Space Of Functions Research Articles

Dynamical mixed boundary-transmission problems of the generalized thermo-electro-magneto-elasticity theory for composed structures

Abstract In the present paper we investigate three-dimensional dynamical mixed boundary-transmission problems for composed body consisting of two adjacent anisotropic elastic components having a common interface surface. The two contacting elastic components are subject to different mathematical models: Green–Lindsay’s model of generalized thermo-electro-magneto-elasticity in one component and Green–Lindsay’s model of generalized thermo-elasticity in the other one. We assume that the composed elastic structure under consideration contains an interfacial crack. We prove the uniqueness and existence theorems in appropriate function spaces.

An inner product on Adelic measures with applications to the Arakelov–Zhang pairing

We define an inner product on a vector space of adelic measures over a number field. We find that the norm induced by this inner product governs weak convergence at each place of K K . The canonical adelic measure associated to a rational map is in this vector space, and the square of the norm of the difference of two such adelic measures is the Arakelov–Zhang pairing from arithmetic dynamics. We find that the norm of a canonical adelic measure associated to a rational map is commensurate with a height on the space of rational functions with fixed degree. As a consequence, we show that the Arakelov–Zhang pairing of two rational maps f f and g g is, when holding g g fixed, commensurate with the height of f f .

Exploring Traditional Nepalese Building Techniques and Timber’s Role Structural Integrity

This paper aims to explore traditional Nepalese building construction techniques and the significant role of timber in enhancing the structural integrity and longevity of these buildings. With a long history of utilizing materials that are readily available locally, particularly wood, clay, stone, Nepal a country renowned for its rich architectural legacy has built buildings employing these resources. The study delves into the various traditional building techniques employed in Nepal, including the intricate craftsmanship and cultural significance associated with them. Additionally, it investigates the unique properties of timber that make it an ideal choice for construction in the Nepalese context. The finding talks about the construction of buildings various techniques which are employed to assemble structures. This includes information, on building materials, functional space allocation and the terminologies used in building construction. These terminologies hold value as they are derived from our tradition, in building construction technology. The findings of this research can serve as a valuable resource for architects, engineers, conservationists, and policymakers involved in the restoration and sustainable development of traditional Nepalese buildings.

Research on The Application of Interactive Design in Subway Public Art

China's urbanization is developing rapidly, and subway space, as an important part of urban construction, is receiving more and more attention from society and the government. The subway has alleviated the city's traffic congestion problem to the greatest extent, and has made rational use of the city's public space system. Public art in underground space has also become a window for urban cultural propaganda. Underground space is transforming from a functional space to a humanistic art space. In recent years, China's subway public art has developed rapidly and presented a diverse state, but there are still some common problems, such as the passive and single communication between space art and passengers, the lack of a certain degree of artistic publicity, and the failure to better meet people's current needs for humanistic art.

Global existence of non-Newtonian incompressible fluid in half space with nonhomogeneous initial-boundary data

In this study, we investigate the global existence of weak solutions of non-Newtonian incompressible fluids governed by (1.1). When u0∈Ḃp,qα−2p(R+n)∩Ḃn+22,n+221−4n+2(R+n)∩Ḃp,11+np(R+n) is given, we will find the weak solutions for the Eq. (1.1) in the function space Cb[0,∞;Ḃp,qα−2p(R+n)∩Cb(0,∞;Ḃn+221−4n+2(R+n))∩L∞(0,∞;Ẇ∞1(R+n)), n+2<p<∞,1≤q≤∞,1+n+2p<α<2. We show the existence of weak solutions in the anisotropic Besov spaces Ḃp,qα,α2(R+n×(0,∞)) (see Theorem 1.2) and we show the embedding Ḃp,qα,α2R+n×(0,∞)⊂Cb[0,∞;Ḃp,qα−2p(R+n) (see Lemma 2.8). For the global existence of solutions, we assume that the extra stress tensor S is represented by S(A)=F(A)A, where F satisfies the assumption (A). Note that S1, S2 and S3 introduced in (1.2) satisfy our assumptions.

