Spaces Of Type Research Articles

Boron-induced phase transformation of ternary cerium boron silicides

Samples of the alloys CeSi2–хBх (x = 0, 0.1, 0.2, 0.4, and 0.5) were prepared and their crystal structures, electrical and magnetic properties were determined. Depending on the amount of boron, x, the phases CeSi2–хBх crystallize in the α-ThSi2 structure type (x = 0, 0.1), or in the α-GdSi2 structure type (x = 0.2, 0.4). Interestingly, as determined by means of X-ray single crystal diffraction crystallizes, CeSi1·5B0.5 crystallizes in the AlB2 structure type (space group P6/mmm, a = 3.9922(2), c = 4.3053(4) Å, 191 reflections with Io ≥ 2σ(Io), R1 = 0.019, wR2 = 0.042). Measurements of the electrical and magnetic properties indicate that phases CeSi2-xBx (x = 0, 0.1, 0.2, 0.4, 0.5) are metallic in character and that phases with B substitution x ≥ 0.2 exhibit correlated magnetic behavior, typically below ∼15 K. Density functional theory calculations were performed to elucidate the change of electronic and physical properties upon boron substitution.

Quantum Chromodynamics and the Hyperbolic Unitary Group SUh(3)

The paper shows that it is possible to construct quantum chromodynamics as a rigorous theory on the basis of employment of hyperbolic unitary group SUh(3), which is a symmetry group for the three-dimensional complex space of the hyperbolic type. Such an approach allows researchers to discover a profound connection between conserved color charges of the quarks and the symmetries of the hyperbolic three-dimensional complex space. Further, it allows a correct introduction of the Hermitian operators to describe the eight gluons, which are carriers of strong interactions.

The exact solutions to a new type space reverse nonlocal Lakshmanan–Porserzian–Daniel equation

The exact solutions to a new type space reverse nonlocal Lakshmanan–Porserzian–Daniel equation

Concerning Fuzzy b-Metric Spaces †

In an article published in 2015, Hussain et al. introduced a notion of a fuzzy b-metric space and obtained some fixed point theorems for this kind of space. Shortly thereafter, Nădăban presented a notion of a fuzzy b-metric space that is slightly different from the one given by Hussain et al., and explored some of its topological properties. Related to Nădăban’s study, Sedghi and Shobe, Saadati, and Šostak independently conducted investigations in articles published in 2012, 2015, and 2018, respectively, about another class of spaces that Sedgi and Shobe called b-fuzzy metric spaces, Saadati, fuzzy metric type spaces, and Šostak, fuzzy k-metric spaces. The main contributions of our paper are the following: First, we propose a notion of fuzzy b-metric space that encompasses and unifies the aforementioned types of spaces. Our approach, which is based on Gabriec’s notion of a fuzzy metric space, allows us to simultaneously cover two interesting classes of spaces, namely, the 01-fuzzy b-metric spaces and the K-stationary fuzzy b-metric spaces. Second, we show that each fuzzy b-metric space, in our sense, admits uniformity with a countable base. From this fact, we derive, among other consequences, that the topology induced by means of its “open” balls is metrizable. Finally, we obtain a characterization of complete fuzzy b-metric spaces with the help of a fixed point result which is also proved here. In support of our approach, several examples, including an application to a type of difference equations, are discussed.

Inclusions and noninclusions of Hardy type spaces on certain nondoubling manifolds

In this paper we establish inclusions and noninclusions between various Hardy type spaces on noncompact Riemannian manifolds M with Ricci curvature bounded from below, positive injectivity radius and spectral gap.Our first main result states that, if L is the positive Laplace–Beltrami operator on M, then the Riesz–Hardy space HR1(M) is the isomorphic image of the Goldberg type space h1(M) via the map L1/2(I+L)−1/2, a fact that is false in Rn. Specifically, HR1(M) agrees with the Hardy type space X1/2(M) recently introduced by the first three authors; as a consequence, we prove that HR1(M) does not admit an atomic characterisation.Noninclusions are mostly proved in the special case where the manifold is a Damek–Ricci space S. Our second main result states that HR1(S), the heat Hardy space HH1(S) and the Poisson–Hardy space HP1(S) are mutually distinct spaces, a fact which is in sharp contrast to the Euclidean case, where these three spaces agree.

Assessing airborne transmission risks in COVID-19 hospitals by systematically monitoring SARS-CoV-2 in the air.

