Space Theory Research Articles

Selected configuration interaction for high accuracy and compact wave functions: Propane as a case study.

Traditionally, because of the limit of full configuration interaction, complete active space (CAS) theory is most often used to model bond dissociation and other dynamical processes where the multi-reference character becomes important. Inconveniently, the CAS method is highly dependent on the choice of active space and, therefore, inherently non-black-box, in addition to the exponential scaling with respect to electrons and orbitals. This illustrates the need for methods that can accurately treat multi-reference electronic structure problems without significant dependence on input parameters. Selected configuration interaction (SCI) methods have experienced a revival in recent years because of their independence of these predicaments. SCI methods aim to exploit the sparsity of the full configuration interaction space to identify all relevant electronic configurations and, therefore, keep the wave function as compact as possible while still representing the total multi-reference electronic structure accurately. In this work, we take the recent achievement by Gao et al. to run full configuration interaction on the propane molecule in a minimal basis set (23 electrons in 26 orbitals) as an occasion to demonstrate that our SCI methods implemented in the GeneralSCI program package can achieve high energetic accuracy in conjunction with very compact wave functions, which considerably alleviate computational cost. Furthermore, we show the good performance of our SCI methods in reproducing a propane bond dissociation surface and energy. This illustrates that SCI methods can be readily applied to problems in chemical reactivity.

Equivariant Infinite Loop Space Theory: The Space Level Story

We rework and generalize equivariant infinite loop space theory, which shows how to construct G G -spectra from G G -spaces with suitable structure. There is a classical version which gives classical Ω \Omega - G G -spectra for any topological group G G , but our focus is on the construction of genuine Ω \Omega - G G -spectra when G G is finite. We also show what is and is not true when G G is a compact Lie group. We give new information about the Segal and operadic equivariant infinite loop space machines, supplying many details that are missing from the literature, and we prove by direct comparison that the two machines give equivalent output when fed equivalent input. The proof of the corresponding nonequivariant uniqueness theorem, due to May and Thomason, works for classical G G -spectra for general G G but fails for genuine G G -spectra. Even in the nonequivariant case, our comparison theorem is considerably more precise, giving an illuminating direct point-set level comparison. We have taken the opportunity to update this general area, equivariant and nonequivariant, giving many new proofs, filling in some gaps, and giving a number of corrections to results and proofs in the literature.

The Rellich-Kondrachov Theorem for Gelfand Pairs Over Hypergroups

Embedding results play important rôles in mathematical analysis. This paper addresses some embedding theorems in the context of Sobolev spaces theory on Gelfand pairs over hypergroups. Mainly, the analogue of the Rellich-Kondrachov theorem is proved.

Direct and inverse theorems of approximation theory in Banach function spaces

Direct and inverse theorems of approximation theory in Banach function spaces

Youth participatory action research (YPAR) to promote educational equity

The article uses theory and qualitative evidence to show how youth participatory action research (YPAR) can advance educational equity. YPAR engages young people and adult allies in research and action on issues in their schools and communities. Interviews with over two dozen YPAR researchers—students and partner teachers—elaborate the mechanisms through which school-based YPAR can affect equity, including through direct changes to policy and practice as a result of YPAR actions, a school culture that values student experiences, transformative teacher-student relationships, and improved individual outcomes for participants. To help theorize a theory of change, we draw on Doreen Massey’s space theory to explain how YPAR done in schools can transform culture, relationships, practice, and policy. Further, we suggest how YPAR can be infused in schools.

An Analysis of Land Use Conflicts and Strategies in the Harbin–Changchun Urban Agglomeration Based on the Production–Ecological–Living Space Theory and Patch-Generating Land Use Simulation

An Analysis of Land Use Conflicts and Strategies in the Harbin–Changchun Urban Agglomeration Based on the Production–Ecological–Living Space Theory and Patch-Generating Land Use Simulation

Kernels of linear maps: A generalization of Duistermaat and Van der Kallen's theorem in dimension one

The theorem of Duistermaat and Van der Kallen from 1998 proved the first case of the Mathieu conjecture. Using the theory of Mathieu-Zhao spaces, we can reformulate this theorem as Ker L is a Mathieu-Zhao space where L is the linear map L:C[X1,…,Xn,X1−1,…,Xn−1]→C,f↦f0. In this paper, we generalize this result (for n=1) to all non-trivial linear maps L:C[X,X−1]→C such that {Xn||n|≥N}⊂KerL for some N≥1.

The Bare Supervening Necessities of Theory Development in Sport Management

This address explores how we can find theory in new spaces and apply it to our own, unique sporting contexts. It first examines how urban regime theory can inform research on the governance of intercollegiate athletics, then discusses how and why some theories in sport management emerge and are adopted while others are not. Borrowing from Winston’s model of technological diffusion, supervening necessities are what allow some prototypes to transform into inventions; in the social sphere of sport management, they are the drivers of new concepts that are adopted and employed as theories in the field. However, Winston notes that within the social sphere are brakes that serve to slow their emergence. In turn, theories develop in sport management under similar conflicting pressures. It is these contrary forces that slow the diffusion of new ideas in the sport management field.

