focus on identifying a type of criminal complicity. In the article, each stage is described. It is emphasized that in each stage there is a special objective. At the same time, all these stages, taken together, constitute a separate module of the program of criminal characterization of an action. From the authors’ point of view, algorithms are necessary not only for detection of crimes and their criminal characterization, but also for answering the question on existence of criminal complicity in each case. Also the authors give their opinions on interpretation of criminal complicity as a legal category. In particular, it is emphasized that not all of crimes merely committed with participation of two or more persons should be understood as jointly committed. It is joint participation that makes a crime jointly committed. Various forms of criminal complicity and types of co-offenders are considered in the article as well. In various crimes, criminal complicity manifests itself differently. Therefore the proposed algorithm can be applied only after identification a specific article of the Russian Criminal Code stipulating the responsibility for the crime committed.

scholarly journals Processing Effect and Characterization of Olive Oils from Spanish Wild Olive Trees (Olea europaea var. sylvestris)

Molecules ◽  
2021 ◽  
Vol 26 (5) ◽  
pp. 1304
Author(s):  
Francisco Espínola ◽  
Alfonso M. Vidal ◽  
Juan M. Espínola ◽  
Manuel Moya
Keyword(s):  
Phenolic Compounds ◽  
Volatile Compounds ◽  
Olive Tree ◽  
Extraction Yield ◽  
Point Of View ◽  
Human Consumption ◽  
Analytical Point ◽  
Wild Olive ◽  
Olive Trees

Wild olive trees have important potential, but, to date, the oil from wild olives has not been studied significantly, especially from an analytical point of view. In Spain, the wild olive tree is called “Acebuche” and its fruit “Acebuchina”. The objective of this work is to optimize the olive oil production process from the Acebuchina cultivar and characterize the oil, which could be marketed as healthy and functional food. A Box–Behnken experimental design with five central points was used, along with the Response Surface Methodology to obtain a mathematical experimental model. The oils from the Acebuchina cultivar meet the requirements for human consumption and have a good balance of fatty acids. In addition, the oils are rich in antioxidants and volatile compounds. The highest extraction yield, 12.0 g oil/100 g paste, was obtained at 90.0 min and the highest yield of phenolic compounds, 870.0 mg/kg, was achieved at 40.0 °C, and 90.0 min; but the maximum content of volatile compounds, 26.9 mg/kg, was obtained at 20 °C and 30.0 min. The oil yield is lower than that of commercial cultivars, but the contents of volatile and phenolic compounds is higher.

scholarly journals Grounding semantic transparency in context

Morphology ◽  
2021 ◽  
Author(s):  
Rossella Varvara ◽  
Gabriella Lapesa ◽  
Sebastian Padó
Keyword(s):  
Large Scale ◽  
Point Of View ◽  
Distributional Semantics ◽  
Semantic Transparency ◽  
Inclusion Measure ◽  
The Difference ◽  
Semantic Point ◽  
The Many ◽  
The Relationship

AbstractWe present the results of a large-scale corpus-based comparison of two German event nominalization patterns: deverbal nouns in -ung (e.g., die Evaluierung, ‘the evaluation’) and nominal infinitives (e.g., das Evaluieren, ‘the evaluating’). Among the many available event nominalization patterns for German, we selected these two because they are both highly productive and challenging from the semantic point of view. Both patterns are known to keep a tight relation with the event denoted by the base verb, but with different nuances. Our study targets a better understanding of the differences in their semantic import.The key notion of our comparison is that of semantic transparency, and we propose a usage-based characterization of the relationship between derived nominals and their bases. Using methods from distributional semantics, we bring to bear two concrete measures of transparency which highlight different nuances: the first one, cosine, detects nominalizations which are semantically similar to their bases; the second one, distributional inclusion, detects nominalizations which are used in a subset of the contexts of the base verb. We find that only the inclusion measure helps in characterizing the difference between the two types of nominalizations, in relation with the traditionally considered variable of relative frequency (Hay, 2001). Finally, the distributional analysis allows us to frame our comparison in the broader coordinates of the inflection vs. derivation cline.

scholarly journals Encephalocele: know it to deal with it

2021 ◽  
Vol 52 (1) ◽  
Author(s):  
Nilkanth Laxman Pal ◽  
Ambika Sumeet Juwarkar ◽  
Sanjaya Viswamitra
Keyword(s):  
Prognostic Factors ◽  
Imaging Modality ◽  
Point Of View ◽  
Extensive Literature ◽  
Resonance Imaging ◽  
Imaging Protocol ◽  
Imaging Protocols ◽  
Associated Malformations ◽  
Associated Abnormalities

Abstract Background Encephaloceles refer to the herniation of intracranial contents through the defect in the dura and calvarium. This article aims to equip the radiologists with all the necessary information to approach a case of encephalocele in a systematic manner and report in an organized format. Thus reduce the reporting time without overlooking any detail. Main text An extensive literature review was performed searching through the standard textbooks and electronic databases to obtain thorough information on the various encephaloceles particularly from a radiological point of view. The author’s observations were also incorporated in the review. Among the available imaging modalities, magnetic resonance imaging is the most versatile and considered the imaging modality of choice because of superior anatomic resolution in the characterization of central nervous system malformation. This study provides the reporting radiologist with a methodical guide to approach a case of encephalocele discussing the imaging protocol, relevant anatomy, classification, associated abnormalities, and imaging prognostic factors. Conclusion Encephalocele has always been a subject of predicament for radiologists. Understanding the relevant terminologies, anatomy, imaging protocols, classification, associated malformations/anomalies, and imaging prognostic factors will help to methodically approach each case and provide a systematic and comprehensive report.

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