The continuous emergence of highly infectious SARS-CoV-2 variants with the capability of immune evasion demands more effective risk assessment and management approaches for infection prevention and control. Controlling nosocomial transmission is critical in response to the COVID-19 pandemic upon the resumption of day-to-day activities. Here, we systematically analyzed the presence of airborne SARS-CoV-2 in the isolation ward and within the contaminant, emergency, and clean zones of a designated COVID-19 hospital. A total of 359 air samples collected in the clean and emergency zones tested negative for SARS-CoV-2, demonstrating the interruption of airborne transmission in a designated COVID-19 hospital by combining the closed-loop management, unidirectional airflow, and negative pressure of isolation wards. In contrast, some air samples in the corridor outside the isolation wards tested positive for SARS-CoV-2. The leakage of virus-containing air from patient rooms to adjoining areas during rounds and meal delivery sheds light on the need for intensive and widespread virus monitoring in designated COVID-19 hospitals. In conclusion, by systematically monitoring viruses in the air, the study provides a starting point for the standardization of transmission risk management in designated hospitals for the future pandemic of a newly emerged respiratory infectious disease.IMPORTANCERisk management and control of airborne transmission in hospitals is crucial in response to a respiratory virus pandemic. However, the formulation of these infection control measures is often based on epidemiological investigations, which are an indirect way of analyzing the transmission route of viruses. This can lead to careless omissions in infection prevention and control or excessively restrictive measures that increase the burden on healthcare workers. The study provides a starting point for standardizing transmission risk management in designated hospitals by systemically monitoring viruses in the air of typical spaces in COVID-19 hospitals. The negative results of 359 air samples in the clean and emergency zones demonstrated the existing measures to interrupt airborne transmission in a designated COVID-19 hospital. Some positive cases in the corridor of the contaminant zone during rounds and meal delivery highlighted the importance of monitoring airborne viruses for interrupting nosocomial infection.

Mixed weak‐type inequalities in Euclidean spaces and in spaces of the homogeneous type

AbstractIn this paper, we provide mixed weak‐type inequalities generalizing previous results in an earlier work by Caldarelli and the second author and also in the spirit of earlier results by Lorente et al. One of the main novelties is that, besides obtaining estimates in the Euclidean setting, results are provided as well in spaces of the homogeneous type, being the first mixed weak‐type estimates that we are aware of in that setting.

N-Best kernel approximation in reproducing kernel Hilbert spaces

By making a seminal use of the maximum modulus principle of holomorphic functions we prove existence of n-best kernel approximation for a wide class of reproducing kernel Hilbert spaces of holomorphic functions in the unit disc, and for the corresponding class of Bochner type spaces of stochastic processes. This study thus generalizes the classical result of n-best rational approximation for the Hardy space and a recent result of n-best kernel approximation for the weighted Bergman spaces of the unit disc. The type of approximations have significant applications to signal and image processing and system identification, as well as to numerical solutions of the classical and the stochastic type integral and differential equations.

Adaptive graph fusion learning for multi-view spectral clustering

Multi-view data suffer from issues related to low quality and heterogeneity, which leads to instability issues in existing learning models for clustering. To overcome the limitations of traditional clustering methods, we propose a novel multi-view spectral clustering based on a contrastive feedback strategy. The proposed method constructs kernelized graphs to obtain higher-order feature representations, mapping primary sample data from different views into an isomorphic feature space and masking differences in type and structure between multiple views. In the meantime, the proposed method leverages a contrastive feedback optimization strategy based on mutual information to iteratively optimize the kernelized graphs of all views and their dynamically fused graph. This method effectively exploits the consistency and complementary information between multi-view, further improving the clustering accuracy. Experiments on multiple datasets demonstrate that the proposed method achieves satisfactory results in terms of clustering, validating the feasibility and effectiveness of the contrastive feedback strategy.

On the completeness of a system of decreasing elementary solutions for one class of fourth-order operator-differential equations on the semi-axis

In this work, we study a homogeneous fourth-order elliptic operator-differential equation with an unbounded operator under non-homogeneous boundary conditions on the semi-axis. We obtain sufficient conditions for the completeness of decreasing elementary solutions of the equation under study in the space of all its solutions from a fourth-order Sobolev type space.

On the uniqueness theorems for transmission problems related to models of elasticity, diffusion and electrocardiography

Abstract We consider a generalization of the inverse problem of the electrocardiography in the framework of the theory of elliptic and parabolic differential operators. More precisely, starting with the standard bidomain mathematical model related to the problem of the reconstruction of the transmembrane potential in the myocardium from known body surface potentials, we formulate a more general transmission problem for elliptic and parabolic equations in the Sobolev type spaces and describe conditions, providing uniqueness theorems for its solutions. Next, the new transmission problem is interpreted in the framework of the elasticity theory applied to composite media. Finally, we prove a uniqueness theorem for an evolutionary transmission problem that can be easily adopted to many models involving the diffusion type equations.

Consonant spaces of countable type and the Menger property

We investigate the connection between consonance and the Menger property. It has been shown that consonant metric spaces are Menger at infinity. We improve this result by showing that completely regular consonant spaces of countable type are Menger at infinity. This result will follow from a number of results about topological games in spaces that are more general than completely regular spaces.

