scholarly journals Dunford-Pettis and strongly Dunford-Pettis operators on L1(μ)

1989 ◽  
Vol 31 (1) ◽  
pp. 49-57 ◽  
Author(s):  
James R. Holub
Keyword(s):  
Positive Operator ◽  
Finite Measure ◽  
Regular Operator ◽  
Mathematical Economics ◽  
Canonical Injection ◽  
Do So ◽  
Convergent Sequences

Motivated by a problem in mathematical economics [4] Gretsky and Ostroy have shown [5] that every positive operator T:L1[0, 1] → c0 is a Dunford-Pettis operator (i.e. T maps weakly convergent sequences to norm convergent ones), and hence that the same is true for every regular operator from L1[0, 1] to c0. In a recent paper [6] we showed the converse also holds, thereby characterizing the D–P operators by this condition. In each case the proof depends (as do so many concerning D–P operators on Ll[0, 1]) on the following well-known result (see, e.g., [2]): If μ is a finite measure, an operator T:L1(μ) → E is a D–P operator is compact, where i:L∞(μ) → L1(μ) is the canonical injection of L∞(μ) into L1(μ). If μ is not a finite measure this characterization of D–P operators is no longer available, and hence results based on its use (e.g. [5], [6]) do not always have straightforward extensions to the case of operators on more general L1(μ) spaces.

scholarly journals The compact range property and C0

1986 ◽  
Vol 28 (1) ◽  
pp. 113-114 ◽  
Author(s):  
Neil E. Gretsky ◽  
Joseph M. Ostroy
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Positive Operator ◽  
Short Note ◽  
Mathematical Economics ◽  
Compact Range ◽  
Convergent Sequences

The purpose of this short note is to make an observation about Dunford–Pettis operators from L1[0, 1] to C0. Recall that an operator T:E→F (where E and F are Banach spaces) is called Dunford–Pettis if T takes weakly convergent sequences of E into norm convergent sequences of F. A Banach space F has the Compact Range Property (CRP) if every operator T:L1]0, 1]→F is Dunford–Pettis. Talagrand shows in his book [2] that C0 does not have the CRP. It is of interest (especially in mathematical economics [3]) to note that every positive operator from L1[0, 1] to C0 is Dunford–Pettis.

ON THE DOMAIN OF SINGULAR TRACES

2002 ◽  
Vol 13 (06) ◽  
pp. 667-674 ◽  
Author(s):  
DANIELE GUIDO ◽  
TOMMASO ISOLA
Keyword(s):  
Positive Operator ◽  
Trace Class ◽  
Regular Operator ◽  
Infinite Rank

The question whether an operator belongs to the domain of some singular trace is addressed, together with the dual question whether an operator does not belong to the domain of some singular trace. We show that the answers are positive in general, namely for any (compact, infinite rank) positive operator A we exhibit two singular traces, the first being zero and the second being infinite on A. However, if we assume that the singular traces are genrated by a "regular" operator, the answers change, namely such traces alway vanish on trace-class, non singularly traceable operators and are always infinite on non trace-class, non singularly traceable operators. These results are achieved on a general semifinite factor and make use of a new characterization of singular traceability (cf. [7]).

scholarly journals Towards Reduced CNNs for De-Noising Phase Images Corrupted with Speckle Noise

Photonics ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 255
Author(s):  
Marie Tahon ◽  
Silvio Montresor ◽  
Pascal Picart
Keyword(s):  
Phase Error ◽  
Speckle Noise ◽  
Experimental Conditions ◽  
Benchmark Data ◽  
Wide Range ◽  
Phase Images ◽  
Different Depths ◽  
Phase Data ◽  
Do So

Digital holography is a very efficient technique for 3D imaging and the characterization of changes at the surfaces of objects. However, during the process of holographic interferometry, the reconstructed phase images suffer from speckle noise. In this paper, de-noising is addressed with phase images corrupted with speckle noise. To do so, DnCNN residual networks with different depths were built and trained with various holographic noisy phase data. The possibility of using a network pre-trained on natural images with Gaussian noise is also investigated. All models are evaluated in terms of phase error with HOLODEEP benchmark data and with three unseen images corresponding to different experimental conditions. The best results are obtained using a network with only four convolutional blocks and trained with a wide range of noisy phase patterns.

