Spaces Of Type Research Articles

Bilinear Calderón-Zygmund operator and its commutator on some variable exponent spaces of homogeneous type

Let $(X,d,\mu)$ be a space of homogeneous type in the sense of Coifman and and Weiss. In this setting, the author proves that a bilinear Calderon-Zygmund operator is bounded from the product of variable exponent Lebesgue spaces $L^{p_{1}(\cdot)}(X)\times L^{p_{2}(\cdot)}(X)$ into spaces $L^{p(\cdot)}(X)$, and it is bounded from the product of variable exponent generalized Morrey spaces $\mathcal{L}^{p_{1}(\cdot),\varphi_{1}}(X)\times \mathcal{L}^{p_{2}(\cdot),\varphi_{2}}(X)$ into spaces $\mathcal{L}^{p(\cdot),\varphi}(X)$, where the Lebesgue measure functions $\varphi(\cdot,\cdot), \varphi_{1}(\cdot,\cdot)$ and $\varphi_{2}(\cdot,\cdot)$ satisfy $\varphi_{1}\times\varphi_{2}=\varphi$, and $\frac{1}{p(\cdot)}=\frac{1}{p_{1}(\cdot)}+\frac{1}{p_{2}(\cdot)}$. Furthermore, by establishing sharp maximal estimate for the commutator $[b_{1},b_{2},BT]$ generated by $b_{1}, b_{2}\in\mathrm{BMO}(X)$ and $BT$, the author shows that the $[b_{1},b_{2},BT]$ is bounded from the product of spaces $L^{p_{1}(\cdot)}(X)\times L^{p_{2}(\cdot)}(X)$ into spaces $L^{p(\cdot)}(X)$, and it is also bounded from product of spaces $\mathcal{L}^{p_{1}(\cdot),\varphi_{1}}(X)\times \mathcal{L}^{p_{2}(\cdot),\varphi_{2}}(X)$ into spaces $L^{p(\cdot),\varphi}(X)$.

Static spacers play a crucial role in the treatment of complex periprosthetic joint infections of the knee.

To determine the superior spacer design, a growing number of studies are comparing treatment results between patients having been treated with articulating and static knee spacers in the setting of two-stage revision for periprosthetic joint infection (PJI). In contrast, the primary objective of this study was to compare preoperative characteristics between patients from both spacer groups and examine whether significant differences were present prior to spacer implantation. This retrospective, single-centre, cohort study examined the preoperative situation of 80 consecutive knee PJIs between 2017 and 2020. All patients underwent two-stage revision, with 35 (44%) receiving an articulating and 45 (56%) a static spacer. No significant differences were observed in terms of patient gender (p = 0.083), age (p = 0.666), comorbidity (p = 0.1) and preoperative clinical function (p = 0.246). Static spacers were significantly more often used in the presence of a periarticular fistula (p = 0.033), infection of a revision implant (p < 0.001), higher degree of bone loss (p < 0.001) and infection caused by a difficult-to-treat pathogen (p = 0.038). Complication and revision rates were similar for both spacer types during the interim period, while patients with articulating spacers demonstrated a superior clinical function (p < 0.001) during the interim period and after reimplantation. Static spacers are being utilised in significantly more complex and unfavourable preoperative scenarios. Therefore, a preoperative selection bias may be at least partially accountable for any disparities observed in postoperative outcomes. To achieve the best possible results, surgeons should know and respect the distinct indications of static and articulating spacers and consequently understand and use them as complementary surgical options. Level III.

Weighted estimates for product singular integral operators in Journé’s class on RD-spaces

Abstract An RD-space 𝑀 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in 𝑀. In this paper, firstly, the authors give the Plancherel–Pôlya characterization of product weighted Triebel–Lizorkin spaces and product weighted Besov spaces on RD-spaces and make some estimates for the product singular integral operators in Journé’s class on these function spaces. As a result of these conclusions, they present some sufficient conditions for the boundedness of product singular integral operators on the product Lipschitz spaces and product weighted Hardy spaces. Secondly, by the boundedness of lifting and projection operators, they also obtain that the dual spaces of the product weighted Hardy spaces are product weighted Carleson measure spaces. Using the idea of dual, the authors obtain the weighted boundedness of singular integral operators on the product weighted Carleson measure spaces.

