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Each family M of means has a natural, partial order (point-wise order), that is M ≤ N iff M(x) ≤ N(x) for all admissible x. In this setting we can introduce the notion of interval-type set (a subset I ⊂ M such that whenever M ≤ P ≤ N for some M,N ∈ I and P ∈ M then P ∈ I). For example, in the case of power means there exists a natural isomorphism between interval-type sets and intervals contained in real numbers. Nevertheless there appear a number of interesting objects for a families which cannot be linearly ordered. In the present paper we consider this property for Gini means and Hardy means. Moreover some results concerning L∞ metric among (abstract) means will be obtained.

In this paper, we consider homogeneous quasideviation means generated by real functions (defined on (0, ∞)) which are concave around the point 1 and possess certain upper estimates near 0 and ∞. It turns out that their concave envelopes can be completely determined. Using this description, we establish su˚cient conditions for the Hardy property of the homogeneous quasideviation mean and we also furnish an upper estimates for its Hardy constant. [ABSTRACT FROM AUTHOR]

The extension of the Hardy-Knopp-Carleman inequality to several classes of means was the subject of numerous papers. In the class of Gini means the Hardy property was characterized in 2015 by the second author. The precise value of the associated Hardy constant was only established for concave Gini means by the authors in 2016. The determination of the Hardy constant for nonconcave Gini means is still an open problem. The main goal of this paper is to establish sharper upper bounds for the Hardy constant in this case. The method is to construct a homogeneous and concave quasideviation mean which majorizes the nonconcave Gini mean and for which the Hardy constant can be computed. [ABSTRACT FROM AUTHOR]

For a given weighted mean M defined on a subinterval of ℝ+ and a sequence of weights λ= (λn)n=1 we define a Hardy constant H ( λ) as the smallest extended real number such that .... The aim of this note is to present a comprehensive study of the mapping H. For example we prove that it is lower semicontinuous in the pointwise topology. Moreover we show that whenever M is a monotone and Jensen-concave mean which is continuous in its weights then H is monotone with respect to the partitioning of the vector. Finally we deliver some sufficient conditions for λ to validate the equality H ( λ) = sup H for every symmetric and monotone mean. [ABSTRACT FROM AUTHOR]∞ we define a Hardy constant H ( λ) as the smallest extended real number such that .... The aim of this note is to present a comprehensive study of the mapping H. For example we prove that it is lower semicontinuous in the pointwise topology. Moreover we show that whenever M is a monotone and Jensen-concave mean which is continuous in its weights then H is monotone with respect to the partitioning of the vector. Finally we deliver some sufficient conditions for λ to validate the equality H ( λ) = sup H for every symmetric and monotone mean. [ABSTRACT FROM AUTHOR]

Purpose: This study investigated the factors that influence parenting stress, including hardiness, parent-child interactions, and social support, to provide basic data for developing a program to reduce parenting stress in North Korean refugee mothers. Methods: A descriptive study design was used. Data were collected between September and December 2021, and 123 North Korean refugee mothers participated. Results: The mean scores were 69.42 out of 135 for hardiness, 48.45 out of 144 for interactions, 47.32 out of 90 for social support, and 51.84 out of 90 for parenting stress. The parental distress score was higher than that of child-related stress. Hardiness was significantly related to North Korean refugee mothers' parenting stress. Multiple regression analysis indicated that the explanatory power for hardiness and the number of supporters was approximately 19% for parenting stress (F=6.84, p<.001). As such, the factors with a relatively strong influence on parenting stress were hardiness (β =-.40, p<.001) and having four or more supporters (β=-.27, p=.027). Conclusion: This study's findings suggest the need to identify ways to increase North Korean refugee mothers' psychological hardiness and encourage them to extend their sources of social support and enhance their style of parenting. [ABSTRACT FROM AUTHOR]

The article explores In ‘The Mayor of Casterbridge' Thomas Hardy describes Dorchester as ‘compact as a box of dominoes. It had no suburbs in the ordinary sense. Country and town met at a mathematical line'. I am writing to you to protest most profusely at the proposed development for the North of Dorchester spanning land from Charminster across the water-meadows to the Stinsford bypass.

