Space Form Research Articles

Bounds for Eigenvalues of q-Laplacian on Contact Submanifolds of Sasakian Space Forms

This study establishes new upper bounds for the mean curvature and constant sectional curvature on Riemannian manifolds for the first positive eigenvalue of the q-Laplacian. In particular, various estimates are provided for the first eigenvalue of the q-Laplace operator on closed orientated (l+1)-dimensional special contact slant submanifolds in a Sasakian space form, M˜2k+1(ϵ), with a constant ψ1-sectional curvature, ϵ. From our main results, we recovered the Reilly-type inequalities, which were proven before this study.

Evolution of the first eigenvalue along the inverse mean curvature flow in space forms

In this paper, we show that the first nonzero eigenvalues λ1 of the Laplacian and the p-Laplacian are decreasing along the inverse mean curvature flow in the hyperbolic space and in the sphere. For a convex closed surface M⊂S3, we show that the geometric quantity λ1⋅Area(M) is monotonically decreasing along the inverse mean curvature flow in S3.

Futures Studies for Design Systems and Social Transformation from Time/Space-Based Perspectives

Analyses of disciplines encompassing futures studies reveal a prevailing tendency to perceive time as a linear sequence of projections. However, this perspective is not applicable to the current context of social transformation in the age of globalization and digitization, such as sustainable development. Preliminary investigations into time-based design and futures studies have shown the potential of time-based paradigms for predicting reliable future scenarios and redesigning current forms of spaces, relationships, and services in response to these desired futures. In this paper, we describe a project of an Ephemeral and Temporary Space Design Laboratory, which has been a pedagogical experiment for 3 years to date in the School of Design at the Politecnico di Milano. The objective of this project is to systematically design an area of the city by reflecting on the relationship between design systems and social change, using participatory design methods such as field research and interviews with local residents to systematically redesign the urban space of the Lodi/Corvetto area in the city of Milan. This research aims to investigate the systematic influence of time factors on the spatial design of urban communities through futuristic and time/space-based design perspectives. The findings demonstrate that the utilization of time-based paradigms and tools can effectively enhance the time-based design approach, resulting in its increased integration within the design process. This integration plays a pivotal role in the construction of systems that have the capability to interact with and catalyze social transformation within the broader public and shared community.

The impact of transformations of the space of tenement houses on the architectural form of the building

The study examined transformations of tenement houses carried out by development companies conducting their investments in the city of Warsaw. The tenement houses that were originally erected in the second half of the 19th century or at the beginning of the 20th century and were renovated in the last 20 years, i.e. since 2003, were examined.
 The results of the study showed the existence of four main types of transformations that affect the architectural form of buildings: changing the function of the ground floor from residential to commercial, adaptation/reconstruction of attics for residential purposes, superstructures and transformations of courtyards. The impact of individual transformations on the architectural form of space is described. These changes have been illustrated with examples of Warsaw projects.

ARCHITECT YO MING PEI. THE ART OF ARCHITECTURE OF MUSEUM BUILDINGS

Famous Chinese-American architect I.M. Pei was born in Guangdong, China in 1917.He traveled to the United States in 1935. Initially educated at the University of Pennsylvania, he continued his studies at the Massachusetts Institute of Technology (Bachelor of Architecture in 1940) and Harvard Graduate School of Design (Master of Architecture in 1946). I.M. Pei is widely praised for his bold design and clear geometric forms in his project. His career spanned 60 years and left many outstanding architectural works. I.M. Pei, revered as "the consummate master of modern architecture," his architectural philosophy was deeply influenced by modern art. During that era, New York City was known as the center of modern art. Among them, abstract expressionism, conceptualism and minimalism were on full display here. Many famous artists held grand exhibitions here and established their own studios. I.M. Pei spent most of his life in this place. When American modern art reached its peak in New York, many architects decided to use primitive forms to convey a concise and powerful artistic language, which also became their iconic design style. I.M. Pei's design philosophy is global. He emphasized: "In the architectural design process, there are three key aspects that require special attention: the first is the integration of the building with its environment; the second is how to handle space and form; and finally, from the user's point of view, to correctly solve functional problems. In this paper, the study analyzes the structural features of 12 architectural spaces of art museums designed by I.M. Pei in the context of the time line. It compares the similarities and differences in the spatial structure of the architecture of art museums built in the same time period as well as between different historical eras. The study focuses on analyzing the form and content of space and draws on the theoretical framework of contemporary architecture, namely the concepts of space within modernism. As a result of the analysis, two key characteristics of Pei's architecture are highlighted: sculptural and geometric.