Multiplication between elements in martingale Hardy spaces and their dual spaces

In the first part of the paper, we establish continuous bilinear decompositions that arise in the study of products between elements in martingale Hardy spaces Hp(0<p⩽1) and functions in their dual spaces. Our decompositions are based on martingale paraproducts. The second part of the paper concerns applications of the method developed for the classical martingales in the first part. In particular, we build a connection between Hardy spaces on spaces of homogenous type equipped with a doubling measure and Hardy spaces with respect to the corresponding dyadic martingales. Using the method introduced in the first part, we obtain analogous results for dyadic martingales on spaces of homogenous type, which, thanks to the aforementioned connection, yield conclusions for products between elements in Hardy spaces and those in their duals on spaces of homogenous type. The key property of martingale Hardy spaces in the study is that they admit the atomic decomposition, for which we provide an interpretation via duality.

Foundations of the wald space for phylogenetic trees

AbstractEvolutionary relationships between species are represented by phylogenetic trees, but these relationships are subject to uncertainty due to the random nature of evolution. A geometry for the space of phylogenetic trees is necessary in order to properly quantify this uncertainty during the statistical analysis of collections of possible evolutionary trees inferred from biological data. Recently, the wald space has been introduced: a length space for trees which is a certain subset of the manifold of symmetric positive definite matrices. In this work, the wald space is introduced formally and its topology and structure is studied in detail. In particular, we show that wald space has the topology of a disjoint union of open cubes, it is contractible, and by careful characterisation of cube boundaries, we demonstrate that wald space is a Whitney stratified space of type (A). Imposing the metric induced by the affine invariant metric on symmetric positive definite matrices, we prove that wald space is a geodesic Riemann stratified space. A new numerical method is proposed and investigated for construction of geodesics, computation of Fréchet means and calculation of curvature in wald space. This work is intended to serve as a mathematical foundation for further geometric and statistical research on this space.

Prototypes of SARS-CoV-2 virus “traps” based on enterosorbents

Background. Despite the ongoing mutations of the SARS-CoV-2 virus, the causative agent of the COVID-19 disease, its mechanism of entry into the cell remains unchanged, which can be used to create virus “traps”. Intravenous medications aggravate the symptoms of the disease. An alternative means of combating the virus could be enterosorbents synthesized on nanosized carriers that intercept SARS-CoV-2 directly at the site of its introduction into the body, namely in the gastrointestinal tract. Objective. To study and refine the methods of synthesis of different spacer types on the surface of aerosil nanoparticles, immobilization of model protein with the possibility of using the compounds as enterosorbents of SARS-CoV-2 virus. Design and method. Aerosil A-200 grade was used as carrier nanoparticles. The chemical composition of the obtained compounds was studied by FTIR spectroscopy. The absorption spectra of the samples were studied using a spectrophotometer. The dimensions of nano-objects were determined by dynamic light scattering. Qualitative and quantitative determination of protein chemisorption on the synthesized particles was carried out. Results. Prototypes of SARS-CoV-2 enterosorbents on aerosil particles were developed. The efficacy of the spacers was tested on the model protein, albumin. Conclusion. Further research may be directed to the development of an oral drug that reduces the viral load of SARS-CoV-2.

Effects of thermal and acoustic environments on human comfort in urban and suburban campuses in the cold region of China.

In this study, we investigated the effects of thermal-acoustic environments on human comfort in a cold region by focusing on Xi'an in China as a representative city. Four typical open spaces were identified within two universities, with one located in an urban area and the other in a suburban area. Surveys were conducted using questionnaires and environmental parameters were measured to assess thermal-acoustic perception. The physiological equivalent temperature (PET) and noise sound pressure levels were employed to measure the thermal-acoustic environments in the four open spaces. The results showed that the neutral PET was 19.1°C in Xi'an from March to May, and the neutral temperature range was 14.9-23.4°C. The preferred temperature was 20.0°C. Acoustic sensation votes were lower in suburban areas than urban areas. Respondents in urban areas exhibited significantly higher sensitivity to the thermal and acoustic environments compared with those in suburban areas. Sensitivity to the thermal environment decreased as the environmental noise levels decreased. The temperature perceived as most suitable increased as the sensitivity to the thermal environment decreased. Acoustic comfort evaluations were generally higher in colder and warmer environments. Warmer environments heightened the sensitivity to the acoustic environment and this effect gradually decreased as the sound pressure levels increased. Thus, based on empirical analyses, we compared the effects of outdoor thermal-acoustic parameters on comfort to provide experimental data support for further outdoor thermal comfort research.

