Mapping Properties Research Articles

On sharp heat kernel estimates in the context of Fourier–Dini expansions

We prove sharp estimates of the heat kernel associated with Fourier–Dini expansions on (0,1) equipped with Lebesgue measure and the Neumann condition imposed on the right endpoint. Then we give several applications of this result including sharp bounds for the corresponding Poisson and potential kernels, sharp mapping properties of the maximal heat semigroup and potential operators and boundary convergence of the Fourier–Dini semigroup.

Hardy–Littlewood maximal operator in a new vanishing Orlicz–Morrey space

We study mapping properties of maximal operator in a new vanishing subspace of Orlicz–Morrey spaces. We show that the vanishing property defining that subspace is preserved under the action of maximal operator. As an application, we also investigate the behavior of fractional operators.

Electrographic flow mapping of atrial fibrillation.

A low ceiling of efficacy exists for the treatment of persistent atrial fibrillation via pulmonary vein isolation without adjunctive ablations, which is likely because they do not target an individual patient's specific underlying disease mechanisms. Electrographic flow (EGF) mapping is the first system that reliably displays wavefront propagation through the atria. It is a promising tool for localizing sources of atrial fibrillation, guiding targeted ablation, and visualizing conduction through the atrial substrate. We describe EGF mapping with emphasis on contemporary studies examining map reproducibility and use cases in the preclinical and clinical environment. Animal experiments demonstrated that maps were interpretable across increasingly complex rhythms with pacing during spontaneously persistent atrial fibrillation reliably simulating EGF sources. The FLOW-AF randomized controlled trial showed that source ablation improved outcomes and that EGF map properties may be used to phenotype patients based on their atrial fibrillation mechanisms and recurrence likelihoods. Targeted ablation strategies balance the risks of insufficiently ablating atrial fibrillation triggers with exacerbating disease through additional scar formation. EGF mapping leverages spatiotemporal relationships in voltage to localize sources and quantify substrate health. Further research is needed to optimize phenotyping and treatment efforts.

The Teodorescu and the Π-operator in octonionic analysis and some applications

In the development of function theory in octonions, the non-associativity property produces an additional associator term when applying the Stokes formula. To take the non-associativity into account, particular intrinsic weight factors are implemented in the definition of octonion-valued inner products to ensure the existence of a reproducing Bergman kernel. This Bergman projection plays a pivotal role in the L2-space decomposition demonstrated in this paper for octonion-valued functions. In the unit ball, we explicitly show that the intrinsic weight factor is crucial to obtain the reproduction property and that the latter precisely compensates an additional associator term that otherwise appears when leaving out the weight factor.Furthermore, we study an octonionic Teodorescu transform and show how it is related to the unweighted version of the Bergman transform and establish some operator relations between these transformations. We apply two different versions of the Borel-Pompeiu formulae that naturally arise in the context of the non-associativity. Next, we use the octonionic Teodorescu transform to establish a suitable octonionic generalization of the Ahlfors-Beurling operator, also known as the Π-operator. We prove an integral representation formula that presents a unified representation for the Π-operator arising in all prominent hypercomplex function theories. Then we describe some basic mapping properties arising in context with the L2-space decomposition discussed before.Finally, we explore several applications of the octonionic Π-operator. Initially, we demonstrate its utility in solving the octonionic Beltrami equation, which characterizes generalized quasi-conformal maps from R8 to R8 in a specific analytical sense. Subsequently, analogous results are presented for the hyperbolic octonionic Dirac operator acting on the right half-space of R8. Lastly, we discuss how the octonionic Teodorescu transform and the Bergman projection can be employed to solve an eight-dimensional Stokes problem in the non-associative octonionic setting.

Hardy–Littlewood maximal function on Lorentz–Herz spaces

This paper extends the study of the generalized Lorentz spaces to the Lorentz–Herz spaces. The Lorentz–Herz spaces consist of all Lebesgue measurable functions such that theirs non-increasing rearrangements belong to the weighted Herz space. The main result of this paper establishes the mapping properties of the Hardy–Littlewood maximal function on the Lorentz–Herz spaces.

