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AbstractDue to its significance in reconstructing signals, the theory of dual frames has attracted the interest of many mathematicians. In this paper, we introduce the concept of approximate Q-oblique dual g-frames. We characterize the approximate Q-oblique dual g-frames of an arbitrarily given g-frame; present a method for constructing approximate Q-oblique dual g-frame pairs that have better approximation from a given approximate Q-oblique dual g-frame pair; and investigate the stability of approximate Q-oblique dual g-frame pairs under the analysis, synthesis and frame operator-perturbation, the gap-perturbation, and the l2 operator portrait-perturbation. Finally, as an application of the above results, we obtain some new results on usual frames which cover some existing results. [ABSTRACT FROM AUTHOR]

A conjugation on a Hilbert space $ \mathcal {H} $ H means an antilinear bounded operator that the squares to the identity, which generalizes the traditional conjugation on complex Euclidean spaces. In this paper, with the help of normalized conjugation we introduce the notion of conjugate phase retrieval on general Hilbert spaces. We characterize frames that do conjugate phase retrieval; prove that every conjugate phase retrieval frame for $ \mathcal {H} $ H consisting of all real vectors has the complement property in $ \mathcal {H} $ H , and the converse is true if $ dim({\mathcal {H}})\leq ~2 $ dim (H) ≤ 2 ; and also prove that a small perturbation of conjugate phase retrieval frame still gives a conjugate phase retrieval frame if $ dim({\mathcal {H}}) \lt \infty $ dim (H) < ∞ , but it is false if $ dim({\mathcal H})=\infty $ dim (H) = ∞. [ABSTRACT FROM AUTHOR]

This article considers the opportunities for learning and inclusive dimensions of role-play based on the reading and interpretation of a canonical text, drawing on a case study involving student-teachers. This exploration of role and learning through drama builds on the foundational work of Bolton and Heathcote. Focusing on students' particular purposes, motivations, and the resources that inform their diverse engagements in drama involves a detailed reflection on the possibilities that role-play offers to support learning in classroom contexts. These findings have implications for a pedagogical approach to teaching texts through drama. [ABSTRACT FROM AUTHOR]

AbstractWe study a variant of extremal disconnectedness in frames, defined by requiring that any two disjoint open sublocales should be separable by disjoint open sublocales each of which is the interior of some zero-sublocale. In spaces, this notion was recently introduced in [1] in order to study some properties of frames of z-ideals of rings of continuous functions. The point-free approach adopted here brings to the fore some topological results not considered in [1], such as that a dense z-embedded subspace of a Tychonoff space has this property if and only if the space containing it has the property. In [1], this was proved only for the embedding X ⊆ βX. We give a ring-theoretic characterization by defining a property of f-rings in a transparent manner which shows why the property should be defined the way we do. The property is that if two annihilator ideals meet trivially, then the annihilator of each of the annihilator ideals contains a positive element such that the sum of the two elements is a non-zerodivisor. [ABSTRACT FROM AUTHOR]

This paper builds on Kohut's creative use of empathy by exploring and delineating the advantages of embracing the concept of permeable boundaries. After describing our theoretical understanding of permeable boundaries, we suggest how its use can facilitate a treatment characterized by an unusual depth, intimacy, and healing. Instead of illustrating the theory using interactions with our patients, we used excerpts from our own therapeutic relationship to capture an experience near understanding of what permeable boundaries looks and feels like in clinical practice. In this way we are proposing a new frame along with a definition which therapists can use to guide and expand their therapeutic work. We then turn to the impact of permeable boundaries on several of the healing processes that occur in many treatments: heightened affective moments, internalization, corrective emotional experiences, the forward edge and interpretative work, and repairing disruptions. [ABSTRACT FROM AUTHOR]

The dissolution (introduced by Isbell in [3], discussed by Johnstone in [5] and later exploited by Plewe in [12, 13]) is here viewed as the relation of the geometry of L with that of the more dispersed T(L) = S(L)op mediated by the natural embedding and its adjoint localic map γL: T(L) → L. The associated image-preimage adjunction (γL)−1 [−] ⊣ γL [−] between the frames T(L) and TT(L) is shown to coincide with the adjunction cT(L) ⊣ γT(L) of the second step of the assembly (tower) of L. This helps to explain the role of T(L) = S(L)op as an "almost discrete lift" (sometimes used as a sort of model of the classical discrete lift DL → L) as a dispersion going halfway to Booleanness. Consequent use of the concrete sublocales technique simplifies the reasoning. We illustrate it on the celebrated Plewe's theorem on ultranormality (and ultraparacompactness) of S(L) which becomes (we hope) substantially more transparent. [ABSTRACT FROM AUTHOR]

We offer here a particularly simple and direct construction of the congruence frame of a given frame, aka its assembly, from the bounded meet semilattice of differences of frame elements. The construction enables economical proofs of two of the assembly's known attributes, namely ultranormality and ultraparacompactness, as well as a proof that the assembly is an essential extension of the frame with the same essential closure as the frame. The major new result is that the assembly is free over its meet semilattice of differences. [ABSTRACT FROM AUTHOR]

