Space Form Research Articles

Rellich inequalities via Riccati pairs on model space forms

We present a simple method for proving Rellich inequalities on Riemannian manifolds with constant, non-positive sectional curvature. The method is built upon simple convexity arguments, integration by parts, and the so-called Riccati pairs, which are based on the solvability of a Riccati-type ordinary differential inequality. These results can be viewed as the higher order counterparts of the recent work by Kajántó, Kristály, Peter, and Zhao, discussing Hardy inequalities using Riccati pairs.

Classification of semi-parallel hypersurfaces of the product of two spheres

It is known that Mendonça and Tojeiro (2013) [19] have established a complete classification of parallel submanifolds in the product manifold Qk1n1×Qk2n2, where Qk1n1 (resp. Qk2n2) is an n1-dimensional (resp. n2-dimensional) real space form with constant curvature k1 (resp. k2). In this paper, motivated by this result with considering further generalization, we study those semi-parallel hypersurfaces in case Qk1n1=Sk1n1 and Qk2n2=Sk2n2 with k1,k2>0. As the main result, we classify semi-parallel hypersurfaces of Sk1n1×Sk2n2 for n1,n2≥2.

A classification of triharmonic hypersurfaces in a pseudo-Riemannian space form

The purpose of this article is to investigate triharmonic hypersurfaces Mtn in a pseudo-Riemannian space form Nt1n+1(c). Assuming that the shape operator is diagonalizable, we show that every CMC triharmonic hypersurface either has constant scalar curvature or it is minimal if cε>0 and every CMC triharmonic hypersurface is minimal if cε<0, where ε is the inner product of the unit normal vector of Mtn. Furthermore, we prove that any CMC triharmonic hypersurface with diagonalizable shape operator in a pseudo-Euclidean space Et1n+1 is actually minimal provided that zero is a principal curvature of multiplicity at most one.

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

Homology of Warped Product Semi-Invariant Submanifolds of a Sasakian Space Form with Semisymmetric Metric Connection

This paper focuses on the investigation of semi-invariant warped product submanifolds of Sasakian space forms endowed with a semisymmetric metric connection. We delve into the study of these submanifolds and derive several fundamental results. Additionally, we explore the practical implications of our findings by applying them to the homology analysis of these submanifolds. Notably, we present a proof demonstrating the absence of stable currents for these submanifolds under a specific condition.

From cakravartin to bodhisattva: Buddhist models for globalization

AbstractThis article examines globalization in an Asian context through the lens of two Buddhist concepts: the cakravartin and the bodhisattva. A cakravartin is a ruler who fuses spiritual and political power in his global reign. This article argues that the cakravartin represents one model of Buddhist globalization where the spread of the religion coincides with the growing military dominion of a BuddhGist king. A bodhisattva, on the other hand, is an enlightened being who has chosen to be reborn out of compassion with the entire suffering world. A bodhisattva watches over a ‘Buddha field’, or spiritual realm. Each Buddha field has its own laws, culture, language, or even separate forms of time and space. The bodhisattva provides a new model for understanding cultural diversity in the absence of a unified political power: the Buddhist world is a transnational network where new identities are negotiated.

System modeling and temperature control for a fuel cell system based on local model networks

ABSTRACT Fuel cells have been studied for use in stationary power generation and vehicle propulsion systems. The fuel cell thermal management subsystem is coupled and nonlinear, posing challenges for modeling and temperature control. This paper aims to integrate the physical models of the fuel cell stack, pump, thermostat, and other components combined with intelligent algorithms into an efficient system-level thermal management model framework and develop a model predictive controller to solve the temperature control problem. First, a physics-based nonlinear model of the fuel cell system is developed and used as a basis to identify the linearized model for different operating points. Then, the global model is obtained by fusing the local models with Gaussian validity functions using the local linear model tree method. Third, a multi-step prediction model is derived based on the local model networks, and a parameterized linear state space form is obtained and used for controller design. Furthermore, an online correction method is developed to reduce the model discrepancy. Finally, the accuracy of the system model and the performance of the proposed controller are verified by open-loop experimental data and a series of closed-loop simulation cases.

Recent Developments on the First Chen Inequality in Differential Geometry

One of the most fundamental interests in submanifold theory is to establish simple relationships between the main extrinsic invariants and the main intrinsic invariants of submanifolds and find their applications. In this respect, the first author established, in 1993, a basic inequality involving the first δ-invariant, δ(2), and the squared mean curvature of submanifolds in real space forms, known today as the first Chen inequality or Chen’s first inequality. Since then, there have been many papers dealing with this inequality. The purpose of this article is, thus, to present a comprehensive survey on recent developments on this inequality performed by many geometers during the last three decades.