On the existence and Lipschitz-like property of the solution map to parametric equilibrium problems governed by trifunction with applications

In this paper, we study a class of parametric equilibrium problems governed by a trifunction. We apply the Fan-KKM theorem under new type of monotonicity and coercivity conditions for trifunctions to obtain the existence result of a solution for the equilibrium problem. For the solution map of parametric equilibrium problems, we obtain the Hölder-type Lipschitz-like property relative to a closed and convex set, which generalizes some existing results in the literature. We illustrate the application of our abstract results in the study of a new model of a fluid flow problem with slip and leak boundary conditions of frictional type.

I-Symmetric Spaces and the π-Images of Metric Spaces

Symmetric spaces and sn-symmetric spaces, as a generalization of metric spaces, have many important properties and have been widely discussed. We consider characterizations and mapping properties of sn-symmetric spaces under ideal convergence. I-symmetric spaces and I-sn-symmetric spaces are defined and studied. These not only generalize some classical results on symmetric spaces but also provide new directions to study generalized metric spaces using the notion of ideal convergence. As an application of I-sn-symmetric spaces, some relevant properties of statistical convergence are obtained. Some unanswered questions in this field are raised.

Adapting high-speed indentation mapping for investigating microstructure-property correlations in chromium carbide-nickel alloy coatings: Challenges and solutions

This study investigates the microstructural and mechanical characteristics of chromium carbide‑nickel rich alloy coatings produced through laser cladding, detonation spraying, and plasma spraying techniques. While all three processing techniques used the same feedstock powder, each method yields coatings with unique microstructures encompassing varying compositions and length scales. Employing Field Emission Scanning Electron Microscopy (FE-SEM) in combination with Energy Dispersive Spectroscopy (EDS) and nanoindentation mapping, local microstructure and mechanical properties were assessed at the micrometre length scale. Laser-clad coatings exhibit a typical metal matrix composite microstructure with high carbide content, distinct (MoNb)C2 phases, and Fe in the metallic matrix, while the thermal sprayed coatings showed carbides of varying sizes and metallic matrix with varying degrees of chromium dissolved in it. The instrumented indentation technique helped precisely record the microstructural features in all the coatings. Chromium carbide consistently emerges as the hardest phase across all coatings, with variations in metallic matrix hardness. Higher matrix hardness in thermal sprayed coatings correlates with increased Cr content, attributed to extended solid solubility of Cr and the presence of Mo and Nb. Energy dispersive spectroscopy and transmission electron microscopy provided clearer insight into the microstructure. This study highlights a direct one-to-one correlation between microstructure and mechanical properties mapped using instrumented indentation techniques in chromium carbide‑nickel rich coatings across different deposition methods.

Mappings of finite distortion on metric surfaces

AbstractWe investigate basic properties of mappings of finite distortion$$f:X \rightarrow \mathbb {R}^2$$ f : X → R 2 , where X is any metric surface, i.e., metric space homeomorphic to a planar domain with locally finite 2-dimensional Hausdorff measure. We introduce lower gradients, which complement the upper gradients of Heinonen and Koskela, to study the distortion of non-homeomorphic maps on metric spaces. We extend the Iwaniec-Šverák theorem to metric surfaces: a non-constant $$f:X \rightarrow \mathbb {R}^2$$ f : X → R 2 with locally square integrable upper gradient and locally integrable distortion is continuous, open and discrete. We also extend the Hencl-Koskela theorem by showing that if f is moreover injective then $$f^{-1}$$ f - 1 is a Sobolev map.

Localized operators on weighted Herz spaces

AbstractWe introduce the notion of localized operators. We extend the boundedness of the localized operators from the weighted Lebesgue spaces to the weighted Herz spaces. The localized operators include the Hardy operator, the Riemann–Liouville fractional integrals, the general Hardy‐type operators, the geometric mean operator, and the one‐sided maximal function. Therefore, this paper extends the mapping properties of the the Hardy operator, the Riemann–Liouville fractional integrals, the general Hardy‐type operators, the geometric mean operator, and the one‐sided maximal function to the weighted Herz spaces.