Exact-exchange relativistic density functional theory in three-dimensional coordinate space

Exact-exchange relativistic density functional theory in three-dimensional coordinate space

Polynomial-based kernel reproduced gradient descent for stochastic optimization

Stochastic gradient descent (SGD) is widely applied to machine learning tasks. However, the existence of gradient variance degrades the convergence performance of SGD, which cannot be tackled well for tasks with one-time data sampling per sample. In this paper, a kernel reproduced gradient descent algorithm is proposed where the gradient of the risk function is estimated by utilizing the Reproducing Kernel Hilbert Space (RKHS) theory. Meanwhile, to ensure a low storage requirement, a kernel function linearization strategy is used to design the polynomial form of the kernel learning algorithm. It is shown that the error resulting from linearization decreases as the model parameter size increases, and the proposed polynomial-like kernel reproduced gradient descent (PKRGD) algorithm can converge faster than SGD. From experiments on models such as the latest image matching model, LightGlue, it is verified that the reproduced gradients have lower variances, and existing optimizers using the reproduced gradients can further accelerate model training.

Research on fault factors of engineering simulators based on quotient space theory

Research on fault factors of engineering simulators based on quotient space theory

A Study on the Characters’ Self-Identity of the Film “YiYi” (2000) from the Perspective of Heterotopia Space Theory

A Study on the Characters’ Self-Identity of the Film “YiYi” (2000) from the Perspective of Heterotopia Space Theory

EXISTENCE OF SOLUTIONS FOR NONHOMOGENEOUS DIRICHLET PROBLEMS IN ORLICZ-SOBOLEV SPACES

In this paper, by using variational methods and critical point theory in an appropriate Orlicz-Sobolev space, we establish the existence of infinitely many nontrivial solutions to a nonhomogeneous problem. Precisely, we use the Z_2-symmetric version for the well-known Mountain Pass theorem, to prove the existence of such solutions.

Rhetoric of Violence in Political Discourses: A Comparative Study of Pakistani Politicians’ Speeches

Language plays a significant role in determining what goes on in an individual's mind. Politicians use language insidiously and persuasively to impart their ideologies and to win the consent of the general masses. Moreover, they also use certain lexicons to otherize the others. Speeches are delivered by politicians for positive self-representation and negative others representation. The aim of this study is to provide a comprehensive analysis of political discourses. For this purpose, the speeches of three Pakistani politicians, namely Imran Khan, Maryam Nawaz and Bilawal Bhutto, have been analysed from Sept. 2021 to May 2023. It is analysed how they exercise political rhetoric using different linguistic spins. The theoretical framework, including Paul Chilton (2004) Discourse Space Theory, is employed for this study. The data is taken from the YouTube channel of Pakistani news channels, namely ARY and SAMMA TV. The findings reveal that politicians make use of various discursive spins and rhetorical strategies to others.

An Interactionist’s View

This essay examines the unbuildable architectural and interior design drawings of Love/House (1984) by architect and professor Lars Lerup. Developed at University of California, Berkeley, and the Canadian Centre for Architecture, Lerup’s work is shown to use fictional narratives in drawings to explore certain poetic ideas about the human experience from Roland Barthes’s 1977 book, A Lover’s Discourse: Fragments. His deliberate exploration of artistic, fictional, and unrealisable aesthetic effects aimed to offer a critical revision to the rise of American West-Coast suburbanisation, and the commercialisation of domestic, social behaviours in an increasingly commoditised media culture of the 1980s. Through a close reading of several of Lerup’s lesser known texts from the 1970s and 1980s that foregrounded the Love/House project, this essay shows there was more to his work than the somewhat cryptic and idiosyncratic employment of fictional drawings to challenge the commercial rhetoric of late-capitalism. It argues that his largely unexamined approaches to spatial design resulted from a deeper theoretical derivation that human action was irreducibly unpredictable, and unable to be categorised into behaviourist models or functional planning. By unpacking the qualities of his ‘interactionist view’ of people, objects, and the built environment from his first theoretical text, Building the Unfinished (1977), the unbuildable compositional effects of the Love/House drawings are shown to have resulted from his earlier attempts to establish the complex and unpredictable nature of human action as the central tenet of spatial design. For Lerup, exploring ideas of poetry and fiction in drawings played a crucial role in cultivating his theory of space that reflects people’s unfinished search for meaning.

