Properties Of Operators Research Articles

Justification of key factors regarding the application of prospective ecological transport in the urban passenger transportation system

Research objective. Justification of the key factors that have an impact on the introduction of promising ecological transport in the system of urban passenger transport in order to improve the quality of transport services for passengers and improve ecology in densely populated cities. Materials and methods. To achieve the goal, the fuzzy Dematel method is used, which is based on graph theory and allows to classify all available factors that influence decision-making based on cause-and-effect relationships. Results. The eight key factors that form the transport project and the factors that have a significant impact on them are substantiated for the implementation of the transport project of the implementation of promising ecological passenger transport on urban routes into the transport system of urban passenger transportation. These include the level of development of modern transport technologies when transporting passengers on city routes and the availability of their support centers; the availability of financial programs for updating/restructuring the rolling stock fleet of the motor vehicle enterprise and the availability of the appropriate legal framework for preferential operation of electric passenger transport; rapid adaptation of the transport infrastructure of a modern city for the operation of ecological transport; compliance of ecological transport with the transport characteristics of the passenger transportation route; operational properties of a modern electric bus; the effect of relevant legislative initiatives regarding benefits for the purchase and costs of operating electric vehicles. Scientific novelty consists in identifying the interrelationships between the factors that form the transport project and the factors that have a significant influence on them, on the implementation of the transport project of the implementation of promising ecological passenger transport on urban routes into the transport system of urban passenger transport, which allows to estimate the possible economic costs of road transport enterprises carrying out passenger transportation. Practical significance lies in the determination of key factors that can be used for the implementation of a transport project for the use of promising ecological passenger transport in the system of urban passenger road transport

On [formula omitted]-Gamma type operators in a polynomial weighted space

The objective of this paper is to examine various approximation properties of the q-Gamma operators developed by Cheng et al. (2020) in the context of a polynomial weighted space. Following that, we modify these operators to investigate the approximation properties of differentiable functions in the same space, providing evidence that the modified operators have a better rate of convergence.

Dirichlet Problem for Nonlinear Higher-Order Equations in Upper Half Plane

In this article, we consider the Dirichlet problem for nonlinear higher-order equations in upper half plane. Firstly we introduce the solutions of inhomogeneous polyanalytic equation in upper half plane. Then we investigate the properties of relevant integral operators. Lastly we transform the Dirichlet problem for nonlinear higher-order equations in upper half plane into the system of integro-differential equations and we obtain the existence of unique solution using Banach fixed point theorem.

On the evolution of the volume in Loop Quantum Cosmology

The dynamics of the expectation value of the volume is one of the key ingredients behind the replacement of the Big Bang singularity by a bounce in Loop Quantum Cosmology. As such, it is of great importance that this quantity is mathematically well-defined in the space of physical states of the theory. A number of caveats have been raised about such a definition entering in conflict with the quantum evolution of states, motivated by the situation found in quantum geometrodynamics. We show that there are ways around these caveats, all of which are related to the existence of quantization prescriptions leading to a nondegenerate curvature operator in Loop Quantum Cosmology. Interestingly, the properties of the curvature operator that may allow for a good behavior of the volume are only possible thanks to the discreteness of the geometry characteristic of the loop quantization procedure.

Qualitative properties of fractional convolution elliptic and parabolic operators in Besov spaces

The maximal Bp,qs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{p,q}^{s}$$\\end{document}-regularity properties of a fractional convolution elliptic equation is studied. Particularly, it is proven that the operator generated by this nonlocal elliptic equation is sectorial in Bp,qs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ B_{p,q}^{s}$$\\end{document} and also is a generator of an analytic semigroup. Moreover, well-posedeness of nonlocal fractional parabolic equation in Besov spaces is obtained. Then by using the Bp,qs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{p,q}^{s}$$\\end{document}-regularity properties of linear problem, the existence, uniqueness of maximal regular solution of corresponding fractional nonlinear equation is established.

Research on the resistance of protective coatings for concrete to the effects of atmospheric moisture

The development of the construction industry has led to increased requirements for the operational properties of building materials in general and concrete in particular. Although concrete is designed primarily to withstand structural loads, it must also resist environmental influences to increase its durability. This article presents the results of the influence of the components of protective coatings on the hydro-physical properties of concrete. The edge wetting angle in concrete with a protective coating ranges from 95 to 101 degrees, which is about twice that of uncoated concrete. The mass of concrete under the influence of hygroscopic moisture increases, and after 30 days of exposure, it is 1.1–1.6 wt. % compared to 5.7–5.8 wt. % for control samples. The minimum increase (1.1–1.2 wt. %) is achieved when using coatings with the largest amount of heat-resistant varnish KO-08. The water absorption of the developed coating compositions decreases after 30 days of being in water from 5.2 to 1.6–2.2 wt. % for C20/25 concrete. Low temperatures negatively affect the hydrophysical properties of protective coatings, but only slightly. It has been found that water absorption increases by approximately 20 %.