Power comes not only as conventional Compulsory Power but also as Institutional, Structural, or Productive Power. We focus on under-explored Productive Power (the ability to produce and give meaning to social identities and capacities through discursive processes and practices) and the related strategy of rhetorical framing (using particular words or terms to characterise an issue and imply appropriate actions in line with that characterisation). Spotlighting the strategy's dual offensive/defensive utility and relatively low resource requirements, we expect the strategy of rhetorical framing (and counter-framing) to be: (1) prevalent in inter-governmental negotiations, and (2) used even by conventionally 'very weak' states. Employing text analysis on over 5000 observations from the World Trade Organization's (WTO) negotiation transcripts between 1995 and 2020, we confirm that states 'weak' in Compulsory Power are nevertheless wielding Productive Power and its related strategy of rhetorical framing. Whilst conventionally strong states emphasise a Reciprocation Frame (mutual concessions between states), conventionally weak states emphasise a Redistribution Frame (one-way concessions from some states to other states). Such findings make two important contributions: we exhibit the mechanics of an under-explored type of power and show what happens in international institutions when no single rhetorical frame dominates. [ABSTRACT FROM AUTHOR]

Frontline workers engaged in enabling employment and activist entrepreneurs strive to reframe disability as they facilitate work inclusion. They do so in an organisational and societal context that emphasises labour-market participation. Frontline workers facilitate this inclusion when they implement and construct disability employment policies at the street level, while activist entrepreneurs do so when they privilege hiring disabled people. Based on interviews in this study within a Norwegian welfare context, I show how both groups of actors strive to abolish a deficit approach in distinct yet overlapping ways. They do so by framing disabled people in terms of their assets and contributions rather than foregrounding their needs and challenges. While the entrepreneurs brought up ways in which disability can be a central part of identity that should be recognised and talked about, the frontline workers promoted assets in an individualised manner. Nevertheless, the deficit approach is maintained in subtle ways. The social political context that emphasises employment for all encourages key stakeholders to abolish the deficit approach to disability. Social actors use different angles or perspectives to understand complex social phenomena, such as disability. Both frontline workers and activist entrepreneurs provide perspectives that highlight disabled people's assets and contributions rather than foregrounding their needs and challenges. Despite engagement in highlighting disabled people's assets, the deficit approach is still maintained in subtle ways. Activist entrepreneurs could provide input into the design of disability employment policies. [ABSTRACT FROM AUTHOR]

The stereotype and stigma that disabled people experience is a communication proposition that deserves academic attention. How the media reports people with disabilities reflects society's overall perception and evaluation of people with disabilities. This study uses content analysis to demonstrate how People's Daily, the mainstream media in mainland China, has undergone a process in the designation of people with disabilities from canfei (disabled and waste) to canji (disabled and ill) to canzhang (people encountering obstacles). News reports related to the image of people with disabilities often relate to terms such as 'heroes', 'role models', 'builders', 'beneficiaries', and 'free riders'. How the media reports people with disabilities reflects, to some extent, what society thinks and feels about people with disabilities. This study demonstrates how People's Daily, the mainstream media in mainland China, has built and reproduced the image of people with disabilities in different historical periods since 1946. With the development of the Chinese society, People's Daily has been going through a process of naming people with disabilities from canfei (disabled and waste) to canji (disabled and ill) to canzhang (people encountering obstacles). While highlighting the positive aspects of people with disabilities, they are also perceived as weak people who require help from all sectors of society. People with disabilities need to be understood from a 'human' perspective to establish approaches based on equality and pluralism to human values. [ABSTRACT FROM AUTHOR]

Recent advances in behavioural and communication sciences generated enthusiasm in public policy for new ways of 'framing' messages and 'nudging' individual behaviour. Wide research and practice of behavioural interventions that have since ensued triggered the rise of a new sub-field called Behavioural Public Policy (BPP). At the same time, nudges – a part and parcel of BPP, have received criticism for being paternalistic, non-democratic and lacking evidence of long-term effectiveness. More recently, the whole project of BPP has come under criticism as construed too narrowly. Critics have argued for a new approach to BPP that is pluralistic, multi-disciplinary and multi-method. One key pillar of it is a 'policy mix' – a combined application of behavioural and non-behavioural policy tools. Little is known, however, about 'policy mixes' in practice. This paper conducts a scoping non-exhaustive review of the academic and policy literature published between 2008 and 2020 that discusses policy mixes of behavioural policy tools (defined in this paper as 'nudges' and 'frames') and reflective policy tools (defined in this paper as 'deliberative' events and incentives for individuals to 'think') employed within environmental policy. Two questions guide this review: (a) what are the characteristics of policy mixes in terms of their types, geography, sectors of application, and empirical detail of exposition?; (b) to what extent do existing policy mixes include broader governance aspects of politics, awareness of contextuality and flexibility? By taking stock of experiences of empirical place-based policy mixes of behavioural and reflective tools, we provide insights into a fast-developing body of scholarship and point to ways forward with policy mixes. The paper is also relevant to policy studies beyond the domain of the environment. [ABSTRACT FROM AUTHOR]