A characterization of Ricci solitons in Lorentzian generalized Sasakian space forms

In this paper, we study Lorentzian generalized Sasakian space forms admitting Ricci soliton, conformal gradient Ricci soliton and Ricci Yamabe soliton. We also study the conditions for the soliton to be steady, shrinking and expanding. We also provide some applications of Ricci Yamabe solitons.

The lifts of surfaces in neutral 4-manifolds into the 2-Grassmann bundles

A twistor lift of a space-like or time-like surface in a neutral hyperKähler 4-manifold with zero mean curvature vector is given by a (para)holomorphic function, which yields (para)holomorphicity of the Gauss maps of space-like or time-like surfaces in E24 with zero mean curvature vector. For a space-like or time-like surface in an oriented neutral 4-manifold with zero mean curvature vector such that both twistor lifts belong to the kernel of the curvature tensor, its (para)complex quartic differential is holomorphic. If both twistor lifts of a time-like surface with zero mean curvature vector have light-like or zero covariant derivatives, then either the shape operator with respect to a light-like normal vector field vanishes or all the shape operators of the surface are light-like or zero. Examples with the former (resp. latter) property are given by the conformal Gauss maps of time-like surfaces of Willmore type with zero paraholomorphic quartic differential (resp. time-like surfaces in 4-dimensional neutral space forms based on the Gauss-Codazzi-Ricci equations).

Quasi-Statistical Schouten–van Kampen Connections on the Tangent Bundle

We determine the general natural metrics G on the total space TM of the tangent bundle of a Riemannian manifold (M,g) such that the Schouten–van Kampen connection ∇¯ associated to the Levi-Civita connection of G is (quasi-)statistical. We prove that the base manifold must be a space form and in particular, when G is a natural diagonal metric, (M,g) must be locally flat. We prove that there exist one family of natural diagonal metrics and two families of proper general natural metrics such that (TM,∇¯,G) is a statistical manifold and one family of proper general natural metrics such that (TM∖{0},∇¯,G) is a quasi-statistical manifold.

Proactive health interventions in the workplace: The role of spatial playfulness in promoting mental health.

The high prevalence of mental illnesses has a serious impact on productive life and there is an urgent need to intervene using a variety of active and effective measures. The concept of playfulness in space is introduced into the design of work spaces oriented towards active health interventions, creating a close interaction between the body and the space through play, thus developing a positive effect on the promotion of the physical and mental health of the staff. With the help of the spatial order theory, the analysis of the interaction between body and space is attempted to explore the form, structure and scene of space in order to optimize the body's perception, cognition and behavior in the space, thus creating an indoor workspace model with positive intervention effects on human health. Based on the idea of spatial playful participation in active health interventions, this study explores the interaction between the body and the architectural space to enhance the perception and cognitive guidance of the space for the individual and to have a pleasant spiritual experience in the interaction to relieve work stress and enhance mental health. This series of discussions on the relationship between architectural space and the human body is of great relevance in improving the public health of occupational groups.

Spatiotemporal evolution and influencing factors of water resource green efficiency in the cities of the Yangtze River Economic Belt.