Navigating multiple displacements: encounters and emplacement practices at municipal service centres in marginalised communities in Sweden

ABSTRACT This article contributes to the understanding of how residents and social guides collaboratively navigate multiple forms of displacement within Municipal Service Centres (MSC) situated in marginalised communities in Sweden. Drawing on critical theories of the production space, the paper posits that social work can be understood as an emplacement practice in response to displacement from vital resources such as jobs, housing, and residence permits. The article identifies two pivotal emplacement practices operating at MSCs: reclaiming and enclosing. MSCs are perceived as institutional spaces that provide residents with agential power to navigate challenging realities, conditional welfare systems, and bordering practices. The study draws on nine months of ethnographic fieldwork conducted in a specific MSC located in a marginalised community, along with interviews with 23 social guides and 6 managers in four other MSC within similar settings. Employing a relational ethnographic approach, the study observes face-to-face encounters, collaboration, and education between residents and social guides.

Kinetic Theory with Casimir Invariants—Toward Understanding of Self-Organization by Topological Constraints

A topological constraint, characterized by the Casimir invariant, imparts non-trivial structures in a complex system. We construct a kinetic theory in a constrained phase space (infinite-dimensional function space of macroscopic fields), and characterize a self-organized structure as a thermal equilibrium on a leaf of foliated phase space. By introducing a model of a grand canonical ensemble, the Casimir invariant is interpreted as the number of topological particles.

Tosaka Jun: Problems of Space and Time in the Philosophy of Everydayness

The article is focused on the analysis of the theory of space and time by the Japanese neoMarxist philosopher Tosaka Jun. Tosaka was one of the first in his country to act as a critic of Western philosophy, whilst also being a follower of one of its directions. The relevance of studying this cultural phenomenon lies in the possibility of supplementing knowledge about Asian philosophies in the context of the ongoing pivot to the East. The empirical basis of the research was a series of Tosaka’s essays written in 1920-30s focused on the problems of space and time, as well as his monograph “Japanese Ideology.” The main methods used in the article were the methods of comparative analysis, discourse analysis, and (based on the analysis of concepts and terms) the techniques of logical and semantic reconstruction of the system of ideas associated with a particular problem. The author sets the goal of investigating the content and features of the interpretation of space and time in Japanese thought of the 20th century using the example of Tosaka’s philosophy in the context of discussing the role of everydayness as an epistemological basis for philosophical teachings. In this regard, the task of identifying the original solutions and approaches of the Japanese thinker was realized, allowing us to consider his legacy a significant part of the historical and cultural process, as well as to understand the significance of his philosophical ideas in modern discussions. Another important task of the study was to determine the paths of transfer and transformation of ideas, in particular, the refraction and critical rethinking of Western concepts in the Japanese intellectual space. As a result, for the first time in scientific literature, a detailed reconstruction of the problems of space and time, based on the entire body of Tosaka’s works is presented. The conclusion is substantiated that by introducing a number of concepts (everyday space, historical time, character, configuration, relevance, etc.) and rejecting traditional Marxist ideas about the linearity of time and the value approach to history, the Japanese philosopher rethought the Marxist philosophy of history from the position of his theory of everyday life and common sense, creating an original model of unequal cycles formed from within the historical whole and possessing internal completeness, and, thus, presented history as a non-linear and uneven process that has not only a temporal but also a spatial dimension.

Third places and national contexts among Generation Z in a mobile game: Quantitatively examining third place characteristics and well-being of players from Brazil, China, and the United States

Youth online engagement and well-being are especially important in emerging countries, but they tend to be understudied. Rather, the existing research tends to be more on the United States. This study examined third place theory of virtual spaces on individual-level well-being among the Generation Z from Brazil and China, especially comparing them to their U.S. counterparts. Well-being, both related to realizing your full potential and lowering psychopathology, is relevant to youth engagement in online spaces, because the spaces can help the youth express their true selves and engage in supportive online communities. The participants were players of a mobile video game whose three months of pre-survey gameplay data and survey data (N = 986) were analyzed. We compared countries on several third place characteristics, on well-being, and how the third place characteristics predicted well-being. We found that players from the three countries were significantly different in several third place characteristics (i.e., neutral ground, leveler, and conversation). Well-being was also higher among the Chinese players. Moreover, the leveler characteristic–commonality of game levels among players and their in-game friends–significantly predicted well-being. These findings from a mobile game help better understand youth online perceptions and behaviors in different countries, correlates to well-being, and contribute to the theory development of virtual third places and digital public spheres.

Attractive Space Evaluation Method for HVDC Transmission Lines

High-voltage direct current (HVDC) transmission lines are increasing in number and overall length. This means their lightning protection must be of higher importance as well. Probability-modulated attractive space (PMAS) theory is a proven geometry-based method for lightning protection calculations. However, it cannot accurately assess the number and parameters of direct lightning strikes to the phase conductor of HVDC lines, because the effect of pole voltage on lightning attachment cannot be considered. This effect can be taken into account with leader progression models, which feature lightning physics models that can quantify the effect of the electric field around the phase conductor, which can be quite complex compared to geometric models in general. In this paper, a novel method, called the attractive space matrix, is presented to examine the effect of the DC electric field around the conductor on the attractive space. The algorithm is based on the physical background of the self-consistent leader inception and propagation model. The results could lead to improved lightning protection of HVDC lines and reduce the outages caused by direct lightning strikes.