Frames can have an essential role in the (re)production of the ‘shared ideologies’ concerning several social categories, including migrants. The overall aim of this work is to investigate the discursive construction of frames concerning migration, as rhetoric tools (a) connected to editorial orientations; (b) related to both specific events and more general thematic news articles; (c) having socio-cultural and emotional connotations. The qualitative analysis of 235 Italian news articles enabled us to outline different configurations of discursive elements as well as to identify different emotional pathways. Reflections about the critical role of framing in the social knowledge construction are proposed. [ABSTRACT FROM AUTHOR]

This paper attempts to expand José Bleger’s classic, metapsychological descriptions of the psychoanalytic frame to formulate and emphasize the role of the analyst’s internal frame in establishing a psychoanalytic observational perspective in the analytic situation. The rationale for doing so follows from clinical necessity, especially when working with patients and psychic organizations that are ‘beyond neurosis’ and in non-traditional settings such as distance and telemetric analyses. Clinically speaking, in its most effective state, the analyst’s internal frame can inform the possibility of an observational vertex aimed at the intuitive grasp of psychic reality rather than a sense-based, empirical observation of parameters denoted by the elements of a consensually validatable social reality. [ABSTRACT FROM AUTHOR]

The author addresses the theme of frame and setting in psychoanalysis, suggesting that they are “functions” of the psychoanalytic process. Frame is defined as the external components of the context that enable the development of a process, and setting as the primarily psychoanalytic elements within the analyst’s mind, necessary for establishing an analysing situation where a process should take place. The author emphasizes that the characteristics of both also define the outline of the process, while discussing attributes that would aid in its development. The author proposes the creation of an imaginary model regarding possible invariants in psychoanalytic theories and theories of technique with the intention of deepening the understanding of the relationship between frame, setting and process. The author concludes with a reflection on the effect of implicit theories on the construction of frame and setting. [ABSTRACT FROM AUTHOR]

Reforms within science education strive to shift early science instruction (K − 2) so students have ample sense-making opportunities to construct scientific explanations. Classroom discussions play a key role in supporting these endeavors. This requires that classroom discussions are shaped in ways that foster scientific instruction and learning. In this study, we take a social semiotic perspective on Goffman's notions of frames and participation framework to explore how a first-grade teacher accessed and supported his students' scientific explanation construction within whole-class discussions. Our research questions ask how scientific explanations are framed during science discussions and how this framing influences student scientific explanations and participation in science talk. Evidence suggests that the teacher's framing resulted in miscues regarding the frame and participation framework necessary to participate in the discussion. When students encountered these miscues, their participation was thwarted and opportunities for articulating scientific sense-making were lost. Implications for this study identify the importance of semiotic resources for framing science instruction during classroom discussions and the architecture of interactional spaces. [ABSTRACT FROM AUTHOR]

This study investigates the elastoplastic deformation behaviour of a motorcycle frame under quasi-static mechanical loading. We present a novel test rig to analyse the mechanical integrity of a motorcycle frame under four different load configurations. These four load configurations reproduce longitudinal forces, lateral forces, torques and bending moments that act on the frame in normal operation as braking, acceleration or cornering. Additionally, the four load configurations represent loads that act on the frame in the most frequent crash scenarios in urban areas, such as a motorcycle's frontal or inclined collision against a car. We conducted three repetitions of each load configuration with a frame from a motorcycle, especially for the urban area. The compliance of the measured load–displacement curves is rated by an objective assessment method. All tested frames show a similar elastoplastic deformation pattern; specifically, the longitudinal tubes are pressed outside, and fractures occur predominantly at areas of welding spots while the inner part remains scarcely deformed. The load–displacement curves, mechanical failures, weak points and deformation behaviour of the frames can be used in future to validate a numerical model of a motorcycle frame and improve the crashworthiness of a motorcycle frame. Novel experiments on the elastoplastic characterisation of motorcycle frames Multidirection deformation and failure behaviour Motorcycle frame as protection for sensitive components such as batteries Approach to validate deformation patterns and mechanical resistance of simulation models Validation of the test reproducibility by compliance assessment of measurement data [ABSTRACT FROM AUTHOR]

In last decades, the operator theory of Krein spaces, Krein space approaches, and various generalizations of frames have interested many mathematicians due to their potential applications in mathematics and engineering. This paper addresses the frame theory for Krein spaces. We present some properties of J-orthonormal bases, Parseval frames and frames for Krein spaces, and a parametric expression of all duals of an arbitrarily given frame in Krein spaces. This study shows that the frame theory for Krein spaces is not a direct generalization of the frame theory for Hilbert spaces. [ABSTRACT FROM AUTHOR]