Effectively utilizing water resources, which is a fundamental natural resource and a vital economic resource, directly impacts how a country's economy develops. In this study, the Super-SBM model is used to calculate the city water resource green efficiency (CWRGE) of the Yangtze River Economic Belt (YREB), 108 cities that are prefecture level or higher, from 2006 to 2021. And its temporal and spatial evolution as well as its affecting variables are examined. The results indicate that, as a whole, the YREB's CWRGE has not yet achieved an effective level. The CWRGE in the YREB generally exhibits a trend of "first decreasing and then increasing, then decreasing and then increasing" and shows a "W"-shaped evolution law, and the overall trend is upward. There are just seven cities with effective data envelopment analysis (DEA), namely Changzhou, Hangzhou, Shanghai, Xuzhou, Changde, Changsha, and Yuxi. During the reporting period, the CWRGE of cities of various scales showed significant gaps: mega cities > big cities > small and medium-sized cities. From a regional perspective, the highest rate of CWRGE was found downstream of the YREB cities, then upstream, and the middle was the lowest. Spatial correlation findings demonstrated that both the agglomeration range and the outlier range were distributed, and there were mainly two positive aggregations of space forms ("high-high (H-H) type" and "low-low (L-L) type"), and the spatial distribution changed. The results of the spatiotemporal evolution demonstrate that there are more and more cities with high efficiency, as well as cities with low efficiency. From the results of the Tobit regression model, the CWRGE in the YREB are significantly improved by the economical development level, industrial scale, and water usage structure. While foreign direct investment and environmental regulation have considerable detrimental impacts, the impact of scientific and technological investment is not significant.

The hegemony of values: Revisiting Stanisław Pietraszko’s concept of culture with Antonio Gramsci’s theory of hegemony

In my reinterpretation of Stanisław Pietraszko’s writings, I seek to identify their elements that exhibit some affinity with the concept of cultural hegemony, which germinated from entirely different ideological soil and has been developed under different historical circumstances. The idea of hegemony is usually traced back to Antonio Gramsci’s texts, though also to the work of other scholars inspired by Karl Marx’s thought, including the British philosophers who founded cultural studies. I argue that in distancing himself from all Marxism-underpinned theories, therein those that evolved toward semiology, Pietraszko was prompted not only by his philosophical views on the ontology of culture and possibilities of studying it but also by the social and political conjuncture in which hedeveloped his conception of culture (specifically, the socialist or communist regimes in Eastern Europe). I ponder how the two divergent models of understanding culture (i.e. culture defined in terms of ways of life and the idea of cultural hegemony) can be brought together. In my argument, I consider various media and communication forms in public space, such as murals, graffiti, posters, billboards, monuments and the like. It is in them that I see manifestations of values.

Rigidity of weighted Einstein smooth metric measure spaces

We study the geometric structure of weighted Einstein smooth metric measure spaces with weighted harmonic Weyl tensor. A complete local classification is provided, showing that either the underlying manifold is Einstein, or decomposes as a warped product in a specific way. Moreover, if the manifold is complete, then it either is a weighted analogue of a space form, or it belongs to a particular family of Einstein warped products.

The Restorative Potential of Green Cultural Heritage: Exploring Cultural Ecosystem Services’ Impact on Stress Reduction and Attention Restoration

Green cultural heritage is an important form of natural space in cities. Only a few studies have conducted restorative studies in a historical environment as most have focused on natural environments. Moreover, few studies on cultural ecosystem services (CESs) have addressed cultural heritage. Based on an onsite questionnaire distributed to green cultural heritage users (N = 64) in Hamarikyu Garden, this paper explores the value of CESs in a green cultural heritage site and the relationship between cultural ecosystem values and perceived attention restoration/stress reduction. A multiple linear regression analysis and simple linear regression analyses were used to examine the data. The results showed that (1) the cultural ecosystem values of the green cultural heritage site were all rated highly except for the sense of place; (2) spending time in green cultural heritage provided respondents significant perceived attention restoration and stress reduction; (3) aesthetics and cultural heritage significantly affected perceived stress reduction, while attention restoration showed a significant positive correlation with aesthetic value and sense of place; and (4) the more visitors perceived the value of CESs, the more significant the perceived stress reduction and attention recovery were. This study indicates that CESs represent a useful tool for measuring the environmental characteristics of green cultural heritage sites and can predict perceived psychological recovery in green cultural heritage sites. Our findings enhance our knowledge about restorative environmental attributes through objective descriptions of potential health-promoting qualities and can be utilized as inspiration for designing restorative environments in green cultural heritage sites.

Art and Philosophy: Harmony of Giring-Giring Dance, Manganjan Dance, Tambun Bungai Dance of Kalimantan Tengah

The possibility of tradition collaborating with dance, music and performance art is an amazing art. However, it becomes problematic if the space to perform one of the parts of tradition, namely dance as an art or work in certain regions or localities, is still minimal. Either from the history of dances from certain regions, for example Central Kalimantan, especially the Ma'anyan Dayak community, or the method of usage or meaningful values in the form of ribut rukun, togetherness, care and exploration space. This research method uses a literature review that examines the results of previous studies as secondary sources, online media, and accompanying photos of dances originating from Central Kalimantan. The findings show that the Dayak Giring-Giring dance, Manganjan Dance and Tambun Bungai Dance have a variety of cultural richness, the meaning of friendship, as well as a rich history that must get space from generation to generation to the global community as a cultured, dignified, valuable and communal dance.

