Type Operators Research Articles

Asymptotics of the Spectrum of a Hartree Type Operator with Self-Consistent Potential Including the Macdonald Function

Asymptotics of the Spectrum of a Hartree Type Operator with Self-Consistent Potential Including the Macdonald Function

On the Homogenization of Nonlocal Convolution Type Operators

On the Homogenization of Nonlocal Convolution Type Operators

Variational Principles in Quaternionic Analysis with Applications to the Stationary MHD Equations

In this paper we aim to combine tools from variational calculus with modern techniques from quaternionic analysis that involve Dirac type operators and related hypercomplex integral operators. The aim is to develop new methods for showing geometry independent explicit global existence and uniqueness criteria as well as new computational methods with special focus to the stationary incompressible viscous magnetohydrodynamic equations. We first show how to specifically apply variational calculus in the quaternionic setting. To this end we explain how the mountain pass theorem can be successfully applied to guarantee the existence of (weak) solutions. To achieve this, the quaternionic integral operator calculus serves as a key ingredient allowing us to apply Schauder’s fixed point theorem. The advantage of the approach using Schauder’s fixed point theorem is that it is also applicable to large data since it does not require any kind of contraction property. These considerations will allow us to provide explicit iterative algorithms for its numerical solution. Finally to obtain more precise a-priori estimates one can use in the situations dealing with small data the Banach fixed point theorem which then also grants the uniqueness.

The tangential k-Cauchy–Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group

The tangential k-Cauchy–Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group

Essential norm of linear operators from general weighted‐type spaces to Banach spaces and some applications

We present a result concerning the essential norm of linear operators mapping some general weighted‐type spaces of holomorphic functions on the open unit ball in to Banach spaces. As some applications, we compare essential norms of a product‐type operator of integral type and a weighted composition operator between some of the general weighted‐type spaces.

Commutators for certain fractional type operators on weighted spaces and Orlicz–Morrey spaces

Commutators for certain fractional type operators on weighted spaces and Orlicz–Morrey spaces

Steklov Type Operators and Functional Equations

Abstract We consider sequences of Steklov type operators and an associated functional equation. For a suitable sequence, we establish asymptotic formulas.

P(x)-biharmonic equations involving Leray–Lions type operators with Hardy potentials

In this article, we investigate p ( x ) -biharmonic equations involving Leray–Lions type operators with Hardy potentials. New criteria for the existence of at least one or at least three generalized solutions are established via variational methods when the Leray–Lions type operator and the nonlinearity f satisfying suitable hypotheses in variable-exponent Lebesgue spaces.

Inverse problems for real principal type operators

abstract: We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems.

Construction of New Operators by Composition of Integral-Type Operators and Discrete Operators

In this paper, we propose some new positive linear approximation operators, which are obtained from a composition of certain integral type operators with certain discrete operators. It turns out that the new operators can be expressed in discrete form. We provide representations for their coefficients. Furthermore, we study their approximation properties and determine their moment generating functions, which may be useful in finding several other convergence results in different settings.

A unified approach to three themes in harmonic analysis (I & II): (I) The linear Hilbert transform and maximal operator along variable curves (II) Carleson type operators in the presence of curvature

This paper constitutes the first part of a study that addresses three rich historical themes in harmonic analysis that, in the non-zero curvature setting, investigate the boundedness properties along variable curves for(I) the linear Hilbert transform and analogous maximal operator,(II) the Carleson-type operators, and(III) the bilinear Hilbert transform and analogous maximal operator.Our Main Theorem in this paper states that, given a general variable curve γ(x,t) in the plane that is assumed only to be measurable in x and to satisfy suitable non-zero curvature in t and extra (mild) non-degeneracy conditions, the operators at (I) and (II) defined along the curve γ are Lp-bounded for 1<p<∞.Our result provides a new and unified treatment of the first two themes as well as a unitary approach within the x-variable setting for both the singular integral and the maximal operator versions of (I).At the heart of our approach is the LGC–methodology introduced here, which encompasses three key ingredients:(1)phase/space discretization that confines the phase of the multiplier to oscillate at the linear level,(2)adapted Gabor frame discretization of the input function(s), and(3)cancelation extraction via the analysis of the time-frequency correlation(s) capturing the non-zero curvature of γ.