The author describes how a teaching forum was started at his local institute, with the goal of helping to support and sustain faculty in their work as psychoanalytic teachers. Psychoanalytic teachers receive little training or mentorship, and there are few opportunities to discuss their classroom experiences, despite the challenges of shifting from the dyadic experience of the therapist's office to the group dynamics of the classroom. The author discusses various challenges for psychoanalytic teachers in making that transition, while also considering how our awareness of the frame, the risks of idealization and transference can aid us as teachers. An example of a forum meeting about the use of assigned readings demonstrates how a focus on the process of reading can be a more effective form of teaching foundational psychoanalytic concepts than simply teaching content or concepts from papers. [ABSTRACT FROM AUTHOR]

Dynamic Magnetic Resonance Imaging (dMRI) is a valuable tool for understanding changes in human physiology, but its temporal and spatial resolution can be limited. Compressed sensing (CS) has been used to enhance temporal resolution by acquiring partial k-spaces of each time frame and exploiting sparsity to retain spatial resolution. Invoking CS in dMRI necessitates algorithms that can leverage both spatial sparsity within each time frame and temporal sparsity across time frames. A tensor decomposition-based multi-mode dictionary learning algorithm has been proposed to learn the spatial and temporal features of dMRI data and reconstruct it more efficiently. The extensive quantitative simulations reveal the improvement induced by the proposed method in various settings compared to state-of-the-art methods in dMRI. Further, it considerably advances reconstruction speed from trained dictionaries over the state-of-the-art, permitting faster scans catering to a larger patient group. [ABSTRACT FROM AUTHOR]

In this paper we introduce generalized phase retrievable frames or simply g-phase retrievable frames in real or complex n-dimensional Hilbert space H n , which include ordinary phase retrievable frames in H n . Specifically, a g-phase retrievable frame is a λ-phase retrievable frame, where λ is an special function, which is called phase coefficient function. Using the λ-phase retrievable frames, every vector in H n can be reconstructed up to a constant phase coefficient factor from the action of λ on the its frame coefficients, which can be bounded for bounded phase coefficient functions. We obtain some equivalent conditions to g-phase retrievable frames and we study on stability of special g-phase retrievable frames under small perturbation of their vectors and under small perturbation of their phase coefficient functions. [ABSTRACT FROM AUTHOR]

The property of subfitness used in point-free topology (roughly speaking) to replace the slightly stronger T1-separation, appeared (as disjunctivity) already in the pioneering Wallman's [16], then practically disappeared to reappear again (conjunctivity, subfitness), until it was in the recent decades recognized as an utmost important condition playing a very special role. Recently, it was also observed that this property (or its dual) appeared independently in general poset setting (e.g. as separativity in connection with forcing). In a recent paper [2], Delzell, Ighedo and Madden discussed it in the context of semilattices. In this article we discuss it on the background of the systems of meet-sets (subsets closed under existing infima) in posets of various generality (semilattices, lattices, distributive lattices, complete lattices) and present parallels of some localic (frame) facts, including a generalized variant of fitness. [ABSTRACT FROM AUTHOR]

H-S-frame is in essence a more general operator-valued frame than generalized frames. In this paper, we aim at studying the characterizations and representations of H-S-frames in H (Hilbert space). We first introduce the notion of H-S-preframe operator, and characterize the H-S-frames, Parseval H-S-frames, H-S-Riesz bases, H-S-orthonormal bases and dual H-S-frames with the help of H-S-preframe operators, and obtain the accurate expressions of all dual H-S-frames of a given H-S-frame by drawing support from H-S-preframe operators. Then we discuss the sum of H-S-frames through the properties of H-S-preframe operators. Finally, with the help of the approaches and skills of frame theory, we present the representations of H-S-frames and H-S-Bessel sequences. Specifically, the necessary and sufficient condition for the H-S-frame to be represented as a combination of two H-S-orthonormal bases is that the H-S-frame is an H-S-Riesz basis. [ABSTRACT FROM AUTHOR]

The new type of prefabricated embedded concrete-filled steel tube (CFST) special-shaped column structure delivers green and environmentally-friendly strengths and high space. In this study, a full-scale frame test piece with one frame façade, two stories and two spans are designed and fabricated for purposes of exploring the seismic performance and node connection safety of filled built-in steel tube concrete-filled special-shaped column, and low cyclic load testing is implemented. The bearing characteristics, deformation capacity, energy-dissipating capacity, ductility and stiffness degradation of the test piece are analyzed. The results showed that the failure mechanism is typical beam hinge mechanism. The fabricated beam-column and column-column connection nodes in this paper are safe and reliable. The hysteretic curve of fabricated embedded CFST special-shaped column is full, the ductility and energy dissipation capacity of fabricated embedded CFST special-shaped column are better than such indexes of ordinary reinforced concrete special-shaped column. The inter-story displacement angle is 1/32 when the test piece is damaged, being significantly higher than the limit value of elastic-plastic inter-story displacement angle of 1/50 under strong earthquake. The precast embedded steel-reinforced concrete special-shaped column structure is only required to be connected with steel ribs to significantly improve the construction speed and quality, delivering great economy. [ABSTRACT FROM AUTHOR]