Continuous dependence on initial data for the solutions of 3-D anisotropic Navier-Stokes equations

In this paper, we prove the continuous dependence on the initial data for the solutions of 3-D incompressible anisotropic Navier-Stokes equations in the functional space Xs(T)=def{u:u∈C([0,T];H0,s)with∇hu∈L2(]0,T[;H0,s)} for s>12. We also show the non-uniform continuity of the data-to-solution map in C([0,T];H0,s) for s>12, which makes sharp contrast with the corresponding result for the classical 3-D Navier-Stokes equations.

Variegated urban and rural spaces: Defining village types in China

China’s system of territorial spatial planning requires an integrated layout of ecological, agricultural, and urban functional space. This paper examines urban and rural villages and finds that villages can be classified into five types: urban villages, suburban villages, rural villages, semi-ecological villages, and eco-villages. These villages have multiple functions such as ecological services, agricultural production, and town services, according to the relationship between villages and territorial space. Urban villages refer to villages within the urban space, which have certain urban socio-ecological service functions; suburban villages are villages located at the junction of urban and agricultural spaces, which adapt their functions to the needs of the town; rural villages refer to villages located in the vast agricultural space, which are dominated by large-scale agriculture, and which need to undertake the function of guaranteeing food security; semi-ecological villages refer to villages at the junction of the agricultural space and the eco-villages, which can develop diversified ecological services; and eco-villages refer to villages that are in, or essentially in, eco-space, and have an important role to play in the maintenance of natural ecosystems.

Fractional Hermite–Hadamard, Newton–Milne, and Convexity Involving Arithmetic–Geometric Mean-Type Inequalities in Hilbert and Mixed-Norm Morrey Spaces ℓq(·)(Mp(·),v(·)) with Variable Exponents

Function spaces play a crucial role in the study and application of mathematical inequalities. They provide a structured framework within which inequalities can be formulated, analyzed, and applied. They allow for the extension of inequalities from finite-dimensional spaces to infinite-dimensional contexts, which is crucial in mathematical analysis. In this note, we develop various new bounds and refinements of different well-known inequalities involving Hilbert spaces in a tensor framework as well as mixed Moore norm spaces with variable exponents. The article begins with Newton–Milne-type inequalities for differentiable convex mappings. Our next step is to take advantage of convexity involving arithmetic–geometric means and build various new bounds by utilizing self-adjoint operators of Hilbert spaces in tensorial frameworks for different types of generalized convex mappings. To obtain all these results, we use Riemann–Liouville fractional integrals and develop several new identities for these operator inequalities. Furthermore, we present some examples and consequences for transcendental functions. Moreover, we developed the Hermite–Hadamard inequality in a new and significant way by using mixed-norm Moore spaces with variable exponent functions that have not been developed previously with any other type of function space apart from classical Lebesgue space. Mathematical inequalities supporting tensor Hilbert spaces are rarely examined in the literature, so we believe that this work opens up a whole new avenue in mathematical inequality theory.

Urban parks in developing countries: Challenges and opportunities in Addis Ababa, Ethiopia

The scarcity of well-functioning green spaces in the rapidly growing urban centers of developing countries poses significant challenges, hindering the well-being and quality of life for urban populations. Urban parks, often referred to as the "lungs of the city," have the potential to alleviate these challenges, yet their benefits are not always evident. This study explores the challenges and opportunities faced by urban parks in developing countries through a comparative analysis of Janmeda Park and Entoto Park in Addis Ababa, Ethiopia. The research assesses key dimensions, including accessibility, sociability, comfort, image projection, and management/maintenance. These elements are vital for understanding how well urban parks serve their communities and contribute to urban development. While Janmeda Park, despite its historical importance, struggles with physical and operational challenges, Entoto Park’s well-designed amenities, management, and safety provide a model for future park developments. The study offers recommendations to improve urban parks, such as enhancing accessibility, fostering sociability, ensuring user comfort and safety, strengthening image projection, integrating cultural and historical elements, and improving management and maintenance. It also highlights the importance of monitoring and evaluating park performance. These recommendations aim to guide urban planners and policymakers in enhancing urban parks, thereby supporting community well-being and promoting effective urban development. The insights provided are intended to inform better practices for urban park planning and management, contributing to more vibrant and functional green spaces in developing cities.

