Framework Of Spaces Research Articles

Quantitative estimates for Durrmeyer-sampling series in Orlicz spaces

In this paper, we establish a quantitative estimate for Durrmeyer-sampling type operators in the general framework of Orlicz spaces, using a suitable modulus of smoothness defined by the involved modular functional. As a consequence of the above result, we can deduce quantitative estimates in several instances of Orlicz spaces, such as L^p-spaces, Zygmund spaces and the exponential spaces. By using a direct approach, we also provide a further estimate in the particular case of L^p-spaces, with 1le p <+infty , that turns out to be sharper than the previous general one. Moreover, we deduce the qualitative order of convergence, when functions belonging to suitable Lipschitz classes are considered.

Confinement and spatial entanglement: phenomenology of a new interference principle

Recently, the novel confinement principle in spatially-structured Lorentzian wells was reported to describe in a unified way the interference of classical waves and singular quantum particles in a causal framework in ordinary space. The phenomenology derived from this principle offers significant advantages over the conventional classical and quantum formalisms of interference founded on wave superposition. This paper presents a conceptual analysis of such a principle and its main implications indicating its fundamental differences from the standard descriptions.

The role of cultural safety and ethical space within postcolonial healthcare for Maasai in Tanzania

The history of the Maasai tribe in northern Tanzania is characterised by marginalisation, discrimination and political subjugation. Inequities, enacted through power relations, influence healthcare access, practices and outcomes among the...

The Issue of Ethnic Formation of the Population of the Southern Regions of Uzbekistan in the Works of B.Kh.Karmisheva

It is known that the territory of Uzbekistan is a developed region, preserving its autochthonous basis as a result of long-lasting historical and ethnic processes. The socio-cultural basis of the Uzbek people formed in this ancient region was created in the distant past and has followed its own historical path. Undoubtedly, the formation of the Uzbek nation did not take place within the framework of one country or a small region, but within the framework of the vast space in which the Uzbek people historically formed and developed - the Central Asian region.

Reciprocal space study of Heisenberg exchange interactions in ferromagnetic metals

The modern quantum theory of magnetism in solids is getting commonly derived using Green's functions formalism. The popularity draws itself from remarkable opportunities to capture the microscopic landscape of exchange interactions, starting from a tight-binding representation of the electronic structure. Indeed, the conventional method of infinitesimal spin rotations, considered in terms of local force theorem, opens vast prospects of investigations regarding the magnetic environment, as well as pairwise atomic couplings. However, this theoretical concept practically does not devoid of intrinsic inconsistencies. In particular, naturally expected correspondence between single and pairwise infinitesimal spin rotations is being numerically revealed to diverge. In this work, we elaborate this question on the model example and canonical case of bcc iron. Our analytical derivations discovered the principal preference of on-site magnetic precursors if the compositions of individual atomic interactions are in focus. The problem of extremely slow or even absent spatial convergence while considering metallic compounds was solved by suggesting the original technique, based on reciprocal space framework. Using fundamental Fourier transform-inspired interconnection between suggested technique and traditional spatial representation, we shed light on symmetry breaking in bcc Fe on the level of orbitally decomposed total exchange surrounding.

Decay estimates of solutions to nonlinear elastic wave equations with viscoelastic terms in the framework of Lp-Sobolev spaces

The Cauchy problem for nonlinear elastic wave equations with viscoelastic damping terms is investigated in the Lp framework. Sharp estimates of the global solutions in t for the higher order derivatives are established. The proof is based on the Gronwall type argument for 1<p<∞, the use of the difference of the propagation speed of the fundamental solutions for p=1 and the bootstrap argument for p=∞, combined with the sharp estimates for the linearized solutions.

Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results

This paper deals with the question of achieving a suitable extension of the notion of Suzuki-type contraction to the framework of quasi-metric spaces, which allows us to obtain reasonable fixed point theorems in the quasi-metric context. This question has no an easy answer; in fact, we here present an example of a self map of Smyth complete quasi-metric space (a very strong kind of quasi-metric completeness) that fulfills a simple and natural contraction of Suzuki-type but does not have fixed points. Despite it, we implement an approach to obtain two fixed point results, whose validity is supported with several examples. Finally, we present a general method to construct non-T1 quasi-metric spaces in such a way that it is possible to systematically generate non-Banach contractions which are of Suzuki-type. Thus, we can apply our results to deduce the existence and uniqueness of solution for some kinds of functional equations which is exemplified with a distinguished case.