The GameStop saga aroused the emotion and indignation of a large part of the financial community. This paper accounts for this reaction by exposing the conflict of expertise at the heart of the saga: the Bloomberg Terminal of market professionals and the forum of retail investors supported antagonistic perceptions of events. It then generalizes these findings by characterizing the framing operated by the Terminal mobilized by traders, and by underlining its essential divergences from the framing of the internet forum. Through their selection, weighting and ranking operations, these devices offer different points of view on the financial markets. This pluralization of the informational bases guiding investors' decisions allows this paper to address the issue of the democratization of finance, its conditions of feasibility and desirability. [ABSTRACT FROM AUTHOR]

Vona Groarke has long evoked domestic spaces as a means of self-definition in face of a fluid world. Unlike her earlier work, though, in Four Sides Full and X, she finds in architectural constructions, gardens and visual arts a liminal space in which the persona withdraws from the world of action and actuality into a state of potentiality. Although this state is fraught with painful feelings of loneliness, Groarke, in order to resist the seclusion that threatens to engulf her, strives after a radical openness, employing the frames of poetic form inside of which the persona arises as it always already disappears into the framing whiteness of the page. [ABSTRACT FROM AUTHOR]

This paper considers the compact hedgehog as a frame presented by generators and relations, based on the presentation of the frame of extended real numbers. The main focus will be on the point-free version of continuous and semi-continuous functions that arise from it, and their application in characterizations of variants of collectionwise normality. The variants to be considered are defined by selections of adequate families of sublocales and their characterizations depend on lattice-theoretic properties of the selected families. This way insertion and extension results for semicontinuous and continuous functions with values in the compact hedgehog frame are generalized and unified. [ABSTRACT FROM AUTHOR]

The concept of prospective memory has been suggested as a way of theorising the importance of forward-looking memory in mediated accounts of past events. As yet, however, there was insufficient work to analyse the relationship between retrospective and prospective memory especially in collaborative journalistic cultures where one might expect the importance of prospective memory to be significant. Here, we apply the concept of mediated prospective memory, together with retrospective memory, to understand the commemoration of the end of the Second World War in China. We compare the commemoration—or indeed the absence of commemoration—in the People's Daily over the last seven decades, showing how the Second World War was retrospectively remembered, which remaining geopolitical or domestic tasks the Chinese people were reminded of prospectively, and how retrospective memory has been reinterpreted over time in order to construct a narrative suiting the perceived changing needs of the future. Through doing so we contribute methodological and conceptual resources for the analysis of the relationship between retrospective and prospective mediated memory and commemorative journalism beyond China. [ABSTRACT FROM AUTHOR]

The article explores the impact of Israeli policies and practices on Palestinian urban nodes in occupied East Jerusalem focusing on Kubsa junction. It argues that the Segregation Wall has created spaces where Palestinian life is expendable and where the practice of eliminating the Arab Palestinian character of the city has transformed a once vibrant Palestinian urban node into a dead end. Kubsa Junction illustrates settler-colonial military spatial policies and urban planning to control the urban space of Kubsa Junction which have created a 'frame' to segregate and control the colonized Palestinians. Such policies, the article argues, are better interpreted by settler-colonial state strategies than racialized global capitalism. Yet, while different layers of daily lives and memory of the colonized on both sides of the Segregation Wall have been harmed, the spiritual and collective memory layers maintain meaning and purpose to the colonized's steadfastness or Sumoud. [ABSTRACT FROM AUTHOR]

The fractional Fourier transform, which is a generalization of the Fourier transform, has become the focus of many research papers in recent years because of its applications in electrical engineering and optics. In this paper, we introduce the notion of fractional biorthogonal wavelets on R and obtain the necessary and sufficient conditions for the translates of a single function to form the fractional Riesz bases for their closed linear span. We also provide a complete characterization for the fractional biorthogonality of the translates of fractional scaling functions of two fractional MRA's and the associated fractional biorthogonal wavelet families. Moreover, under mild assumptions on the fractional scaling functions and the corresponding fractional wavelets, we show that the fractional wavelets can generate Reisz bases for L 2 (R). [ABSTRACT FROM AUTHOR]

This paper is concerned with the lower and upper redundancy of infinite frames in a separable Hilbert space. Using unit norm linear operators, a new representation of upper redundancy is given. Also, we show that there is no frame such that its lower redundancy is less than one and its upper redundancy is one. Moreover, for given (μ , λ) ∈ M := { (μ , λ) ; 1 ≤ ⌈ μ ⌉ ≤ ⌊ λ ⌋ } ∖ { (μ , 1) ; 0 < μ < 1 } , we construct a frame such that its lower redundancy is μ and its upper redundancy is λ. [ABSTRACT FROM AUTHOR]

Recently, duality principles in g-frame theory were studied. This paper addresses a relaxation of g-R-duals. We introduce the notion of weak g-R-dual in g-frame theory setting, and present the link between frame properties of a bounded operator sequence and its weak g-R-duals. Using weak g-R-duals, we characterize g-frames and (unitary) equivalence between g-frames. And using pseudo-inverse operators, we represent the canonical duals of weak g-R-duals. Some examples are also provided. [ABSTRACT FROM AUTHOR]