Managing dental and skeletal development in patients with hemifacial microsomia

Hemifacial microsomia (HFM) is a congenital condition characterized by the underdevelopment of one side of the face, impacting the ear, mouth, and jaw areas. This anomaly, second only to cleft lip and palate in prevalence, presents significant challenges in dental and skeletal development. Early diagnosis, primarily through advanced imaging techniques such as 3D computed tomography (CT) scans and magnetic resonance imaging (MRI), is crucial for identifying the extent of anomalies and planning effective interventions. The condition involves complex dental issues including malocclusion, missing teeth, and delayed dental eruption, necessitating early and targeted orthodontic treatments. Functional appliances, space maintainers, and braces are commonly used to guide dental arch development and correct alignment, leveraging the natural growth phase of the patient. Surgical interventions play a pivotal role in managing severe skeletal deformities. Preventive strategies, including regular dental check-ups, proper oral hygiene practices, and preventive treatments such as fluoride applications and dental sealants, are vital in minimizing complications and ensuring long-term oral health. Educating patients and their families on the importance of oral hygiene and routine dental care is crucial for maintaining dental health and preventing future issues. Continuous monitoring and follow-ups allow for timely adjustments to treatment plans, enhancing the effectiveness of interventions and supporting optimal growth and development. Overall, the management of dental and skeletal anomalies in hemifacial microsomia involves a combination of early diagnosis, orthodontic and surgical treatments, and preventive care, all of which are integral to improving outcomes and quality of life for affected individuals.

Classifying post-Minkowskian geometries for gravitational waves via loop-by-loop Baikov

We use the loop-by-loop Baikov representation to investigate the geometries in Feynman integrals contributing to the classical dynamics of a black-hole two-body system in the post-Minkowskian expansion of general relativity. These geometries determine the spaces of functions to which the corresponding Feynman diagrams evaluate. As a proof of principle, we provide a full classification of the geometries appearing up to three loops, i.e. fourth post-Minkowskian order, for all diagrams relevant to the conservative as well as the dissipative dynamics, finding full agreement with the literature. Moreover, we show that the non-planar top topology at four loops, which is the most complicated sector with respect to integration-by-parts identities, has an algebraic leading singularity and thus can only depend on non-trivial geometries through its subsectors.

Predicting Inhibition of CDK2 with SAnDReS: The Application of Machine Learning to Navigate the Scoring Function Space.

CDK2 plays a pivotal role in controlling the progression of the cell cycle and is a target for anticancer drugs. The last 30 years of structural studies focused on CDK2 provided the basis for understanding its inhibition and furnished the data to develop machine-learning models to study intermolecular interactions. This review addresses the application of computational models to estimate the inhibition of CDK2. It focuses on machine-learning models developed to predict binding affinity against CDK2 using the program SAnDReS. A search of previously published articles on PubMed showed machine-learning models built to evaluate CDK2 inhibition. BindingDB information for CDK2 furnished the data to generate updated machine-learning models to predict the inhibition of this enzyme. The application of SAnDReS to model CDK2-inhibitor interactions showed that this approach can build machine-learning models with superior predictive performance compared with classical and deep-learning scoring functions. Also, the innovative DOME analysis of the predictive performance of machine learning and universal scoring function indicates that this method is adequate to select computational models to address protein-ligand interactions. The available structural and functional data about CDK2 is a rich source of information to build machine-learning models to predict the inhibition of this protein target. SAnDReS can build superior models to predict pKi and outperform universal scoring functions, including one developed using deep learning.