Biochemical characterization of a cortexless mutant of a variant of Bacillus cereus

1976 ◽  
Vol 22 (7) ◽  
pp. 1007-1012 ◽  
Author(s):  
Susanne M. Pearce
Keyword(s):  
Cell Wall ◽  
Fatty Acid Composition ◽  
Fatty Acid ◽  
Bacillus Cereus ◽  
Biochemical Characterization ◽  
Diaminopimelic Acid ◽  
Peptidoglycan Synthesis ◽  
Biochemical Lesion ◽  
Do So

Previous studies on this cortexless mutant of Bacillus cereus var. alesti indicated that the forespore membrane was the site of the biochemical lesion. This hypothesis is supported by the results presented here: fatty acid composition of sporulating cells of the mutant is altered, while in vegetative cells it is comparable to the parent; soluble precursors of peptidoglycan synthesis are accumulated in the mutant, at the time of cortex formation; homogenates of the mutant prepared at the time of cortex formation are unable to incorporate tritiated diaminopimelic acid into peptidoglycan, while homogenates of cells forming germ cell wall do so to an extent comparable to that of the parent; lipid-linked intermediates are formed by the mutant as in the parent. Apparently the mutant is unable either to transfer disaccharide penta-peptide units from the carrier lipid to the growing peptidoglycan acceptor, or to transport lipid-linked intermediates across the forespore membrane.

scholarly journals Orderability of topological spaces by continuous preferences

2001 ◽  
Vol 27 (8) ◽  
pp. 505-512 ◽  
Author(s):  
José Carlos Rodríguez Alcantud
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Properties ◽  
Linear Orders ◽  
Mathematical Economics

We extend van Dalen and Wattel's (1973) characterization of orderable spaces and their subspaces by obtaining analogous results for two larger classes of topological spaces. This type of spaces are defined by considering preferences instead of linear orders in the former definitions, and possess topological properties similar to those of (totally) orderable spaces (cf. Alcantud, 1999). Our study provides particular consequences of relevance in mathematical economics; in particular, a condition equivalent to the existence of a continuous preference on a topological space is obtained.

scholarly journals Introduction to Formal Preference Spaces

2013 ◽  
Vol 21 (3) ◽  
pp. 223-233
Author(s):  
Eliza Niewiadomska ◽  
Adam Grabowski
Keyword(s):  
Binary Relation ◽  
Preference Relation ◽  
Consumer Preference ◽  
Consumer Theory ◽  
Mathematical Economics ◽  
Characteristic Relation ◽  
Finite Set ◽  
Preference Structures ◽  
Equal Interest

Summary In the article the formal characterization of preference spaces [1] is given. As the preference relation is one of the very basic notions of mathematical economics [9], it prepares some ground for a more thorough formalization of consumer theory (although some work has already been done - see [17]). There was an attempt to formalize similar results in Mizar, but this work seems still unfinished [18]. There are many approaches to preferences in literature. We modelled them in a rather illustrative way (similar structures were considered in [8]): either the consumer (strictly) prefers an alternative, or they are of equal interest; he/she could also have no opinion of the choice. Then our structures are based on three relations on the (arbitrary, not necessarily finite) set of alternatives. The completeness property can however also be modelled, although we rather follow [2] which is more general [12]. Additionally we assume all three relations are disjoint and their set-theoretic union gives a whole universe of alternatives. We constructed some positive and negative examples of preference structures; the main aim of the article however is to give the characterization of consumer preference structures in terms of a binary relation, called characteristic relation [10], and to show the way the corresponding structure can be obtained only using this relation. Finally, we show the connection between tournament and total spaces and usual properties of the ordering relations.