This paper concerns the congruence frame in the setting of partial frames, which, in contrast to full frames, do not necessarily have all joins. Examples of these include bounded distributive lattices, σ- and κ-frames. A new class of congruences, called Heyting congruences, helps to illuminate the structure of these congruence frames. Defining these involves the very useful free frame over a partial frame. We investigate the relationship between Heyting congruences and co-atoms of the congruence frame, showing how different the cases of full and partial frames can be. The Madden congruence, which yields the least dense quotient, is recognized as a particular Heyting congruence. While the collection of all Heyting congruences on a partial frame is in general not even a meet-semilattice, joining each of them with the Madden congruence results in a collection with considerably more interesting structure. [ABSTRACT FROM AUTHOR]

Public perceptions of emergent low-carbon technologies, such as geothermal energy, impact the speed of energy transitions. Such perceptions are largely shaped by how the media portray such technologies. This paper reports on how geothermal energy has been framed in two prominent national newspapers in Indonesia, a country with large geothermal potential due to its volcanic geology. We examined articles on geothermal energy written over ten years. Applying a quantitative framing analysis, we investigated the salience of six frames indicated in the literature as often used in communications on geothermal energy: energy security, economy, legislation, environment, knowledge, and social issues. We also examined the tone and source of the frames. The analysis reveals an overall positive tone in the newspaper articles, especially regarding the technology's energy security and economic potential, with the primary source being the national government. Possible adverse effects of geothermal technology are covered less often, particularly those related to social issues at the local level. We describe the different frames identified, provide examples and discuss implications. [ABSTRACT FROM AUTHOR]

It is constructed infinite frames with some given redundancy. In this paper, the solution of the construction problem of infinite frames with given redundancy, is completed. More precisely, all possible infinite frame redundancies are characterized. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has been the most mediatised health crisis in human history, involving a rapid circulation of knowledge in global networks and a continuous flow of spectacular images and narratives that have rendered the pandemic graspable in cultural, political, and moral terms. This article proposes that the intertwined nature of two opposite trends of knowledge production – scientific reasoning and affective storytelling – can be analytically approached through the concept of 'outformation' that provides explanatory power and conceptual clarity to make sense of the disorderly flows of knowledge in the pandemic-era. Using frame analysis, the article examines how one key term of the pandemic era, herd immunity, is taken from its scientific context and mobilised across different epistemic arenas from journalistic media to parliamentary debates as a vehicle for mistrust towards political and expert authorities in Finland that is a country characterised by high levels of trust towards authorities. The Finnish case is not only a national case about the framing of a specific term in times of epistemic instability but also provides a valuable lens to knowledge production during the pandemic era. [ABSTRACT FROM AUTHOR]

Let P be a prime ideal of the ring of continuous real-valued functions on a completely regular frame L, i.e., L. We study many new results about the residue class domains L/P with an emphasis on determining when the ordered L/P is a valuation domain (i.e., when given any two non-zero elements of L/P , one divides the other). A prime ideal P of L is called a valuation prime ideal if L/P is a valuation domain. A frame L is called an SV-frame if every prime ideal of L is a valuation prime ideal. We introduce and study two new generalizations of the SV-frames. The first is that of a quasi SV-frame in which every real maximal ideal of L that is not a minimal prime ideal contains a non-maximal prime ideal P such that L/P is a valuation domain. In the second, we define a frame L to be an almost SV-frame if every maximal ideal of L contains a minimal valuation prime ideal. A point I ∈ Pt(βL) is called a special βF -point if OI = {δ ∈ L : coz δ ∈ I} is a valuation prime ideal of L. It is shown that I is a special βF -point if and only if the pseudo-prime ideals of L containing OI that are not primary form a chain under set inclusion. [ABSTRACT FROM AUTHOR]

In practice, the time variable cannot be negative. The square integrable function space L 2 (R +) defined on the half real line R + = (0 , ∞) models the causal signal space. Given a>1, this paper addresses F a -frames in the setting of subspaces of L 2 (R +). We establish the connection between subspace F a -frames and orthogonal projections; characterize all bounded linear operators on L 2 (Z × T a) that transform F a -frames into other F a -frames for a subspace V of L 2 (R +) ; and obtain some sufficient conditions for constructing F a -frames for V from an arbitrarily given one. [ABSTRACT FROM AUTHOR]