An integrated assessment method of real-time source term for high temperature gas-cooled reactor

To address high temperature gas-cooled reactor (HTR) nuclear power plant (NPP) safety analysis and emergency response, this paper proposes an integrated source term assessment (ISTA) method, guided by the principles of reality, rapidity and rationality. The fundamental concept of ISTA is to establish a connection between the theoretical model of source term (ST) calculation and actual conditions of HTR NPPs. According to the ISTA method, STs can be evaluated by mapping key parameters through monitoring variables during any abnormal operational conditions or accident conditions, resulting in a more realistic representation. Furthermore, the output of STs in various typical spaces within an HTR NPP further expands the application scope beyond the development of nuclear emergency protection strategies. In addition, a corresponding tool (ISTAT) for engineering application is developed and the case is given to verify the feasibility. This research highlights the technological advancement affecting radiological release scenarios and avoiding unnecessary conservatism, which also can give reference for other advanced reactor NPPs.

Embeddings of a Multi-Weighted Anisotropic Sobolev Type Space

Parameters such as various integral and differential characteristics of functions, smoothness properties of regions and their boundaries, as well as many classes of weight functions cause complex relationships and embedding conditions for multi-weighted anisotropic Sobolev type spaces. The desire not to restrict these parameters leads to the development of new approaches based on the introduction of alternative definitions of spaces and norms in them or on special localization methods. This article examines the embeddings of multi-weighted anisotropic Sobolev type spaces with anisotropy in all the defining characteristics of the norm of space, including differential indices, summability indices, as well as weight coefficients. The applied localization method made it possible to obtain an embedding for the case of an arbitrary domain and weights of a general type, which is important in applications in differential operators’ theory, numerical analysis.

On the Legal Concept of Metaverses

The paper offers a detailed model of the legal concept of metaverses. The scientific impetus for this discourse was the foreign practice of developing metaverses, which have become national priorities for a number of states. According to the author’s position, the metaverse is a direction (area) of digital technology development for the formation of a digital space for various types of social and public activities with imitation of the personal presence of the user. The components of the metaverse interact with each other, are in dynamic balance, creating a digital industry. The industry of the metaverse is at a stage of continuous evolution and development. It consists of five main systems, including a technological system, a system of standards, a system of digital products, a service and warranty system. Based on this conclusion, the author systematizes approaches to the development of legal regulation of relations in the metaverses in order to consolidate the country’s technological leadershipin this promising direction. As the metaverse evolves, it may become a promising space for the circulation of digital data and the implementation of other ambitious projects of the digital economy. However, the emergence of new threats and risks in artificial virtual worlds requires the development and adoption of a concept of legal understanding of metaverses, as well as the advanced study of Russian legislation guaranteeing human rights and freedoms in metaverses.

A Study on the Dust Retention Effect of the Vegetation Community in Typical Urban Road Green Spaces—In the Case of Ying Tian Street in Nanjing City

This study aimed to investigate the association between the plant community structure, leaf surface microstructure, nutrient element content, and the dust-retention capacity of garden plants in urban road green spaces. The plant community located along Ying Tian Street in Nanjing City was selected as the focal point of the investigation. Random sampling was performed on the urban road green spaces, determining the amount of dust trapped in plant leaves. Subsequently, the microstructure of the leaf surface was observed, and the content of nutrient elements in the plant leaves was determined. The study also entailed an analysis of the interrelationships between the leaf surface microstructure, plant nutrient element content, and the dust-retention ability of the plants. The findings of this study revealed notable variations in the dust-retention capacity of garden plants and the community structure observed along Ying Tian Street. Among the tree species, Cedrus deodara and Ginkgo biloba exhibited a remarkable dust-retention ability per unit leaf area. Among the shrub species, Abelia × grandiflora and Loropetalum chinense displayed a strong dust-retention capacity per unit leaf area. Similarly, Ophiopogon japonicus and Cynodon dactylon exhibited a robust dust-retention ability per unit leaf area among the herbaceous plants. Furthermore, the dust-retention ability of the plants exhibited a strong positive correlation with the dimensions of leaf stomata, specifically the length and width, while displaying a moderate positive correlation with the width of grooves on the upper and lower surfaces of the leaves. Conversely, the thickness of the leaves did not exhibit a significant correlation. Additionally, the nitrogen content of the leaves exerted a significant influence on the dust-retention ability of the plants (p &lt; 0.05), although the phosphorus and potassium content factors did not exhibit a significant influence (p &gt; 0.05). Based on the findings, it is recommended to prioritize the utilization of plants with robust dust-retention abilities, such as C. deodara, A. grandiflora, O. japonicus, and C. dactylon, and implement a mixed planting approach encompassing a combination of trees, shrubs, and herbaceous plants within urban road green spaces.