scholarly journals Mathematics Classroom Assessment: A Framework for Designing Assessment Tasks and Interpreting Students’ Responses

2021 ◽  
Vol 11 (3) ◽  
pp. 1088-1106
Author(s):  
Eleni Demosthenous ◽  
Constantinos Christou ◽  
Demetra Pitta-Pantazi
Keyword(s):  
Teaching And Learning ◽  
Classroom Assessment ◽  
Mathematics Classroom ◽  
Mathematics Learning ◽  
Fourth Grade ◽  
Mathematics Assessment ◽  
Assessment Tasks ◽  
Grade Classroom ◽  
Do So

Classroom assessment could contribute substantially to improving students’ mathematics learning. The process of classroom assessment involves decisions about how to elicit evidence, how to interpret it, and how to use it for teaching and learning. However, the field still needs to further explore how assessment tasks could guide forthcoming instructional adjustments in the mathematics classroom. Towards the endeavor of unpacking the classroom assessment, we present a framework that provides a lens to capture the interplay between the design of mathematics assessment tasks and the analysis of students’ responses. To do so, we relied on existing frameworks of mathematics assessment tasks, and on issues that pertain to the design of tasks. The proposed framework consists of three types of mathematics assessment tasks, their respective competencies, and the characterization of students’ responses. The framework is exemplified with students’ responses from a fourth-grade classroom, and is also used to sketch different students’ profiles. Issues regarding the interpretation of students’ responses and the planning of instructional adjustments are discussed.

scholarly journals A Viral Ecogenomics Framework To Uncover the Secrets of Nature’s “Microbe Whisperers”

mSystems ◽  
2019 ◽  
Vol 4 (3) ◽  
Author(s):  
Simon Roux
Keyword(s):  
Cell Metabolism ◽  
Ecosystem Functions ◽  
Biological Knowledge ◽  
Viral Sequence ◽  
Molecular Tools ◽  
Microbial Cells ◽  
Health And Disease ◽  
Virus Genomes ◽  
Do So

ABSTRACTMicrobes drive critical ecosystem functions and affect global nutrient cycling along with human health and disease. They do so under strong constraints exerted by viruses, which shape microbial communities’ structure and shift host cell metabolism during infection. While the majority of viruses and their associated impacts remain poorly characterized, a number of mechanisms by which viruses alter microbial cells and ecosystems have already been revealed. Here I outline how a comprehensive host-resolved mapping of viral sequence space will enable a thorough characterization of virus-encoded mechanisms for microbial manipulation. With soon-to-be millions of virus genomes obtained from metagenomes, one of the major challenges resides in the development of methods for high-throughput and high-resolution virus-host pairing, before multi-omics approaches can be leveraged to fully decipher virus-host dynamics in nature. Beyond novel fundamental biological knowledge, these studies will likely provide new molecular tools enabling a precise engineering of microbial cells and communities.

‘To be or not to be’: Hamlet’s Humanistic Quaestio

2019 ◽  
Vol 70 (296) ◽  
pp. 640-658
Author(s):  
Vanessa Lim
Keyword(s):  
Rhetorical Theory ◽  
The Subject ◽  
The Right ◽  
The University ◽  
Scholarly Attention ◽  
Do So

Abstract Hamlet’s ‘To be or not to be’ speech has long been the subject of intense scholarly attention. By situating the speech against the backdrop of classical and Renaissance rhetorical theory, this essay demonstrates that there is still much more to be said about it. The speech ostensibly examines a quaestio infinita or a thesis, and follows the rhetorical rule that the right way to do so is by the invocation of commonplaces. This reading of Hamlet’s speech is not only consistent with Shakespeare’s characterization of the university-educated prince, who frequently invokes commonplaces, but also has significant implications for our understanding of the play and Shakespeare’s own practice as a writer. The book that Hamlet is reading could well be his own commonplace collection, and it is perhaps in looking up his entries under the heading of ‘Death’ that Hamlet finds what he needs in order to examine his quaestio.

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