The assembly of frames into the structure of aircraft fuselages requires adhesive shimming to fill occurring joint gaps above 0.3 mm. Gap measurement and gap filler application tasks are time-consuming manual processes. Up to now, the frame elements form the interface between frame and shell adjusting any form deviations. Stiffness elements are added to support the shape of the frame. To save process efforts, new frames under development are thermoplastic integrals with main body, feet, and stiffness elements made of one part. These parts are easier to form and re-shape during production but have to be adequately produced to fit to the shell, avoiding joining forces and deformations. In this paper, it is presented that the gaps can be measured with an automated method. Novel developments are the automated gap body measurement of rigid parts in a pre-assembly station, the measurement method by avoiding joining forces and the automated procedure of measuring gaps for applying the gap filler. The gaps between two joining parts are reconstructed virtually by measuring the joining surfaces of the produced parts with a laser tracker and a line scanner (T-Scan) before joining. These points are combined with the CAD model of each part. The parts are then virtually joined. The exact opposite points of each joining surface are either in contact or have a distance resulting in the gap value. Virtual joining gives insight into the results of the process and helps decide on the gap-filling strategy. The effects of contact during assembly can be avoidable using a design gap or a shape best-fit. The resulting point cloud is then processed and transmitted to a robot-guided 3D printer reproducing the surface structure with thermoplastic PEEK gap filler material directly onto the frame feet surfaces. [ABSTRACT FROM AUTHOR]

The paper focuses on the changing status of the moral framing of animals in Western visual culture in the last four decades. The author proposes to revise John Berger's critique of the marginal way of seeing animals in modern museums and zoos. Both institutions presented animals as strangers to urban culture by keeping them isolated in showcases and cages. Mass media that disseminated wildlife documentaries kept on separating animals from human culture by picturing them as representatives of "wild" species. The paper brings attention to a decisive moment in the reframing of the public gaze, which occurred with the birth of two new visual genres. First, investigative documentaries and activist blogs allowed the human right to exploit animals to be criticized. Second, the rise of social networks allowed animals to be pictured as companions. The author argues that both genres caused an inclusive turn of public gaze that visually integrated animals into urban culture. [ABSTRACT FROM AUTHOR]

Months following the traumatic termination of my analysis I engaged in self-analytic work in which I was able to rework the events of the termination and their significance in terms of my history. Fundamental differences between my self-analytic process and that of my formal analysis led me to consider how termination may affect the ensuing self-analytic process. In this paper, I look at aspects of termination that have to do with the dissolution of symbiotic ties with the analyst; I will try to show that relinquishment of the frame provides an impetus both for consolidation and reworking of an identification with the analyst, which may enable the analysand to develop a personal way of thinking about the unconscious that differs from that of the analyst. I further suggest that there are inevitable limitations to the analytic process which manifest in the development of irreducible bastions, and that the dissolution of the frame at termination provides an opportunity for self-analytic resolution of those bastions which may allow self-understanding beyond what could have been attained within the formal analytic setting. Finally, I offer some speculations on how these processes may have played out between Freud and Fliess in Freud's self-analysis. [ABSTRACT FROM AUTHOR]

In order to see how Asian countries in this special volume (Japan, South Korea, Vietnam, Singapore, and Indonesia) are looking at China in chronological and comparative perspectives, using Global Attitudes Survey data conducted by Pew Research Center would be the best way because they cover the data from 2002 to 2019 as of now. We can get a lot of insights on different views of the rise of China in Asia through the analysis of Pew Research Center's Global Attitudes Survey data, but there are some inconveniences. Some data in Asian countries are lacking, and the timing of survey is different from one country to another, which makes it difficult to compare the results across the countries. In order to overcome such limitations, this paper uses the second wave and third wave data of Asian Student Survey. Main findings of the analysis are as follows. As of 2018, Singapore and Indonesia were comparatively positively viewing the influence of China, while Vietnam was viewing it negatively, and Japan and South Korea were in-between. The changes in these five years, however, were different from country to country. Changing views of Chinese toward Asian countries were basically symmetrical to those of Asian countries toward China. In these surveyed countries, "peaceful rise frame" was the most powerful determinant of the views of China, which explains why views of China were worsening in these countries. But the concrete determinants of the views were different from one country to another. [ABSTRACT FROM AUTHOR]

The article reports a comparative study of the representation of migration in media from three countries (Greece, Italy, and Turkey), over 2001–2018 period. Analysis showed the salience of two main frames – the view of migration as a matter of security and human beings as well. Themes framing the media discourses on migration are grounded on a semantic structure that is quite similar across the three countries compared, despite their considerable socio-cultural and geo-political differences. These semantic structures appear not to be associated with time of publication or with the political orientation of newspapers. Implications from these findings are discussed. [ABSTRACT FROM AUTHOR]

This paper considers some of the paradoxes, challenges and opportunities we face in the shadow of the COVID-19 pandemic. I consider the ways in which masks serve necessary protective functions, while at the same time serving defensive roles in a different register. The ways in which "remote" work can function as an obstacle to therapeutic intimacy at the same time that it can deepen it, are considered. [ABSTRACT FROM AUTHOR]

The COVID-pandemic has meant that we, as therapists, go through the same experiences as our patients. Bass's paper enables us to digest these last months' experience, not only from a professional perspective, but from both emotional and practical perspectives as well. In this paper, we zoom into the new opportunities frame alterations have brought, such as more intimacy and openness, both for patients and therapists. [ABSTRACT FROM AUTHOR]