Convergence and high order of approximation by Steklov sampling operators

In this paper we introduce a new class of sampling-type operators, named Steklov sampling operators. The idea is to consider a sampling series based on a kernel function that is a discrete approximate identity, and which constitutes a reconstruction process of a given signal f, based on a family of sample values which are Steklov integrals of order r evaluated at the nodes k/w, k∈Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k \\in {\\mathbb {Z}}$$\\end{document}, w>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$w>0$$\\end{document}. The convergence properties of the introduced sampling operators in continuous functions spaces and in the Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document}-setting have been studied. Moreover, the main properties of the Steklov-type functions have been exploited in order to establish results concerning the high order of approximation. Such results have been obtained in a quantitative version thanks to the use of the well-known modulus of smoothness of the approximated functions, and assuming suitable Strang-Fix type conditions, which are very typical assumptions in applications involving Fourier and Harmonic analysis. Concerning the quantitative estimates, we proposed two different approaches; the first one holds in the case of Steklov sampling operators defined with kernels with compact support, its proof is substantially based on the application of the generalized Minkowski inequality, and it is valid with respect to the p-norm, with 1≤p≤+∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\le p \\le +\\infty $$\\end{document}. In the second case, the restriction on the support of the kernel is removed and the corresponding estimates are valid only for 1<p≤+∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 < p\\le +\\infty $$\\end{document}. Here, the key point of the proof is the application of the well-known Hardy–Littlewood maximal inequality. Finally, a deep comparison between the proposed Steklov sampling series and the already existing sampling-type operators has been given, in order to show the effectiveness of the proposed constructive method of approximation. Examples of kernel functions satisfying the required assumptions have been provided.

Ulam–Hyers–Rassias Mittag-Leffler stability of ϖ–fractional partial differential equations

This paper offers a comprehensive analysis of solution representations for ϖ-fractional partial differential equations, specifically focusing on the linear case of the Darboux problem. We exhibit a representation of the solutions for the Darboux problem of ϖ-fractional partial differential equations in the linear case in the space of continuous functions. Through the application of the generalized Gronwall inequality, we establish the Ulam–Hyers–Rassias Mittag–Leffler stability in the space of continuous functions. Three numerical examples are presented to show the effectiveness and the applicability of our results.

Environmental influence on the functional ecological structure of benthic macrofaunal communities of the northwest Iberian coast

Evaluating the functional structure of benthic macrofaunal communities provides insights into how environmental drivers shape the ecosystem and establishes a baseline knowledge of the communities’ dynamics and functioning. This understanding allows the prediction of responses to environmental changes and the implementation of efficient conservation and management strategies. Here we examine the structures and functions of benthic macrofaunal communities on the Northwest Iberian coast concerning environmental factors such as depth, hydrodynamic energy, and bottom type. The results suggest that the community assemblages and their function are structured by factors which influence food availability and habitat heterogeneity. The different sites exhibited different trait compositions and functional structures, indicating that distinct functions are performed according to environmental conditions. The communities found in sandy bottom areas with low hydrodynamic conditions presented frail functionality and demonstrated high vulnerability to alterations in their environment. Conversely, the communities found in rocky bottoms with high hydrodynamic conditions exhibited a fulfilled functional niche space, rendering them more resilient to such changes and less prone to loss of function. Although the analyses did not reveal significant differences in the factor depth, its influence on several factors seems relevant in shaping the functional structure of the communities. These findings highlight the importance of understanding the impact of local environmental conditions on ecosystem functioning, to effectively implement monitoring, management, and conservation strategies.

MODELLING STUDY ON CENTRAL COURTYARD SHADING STRATEGY IN TROPICAL CLIMATE REGION MALAYSIA

A courtyard is an open multi-functional space and an effective daylight passive design strategy in a building. However, to have a courtyard in a tropical country, it had to deal with the issue of visual discomfort, which requires some consideration in adaptation to the climate condition. These visual comfort issues include inconsistent light distribution, inappropriate illuminance levels, glare, and a lack of shaded areas. The focus of this research paper is to address the solution of shading strategies towards the visual discomfort issues associated with courtyard spaces. The solution is done by modelling study method on courtyard ratios and courtyard configuration to determine the effect on the internal courtyard percentage shaded area. This research aims to explore the potential benefits of using courtyards as a daylight shading design as a strategy in buildings. Besides, it is also to examine courtyard design variables in enhancing visual comfort, particularly in the context of commercial building design in Malaysia. Kuala Lumpur is chosen to represent the tropical climate region. The aim is achieved by identifying optimum courtyard ratios that can improve daylight, shading, and visual comfort that make courtyards functional and usable spaces. Results show that a small and deep courtyard is found to be best suited to tropical climate conditions with the configuration of the courtyard’s height being double the size or more than the size of the courtyard’s width. This courtyard ratio is able to produce a full shaded area during daytime. While courtyard length does not have any impact on the percentage of shaded area, wide and narrow courtyard need to adapt to the tropical climate constraint by having aided shading strategies such as multi-layered height of trees, independent covered structures like a canopy or gazebo, shading panels, awnings, and extended roof overhangs.

