Ideal Extensions of Topological Semigroups

A semigroup S is called an absolute coretract if for any continuous homomorphism f from a compact Hausdorff right topological semigroup T onto a compact Hausdorff right topological semigroup containing S algebraically there exists a homomorphism g \colon S→ T such that f\circ g=idS. The semigroup β\ben contains isomorphic copies of any countable absolute coretract. In this article we define a class C of semigroups of idempotents each of which is a decreasing chain of rectangular semigroups. It is proved that every semigroup from C is an absolute coretract and every finite semigroup of idempotents, which is an absolute coretract, belongs to C .

The known theory for a discrete oid \(T\) shows that how to find a subset \(T^{\infty}\) of \(\beta T\) which is a compact right topological semigroup (see section 2 for details).In this paper we try to find an analogue of almost periodic functions for oids. We discover, new compact semigroups by using a certain subspace of functions \(u^{\infty}(T)\) of \(C(T)\) for an oid \(T\) for which \(f\beta\) is continuous on \(T^{\infty}\times(T\cup T^{\infty}\cup TT^{\infty})\),where \((T\cup T^{\infty}\cup TT^{\infty})\) is a suitable subspace of \(\beta T\) for a wide range.

Algebraic and topological equivalences in the Stone-Čech compactification of a discrete semigroup

In this paper we present a number of sufficient conditions on a sequence of probability measuresµ n on a locally compact (second countable) Hausdorff topological semigroupS that guarantee the weak convergence of the sequence of convolution productsµ k,n ≡µ k + 1 *···*µ n (k<n), asn→∞, for allk≥0.

Let S be a topological semigroup, ω be a weight function on S, and M a (S, ω) be the weighted semigroup algebra of S. Let (S; M a (S, ω)) be the C *-algebra of all M a (S, ω)-measurable functions g on S such that g/ω vanishes at infinity. Here, we consider (S; M a (S, ω))* as a closed subalgebra of M a (S, ω)** equipped with the first Arens product, and study the relation between these two algebras. In particular, we show that (S; M a (S, ω))* is a closed ideal of M a (S, ω)** only when S is compact.

LetS be a uniform semigroup (this includes all topological groups and affine semigroups). We show that a certain space of uniformly continuous functions onS has a left invariant mean iffS has the fixed point property for uniformly continuous affine actions ofS on compact convex sets. This is closely related to but independent of the results of T. Mitchell in [13] and A. Lau in [10]. Interesting examples and consequences are given for the special cases of topological groups and affine convolution semigroups of probability measures on a locally compact semigroup or group.

Introduction. Limit properties of the convolution sequence of a regular measure on a compact topological semigroup are examined in this paper. Similar questions, as they arise in the case of a compact group, were examined byKAWADA & ITO [4], Recently BELLMAN [1] and GRENANDER [3] considered special limit theorems for products of independent identically distributed random operators. Such problems are closely related to those in this paper. It should be noted that similar questions arise when considering the structure of stationary stochastic processes [7]. Various results on compact semigroups are used in characterizing the class of limit measures [5], [6], [8].

It has been shown that, for a compact totally ordered set X, the category of irreducible semigroups with idempotents X and idempotent separating homomorphisms has a generator, Irr(X) [7]. In this article we outline the proof of the existence of Irr(X), along with the results obtained previously about the existence of Irr(X). We also survey the known results about the structure of an Irr(X) and about its uniqueness. These latter results were obtained by K. H. Hofmann and the author in a seminar on compact semigroups at Tulane University during the academic year 1970–1971.

China's urban areas are entering an era of stock renewal, where street renewal is receiving policy attention and practical project implementation. However, the challenges posed by spatial constraints and insufficient functional activities on the streets have led to street renewal failing to meet public demands. Small Variable Modular Installations (SVMI) possess a high degree of adaptability to constrained spaces and a flexible capacity to shape diverse functions, making them a targeted strategy in theory to address the challenges of street renewal. Nevertheless, there is a research gap in the context of Chinese street renewal (CSR) concerning the design, and construction of SVMI: an insufficient exploration of combined variable and modular technology solutions and practical construction techniques and methods. In response to this research gap, this study focuses on the "Jing-Zhang Box" (JZB) service installation in Beijing, providing specific analysis of its design concept, design technical points, application functions, spatial structure and connection methods, construction methods, and construction outcomes. This study aims to provide specific supplementation to the research on SVMI design and construction in the context of CSR and to offer theoretical and engineering foundations for the future design and practical construction of SVMI in various scenarios.

