Indefinite Space Research Articles

Adaptive indefinite kernels in hyperbolic spaces

Learning embeddings in hyperbolic space has gained increasing interest in the community, due to its property of negative curvature, as a way of encoding data hierarchy. Recent works investigate the improvement of the representation power of hyperbolic embeddings through kernelization. However, existing developments focus on defining positive definite (pd) kernels, which may affect the intriguing property of hyperbolic spaces. This is due to the structures of hyperbolic spaces being modeled in indefinite spaces (e.g., Kreĭn space). This paper addresses this issue by developing adaptive indefinite kernels, which can better utilize the structures in the Kreĭn space. To this end, we first propose an adaptive embedding function in the Lorentz model and define indefinite Lorentz kernels (iLks) via the embedding function. Due to the isometric relationship between the Lorentz model and the Poincaré ball, these iLks are further extended to the Poincaré ball, resulting in the development of what are termed indefinite Poincaré kernels (iPKs). We evaluate the proposed indefinite kernels on a diversity of learning scenarios, including image classification, few-shot learning, zero-shot learning, person re-identification, knowledge distillation, etc. We show that the proposed indefinite kernels can bring significant performance gains over the baselines and enjoy better representation power from RKKSs than pd kernels.

Space and Place in Tao Qian’s Tianyuan Poetry

Abstract Tao Qian is one of the central figures in Chinese literary history and the founding father of the so-called tianyuan (farmstead) poetry. Traditionally, Tao’s writings have been read biographically, which has limited our understanding of their deeper structural and experiential dimensions. In this article, I turn my attention to the place-consciousness of his poetry and analyze how he repeatedly creates experiences of belonging in his verses. As a theoretical frame of reference, I utilize the concepts “space” and “place” as they are defined by Yi-Fu Tuan in his study Space and Place. In Tao’s tianyuan poetry, the surrounding, indefinite space turns constantly into a lived and meaningfully organized place which functions as the epicenter of the agrarian lifestyle and worldview. As I seek to demonstrate, a place is not only a physical location but is a complex and multilayered phenomenon that can appear as a means of knowing, a source of truthful living, and even as an event. In Tao’s writings, the experience of place is predominantly positive and empowering but can also at times cause feelings of loss and grief.

Semiosis of Political Action

Aristotle, calling man “political by nature,” predetermined the actual opportunity to consider politics through the prism of practical action, through specific ways of equitable arrangement of public life. Thrown into a digital existence, where the ambivalent task of realizing one’s vulnerable position arises, exposing oneself to risk, while simultaneously navigating the indefinite space of a dynamically developing community. The modern territory of politics is being mastered by actants with the help of a renewed arsenal of means, taking into account the meaning of design (de + signare), the signs of which acquire multiplication of ideas about complexly organized integrity of its image. Integration ties of semiosis “sew through” the heterotopy of the renewed territory of political action, putting down the chronological framework of events in sign expression (index, symbol, code, number), to compare and supplement possible transformational semiotic shifts and confusions, thus creating a plausible and recognizable semiotic image of the current state of affairs in society. Semiotic representation emphasizes the sign, symbolic nature of political action as a political event, realized by its subject in the process of normogenesis and anchored in the pragmatics of everyday activity. Conditional analytical dismemberment of the process of semiosis (syntactics, semantics, pragmatics) of political action initiates the synchronization of methodological synthesis, which leads to the co-creation of the subject and structure at the level of reflective analysis. This allows us to add the “included third”, traditional for the transdisciplinary methodological approach, into the agent-structure dichotomy, which is classic for the science of politics, serving as a target reason for creating integral image of political action. It should be noted that the “included third” as the target cause does not guarantee the unambiguity of the outcome of the formation of the specified action, but only adjusts the optics of tracking its possible configurations, taking into account both contextual and environmental conditionality.