Semi-slant submanifolds in a locally conformal Kaehler space form

In this paper, we consider semi-slant submanifolds in a locally conformal Kaehler manifold and a locally conformal Kaehler space form. We give inequalities for the length of the second fundamental form and the mean curvature and, using Gauss and Codazzi equations, we get many useful results in locally conformal Kaehler space form.

Identification of polynomial nonlinear systems based on center manifold

A center-manifold (CM) based system identification (SID) method is developed to identify multi-input-multi-output continuous-time polynomial nonlinear systems in the state–space form. On one hand, the CM method is a natural extension of the frequency-domain subspace method to nonlinear SID problems. It decomposes the nonlinear SID problem into a series of linear least-square problems (in a precise sense), which can be solved analytically. This is in contrast to many existing methods that rely on iterative search of the global minimum. On the other hand, it is also a generalization of the invariant-subspace (ISP) based SID method. It inherits the nice property of the ISP method that the advantages of time-domain and frequency-domain SID methods are combined. In the paper, a persistence of excitation (PE) condition for the CM method is derived, which is described by the rank of certain Khatri–Rao product. Under the PE condition, the identification error is shown to be bounded within an arbitrarily small neighborhood of the origin when measurement noise is presented.

Desain Interior Perpustakaan Fakultas Bahasa Dan Seni Universitas Negeri Padang Dengan Konsep Minimalis

The low interest in reading has hampered intellectual abilities in society, especially students, so that libraries are required to be able to keep up with the pace of development of the times with services and infrastructure that meet the needs of space users, but the FBS UNP library has not been optimal in terms of interior design standards. Student complaints such as unstable air circulation, lack of reading space, and incomplete facilities have caused inconvenience, so an interior design of the FBS UNP Library was held with a minimalist concept. The purpose of interior design is to design a library layout that is representative and in accordance with interior design standards in order to create a sense of security and comfort for visitors while in the room. The interior design of the FBS UNP Library refers to the application of library interior design standards in the form of space, variety, hierarchy, lighting, personal areas, and comfort. The design method uses the 4D design method, namely Define (Defining) Design (Design), Develop (Development) and Dissaminate (Dissemination). Data collection is done by way of interviews, observation and documentation. Works are presented in the form of an Artwork Report with the main works being Presentation Mockups, Animation Videos and Presentation Posters.

The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$

We study the second fundamental form of the Siegel metric in $\mathcal A_5$ restricted to the locus of intermediate Jacobians of cubic threefolds. We prove that the image of this second fundamental form, which is known to be non-trivial, is contained in the kernel of a suitable multiplication map. Some ingredients are: the conic bundle structure of cubic threefolds, Prym theory, Gaussian maps and Jacobian ideals.

Concircular Hypersurfaces and Concircular Helices in Space Forms

In this paper, we find a full description of concircular hypersurfaces in space forms as a special family of ruled hypersurfaces. We also characterize concircular helices in 3-dimensional space forms by means of a differential equation involving the concircular factor and their curvature and torsion, and we show that the concircular helices are precisely the geodesics of the concircular surfaces.

A new geometric flow on 3-manifolds: the K-flow

We define a new geometric flow, which we shall call the K-flow, on 3-dimensional Riemannian manifolds; and study the behavior of Thurston’s model geometries under this flow both analytically and numerically. As an example, we show that an initially arbitrarily deformed homogeneous 3-sphere flows into a round 3-sphere and shrinks to a point in the unnormalized flow; or stays as a round 3-sphere in the volume normalized flow. The K-flow equation arises as the gradient flow of a specific purely quadratic action functional that has appeared as the quadratic part of New Massive Gravity in physics; and a decade earlier in the mathematics literature, as a new variational characterization of three-dimensional space forms. We show the short-time existence of the K-flow using a DeTurck-type argument.