A Data Quality Framework for the European Health Data Space for secondary use

Abstract A cornerstone in the development of the European Health Data Space for secondary use of data (EHDS2) is the design, implementation and assessment of a Data Quality Framework (DQF). Consistently, the Joint Action TEHDAS has a dedicated work program where, learning from others’ experiences across Europe and abroad, the work package is building the concepts and methods for such a DQF. The scope of this work program is to provide recommendation to the Member States and the European Commission on the concept of DQF to foster, where (institutions) the DQF should be implemented, when in data life cycle, how should be implemented and by whom. In terms of the concept, the DQF raises the importance of quality assurance procedures at data processor level and the level of quality of the data collections in terms of reliability, relevance, timeliness, coherence, coverage and completeness. When it comes to when along the data life cycle, DQF is expected operate when data needs harmonization at data processor level (ie, the effective application of interoperability standards), in the publication of the data sources (ie providing users knowledge on the provenance of data and the content of data source); or, when data sources have to be integrated and sensitive data pseudonymized (ie, the quality of the linkage and losses after pseudonymisation). Finally, when it comes to the methodology, TEHDAS suggests a three-fold approach - some quality measures in the DQF could be translated into legislation (eg, the requirement of regular auditing for a data processor to be a trusted party in the EDHS2); some could be kept as good-practices (eg, recommendation of archival procedures when a research project finalizes); and, under the assumption of continuous data quality improvement, an assessment, benchmarking and promotion methodology (eg, a grading system at data processor level).

Optimal Recovery from Inaccurate Data in Hilbert Spaces: Regularize, But What of the Parameter?

In Optimal Recovery, the task of learning a function from observational data is tackled deterministically by adopting a worst-case perspective tied to an explicit model assumption made on the functions to be learned. Working in the framework of Hilbert spaces, this article considers a model assumption based on approximability. It also incorporates observational inaccuracies modeled via additive errors bounded in $$\ell _2$$ . Earlier works have demonstrated that regularization provides algorithms that are optimal in this situation, but did not fully identify the desired hyperparameter. This article fills the gap in both a local scenario and a global scenario. In the local scenario, which amounts to the determination of Chebyshev centers, the semidefinite recipe of Beck and Eldar (legitimately valid in the complex setting only) is complemented by a more direct approach, with the proviso that the observational functionals have orthonormal representers. In the said approach, the desired parameter is the solution to an equation that can be resolved via standard methods. In the global scenario, where linear algorithms rule, the parameter elusive in the works of Micchelli et al. is found as the byproduct of a semidefinite program. Additionally and quite surprisingly, in case of observational functionals with orthonormal representers, it is established that any regularization parameter is optimal.

(ψ,ϕ)-Contractions under a Class of Transitive Binary Relations

The present article is devoted to prove some fixed point results for (ψ,ϕ)-contractions in the framework of metric space equipped with a locally finitely G-transitive relation. The results proved in this article improve and weaken some existing fixed point results available in the literature. Finally, an example is provided for attesting to the credibility of my results.

A Fixed Point Approach to Lattice Fuzzy Set via F-Contraction

In this work, we design and demonstrate the occurrence of L-fuzzy common fixed points of L-fuzzy mappings (L-FM) meeting contractive criteria in the framework of complete b-metric spaces (b-MS) employing F-contractions and a certain class of continuous functions. We also conduct a case study to determine the implementation of our derived principles. A few other concepts which are the direct consequences of our findings are explained in this paper.

Asynchronous functional linear regression models for longitudinal data in reproducing kernel Hilbert space.

Motivated by the analysis of longitudinal neuroimaging studies, we study the longitudinal functional linear regression model under asynchronous data setting for modeling the association between clinical outcomes and functional (or imaging) covariates. In the asynchronous data setting, both covariates and responses may be measured at irregular and mismatched time points, posing methodological challenges to existing statistical methods. We develop a kernel weighted loss function with roughness penalty to obtain the functional estimator and derive its representer theorem. The rate of convergence, a Bahadur representation, and the asymptotic pointwise distribution of the functional estimator are obtained under the reproducing kernel Hilbert space framework. We propose a penalized likelihood ratio test to test the nullity of the functional coefficient, derive its asymptotic distribution under the null hypothesis, and investigate the separation rate under the alternative hypotheses. Simulation studies are conducted to examine the finite-sample performance of the proposed procedure. We apply the proposed methods to the analysis of multitype data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, which reveals significant association between 21 regional brain volume density curves and the cognitive function. Data used in preparation of this paper were obtained from the ADNI database (adni.loni.usc.edu).

Fixed point theorems for F- contraction mapping in complete rectangular M-metric space

In this paper, we prove a fixed point result for F- contraction principle in the framework of rectangular M-metric space. An example is also adopted to exhibit the utility of our result. Finally, we apply our fixed point result to show the existence of solution of Fredholm integral equation.

Sequential estimation of temporally evolving latent space network models

Dynamic network data describe interactions among a fixed population through time. This data type can be modelled using the latent space framework, where the probability of a connection forming is expressed as a function of low-dimensional latent coordinates associated with the nodes, and sequential estimation of model parameters can be achieved via Sequential Monte Carlo (SMC) methods. In this setting, SMC is a natural candidate for estimation which offers greater scalability than existing approaches commonly considered in the literature, allows for estimates to be conveniently updated given additional observations and facilitates both online and offline inference. A novel approach to sequentially infer parameters of dynamic latent space network models is proposed by building on techniques from the high-dimensional SMC literature. The scalability and performance of the proposed approach is explored via simulation, and the flexibility under model variants is demonstrated. Finally, a real-world dataset describing classroom contacts is analysed using the proposed methodology.