Some characterizations on indefinite space forms admitting almost contact structures

In this paper, the projective curvature tensor field of a generalized indefinite Sasakian space form is investigated. Some results dealing with projectively semi-symmetric and [Formula: see text]-projectively semi-symmetric generalized indefinite Sasakian space forms are obtained. Furthermore, biharmonic Legendre Frenet curves are discussed on these manifolds.

Some remarks on invariant lightlike submanifolds of indefinite Sasakian manifold

PurposeThe author considers an invariant lightlike submanifold M, whose transversal bundle tr(TM) is flat, in an indefinite Sasakian manifold M¯(c) of constant φ¯-sectional curvature c. Under some geometric conditions, the author demonstrates that c=1, that is, M¯ is a space of constant curvature 1. Moreover, M and any leaf M′ of its screen distribution S(TM) are, also, spaces of constant curvature 1.Design/methodology/approachThe author has employed the techniques developed by K. L. Duggal and A. Bejancu of reference number 7.FindingsThe author has discovered that any totally umbilic invariant ligtlike submanifold, whose transversal bundle is flat, in an indefinite Sasakian space form is, in fact, a space of constant curvature 1 (see Theorem 4.4).Originality/valueTo the best of the author’s findings, at the time of submission of this paper, the results reported are new and interesting as far as lightlike geometry is concerned.

On pseudo-umbilical spacelike submanifolds in indefinite space form $$\mathcal {M}_p^{n+p}(c)$$

An intrinsic condition for Pseudo-umbilical spacelike submanifold immersed in indefinite space form is derived, which is used to show that such submanifold is totally geodesic. Next, using a result of Aiyama (Tokyo J Math 18:81–90, 1995), it is proved that Pseudo-umbilical spacelike submanifold is totally umbilical.

ОСВІТНЬО-ПРОФЕСІЙНЕ СЕРЕДОВИЩЕ ПЕДАГОГІЧНОЇ ПРАКТИКИ ЯК УМОВА НАБУТТЯ ПРОФЕСІОНАЛІЗМУ МАЙБУТНІМИ ВЧИТЕЛЯМИ ПРИРОДНИЧИХ ДИСЦИПЛІН

The article analyzes the models of educational environment represented in psychological and pedagogical research studies. It is stated that in order to acquire professional skills by teacherstrainees a special educational training environment during pedagogical practice should be created. The professional training environment during pedagogical practice is defined as a special set of influences and conditions which provides creation of a variable, indefinite space full of problem situations and opportunities. It helps to launch professional development mechanism, development of new ideas, forming of life perspectives as well as an ability of self-projection. The model of professional training environment comprises the following components: space and subject referenced, social and psycho-didactical. The resources of the space and subject referenced component (distant learning means, electronic libraries, software systems) are the material basis of professional training environment functioning. The social component includes interrelated key subjects of educational process: a professional teacher, a teacher-trainee, a supervisor of pedagogical practice, students. A teacher being an example of professionalism supervises the process and consults a teacher-trainee. A priority of a dialogue in the system of relations of a teacher-trainee and students as well as the role of a supervisor of pedagogical practice in projection and implementation of individual educational trajectory is specified. Psycho-didactic component provides correspondence of education objectives, syllabus and applied methods to physiological characteristics of trainees. Factors which influence the successful implementation of individual educational trajectory of a teacher-trainee are related to the components of professional training environment during pedagogical practice. The ways to enrich the professional training environment with opportunities to meet individual educational needs and intentions of trainees in acquiring their professional skills are discussed. The effectiveness of professional training environment functioning during pedagogical practice is defined according to the level of professional competences formation of teachers-trainees at the after action review and assessment stage.

Weighted Moore–Penrose Inverses Associated with Weighted Projections on Indefinite Inner Product Spaces

Let H be a Hilbert $$C^*$$ -module, and let $$H_M$$ be the indefinite inner space induced by a self-adjointable and invertible operator M on H. Given weighted projections P and Q on $$H_M$$ , let $$S_{\lambda ,k}=(PQ)^k-\lambda (QP)^k$$ for a pair $$(k, \lambda )$$ , where k is a natural number and $$\lambda $$ is a complex number. It is proved that $$PQ-QP$$ is weighted Moore–Penrose invertible if and only if $$S_{\lambda ,k}$$ is weighted Moore–Penrose invertible for every pair $$(k, \lambda )$$ .

Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an (<img src=image/13415329_01.gif>)-type Connection

Jin [1] defined an ( )-type connection on semi-Riemannian manifolds. Semi-symmetric nonmetric connection and non-metric ∅-symmetric connection are two important examples of this connection such that ( ) = (1; 0) and ( ) = (0; 1), respectively. In semi-Riemannian geometry, there are few literatures for the lightlike geometry, so we expose new theories for non-degenerate submanifolds in semi-Riemannian geometry. The goal of this paper is to study a characterization of a (Lie) recurrent lightlike hypersurface M of an indefinite Kaehler manifold with an ( )-type connection when the charateristic vector field is tangnet to M. In the special case that an indefinite Kaehler manifold of constant holomorphic sectional curvature is an indefinite complex space form, we investigate a lightlike hypersurface of an indefinite complex space form with an ( )-type connection when the charateristic vector field is tangnet to M. Moreover, we show that the total space, the complex space form, is characterized by the screen conformal lightlike hypersurface with an ( )-type connection. With a semi-symmetric non-metric connection, we show that an indefinite complex space form is flat.

Isometry Lie algebras of indefinite homogeneous spaces of finite volume

Let $\mathfrak{g}$ be a real finite-dimensional Lie algebra equipped with a symmetric bilinear form $\langle\cdot,\cdot\rangle$. We assume that $\langle\cdot,\cdot\rangle $ is nil-invariant. This means that every nilpotent operator in the smallest algebraic Lie subalgebra of endomomorphims containing the adjoint representation of $\mathfrak{g}$ is an infinitesimal isometry for $\langle\cdot,\cdot\rangle $. Among these Lie algebras are the isometry Lie algebras of pseudo-Riemannian manifolds of finite volume. We prove a strong invariance property for nil-invariant symmetric bilinear forms, which states that the adjoint representations of the solvable radical and all simple subalgebras of non-compact type of $\mathfrak{g} $ act by infinitesimal isometries for $\langle\cdot,\cdot\rangle $. Moreover, we study properties of the kernel of $\langle\cdot,\cdot\rangle $ and the totally isotropic ideals in $\mathfrak{g} $ in relation to the index of $\langle\cdot,\cdot\rangle $. Based on this, we derive a structure theorem and a classification for the isometry algebras of indefinite homogeneous spaces of finite volume with metric index at most two. Examples show that the theory becomes significantly more complicated for index greater than two.

Characterizations of the Total Space (Indefinite Trans-Sasakian Manifolds) Admitting a Semi-Symmetric Metric Connection

We investigate recurrent, Lie-recurrent, and Hopf lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a semi-symmetric metric connection. In these hypersurfaces, we obtain several new results. Moreover, we characterize that the total space (an indefinite generalized Sasakian space form) with a semi-symmetric metric connection is an indefinite Kenmotsu space form under various lightlike hypersurfaces.

‘You Say “Performance Poet”, I Hear “Dance Nigger, Dance”’: Problematizing the Notion of Performance Poetry in South Africa

This article analyzes how the notions of what counts as ‘performance poetry’ and who counts as a ‘performance poet’ differ according to context, and its focus lies on how these terms are postulated and disseminated within the South African literary scene. It offers an analysis of circumstantial factors within the South African literary community, which is explored as a site of epistemic violence. This epistemic violence unfolds through the racial micro-invalidations which are produced each time academia and media use the terms ‘performance poet’ and ‘performance poetry’ in relation to black poets and their work, without being aware of the negative implications of this. This pernicious ignorance is exposed and addressed, and so too is the conceptual system underscoring an approach that sees poetry as synonymous with the written word and which privileges the written over the oral, thereby relegating ‘performance poetry’ to an indefinite space, existing somewhere outside the national written traditions.