Sobolev embeddings for kinetic Fokker-Planck equations

We introduce intrinsic Sobolev-Slobodeckij spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak Hörmander condition. We prove continuous embeddings into Lorentz and intrinsic Hölder spaces. We also prove approximation and interpolation inequalities by means of an intrinsic Taylor expansion, extending analogous results for Hölder spaces. The embedding at first order is proved by adapting a method by Luc Tartar which only exploits scaling properties of the intrinsic quasi-norm, while for higher orders we use uniform kernel estimates.

The proposed model for analyzing off-street parking Dynamics: A case study of Taipei City

To reduce traffic congestion, air pollution, and lost revenue due to wasted driving around looking for parking spaces, effective parking management has become a crucial issue in urban areas. Previous studies have shown that parking demand is related to the location of parking spaces/lots, parking fees, time spent looking for spaces, and various driver and environmental characteristics. However, there have been more studies of on-street rather than off-street parking. Also, the spatio-temporal variance between variables and turnover rate (such as the hours of operation for various types of Points of Interest (POIs) as well as the causes of bias estimators has been largely overlooked.To solve the above problems, the Geographical and Temporal Weighted Regression (GTWR) model was utilized in this study to predict the hourly parking turnover rate in off-street parking lots. The flexible coefficient setting of this model can be used to capture the spatial and temporal variance. In addition to this model, the Geographically Weighted Regression (GWR) and the Ordinary Least Squares (OLS) models were used as a basis for comparison. The study included 346 public off-street parking lots in Taipei and 10 types of nearby POIs. The study period was for 24 h on August 31, 2021. Due to the dissimilar trend of the turnover rate, the researchers separated all parking lots into three groups for regression analysis: those that experience a daytime decrease, remain stable, and those with an increase during the day.Our results show the following: (1) For the types of parking lots that experienced increases and decreases, the GTWR model performed best for the prediction of hourly turnover rate, while all models performed similarly for the prediction of the stable type parking lot. (2) With regard to related factors (the type 1 parking lot for example), parking lots in areas with more traditional markets, MRT stations, and with fewer schools, supermarkets, hotel bus stops, and lower parking fees tended to have higher turnover rates. (3) Incorporating a more precise POI dataset (the number and types of POIs as well as their business hours) and applying a suitable spatial temporal model improved the parking demand model’s performance. However, the GTWR model’s limitations may hamper its performance, especially with regard to analysis of the time-stable parking lots or variables. Future studies might include other datasets, such as nearby private parking lots or holiday data to improve the model fit.

New Multivariate and Univariate Aldaz–Kounchev–Render Type Operators

New Multivariate and Univariate Aldaz–Kounchev–Render Type Operators

Study on the Basic Form of Reservoir Operation Rule Curves for Water Supply and Power Generation

Reservoir operation rule curves are crucial for managing water supply and power generation in reservoirs. As the number of objectives and management requirements increase, there is a growing demand for optimized operation rule curves. The objective of this study is to explore the most effective forms of reservoir operation rule curves, focusing on the case of the Nierji Reservoir and considering the dual objectives of water supply and power generation. The parameter–simulation–optimization framework, specifically employing the NSGA-II algorithm, was used to analyze and compare two basic forms of operation rule curves: the shared type and independent type. The impact of these curves on water supply potential and multi-objective optimization results with various water demand scenarios was assessed. The analysis revealed that the choice of operation rule curve form can influence the maximum water supply potential of the reservoir to some extent. The independent type operation rule curve was significantly more effective in enhancing the water supply potential for industrial and domestic users, resulting in a notable increase of 3.5 × 108 m3. Additionally, it also proved beneficial for environmental users, with an increase of 1 × 108 m3. Conversely, the shared type operation rule curve demonstrated similar functionality to the independent type curve with fewer decision variables, particularly when the water demand was relatively low. In scenarios with high water demand, the independent type curve outperformed the shared type curve by generating 6549 superior, non-dominated solutions for multi-objective optimization, specifically focused on maximizing reservoir operation benefits. In conclusion, selecting the appropriate form of reservoir operation rule curve is crucial to balance different reservoir functional objectives and achieve optimal results. Further research could focus on quantifying the specific benefits and trade-offs associated with each type of curve in order to provide more robust evidence for the advantages of a complex reservoir system.