Phase transition and quantum corrections of quintessential Kerr–Newman black hole with cloud of strings

The purpose of this manuscript is to inspecting the phase transition and the critical phenomenon of charged quintessential Kerr-Newman-anti-de Sitter black hole with cloud of strings. In this regard, we evaluate the thermodynamic factors (Hawking temperature, angular momentum and entropy) in the framework of extended phase space. These factors fulfill the Smarr-Gibbs-Dehum equation in the existence of quintessence and cloud of strings. The critical behavior of thermodynamic factors is discussed via two techniques such as Maxwell equal-area law and Van-der Waal like equation of state . It is obtained that the former one is more effective to observe the critical nature of the complex black holes. Further, we study the phase diagram in T − S plane using equal-area law and obtain an isobar depicting the coexistence era of two phases. It is concluded that black holes lower than the critical temperature exhibit the phase transition same as that of Van-der Waal fluid. At the end, we analyze the influence of thermal variations on the black hole’s stability. • We inspect the critical phenomenon of quintessential string Kerr-Newman-AdS BH. • The critical behavior via Maxwell equal-area law and Van-der Waal EoS is studied. • Below the critical temperature, BHs show the VdW fluid like phase transition. • At the end, we analyze the influence of thermal variations on the black hole’s stability.

A modified Mann algorithm for the general split problem of demicontractive operators

This work proposes a novel method for solving the general split common fixed point problem of demicontractive operators in the framework of real Hilbert spaces. Our proposed technique is principally based on the Mann algorithm. The proof of the weak convergence theorem is additionally established under some particular conditions. We subsequently verify the convergence of our algorithm via numerical examples.

Invariance of the Gibbs measures for periodic generalized Korteweg-de Vries equations

In this paper, we study the Gibbs measures for periodic generalized Korteweg-de Vries equations (gKdV) with quartic or higher nonlinearities. In order to bypass the analytical ill-posedness of the equation in the Sobolev support of the Gibbs measures, we establish deterministic well-posedness of the gauged gKdV equations within the framework of the Fourier-Lebesgue spaces. Our argument relies on bilinear and trilinear Strichartz estimates adapted to the Fourier-Lebesgue setting. Then, following Bourgain’s invariant measure argument, we construct almost sure global-in-time dynamics and show invariance of the Gibbs measures for the gauged equations. These results can be brought back to the ungauged side by inverting the gauge transformation and exploiting the invariance of the Gibbs measures under spatial translations. We thus complete the program initiated by Bourgain [Comm. Math. Phys. 166 (1994), pp 1–26] on the invariance of the Gibbs measures for periodic gKdV equations.

Extracting Chinese events with a joint label space model.

The task of event extraction consists of three subtasks namely entity recognition, trigger identification and argument role classification. Recent work tackles these subtasks jointly with the method of multi-task learning for better extraction performance. Despite being effective, existing attempts typically treat labels of event subtasks as uninformative and independent one-hot vectors, ignoring the potential loss of useful label information, thereby making it difficult for these models to incorporate interactive features on the label level. In this paper, we propose a joint label space framework to improve Chinese event extraction. Specifically, the model converts labels of all subtasks into a dense matrix, giving each Chinese character a shared label distribution via an incrementally refined attention mechanism. Then the learned label embeddings are also used as the weight of the output layer for each subtask, hence adjusted along with model training. In addition, we incorporate the word lexicon into the character representation in a soft probabilistic manner, hence alleviating the impact of word segmentation errors. Extensive experiments on Chinese and English benchmarks demonstrate that our model outperforms state-of-the-art methods.

On the permutative equivalence of squares of unconditional bases

We prove that if the squares of two unconditional bases are equivalent up to a permutation, then the bases themselves are permutatively equivalent. This settles a twenty-five year-old question raised by Casazza and Kalton in [13]. Solving this problem provides a new paradigm to study the uniqueness of unconditional basis in the general framework of quasi-Banach spaces. Multiple examples are given to illustrate how to put in practice this theoretical scheme. Among the main applications of this principle we obtain the uniqueness of unconditional basis up to permutation of finite sums of spaces with this property, as well as the first addition to the scant list of the known Banach spaces with a unique unconditional bases up to permutation since [14].

A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on 𝑅𝐶𝐷(𝐾,𝑁) spaces

In the framework of (possibly non-smooth) metric measure spaces with Ricci curvature bounded below by a positive constant in a synthetic sense, we establish a sharp and rigid reverse-Hölder inequality for first eigenfunctions of the Dirichlet Laplacian. This generalises to the positively curved and non-smooth setting the classical “Chiti Comparison Theorem”. We also prove a related quantitative stability result which seems to be new even for smooth Riemannian manifolds.