Product type operators acting between weighted Bergman spaces and Bloch type spaces

Product type operators acting between weighted Bergman spaces and Bloch type spaces

Novel secondary pyridinyl amides: Synthesis, in vitro antiproliferative screenings, and molecular docking studies

A novel series of secondary pyridinyl amides, reinforced with the methylsulfonyl pharmacophore unit, was designed and synthesized. Further, we determined the antiproliferative activities of these compounds through experimental assays and analyzed their interactions with Breakpoint Cluster Region/Abelson (bcr/abl), Epidermal Growth Factor Receptor (EGFR), and Human Epidermal Growth Factor Receptor 2 (HER2) tyrosine kinases using molecular autodocking techniques. We grouped these amides into three categories, classified by the type of spacer that binds the pyridine ring to the amide nitrogen atom. Additionally, within each group, we strategically positioned the amide moiety at the ortho, meta, or para position on the pyridyl ring. Among the studied amides, compound 3 exhibited the best overall antiproliferative activity against human immortalized myelogenous leukemia (K562) (IC50 = 26 µM), human leukemia monocytic cell line (THP-1) (IC50 = 81 µM), and human hepatocellular carcinoma (HepG2) (IC50 = 210 µM). Molecular docking studies revealed that compound 3 binds effectively to bcr/abl, EGFR, and HER2 tyrosine kinases, demonstrating strong interactions with crucial active site amino acids, indicative of its targeted antiproliferative mechanism. All investigated compounds showed either very minor or no cytotoxicity against human dermal fibroblast adult cells.

Infinite energy harmonic maps from quasi-compact Kähler surfaces

Abstract We construct infinite energy harmonic maps from a quasi-compact Kähler surface with a Poincaré-type metric into an NPC space. This is the first step in the construction of pluriharmonic maps from quasiprojective varieties into symmetric spaces of non-compact type, Euclidean and hyperbolic buildings and Teichmüller space.

A new weighted spectral geometric mean and properties

In this paper, we introduce a new weighted spectral geometric mean: \begin{equation*}\label{F-mean}F_t(A,B)= (A^{-1}\sharp_t B)^{1/2} A^{2-2t} (A^{-1} \sharp_t B)^{1/2}, \quad t\in [0,1],\end{equation*} where $A$ and $B$ are positive definite matrices. We study basic properties and inequalities for $F_t(A, B)$. We also establish the Lie-Trotter formula for $F_t(A, B)$. Finally, we extend some of the results on $F_t(A, B)$ to symmetric space of noncompact types.

Testing of Electromigration Resistance of Copper and Silver Thick Films

This paper is focused on the electromigration resistance of copper and silver thick films. Electromigration was tested by water drop test. Four common conductive thick film pastes were used for testing – silver paste with low platinum content, and two silver pastes with different content of palladium and copper paste. Electromigration was tested under voltage of 6 and 12 V and time to shortcut was measured. Results of testing including the comparison of electromigration resistance depending on thick film paste type and different electrode spacing are described in this paper.