On Boundary Properties of Conformal Mappings

On Boundary Properties of Conformal Mappings

Hardy–Littlewood fractional maximal operators on homogeneous trees

We study the mapping properties of the Hardy–Littlewood fractional maximal operator between Lorentz spaces of the homogeneous tree and discuss the optimality of all the results.

Bounded cohomology and homotopy colimits

ABSTRACT The comparison map from bounded cohomology to singular cohomology plays an important role in the study of bounded cohomology theory and its applications. The vanishing and covering theorems of Gromov and Ivanov show interesting and useful properties of the comparison map under appropriate assumptions. We discuss an approach to these theorems, based on the general homotopy-theoretic properties of the comparison map, and obtain new proofs and refined versions of these results.

Modeling carbon dioxide emissions reduction

The paper proposes a new scientific approach to modeling carbon dioxide (CO2) emissions in individual countries, based on the tools of Kohonen self-organizing maps and the provisions of economic theory. This work is based on conducted a comprehensive analysis of wide set of indicators influencing carbon dioxide emissions and decarbonization processes in 40 selected countries for 10 years time span from 2013 till 2022. During clustering these nations using self-organizing maps, 14 key indicators were chosen that cover economic and demographic growth, energy consumption, CO2 emission data, and includes trade of energy recourses for wider analysis and identification of countries with similar decarbonization potential, economic development and trade energy recourses possibilities. This approach exposed distinct clusters of nations with varying decarbonization capabilities and tracked the progress of analyzed countries in terms of CO2 emission changes in dynamic.The analysis of clustering was focused on identification leaders and followers in decarbonization activities. The leaders cluster includes Sweden, Norway, New Zealand and other countries exhibited leadership in developing a climate-resilient economy among 40 countries. Hence, all countries positioned closer to the leader cluster on the map demonstrated higher efficiency in their decarbonization pathways. Consequently, these properties of Kohonen maps provide a foundation for formulating general recommendations to achieve an efficient and effective low-carbon economy for followers including Ukraine, Kazakhstan and other energy intensive countries.Distinct countries decarbonization profiles resulting from clustering were used to develop practical recommendations towards estimating and establishing targeted CO2 emission levels for analyzed countries, conducting continued promoting renewable energy utilization, enhancing cross-border energy trade, diversifying energy portfolios, etc. Also, the proposed methodology can be utilized to project future emissions trends for each country based on cluster-specific models and facilitate policy decisions making process related to mitigating carbon emissions.

Production of magnetic photocatalysts from TiO2, Fe(NO3)3 and sucrose and their application for the degradation of model organic contaminants

AbstractBACKGROUNDPhotocatalysis is an efficient method for the removal of organic contaminants in wastewater. In this study, different magnetic photocatalysts for the degradation of organic compounds were prepared.RESULTSTi/C/Fe photocatalysts were prepared by supporting TiO2 (20, 40 and 60% w/w) on a carbon/iron oxide (C/Fe) magnetic carrier. Characterization via Raman spectroscopy, X‐ray diffractometry, thermal analysis, X‐ray fluorescence, scanning electron microscopy and energy‐dispersive X‐ray spectroscopy/elemental mapping and magnetic property analysis by vibrating‐sample magnetometry confirmed the presence of TiO2, Fe3O4, Fe3C and char in the photocatalysts as well as their magnetic properties. The results of specific surface area analysis showed that the C/Fe support had a surface area of 183 m2 g−1 and that this area decreased with an increasing amount of supported TiO2, reaching up to 129 m2 g−1. Diffuse reflectance spectroscopy characterization revealed that the bandgap values obtained for the photocatalysts (Ti/C/Fe) were lower than 3.2 eV. The prepared photocatalysts showed high efficiency in degrading the contaminants Remazol Black (RB5) (99%), paracetamol (77%) and phenol (90%). Recovery and reuse experiments using RB5 showed that after the fourth reaction, the photocatalytic efficiency was reduced by 50%, and the recovery reached up to 70%. Sedimentation kinetics showed that while only 6% of the TiO2 was deposited, up to 89% of the photocatalysts were deposited.CONCLUSIONSThese results indicate that the photocatalysts showed excellent photocatalytic efficiency for different contaminants and can be easily and quickly separated from the reaction medium by magnetic separation. © 2024 Society of Chemical Industry (SCI).