On some spaces via topological ideals

Abstract Our main purpose is to introduce and investigate the concepts of some forms of spaces via topological ideals. Some characterizations of some forms of spaces via topological ideals are established. Moreover, several properties of ⋆ \star -monotonically normal ideal topological spaces are considered.

Identifikasi Pola Sebaran Ruang Terbuka Hijau (RTH) Di Kawasan Lumpur Lapindo

The mud disaster that has occurred in Sidoarjo Regency since May 29 2006 was an event of hot gas and mud coming out of the ground with a temperature of 100°C which has inundated several villages in Sidoarjo Regency. Before the disaster, Porong was a productive area because there were many rice fields, shops and factories. The three districts affected by the Lapindo mudflow, namely Porong District, Tanggulangin District, and Jabon District, previously in 2005, based on satellite imagery, had the form of a spreading Green Open Space (RTH). The impact that resulted from the occurrence of the Lapindo mud disaster was the occurrence of land conversion, especially in the Green Open Space (RTH) sector. Based on these problems, it is necessary to identify the pattern of distribution of green open spaces in the Lapindo Mud Disaster Area. This research discusses the distribution pattern of Green Open Space (RTH) in the Lapindo mud disaster area using the Nearest Neighbor Average (NNA) Analysis method. Based on the results of the Nearest Neighbor Average (NNA), the distribution pattern generated in the Lapindo Mud Disaster Area has a random distribution pattern (Random). Porong clustered (Clustered).

RBF-ARX model-based MPC approach to inverted pendulum: An event-triggered mechanism

The event-triggered predictive control based on RBF-ARX model (state-independent autoregressive with exogenous inputs constructed by radial basis function network) is designed in this paper, which is aiming at the issue of accumulating computational burden associated with solving the optimization problems at each sampling time. To alleviate the computational burden while the performance of model predictive control (MPC) cannot be simultaneously sacrificed, from the perspective of model building, the data-driven RBF-ARX model presented by a new state space form is combined into the event-triggered model predictive control (ETMPC) method instead of the mechanistic model. Therefore, we attempt to expand the results of ETMPC to the complex industrial processes rather than the restricted model described by mechanism in terms of proposing a new event-triggering condition (ETC) with a data-driven model. Additionally, the stability analysis of RBF-ARX model-based ETMPC is demonstrated with a focus on the boundedness of the model’s output. The simulation results presented in this paper serve to illustrate the effectiveness of the proposed method by acting on an inverted pendulum system in this paper, which can be showed that the computational burden is significantly reduced, and the predictive control performance of ETMPC is as well as the MPC roughly.

Real hypersurfaces of nonflat complex space forms with weakly transversal Killing operators

Wang and Zhang in (2022) [20] and (2023) [21] characterized type (A) real hypersurfaces of the nonflat complex space forms as having transversal Killing structure Lie operator Lξ or contact Lie operator Lξϕ. In this note, we extend the above results by showing that the class of real hypersurfaces of type (A), (B) and the ruled real hypersurfaces in the nonflat complex space forms are locally characterized by having weakly transversal Killing operator Lξ or Lξϕ.

Contamination Mechanisms of a Common Illocutionary Space Forming

The study analyzes the main contamination mechanisms of personal and institutional components in the process of forming a common illocutionary space of counter-communicators in the conditions of borderline communication of social work discourse. The basis for creating a common sphere of goal-setting is not only the intention of agents and clients to ensure the realization of the dominant goal, but also the presence of a conventionalizing “tertiary agent” (tertiariis agens), which contributes to the constant comparison of their own communicative actions with model samples. As part of the description of the strategies and tactics of consolidation, based on the discursive-modus analysis, not only the key speech-actual characteristics of the harmonization of communication are revealed, but also the interpretive potential of verbalizers of personal illocution elements that do not correspond to the situation of normalized semiosis. For the formation of the card index, the most representative, in terms of the constant change of the coding register, the borderline discourse of social work was chosen. The result of the analysis is a list of the most effective speech acts of direct and hidden implementation of access to the control of discourse development vectors: commissives, promises, declaratives, metacommunicative phatic markers, as well as menasives with a modified illocution as causatives. The contamination of illocutionary spaces occurs on the basis of conditional institutionality with a priori acceptance of the criterion of “equalizing” agents and clients. Agent-client interaction is implemented in similar strategies and tactics for initiating key values; harmonization is achieved by reducing conflict potential during the transformation of the usual functional load. The regulatory potential of tertiariis agens, provided by the presence of conventionalization prototexts, contributes to the reduction of intimization entropy by creating a synergistic goal-setting vector and transforming the countercommunicator’s illocution.