Identification of urban green space availability and utilization in Semarang City

Background: Urban green space land a has been used differently because of Semarang City's rapid development in several sectors, including industry, transportation, and economics. Gajahmungkur Subdistrict determined that the minimum urban green space requirement of 30% had been reached. Methods: The method used in this research is quantitative method with remote sensing. Quantitative methods are used as systematic, rational, measurable, objective, and concrete methods. Findings: However, the identification results may not represent the total amount of urban green space in the village. Conclusion: Therefore, using remote sensing satellite image interpretation of Sampangan Village, the results of urban green space identification amounted to 22.97 ha or 22.6% of the 77.4% non-urban green space area with most of the land being urban green space of riparian type connected to Sampangan Park as a form of utilizing riparian urban green space which is frequently used by visitors to traders. In addition, Kelurahan Sampangan has urban green space utilization in the form of river borders, Sampangan Park, Sampangan Mitra Field, UNNES Labschool Elementary School sports field, Wotgaleh Cemetery, and parking lots. Sampangan Village only has 22.6% of the required minimum of 30% of urban green space, so it still falls short of the standard. Thus, efforts are needed to increase the provision of urban green space in Sampangan Village to become a residential area that is suitable for people to live in from an environmental aspect.

Hausdorff operators on some classical spaces of analytic functions

Abstract In this note, we start on the study of the sufficient conditions for the boundedness of Hausdorff operators $$ \begin{align*}(\mathcal{H}_{K,\mu}f)(z):=\int_{\mathbb{D}}K(w)f(\sigma_w(z))d\mu(w)\end{align*} $$ on three important function spaces (i.e., derivative Hardy spaces, weighted Dirichlet spaces, and Bloch type spaces), which is a continuation of the previous works of Mirotin et al. Here, $\mu $ is a positive Radon measure, K is a $\mu $ -measurable function on the open unit disk $\mathbb {D}$ , and $\sigma _w(z)$ is the classical Möbius transform of $\mathbb {D}$ .

Numerical investigation on boiling crisis in a full-length 5 × 5 fuel assembly under typical pressurized water reactor conditions

Critical heat flux (CHF) presents a research priority in the Pressurized Water Reactor (PWR) safety, as it can lead to the severe accidents and release radioactive materials. In this study, a wall heat flux partition model, proposed by Demarly [1], was employed within the two-fluid model by Computational Fluid Dynamics (CFD) methodology to investigate the characteristics of CHF under typical PWR conditions. A multi-scale interface model was coupled to consider the interfacial transfers in bulk flow during flow regime transition. The models were validated by using experimental data on subcooled flow boiling, boiling crisis in vertical tubes, and rod bundles. The PWR sub-channel and bundle test (PSBT) benchmark, comprising a full-length 5 × 5 fuel assembly with three different types of spacers, was simulated in this study. The CHF value was evaluated, demonstrating an acceptable accuracy compared to the experimental data, with a deviation of less than 10 % in the selected conditions. The CHF location in the cross section was successfully predicted by CFD approach, while the axial location of CHF was underestimated than experimental measurement. Besides, the impacts of mixing vanes with different deflection angles on boiling heat transfer characteristics were analyzed, revealing the crucial role of mixing vanes in the distribution of vapor and dry-patch area fraction in both the circumferential and flow directions.

Experimental and Numerical Analysis for Eccentricity Solution in Double-Layer Space Truss

This paper shows an extensive study on the Typical Connections used in Double-Layer Space Truss. For this structural system, the ends of the bars are flattened to connect the bars. However, the flattening process results in a highly plastic stamping zone susceptible to warping with the appearance of two eccentricities, one of which causes rotation of the connection, with the presence of a bending moment with local rupture resulting in progressive collapse of the entire coverage system, as already evidenced in several countries. Therefore, eccentricity in this paper is studied and an analytical solution to the problem is presented through the use of a new device called a spacer. Furthermore, a preliminary study with complex numerical simulation was carried out with nonlinear analysis in ABAQUS were evaluated. For this study, nine space trusses were experimentally tested with reinforcement spacer in reduced trusses. After confirming the efficiency of the spacer proposal, another six space trusses were tested in the laboratory, this time, on a full-scale. In this study, two types of spacers were evaluated, one made of USI SAC 350 steel and another cheaper one made from recycled tires from heavy vehicles with multiple filaments of steel and nylon wires in the rubber layers. The two devices presented very close resistance capacity values, with a resistance gain of approximately 30% in relation to connections without reinforcement, with structural failure characterized by buckling of the bars. Finally, a numerical study of space trusses with spacers was developed. In practical design terms, from these FE simulations it was possible to determine the normal stresses for different spacers applied in the different modeled spans.