General Fractional Economic Dynamics with Memory

For the first time, a self-consistent mathematical approach to describe economic processes with a general form of a memory function is proposed. In this approach, power-type memory is a special case of such general memory. The memory is described by pairs of memory functions that satisfy the Sonin and Luchko conditions. We propose using general fractional calculus (GFC) as a mathematical language that allows us to describe a general form of memory in economic processes. The existence of memory (non-locality in time) means that the process depends on the history of changes to this process in the past. Using GFC, exactly solvable economic models of natural growth with a general form of memory are proposed. Equations of natural growth with general memory are equations with general fractional derivatives and general fractional integrals for which the fundamental theorems of GFC are satisfied. Exact solutions for these equations of models of natural growth with general memory are derived. The properties of dynamic maps with a general form of memory are described in the general form and do not depend on the choice of specific types of memory functions. Examples of these solutions for various types of memory functions are suggested.

Stability criteria and calculus rules via conic contingent coderivatives in Banach spaces

This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between Banach spaces important in optimization theory and its applications. Our tools of generalized differentiation revolve around the newly introduced concept of ε-regular normal cone to sets and associated coderivative notions for set-valued mappings. Based on these constructions, we establish several characterizations of the central stability notion known as the relative Lipschitz-like property of set-valued mappings in infinite dimensions. Applying a new version of the constrained extremal principle of variational analysis, we develop comprehensive sum and chain rules for our major constructions of conic contingent coderivatives for multifunctions between appropriate classes of Banach spaces.

Enhancing low-light images via dehazing principles: Essence and method

Given the visual resemblance between inverted low-light and hazy images, dehazing principles are borrowed to enhance low-light images. However, the essence of such methods remains unclear, and they are susceptible to over-enhancement. Regarding the above issues, in this letter, we present corresponding solutions. Specifically, we point out that the Haze Formation Model (HFM) used for image dehazing exhibits a Bidirectional Mapping Property (BMP), enabling adjustment of image brightness and contrast. Building upon this property, we give a comprehensive and in-depth theoretical explanation for why dehazing on inverted low-light image is a solution to the image brightness enhancement problem. Further, an Adaptive Full Dynamic Range Mapping (AFDRM) method is then proposed to guide HFM in restoring the visibility of low-light images without inversion, while overcoming the issue of over-enhancement. Extensive experiments validate our proof and demonstrate the efficacy of our method.

Sharp Coefficient Estimates for Analytic Functions Associated with Lemniscate of Bernoulli

The main purpose of this work is to study the third Hankel determinant for classes of Bernoulli lemniscate-related functions by introducing new subclasses of star-like functions represented by SLλ* and RLλ. In many geometric and physical applications of complex analysis, estimating sharp bounds for problems involving the coefficients of univalent functions is very important because these coefficients describe the fundamental properties of conformal maps. In the present study, we defined sharp bounds for function-coefficient problems belonging to the family of SLλ* and RLλ. Most of the computed bounds are sharp. This study will encourage further research on the sharp bounds of analytical functions related to new image domains.

Mapping olfactory cues for wayfinding – a theoretical approach and an empirical study

ABSTRACT Nowadays, navigation systems are widely used to find the shortest path between a starting point and a destination. In order to guide the user these systems rely on visual information. However, consider, e.g. visually impaired or elderly people. They may not be able to navigate using only visual information. Additionally, sometimes there is no visual information (i.e. visual landmark) available. In such a case olfactory information could be a helpful route guidance. To identify possible olfactory cues, we performed two online studies as well as a focus-group interview and identified 13 different smell classes usable for navigation and wayfinding. Based on our results, we gathered data for these classes in an urban environment. We collected 201 smells and mapped their values for the properties temporary, intensity, and notes. We underline the findings of previous studies that the majority of odours in an urban area are gastronomy and waste-related odours. We find a number of smells that have daily or seasonal dependencies and conclude that the temporary property should be captured in more detail in future studies. We also discuss additional properties of smells and smell mapping that should be considered in future work.