Purpose Contemporary construction techniques provide benefits of speed and cost savings on a large scale, and is viable in urban regions with exorbitant housing demand. In rural areas, where scale and access to technology are unavailable, locally prevalent vernacular architecture and methods are more suitable. Although vernacular construction techniques have historically proven more sustainable and climate-sensitive, the lack of skilled labour and lack of versatility in material selection limits its application on large-scale projects. This study explores the choice of building design and technology, from the context of embodied energy, carbon and other life cycle impacts for housing construction. Design/methodology/approach Life cycle assessment (LCA) that evaluates impacts due to the products/processes is used to analyse different construction techniques. Further a detailed estimation of embodied carbon and embodied energy is done for both “vernacular” and “contemporary” choices of construction methodology for a case study project. Findings The building constructed using vernacular techniques has lower embodied carbon and energy by over 30% compared to the other clusters designed using contemporary confined masonry techniques. However, with a few external interventions the contemporary methods can be implemented with improved sustainability. Research limitations/implications The limitation of the study is that it presents a case study-based exploration into comparing construction techniques to provide a practical understanding of making sustainable design choices and, hence, is limited to two construction methods. However, the same method could be extended to compare other construction techniques. Furthermore, it does not present a whole building LCA since the operating phase impacts are assumed to be fairly constant for such housing type, irrespective of the chosen method. Similarly, the demolition phase or the potential of reuse of the waste generated, water consumption and cultural and social heritage are not investigated in comparing the alternatives. Nevertheless, future studies could perform extensive exploratory and modelling studies on the operation phase and demolition phase to understand these impacts further. Practical implications In mass housing projects that belong to the so-called “affordable housing” or low-income housing category, sustainability concerns are not yet at the forefront of the decision-making process. Therefore, this study emphasizes the importance of incorporating sustainability into building design and construction and making sustainability accessible to even low-income communities. Adequate planning, social awareness initiatives and imparting skills and knowledge of sustainability to these communities are of utmost importance. The choice of design and materials should be encouraged by keeping in mind lower upfront costs as well as low maintenance and operational costs. Social implications The primary implications of the study are that the vernacular technologies are much superior in terms of sustainability in comparison to conventional construction of RCC framed structures as well as contemporary construction methods such as confined masonry. However, the implementation of such techniques presents significant challenges such as a lack of skilled forces, increased maintenance and lack of flexibility to minor modifications. Hence, although being a sustainable choice its acceptance and execution present practical difficulties. Therefore, this study primarily aims to reinforce the belief in vernacular architecture and techniques to build sustainable and resilient communities while highlighting the challenges of the modern world in implementing them. Originality/value Most studies advocate using construction methods based on their ease of implementation, maintenance or cost. However, this study highlights the importance of considering the aspect of sustainability in the context of the choice of methods for housing construction in urban and semi-urban areas. This study also addresses the need not to overlook vernacular construction technologies while selecting technology for housing for low-income communities.

Construction industry of Pakistan has a great contribution in uprising the GDP of the country. When compared with the construction industries of some developed countries of the world it still lacks in utilizing the modern methods of construction. Most of the organizations are relying on traditional ways of construction and are not ready to equip themselves with the advanced techniques of construction that may help them do their projects more effectively and efficiently. Prefabrication is the future of modern and sustainable construction which can maximize the capability of constructing the structures without compromising not only the time, cost and quality of project but also the environment. Prefabrication is rapidly increasing in construction, and previous researchers have identified various positive impacts of prefabrication on projects. However, prefabricated construction is less preferred over traditional methods of construction in Pakistan. Therefore, a comparison is required between conventional RCC building and a prefabricated (precast RCC) building to unearth the potential benefits of adopting prefabrication on overall cost of project. To achieve this, a BIM based multi-dimensional model of conventional and prefabricated building is developed using Autodesk Revit. A detailed comparison between both the methods of construction with respect to material, labor, transportation and time made the benefits of prefabricated construction clear over conventional construction. Prefabrication method is 84% faster and costs about 13.46% less than conventional method of construction. This comprehensive contrast will help to better understand and encourage the construction industry to move towards the prefabricated construction.