This paper is concerned with the signal reconstruction without phase by norm retrievable frames in finite dimensional real Hilbert space H . Specifically, we show that the nonlinear analysis maps α , β : H ˆ ⟶ R m are injective, with α (x ˆ) := | x , f k | 1 ≤ k ≤ m and β (x ˆ) := | x , f k | 2 1 ≤ k ≤ m , where { f k } k = 1 m is a norm retrievable frame for H and H ˆ is the quotient space corresponding to a special equivalence relation on H . Using Householder matrices, the members of any x ˆ ∈ H ˆ are characterized. Also, we show that α has upper Lipschitz bound B and local lower Lipschitz bound A , with respect to an appropriate metric d on H ˆ , where A and B are the lower and upper frame bounds of the norm retrievable frame { f k } k = 1 m , respectively. Additionally, we show that β has upper Lipschitz bound 2 B and local lower Lipschitz bound a , with respect to an appropriate metric D on H ˆ , where a = inf ∥ e ∥ = 1 ∑ k = 1 m | e , f k | 4 and B is the upper frame bound of the norm retrievable frame { f k } k = 1 m . [ABSTRACT FROM AUTHOR]

This article builds on the most recent work done on ekphrasis in contemporary fiction and explores its capacities to blur the boundary between visual art and life writing. Since ekphrasis can contest the border of the work of art, this article also draws from Derrida's notion of the parergon (1987). Ekphrasis is most commonly understood as the 'verbal representation of a visual representation' (Heffernan 1993), while the parergon captures the ambiguous, 'ornamental' frame that separates the artwork from the world beyond it. By focusing on Amy Sackville's Painter to the King (2018) and Laura Cumming's The Vanishing Man (2016), two books that use Diego Velázquez's painting Las Meninas (1656) to frame their life narratives, this article shows how ekphrasis can act as a discursive parergon that challenges the borders between art and life, fact and fiction, literature and painting, and inside and outside. These empathetic life narratives—of a Spanish painter and a Victorian bookseller respectively—emulate Velázquez's visual techniques and implicate the reader, who is turned into a quasi-eyewitness through ekphrasis, within their meaning-making structures. In both instances, the enchanting spell of Velázquez's painting is used to push these life narratives into the realm of the imagination. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic forced therapists and patients to physically separate and conduct sessions from afar. This created particular challenges for child and adolescent work, which tends to center around movement and embodiment. As therapists navigated the constraints of their new reality, early skepticism quickly gave way to creative, on-the-spot solutions. Born out of necessity, therapist's flexibility and accommodations brought about changes to the analytic frame that were unprecedented in scope. Common themes include the therapist's loss of control over the structure of psychotherapy, a renegotiation of therapist and patient roles, placing the parent at the center of treatment, findings new ways to play, and virtual treatment as a new mechanism for modulating closeness and intimacy in the therapeutic dyad. Rooted in clinical vignettes of clinicians from the early weeks of the pandemic, this paper will illustrate these themes and consider their implications for the future of psychotherapy with children and adolescents. [ABSTRACT FROM AUTHOR]

This article investigates the ways in which social distancing and home confinement restrictions have been experienced and perceived in the Italian socio-cultural context, in order to assess how they reshaped everyday life, and which are their social implications. Drawing on 60 in-depth semi-structured interviews, this article sheds light on the sense-making processes and the construction of inter-subjective meaning around home confinement and social distancing that emerged during the lockdown. Results support that during the national quarantine individuals had to reframe everyday practices, thereby redefining the boundaries of their experience. Indeed, individuals had to deal with a lack of personal spaces, a following stress overload and a collapse of the typical boundaries between the professional and private sphere, which required a complex management of everyday activities. Implications of these preliminary findings are discussed, as well as suggestions for future research. [ABSTRACT FROM AUTHOR]

In this paper, we first present some simple approaches to obtain dual and approximate dual g-frames. Then, we show that approximate dual g-frames are stable under some conditions. Finally, we give mainly a new characterization for approximate dual g-frames associated with given g-frames and bounded operators. Moreover, we prove that if two g-frames are close to each other, then we can find approximate dual g-frames associated with them which are close to each other. [ABSTRACT FROM AUTHOR]

The atomic decomposition of signals is one of the most important problems in the frame theory. K-dual frame pairs may be used to stably reconstruct elements from the range of bounded linear operators on Hilbert spaces. The purpose of this paper is making K-dual frame pairs and finding common K-dual Bessel sequence. We present a sufficient condition on operators on H which takes a K-dual frame pairs to other ones; characterize bounded linear operators on l 2 (J) that transform K-dual frame pairs to other ones; prove that two Bessel sequences can always be extended to a K-dual frame pair, and that two orthogonal K-frames have a common K-dual Bessel sequence under certain conditions; and obtain a sufficient condition which the K-duals of one K-frame is contained in the ones of another K-frames. Abundant examples are also provided to illustrate the generality of the theory. [ABSTRACT FROM AUTHOR]