TRENDS OF DEVELOPMENT OF PUBLIC SPACE FORMS

The article summarizes the main forms of public space and their types and development trends. Features of open, covered, atrium forms of public space and public space with a complex structure are described.&#x0D; The conditions of the active functioning of a comfortable public space are considered. Examples of progressive projects of the organization of public space, which are implemented in world practice and which illustrate the proposed classification of public spaces by form, are given. Modern possibilities of organizing public space, which can be included inside the building and located outside relative to the buildings, are based on the main groups of forms: open public space (area with design in an open urban environment), covered public space (area with design in an open urban environment with canopy structure), atrium public space (communication and recreation atrium part of a public building) and public space of a complex structure (combination of open, covered and atrium parts: vertically at different levels or by blocking horizontally). The most complicated form of a complex with public space is a multi-level combination of a transport hub, a shopping center and a recreation area on the upper levels.

Quality by Design-Guided Systematic Development and Optimization of Mucoadhesive Buccal Films.

Mucoadhesive buccal films have found increased popularity in pharmaceutical drug delivery due to the several advantages that they possess. The present study strives to develop and optimize chitosan-based mucoadhesive buccal films by relying on quality-by-design (QbD) principles. Previous knowledge and experience were employed to firstly identify the critical quality attributes (CQAs), followed by a thorough risk assessment, which led to the selection of seven critical material attributes and process parameters, namely, the polymer grade and concentration, the plasticizer type and concentration, the citric acid (CA) concentration, the amount of the casted solution, and the drying condition. Their effects on the breaking hardness and mucoadhesivity, selected as CQAs, were investigated in three steps by three designs of the experiment (DoE). The medium molecular weight of chitosan (CH) was the preferred choice in the optimized formulation, and its concentration was the most important factor affecting the CQAs, thickness, and moisture content of the films. It was found that 0.364 g/cm2 was the suitable amount of the casting solution, and its optimum drying conditions were presented in the form of a design space. Glycerol (Gly) was the best choice as a plasticizer, and a design space representing several combinations of CH and CA concentrations that produce films with the required quality was constructed at a fixed concentration of 35% Gly. A formula from this design space was selected and employed to load with two model drugs to test its drug-carrying properties for drugs with different physicochemical characteristics. Uniform drug distribution with an immediate release profile was achieved in both drugs, although one of the CQAs was outside of the specifications in the case of lidocaine-containing film. To summarize, the obtention of the optimum mucoadhesive buccal film based on CH was efficiently facilitated by the rational application of QbD principles and the DoE approach.

Topological complexity of $S^3/Q_8$ as fibrewise L-S category

In 2010, M. Sakai and the first author showed that the topological complexity of a space $X$ coincides with the fibrewise unpointed L-S category of a pointed fibrewise space $\proj_{1} \colon X \times X \to X$ with the diagonal map $\Delta \colon X \to X \times X$ as its section. In this paper, we describe our algorithm how to determine the fibrewise L-S category or the Topological Complexity of a topological spherical space form. Especially, for $S^3/Q_8$ where $Q_8$ is the quaternion group, we write a python code to realise the algorithm to determine its Topological Complexity.

Emlékszerűség és egyöntetűség. Hauszmann, Stróbl, Lotz és a budapesti Igazságügyi palota központi csarnoka

The Palace of Justice opened in 1896 is among the country’s most important public buildings; its central hall is one of the most grandiose spaces of late historicism in size and decoration. A year after its inauguration Alajos Hauszmann, the architect, summed up the construction history and programme of the building, and the work appeared in ornate folio edition in 1901. the architect designed the central hall in the style of Rome’s baroque architecture reviving the spirit of antiquity, and also drew on the tradition of the space type of salles des pas perdus. As regards space forms and structures, its relatives are the halls of the palaces of justice in paris, Antwerp and Strasbourg.The placing of the Justitia statue dominating the space was probably inspired by the central hall of Vienna’s Justizpalast and is permeated with the memory of antique temple interiors abounding in giant cultic statues. With its hieratic character, Stróbl’s statue reminds us of classical Rome’s enthroned Minerva and Dea Roma statues, the modelling of the dress and mantle imitating the Hellenistic and Roman baroque drapery styles.The 19th century reconstructions of the rich mosaic and sculptural decorations of the spaces, walls and vaults of the Roman baths must have fertilized Hauszmann’s imagination and inspired him to envision the colouring and gilding of the surfaces and painted decoration of the ceiling, although the latter was also influenced by Roman baroque fresco painting. Károly Lotz designed the illusory architecture of the ceiling painting after Andrea del Pozzo by taking care to align the painted architectonic details with the framing mouldings and ornaments.A cardinal element of the architectural program was the deliberately monumental effect and “homogeneity” of which – in Hauszmann’s view – fine arts were the “precondition and the instruments”. He himself chose the painter and sculptor for the decoration of the hall, because he deemed it important to give them “direction” and “enlightenment” through his personal influence to achieve a “homogeneously harmonious creation”. As a result, both the sculptor’s and the painter’s adaptation to Roman models and to the grandiosity of the formal idiom and dimensions of the hall can be perceived.