Approximation by nonlinear Meyer-König and Zeller operators based on q-integers

Abstract In this paper, we introduce the nonlinear Meyer-König and Zeller operators based on q-integers. Firstly, we describe the q-Meyer-König and Zeller operators of max-product type. Then, we give an error estimation for the q-Meyer-König and Zeller operators of max-product kind by using modulus of continuity.

Parametric Subtyping for Structural Parametric Polymorphism

We study the interaction of structural subtyping with parametric polymorphism and recursively defined type constructors. Although structural subtyping is undecidable in this setting, we describe a notion of parametricity for type constructors and then exploit it to define parametric subtyping , a conceptually simple, decidable, and expressive fragment of structural subtyping that strictly generalizes rigid subtyping . We present and prove correct an effective saturation-based decision procedure for parametric subtyping, demonstrating its applicability using a variety of examples. We also provide an implementation of this decision procedure as an artifact.

Polyregular Functions on Unordered Trees of Bounded Height

We consider injective first-order interpretations that input and output trees of bounded height. The corresponding functions have polynomial output size, since a first-order interpretation can use a k -tuple of input nodes to represent a single output node. We prove that the equivalence problem for such functions is decidable, i.e. ‍given two such interpretations, one can decide whether, for every input tree, the two output trees are isomorphic. We also give a calculus of typed functions and combinators which derives exactly injective first-order interpretations for unordered trees of bounded height. The calculus is based on a type system, where the type constructors are products, coproducts and a monad of multisets. Thanks to our results about tree-to-tree interpretations, the equivalence problem is decidable for this calculus. As an application, we show that the equivalence problem is decidable for first-order interpretations between classes of graphs that have bounded tree-depth. In all cases studied in this paper, first-order logic and MSO have the same expressive power, and hence all results apply also to MSO interpretations.

The Essence of Generalized Algebraic Data Types

This paper considers direct encodings of generalized algebraic data types (GADTs) in a minimal suitable lambda-calculus. To this end, we develop an extension of System F ω with recursive types and internalized type equalities with injective constant type constructors. We show how GADTs and associated pattern-matching constructs can be directly expressed in the calculus, thus showing that it may be treated as a highly idealized modern functional programming language. We prove that the internalized type equalities in conjunction with injectivity rules increase the expressive power of the calculus by establishing a non-macro-expressibility result in F ω , and prove the system type-sound via a syntactic argument. Finally, we build two relational models of our calculus: a simple, unary model that illustrates a novel, two-stage interpretation technique, necessary to account for the equational constraints; and a more sophisticated, binary model that relaxes the construction to allow, for the first time, formal reasoning about data-abstraction in a calculus equipped with GADTs.

On some algebraic properties related to Heron type operator means on positive definite cones of C⁎-algebras

In this paper we consider certain algebraic properties concerning variants of the Heron mean on positive definite cones of general C⁎-algebras. Those variants are the Kubo-Ando type Heron mean and the Wasserstein mean. The main part of the investigation concerns associativity properties. We present a number of results that show how far operations related to those two kinds of means are from being associative. Many of our results can also be viewed as characterizations of central positive definite elements or as characterizations of commutative C⁎-algebras.