This exploratory case study focuses on the development and implementation of a task called the Inventive English Word Formation in Public Spaces for an undergraduate English Morphology course within the English Language Education program of a university in Indonesia. This task was created based on students' feedback that they disliked the typical memory-based test, which was reported to have a significant strain on them. In that regard, this task was developed to replace the teacher's lectures and achievement test to increase students' learning engagement and understanding of the Word Formation theory. Students were asked to morphologically analyze how Indonesian people invented new English words in commercial signs in linguistic landscapes. Sixty students were involved in the task and they were put into groups of four. Each group was assigned to write a paper reporting how they identified and explained the types and subtypes of word-formation of the invented names. The findings suggested that although students found that the task was more meaningful and engaging than the usual learning procedure, the papers they produced showed that they were still not ready for the demand of academic reading and research skills associated with the task. This task, however, promises positive avenues that can be improved and explored in future studies. [ABSTRACT FROM AUTHOR]

Directing attention to racial ignorance as a core dimension of racialized social systems, this article advances a process-focused Theory of Racial Ignorance (TRI), grounded in Critical Race Theory and the philosophical construct white ignorance. TRI embodies five tenets—epistemology of ignorance, ignorance as ends-based technology, corporate white agency, centrality of praxis, and interest convergence. TRI's tenets explain how racial ignorance reinforces white domination, attending to mechanisms of white knowledge evasion and resistance that facilitate racial reproduction—in everyday life, through institutions, and across societies more broadly. I illustrate TRI's assets by comparison to an extant theory of racial cognition—color-blind theory (CBT). I argue TRI generates returns by shifting from racial ideology to racial ignorance, and from era-defined structures to ongoing historical processes; and demonstrate TRI's unique capacity to explain and predict changes in dominant logics, supporting more strategic resistance. [ABSTRACT FROM AUTHOR]

The aim of this paper is to find a broad family of means defined on a subinterval of $I\subset [0,+\infty)$ such that $$\begin{eqnarray}\mathop{\sum }_{n=1}^{\infty }\mathscr{M}(a_{1},\ldots ,a_{n}) Equivalently, the averaging operator $(a_{1},\,a_{2},a_{3}\,,\ldots)\mapsto (a_{1},\,\mathscr{M}(a_{1},a_{2}),\,\mathscr{M}(a_{1},a_{2},a_{3}),\ldots)$ is a selfmapping of $\ell _{1}(I)$. This property is closely related to the so-called Hardy inequality for means (which additionally requires boundedness of this operator). We prove that these two properties are equivalent in a broad family of so-called Gini means. Moreover, we show that this is not the case for quasi-arithmetic means, that is functions $f^{-1}(\sum f(a_{i})/n)$ , where $f:I\rightarrow \mathbb{R}$ is continuous and strictly monotone, $n\in \mathbb{N}$ and $a\in I^{n}$. However, the weak Hardy property is localisable for this family. [ABSTRACT FROM AUTHOR]

The article offers information on the poet Thomas Hardy Birthday Lecture 2019 on "Thomas Hardy in Translation" on June 1, 2019 at the Town Hall, Dorchester, England. Topics discussed include translation of book "Ovid's Epistles" by John Dryden; translation of Dryden by giving importance of metaphrase, paraphrase and imitation; and reference of various Arab poems.

My title is paradoxical, possibly wrong. Refamiliarizing means reintroducing the once known but since forgotten on the assumption that familiarity fosters understanding. The logic on view inheres in the root word, "familiar": "known to a person from long or close association." But Viktor Shklovsky (1893–1984), enfant terrible of the Russian Formalists from the second decade of the twentieth century right to the end of his long life (another paradox), contests that logic. Defamiliarization , his most significant contribution to literary theory, posits that more familiarity with flogging, sex, or the custom of burying the dead—his examples, to which I will return—results in less rather than more of a sense of what they are. In a consequential opposition, Shklovsky claims we lose the ability to see what we encounter frequently; we come instead merely to recognize it by its outlines, "as though it were enveloped in a sack." To see it again, to see it in all its particularity, requires the disorientation that arises when the familiar appears before us as precisely, if temporarily, unrecognizable. Since I aim to render strange, to remove the sack, this little essay should of course be called "Defamiliarizing Viktor Shklovsky." [ABSTRACT FROM AUTHOR]

In the article, the author discusses the activities of the Thomas Hardy Society (THS) as of September 2020, as well as how she became a member of THS. Topics include the feature by the television show "Britain by the Book" of Hardy and his impact to people, and the highlights of the fourth annual THS Study Day, featuring Hardy's novel "The Trumpet-Major."

The article provides information on poems written by Thomas Hardy. The author examines various types of pleasure which one obtains after reading these poems. She discusses the sound symbolism and triplet structure of the poem "The Convergence of the Twain (Lines on the loss of the "Titanic")." The poem "Heiress and Architect" is also examined.