Monte Carlo convergence rates for kth moments in Banach spaces

We formulate standard and multilevel Monte Carlo methods for the kth moment Mεk[ξ] of a Banach space valued random variable ξ:Ω→E, interpreted as an element of the k-fold injective tensor product space ⊗εkE. For the standard Monte Carlo estimator of Mεk[ξ], we prove the k-independent convergence rate 1−1p in the Lq(Ω;⊗εkE)-norm, provided that (i) ξ∈Lkq(Ω;E) and (ii) q∈[p,∞), where p∈[1,2] is the Rademacher type of E. By using the fact that Rademacher averages are dominated by Gaussian sums combined with a version of Slepian's inequality for Gaussian processes due to Fernique, we moreover derive corresponding results for multilevel Monte Carlo methods, including a rigorous error estimate in the Lq(Ω;⊗εkE)-norm and the optimization of the computational cost for a given accuracy. Whenever the type of the Banach space E is p=2, our findings coincide with known results for Hilbert space valued random variables.We illustrate the abstract results by three model problems: second-order elliptic PDEs with random forcing or random coefficient, and stochastic evolution equations. In these cases, the solution processes naturally take values in non-Hilbertian Banach spaces. Further applications, where physical modeling constraints impose a setting in Banach spaces of type p<2, are indicated.

The Tb theorem for some inhomogeneous Besov and Triebel-Lizorkin spaces over space of homogeneous type

In this paper, the authors give some new characterizations of the inhomogeneous Besov spaces and inhomogeneous Triebel-Lizorkin spaces respectively over space of homogeneous type, and establish the Tb theorems for the boundedness of the Calderón-Zygmund singular integral operator with non-convolution kernel on these new inhomogeneous Besov and Triebel-Lizorkin spaces.

Linear canonical wavelet transform and linear canonical wave packet transform on the Schwartz type spaces

Linear canonical wavelet transform and linear canonical wave packet transform on the Schwartz type spaces

Global existence of large solutions for the parabolic–elliptic Keller–Segel system in Besov type spaces

In this paper, we investigate global existence of large solutions for the parabolic–elliptic Keller–Segel system in the homogeneous Besov type spaces. A class of initial data was presented, generating a global smooth solution although the Ḃ∞,∞−2-norm of the initial data may be chosen arbitrarily large.

Weak Contractions via λ-sequences

In this note, we discuss a common fixed point for a family of self-mapping defined on a metric-type space and satisfying a weakly contractive condition. In our development, we make use of the λ-sequence approach and of a certain class of real-valued maps. We derive some implications for self-mappings on quasi-pseudometric type spaces.

Inner functions as strongly extreme points: stability properties

Given a Banach space \(\mathcal X\), let \(x\) be a point in ball\((\mathcal X)\), the closed unit ball of \(\mathcal X\). We say that \(x\) is a strongly extreme point of ball\((\mathcal X)\) if it has the following property: for every \(\varepsilon&gt;0\) there is \(\delta&gt;0\) such that the inequalities \(\|x\pm y\|&lt;1+\delta\) imply, for \(y\in\mathcal X\), that \(\|y\|&lt;\varepsilon\). We are concerned with certain subspaces of \(H^\infty\), the space of bounded holomorphic functions on the disk, that arise upon imposing finitely many linear constraints and can be viewed as small perturbations of \(H^\infty\). It is well known that the strongly extreme points of ball\((H^\infty)\) are precisely the inner functions, while the (usual) extreme points of this ball are the unit-norm functions \(f\in H^\infty\) with \(\log(1-|f|)\) non-integrable over the circle. Here we show that similar characterizations remain valid for our perturbed \(H^\infty\)-type spaces. Also, we investigate to what extent a non-inner function can differ from a strongly extreme point.

Characterization by approximation of homogeneous Besov and Triebel–Lizorkin type spaces

Characterization by approximation of homogeneous Besov and Triebel–Lizorkin type spaces

Evaluating the use of standing seam roof as beam lateral bracing

The standing seam roof (SSR) system is the most commonly used roof system for metal buildings in North America, wherein, SSR panels are attached to Z-shaped or C-shaped purlins with clips, which are in turn connected to rafters (i.e. roof beams). For the design of the rafters against lateral torsional buckling, bottom flange braces in conjunction with the purlin provide torsional bracing. Separately, the purlin provides some amount of lateral bracing to the rafter top flange; although, the degree to which the SSR system can restrain the purlin against lateral movement, and thus laterally brace the rafter, has not previously been studied. The objective of this study is to quantify the in-plane strength and stiffness of the SSR system and identify how this translational resistance can be used to provide lateral bracing to the rafter. A total of 11 standing seam roof specimens were tested to investigate the effects of different standing seam roof configurations: SSR panel type, clip type, thermal insulation, and purlin spacing, on the in-plane stiffness and strength of the SSR system. Results showed that the in-plane load-deformation behavior of SSR systems was governed by clip deformations, and that in-plane strength and stiffness is, therefore, particularly sensitive to SSR panel and clip type. A method for using these experimental results in calculations of rafter bracing is described and can lead to reduced size and frequency of bottom flange braces.