A History of the Locked-In-Syndrome: Ethics in the Making of Neurological Consciousness, 1880-Present

Extensive scholarship has described the historical and ethical imperatives shaping the emergence of the brain death criteria in the 1960s and 1970s. This essay explores the longer intellectual history that shaped theories of neurological consciousness from the late-nineteenth century to that period, and argues that a significant transformation occurred in the elaboration of those theories in the 1960s and after, the period when various disturbances of consciousness were discovered or thoroughly elaborated. Numerous historical conditions can be identified and attributed to the production of the new theories that emerged from that period-on, not least in the broader social and cultural transformations that occurred with decolonialization, pro-democracy movements, and civil and disability rights advocacy, all contexts which exerted pressures on the institutions and professions of medicine. In this telling, the discovery of the locked-in patient is thus the exploration of a transformed vision of medical patients – one that moved them from a liminal indefinite space into a firmly grounded epistemological existence – in a backdrop in which medical professionals in particular and society in general was beginning to see the body differently. With this new vision, came a relational theory of consciousness to, a reading of a body and it signs, that shifted consciousness from an internally-derived state into a relationally-constructed object. The ontology of consciousness, whatever it was, thereby became entangled with the social condition of consciousness, one that bridged the worlds of close relationship with the social movements and anxieties about personhood that emanated out of that fraught period.

1789년의 〈披襟亭圖〉: 강세황의 실경산수화에 관한 모색과 귀결

In 1788, Kang Sehwang (姜世晃, 1713~1791) criticized Jeong Seon (鄭敾, 1676~ 1759), one of the most renowned painters of Diamond Mountain (Mount Geumgang 金剛山), for not depicting its ‘true aspects’ and he displayed the desire to surpass Jeong Seon’s achievement in the painting of Diamond Mountain. BR This paper investigates Topographical Landscape Paintings from Kang’s oeuvre and specifically discusses how he expressed his artistic desire in the case of Pigeumjeong-do (披襟亭圖). The painting, which was executed in 1789, features the Pigeum Pavilion located on the way to the Geumgang mountain range and is one of the most monumental paintings among his artworks. In his earlier representations of landscapes, Kang tried to accurately depict the visible characteristics of the scenery and explored approaches for reproducing his visual experience in painting. In Songdo Gihaengcheop (松都紀行帖) of 1757, a set of topographical paintings of Kaeseong (開城, present North Korea), Kang introduces new techniques from Western art, e.g. linear perspective and shading technique, creating a highly three-dimensional effect. His interest toward this kind of landscape painting persisted for more than 30 years, including the period when he officially ceased any painting activities.BR But Pigeumjeong-do displays that by 1789, Kang was no longer interested in an accurate representation of the external world. Pigeumjeong-do’s main mountain ascends in the middle of the painting, repeatedly opening and closing, rising up and down, and receding into indefinite space. The depiction of the mountain in this manner is based on Dragon Veins (yongmaek 龍脈; Chin. long mai), a traditional concept of Chinese landscape painting originating in fengshui geomantic theory (pungsu jiri, 風水地理). Dragon Veins is a method of artistically expressing the vital energy of nature. Eminent Chinese literati painters like Huang Gongwang, Dong Qichang, and Wang Yuanqi incorporated the Dragon Veins concept into their artworks and turned the concept into one of the traits of literati landscape painting. In conclusion, after travelling to Mount Geumgang in 1788, Kang Sehwang adopted this manner of Chinese literati painters and implemented it in his Topographical Landscape Painting in order to capture the innate power of nature with his brushwork.