Measure theoretic aspects of the finite Hilbert transform

AbstractThe finite Hilbert transform , when acting in the classical Zygmund space (over ), was intensively studied in [8]. In this note, an integral representation of is established via the ‐valued measure for each Borel set . This integral representation, together with various non‐trivial properties of , allows the use of measure theoretic methods (not available in [8]) to establish new properties of . For instance, as an operator between Banach function spaces is not order bounded, it is not completely continuous and neither is it weakly compact. An appropriate Parseval formula for plays a crucial role.

Phenotypic limits of crop diversity: a data exploration of functional trait space.

Relationships between crop genetic and functional diversity are key to addressing contemporary agricultural challenges. Yet, there are few approaches for quantifying the relationship between genetic diversity and crop functional trait expression. Here, we introduce 'functional space accumulation curves' to analyze how trait space increases with the number of crop genotypes within a species. We explore the potential for functional space accumulating curves to quantify genotype-trait space relationships in four common annual crop species: barley (Hordeum vulgare), rice (Oryza sativa), soybean (Glycine max), and durum wheat (Triticum durum). We also employ these curves to describe genotype-trait space relationships in the wild annual Arabidopsis thaliana, which has not been subjected to artificial selection. All five species exhibited asymptotic functional space accumulation curves, suggesting a limit to intraspecific functional crop diversity, likely due to: dominant phenotypes represented by several genotypes;or functional redundancy that might exist among genotypes. Our findings indicate that there is a diminishing return of functional diversity with increasing number of genotypes. Our analysis demonstrates the efficacy of functional space accumulation curves in quantifying trait space occupancy of crops, with implications for managing crop diversity in agroecosystems, and genetic diversity in crop breeding programs.

Diverse Bases for Functional Spaces for Non-Rigid Shape Correspondence

Diverse Bases for Functional Spaces for Non-Rigid Shape Correspondence

Analysis of core functional components in Yinchenhao Decoction and their pathways for treating liver fibrosis

To analyze the core functional component groups (CFCG) in Yinchenhao Decoction (YCHD) and their possible pathways for treating hepatic fibrosis based on network pharmacology. PPI data were extracted from DisGeNET, Genecards, CMGRN and PTHGRN to construct a weighted network using Cytoscape 3.9.1. The data of the chemical components in YCHD were obtained from Traditional Chinese Medicine Systems Pharmacology Database and Analysis Platform (TCMSP), and the potential active components and targets were selected using PreADMET Web server and SwissTargetPrediction. A fusion model was constructed to obtain the functional effect space and evaluate the effective proteins to identify the CFCG followed by GO and KEGG pathway enrichment analyses for all the targets. In cultured human hepatic stellate cells (LX-2 cells), the cytotoxicity of different compounds in YCHD was tested using CCK-8 assay; the effects of these compounds on collagen α1 (Col1a1) mRNA expression and the pathways in 20 ng/mL TGF-β1-stimulated cells were analyzed using RT-qPCR and Western blotting. A total of 1005 pathogenic genes, 226 potential active components and 1529 potential targets in YCHD and 52 potential targets of CFCG were obtained. Benzyl acetate, vanillic acid, clorius, polydatin, lauric acid and ferulic acid were selected for CCK-8 verification, and they all showed minimal cytotoxicity below the concentration of 200 μmol/L. Clorius, polydatin, lauric acid and ferulic acid all effectively inhibited TGF-β1-induced LX-2 cell activation. At the concentration of 200 μmol/L, all these 4 components inhibited PI3K, p-PI3K, AKT, p-AKT, ERK, p-ERK, P38 MAPK and p-P38 MAPK expressions in TGF-β1-induced LX-2 cells. The therapeutic effect of YCHD on hepatic fibrosis is probably mediated by its core functional components including benzyl acetate, vanillic acid, clorius, polydatin, lauric acid and ferulic acid, which inhibit the PI3K-AKT and MAPK pathways in hepatic stellate cells.