In their evaluation ofJude the Obscure (1895), some earlier literary critics have justifiably (given the historical context) judged the text by the standards of the then dominant and sustained New Criticism trend, taking into account its symbiotic relationship with modernist aesthetics. The basic premise behind this conception was the aesthetic notion of structural and thematic unity as well as coherence and integrity of character. These notions were high on the agenda of the New Criticism of the 1940s and onwards. The narrative was found most lacking in this respect. An article entitled, “Hardy and the Fragmentation of Consciousness” (1975) by Harold L. Weatherby, a foremost Hardy critic, serves as an outstanding example of such a critical view. It makes the case that what ails Jude is its unruliness and disjunctiveness: “the brilliance of the novel's peripheries can scarcely compensate for a profound weakness at its center. Indeed the centre cannot hold: the book falls into fragments” (“Hardy” 469). Weatherby continues, arguing that “There is no unified authorial consciousness” (470), that “Hardy as narrator contradicts himself repeatedly in his estimation of what is right or wrong, good or bad, for his characters” (470), and that it is “an artistic failure . . . failing to achieve unity and coherence” (479). Hardy, in addition, is undeservedly dismissed as “the old-fashioned man from Wessex” (483) – which reminds us of the well-known “good little Thomas Hardy” epithets of Henry James's adverse judgment (Cox xxxi). The article also associates incoherence and contradictions in the narrative with attitudinal ambivalences in Hardy's own mind (473, 476). Undeniably, Jude is permeated with incoherence. Who can disagree? It is deeply involved in sustained and unsettled opposition and what may be termed the play of Derridean différance (Positions 14). And, indeed, Hardy himself acknowledges the tangle of disconnections and self-contradictions disrupting the stability of character in a notebook admission (which shows it to be his design): Of course the book is all contrasts . . . Sue and her heathen gods set against Jude's reading the Greek testament; Christminster academical, Christminster in the slums; Jude the saint, Jude the sinner; Sue the Pagan, Sue the saint, marriage, no marriage; &c., &c. (Life 272–73) [ABSTRACT FROM PUBLISHER]

In the 1960s Cargo and Shisha introduced a metric in a family of quasi-arithmetic means defined on a common interval as the maximal possible difference between these means taken over all admissible vectors with corresponding weights. During the years 2013-2016 we proved that, having two quasi-arithmetic means, we can majorize the distance between them in terms of the Arrow-Pratt index. In this paper we are going to prove that this operator can also be used to establish certain lower bounds of this distance. [ABSTRACT FROM AUTHOR]

The article focuses on solving single integrals by using double integrals and focuses on the mathematical proofs related to single integrals.

The Well-Beloved attends to the complexities and anxieties of creative consciousness. While Hardy, characteristically, remains non-committal throughout, a speculation surfaces about the status of the artist, the relationship of the artist and the world, and the tendency of art to falsify. The artist hero Jocelyn Pierston is an explorer feeling his way in an effort to reveal some unknown beauty. It is his desire to find the ideal of woman ("the Well-Beloved") and translate her beauty into a sculptural form that impels him to wander. So among Hardy's preoccupations in the novel is a need to register the notion of wandering as a metaphorical referent for the hero's journey in search of ideal beauty, which is in fact beyond the limits of his own power. This essay invites the reader to consider the nature of Pierston's wandering, thereby aiming to underline that The Well-Beloved reflects Hardy's aesthetic and mores beyond his own fin de siecle, which could be described as distinctively postmodern. [ABSTRACT FROM AUTHOR]

With dramatic developments in the treatment of HIV/ AIDS, life expectancy is increasing, resulting in more middle-aged and older adults living with this disease. Little is known about the problems, and especially the strengths, of those living and aging with HIV. Hardiness is used in the gerontological literature to describe and explain how people age successfully, despite traumatic life events and chronic diseases. Similarly, the concept of hardiness may be used to guide clinicians, researchers, and clients on how to age successfully with HIV. This article provides a review of hardiness in aging and HIV, and emphasizes its importance in facilitating successful aging with this disease. Conceptual and methodological concerns in studying hardiness and successful aging are addressed. Potential interventions and clinical implications for social work are posited for augmenting qualities of hardiness in people aging with HIV. [ABSTRACT FROM AUTHOR]

The article discusses the connection between gold and the monetary system and price level and the gold problem in the U.S. Discussion of the gold standard has been misguided by the experience of the standard's classical period, 1850-1914, and by the wrong interpretation of this experience. If analyzed using statistical methods, the experienced proved that the gold supply governs the trend of the price level. In the current systems of developed countries gold has not been permitted to influence the volume of fiduciary money, but in each of them, an influx of gold created purchasing power corresponding to its physical volume.