A Cognitive Study of Interaction between Noun Boundaries and Articles in English

The purpose of this paper is to analyze the semantic structure of the three types of English articles—indefinite, definite, zero articles―with respect to the supposedly flexible boundaries of English nouns under the framework of Cognitive Grammar (Langacker 1987, 1991a, 1991b, 2000). To facilitate this, a new notion has been proposed: Boundedness Filter (BF), which is thought to play a decisive role in determining the activation or inactivation of noun boundaries in relation with the selection of corresponding articles. BF is supposed to operate in a variety of cognitive domains such as physical space for the indefinite article and psychological space for the definite article. This paper further claims that the count or mass-like property of a given noun is not fixed originally as prescribed in dictionaries or grammar books; rather, its boundary has a flexible feature depending upon the context in which it is used. This is why a common noun with its indefinite article as a boundary marker can sometimes be changed into a mass noun without any article. The BF and flexible characteristics of English noun boundaries can also be used to explain the reason that some apparently visible boundaries are not realized in physical space as indefinite articles.

Suspended Animation: Ace Drummond, Buck Rogers, and the Sustained Desires of Seriality

Despite their traditionally assumed boundaries, the serial media of film, radio, and newspaper comic strips in the 1930s and 1940s were intimately connected. Building upon recent scholarship devoted to the Hollywood film serials of the sound era, this article posits seriality as a kind of “cultural paradigm,” an intermedial bonding agent that serves to engender distinct interconnections between media forms in the mind of the audience and to drive them toward further consumption. The various franchise incarnations of Buck Rogers and Ace Drummond in this period are used here as case studies to underscore what one might term a “plane of suspended animation,” a potentially indefinite imaginative space opened in the mind of the spectator by the narrative disruption of the serial’s cliff-hanger where one might engage in franchise-based play and be encouraged to continue consuming said franchises across media.

Willmore spacelike submanifolds in an indefinite space form Nn+p q(c)

Let Nn+p q(c) be an (n+p)-dimensional connected indefinite space form of index q(1 ? q ? p) and of constant curvature c. Denote by ? : M ? Nn+p q (c) the n-dimensional spacelike submanifold in Nn+p q (c), ? : M ? Nn+p q(c) is called a Willmore spacelike submanifold in Nn+p q(c) if it is a critical submanifold to the Willmore functional W(?) = ?q M ?n dv =?M (S-nH2)n/2 dv, where S and H denote the norm square of the second fundamental form and the mean curvature of M and ?2 = S ? nH2. If q = p, in [14], we proved some integral inequalities of Simons? type and rigidity theorems for n-dimensional Willmore spacelike submanifolds in a Lorentzian space form Nn+p q(c). In this paper, we continue to study this topic and prove some integral inequalities of Simons? type and rigidity theorems for n-dimensional Willmore spacelike submanifolds in an indefinite space form Nn+p q(c) (1 ? q ? p).

Axioms of spheres in lightlike geometry of submanifolds

We prove that if an indefinite Kaehler manifold $\bar {M}$ with lightlike submanifolds satisfies the axioms of holomorphic 2r-spheres, axioms of holomorphic 2r-planes, axioms of transversal r-spheres and axioms of transversal r-planes, then it is an indefinite complex space form.

Spacelike submanifolds with parallel mean curvature vector in S q n+p (1)

Let Mn be a complete spacelike submanifold in an indefinite space form Sqn+p(1). When p = q, there are numerous rigidity results concerning submanifolds with parallel mean curvature vector. However, there are few results concerning the case q < p. In this paper, we will focus on this kind of submanifold and give some classifications of submanifolds with parallel mean curvature vector according to the squared norm of the second fundamental form.

Les voix spectrales chez Antoine Volodine

Ghostly characters, narrative blurriness, mise en abyme processes: these are a few of the most conspicuous features of the spectral phenomenon that structures Antoine Volodine’s work. The themes, linguistic devices and intersubjective relationships are characterized by a systematic discrepancy that relocates the meaning to a marginal, intermediate or indefinite space. In Volodine’s Des anges mineurs, an analysis of the main character’s voice - whose sentence to death is continually postponed - will show how these levels shape the processes of decentralization, dissipation and erosion which, negating the textual univocity, confer to the literary work an original expressiveness assuming the anthropological vulnerability of speech.