Most of researches about the design of the topology and the operation of a wireless sensor network are focusing on how to take advantage of all sensor nodes to collect information that covering the whole sense area. A criticism been ignored that the goal of lengthening lifespan is conflict with the complete coverage strategy due to the overlapping of sensor area among nodes result in unnecessary waste of energy. In this study, we propose another proposition from the idea of partial coverage strategy: a near perfect coverage rate can be achieved by least nodes to save the energy of the whole network. The proposed topology is constructed by clustered structure. According to the simulation results that made by comparing with the classic clustered topology, LEACH, and other related methods proposed recently, the study find that the method proposed in this paper can double the lifespan of a wireless sensor network under the same condition. Furthermore, the construction method can efficiently achieve graceful degradation to maintain the usage of a sensor network in a long period.

Among the many semigroups which can be derived from a given compact (jointly continuous) semigroup S is the semigroup 2s consisting of its non-empty compact subsets; the product is the usual one defined by the rule EF = {xy:xεE, yεF}. The Vietoris or finite topology on 2s (in which a base for the open sets is obtained by taking all sets of the form for l ≦i ≦n} as Vl, V2,…, Vn run over all finite collections of open subsets of S) makes 2s a compact, jointly continuous semigroup. The topology has a long history, having been introduced by Vietoris in 1923 and studied by Michael[4]. The utility of the topological semigroup was established by Hofmann and Mostert [3; see especially Section 3.7]; in fact they prefer to produce directly the uniform structure on 2s rather than the topology.

폴 루돌프의 플로리다 지역 주택은 2차 세계대전 이후 형식적인 근대 건축에서 탈피한 다양한 공간 구성, 지역 재료 및 구법의 사용으로 지역적 특성을 반영한 사례이다. 플로리다 주택 작품은 시대적, 지역적인 특성을 기반으로 하여 공간의 확장 및 연결 그리고 지역 환경을 고려한 재료 및 구법, 구조 시스템을 표현해야 한다는 설계 개념이 반영된 건축이다. 플로리다 주택의 특성은 공간 확장 및 외부 공간 연결 기법으로 목재 구조체를 중심으로 한 공간 확장과 가변적 공간구현 그리고 외부공간의 적극적인 연계성을 유도하기 위하여 다양한 방법(스크린 지붕, 오픈 지붕, 내부 파티오)을 사용하였다. 그리고 지역 재료 사용 그리고 지역 환경에 적합한 디테일 및 구법 사용으로 플로리다 지역의 석회암과 사이프러스 목재를 주된 재료로 사용하고, 고온 다습한 기후에 적합한 디테일과 지역 건설 환경을 고려한 구법을 사용하였다. 폴 루돌프의 플로리다 주택 연구를 통하여 현대 건축의 지역성을 고려한 계획에 구체적으로 적용 가능한 공간적, 기술적 적용 방법에 대한 모범사례로서 제안하는데 그 의미를 찾고자 한다. Paul Rudolph's early work in Florida after World War II is a significant example of the regional transformation of typical Modern Architecture through the spatial composition based on the diversity and use of local material and construction methods. Paul Rudolph's concept of a Florida House design is the expression of regional material, construction, and structural system through the spatial extension & connection based on periodical, regional characteristics. The characteristics of the Florida works is the spatial extension & connection design based on the wood structural framework through the various design factors, such as a screen roof, open roof, and internal patio as the spatial extension and link method. Paul Rudolf designed the house using local materials, such as cypress wood and lime block produced near the Florida Area and provided details & technology considering the Florida climate and construction environment. Through studies of Paul Rudolph's Florida works, the Florida Houses can be a prototype of localization, and can be presented as the spatial & technical transformation of design by the historical, cultural, regional background.

Economic and development growth are mainly supported by the construction industry. Consequently, the escalation and advancement in the building industry had produced massive wastes, affecting the environments’ quality. The problem highlighted is supported by previous studies which proved that it is one of the main concerns to be resolved in future. This paper is based on a review of the construction waste and its scenario in Malaysia. Based on the data collected from previous studies, it can be identified that wood is the main waste materials that are generated in the construction industry due to the high usage of wood in the conventional method of the formwork system. The high amount of construction waste generated also resulted in more illegal waste dumping impacting the environment in Malaysia. This paper discusses on the construction technique that can help in minimising construction waste. Industrialised Building System (IBS) is one of the methods which apply prefabrication and factory-produced construction in Malaysia. It is one of the efforts reducing the production of construction debris on site due to the structural components being produced in a regulated space such as a factory rather than on the construction site. RBM Building System and the new digital IBS is one of the other construction methods that are improvised from the previous IBS which maximise the potential of minimisation of waste construction.