Research on Accessibility of Green Infrastructure Based on GIS: A Case Study of Kunhou Neighborhood Planning

The outbreak of the COVID-19 pandemic in early 2020 has made necessary a re-examination of public health issues and the adoption of life-changing design strategies. By combining quantitative and qualitative methods, the structure and function of community green space can be better evaluated. This study selects the Kunhou neighborhood in Wuhan as the site and proposes to analyze the daily health service function of the community’s green infrastructure. Through GIS spatial analysis, this study evaluates the accessibility of green infrastructure and medical facilities and discusses the ideal green space form based on health indicators. Statistical analyzes were used to visualize the relevance of accessible green infrastructures and medical facilities within walking distance. The findings show that the Kunhou neighborhood is lacking access to green infrastructure for daily activities. The research findings provide a bridge between public health indicators and community space planning and offer design suggestions for green infrastructure planning.

From Monism to Pluralism: Cassirer’s Interpretation of Kant

Kant’s theory of cognition aimed to explain the possibility of scientific knowledge. Aesthetics and life science were not considered by Kant in the context of cognition. By contrast, Cassirer set himself a philosophical task to extend Kant’s theory of cognition to all forms of culture, including pre-scientific knowledge and aesthetics. The present study demonstrates how Cassirer explained the possibility of different objective forms, named symbolic, by employing and transforming Kant’s theory of cognition. For this goal, Cassirer took the following steps: modified the definitions of a priori synthesis (the act of understanding) and pure intuition (the forms of space and time) - main building blocks of Kant’s cognition; indicated the necessary correlation of intuition and synthesis; characterized a priori synthesis and the intuition as notions which include contradicted meanings. Cassirer called this contradiction “twofold oppositions” as characteristic of a priori synthesis. The first argument of the article is that the possibility of various synthetic acts is rooted in the nature of a priori synthesis which carries together two different meanings: the act of uniting elements and the initial unity. One synthetic act forms the world of nature and is connected to scientific space and time, and the other is the product of immediate perceptional space and time, from which the world of myth and aesthetics appears. Thus, Cassirer expanded the scope of “pure” synthesis. The second argument is that Cassirer specified a priori synthesis and pure intuition as a functional concept. The functional concept belongs to the model of concept as-relation that Cassirer has elaborated. It includes moments that are separated and united simultaneously. This definition of concept breaks the rules of consistency. The concept of as-relation justifies the contradictory characteristics of a priori synthesis and pure intuition, which include both the combination of moments in a synthesizing act and the initial unity of intuition.

The Mayflower and Historical Culture in Britain, 1620–2020

Abstract In 2020 the Anglo-American world marked the 400th anniversary of the trans-Atlantic Mayflower voyage with a programme of activities. Intensive and focused interest in the story of the Mayflower is not a new phenomenon—especially in the United States, where it is the bedrock of the nation’s ‘origin story’. But the tale of the Pilgrims has historically also captured the British imagination. This article outlines a chronology for understanding the cultural importance in Britain of this voyage, from the New England chroniclers to the postcolonial critiques of historians today. In between, it offers a thematic analysis of the different groups which could use the story in their construction of morality and identity, from Romanticists and abolitionists to Anglo-American diplomats and civic boosters. Understanding the afterlife of the voyage in this long perspective, we argue, provides us with a more nuanced understanding of how ideas of history develop and evolve within broader arenas of politics and civil society. We use the concept of historical culture: an approach that is attuned to the interplay between memory, public history, heritage and popular history, and across forms of media (novels, plays, film) and spaces of interaction (cities, politics, movements). As the vogue for commemoration continues to exert power in Britain and beyond, and so does an increasing demand for more critical approaches to historical redress, we thus develop a critical framework that understands the powerful draw of ‘history’—both past and present.