Shape preserving fractal multiquadric quasi-interpolation

In this article, we construct a novel self-referential fractal multiquadric function which is symmetric about the origin. The scaling factors are suitably restricted to preserve the differentiability and the convexity of the underlying classical multiquadric function. Based on the translates of a fractal multiquadric function defined on a grid, we propose two fractal quasi-interpolants LCαf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_C^{\\alpha }f$$\\end{document} and LDαf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_D^{\\alpha }f$$\\end{document} to approximate smooth and irregular functions. We study the convergence of LCαf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_C^{\\alpha }f$$\\end{document} and LDαf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_D^{\\alpha }f$$\\end{document} to f using uniform error estimates. We investigate the linear polynomial reproducing property, convexity/concavity and monotonicity features of these quasi-interpolation operators. The advantages of fractal quasi-interpolants over the classical quasi-interpolants are demonstrated by various examples.

A surprising property of nonlocal operators: the deregularising effect of nonlocal elements in convolution differential equations

Abstract We consider nonlocal differential equations with convolution coefficients of the form − M ( a * | u | q ) ( 1 ) μ ( t ) u ″ ( t ) = λ f t , u ( t ) , t ∈ ( 0,1 ) , $$-M\left(\left(a {\ast} \vert u{\vert }^{q}\right)\left(1\right)\mu \left(t\right)\right){u}^{{\prime\prime}}\left(t\right)=\lambda f\left(t,u\left(t\right)\right)\text{,\,}t\in \left(0,1\right),$$ where q > 0, subject to given boundary data. The function μ ∈ C [ 0,1 ] $\mu \in \mathcal{C}\left(\left[0,1\right]\right)$ modulates the strength of the nonlocal element. We demonstrate that the nonlocality has a strong deregularising effect in the specific sense that nonexistence theorems for this problem are directly affected by the magnitude of the function μ. A specific example illustrates the application of the nonexistence results presented herein.

Research on technological parameters affecting the quality of adhesive joints in casting model assemblies and assessment of their operational properties in liquid and humid environments

Modern casting model kits, often created using adhesive technologies, can experience deformations leading to warping and even destruction. This can occur due to differences in thermal expansion and moisture absorption rates between the material and the adhesive. The study evaluated the behavior of the adhesive joint in model kit elements under operational conditions in liquid and humid environments, assessing the hardness and strength of the joint. The analysis revealed a correlation between the density of the plastic and the quality of the adhesive joint.

Homogenization of partial differential equations with Preisach operators

The current work deals with initial boundary value parabolic problems with Preisach hysteresis whose the density functions are allowed to depend on the variable of space. The model contains nonlinear monotone operators in the diffusion term, arising from an energy. Thanks to the properties of Preisach hysteresis operators and to the sigma-convergence method, we obtain the convergence of themicroscopic solutions to the solution of the homogenized problem. The effective operator is obtained in terms of a solution of a nonlinear corrector equation addressed in the usual sense of distributions, leading in an approximate scheme for the homogenizedcoefficient which is an important step towards the numerical implementation of the results from the homogenization theory beyond the periodic setting.

Parameter learning for Wiener systems with time‐delay state‐space model

AbstractThis paper discusses a novel scheme for learning the Wiener output error nonlinear system with time‐delay state‐space model. In the Wiener system, the dynamic linear block is approximated by time‐delay state‐space model, and the static nonlinear block is established using neural fuzzy network. Combined signals designed including separable signal and random signal are devoted to achieving parameters separation learning of the Wiener system, that is, the two blocks are learned independently. Firstly, using the properties of shift operator and transforming state‐space model with time‐delay into a representation with input and output, then linear dynamic block parameters are learned by the virtue of correlation analysis method in the condition of Gaussian signals. Moreover, a recursive extended least squares estimation is carried out to learn parameters of static nonlinear block and colored noise model under the condition of random signals. The efficiency and accuracy of proposed scheme are confirmed on experiment results of a numerical simulation and a typical practical nonlinear process, and experimental simulation results demonstrate that the learning scheme proposed obtains good learning precision.

Truncated Hankel operators on model spaces

The paper by Sarason in 2007 initiated and inspired the study of truncated Toeplitz operators which are the compression of Toeplitz operators to coinvariant subspace of H2. We study the truncated Hankel operators which are the compression of Hankel operators to coinvariant subspace of H2. Several parallel characterizations and properties of such operators are obtained. In addition, boundedness, finite rank and compactness of truncated Hankel operators were characterized in terms of their symbols.

Investigation on hydraulic characteristics of a model and prototype bulb turbine based on similarity criteria

Abstract From the perspective of the world hydropower utilization trend, the medium and high head hydraulic resources are gradually decreasing, and along with much more attention to the ecological environment and land resource constraints, low-head hydropower plants have been becoming particularly prevalent. Benefit from compact structure, less investment, high capacity and wide operation range, bulb tubular turbines have come up to be the optimal option for the development and exploitation of low-head energy resources and been widely applied. In this paper, based on measurement data and CFD simulation results of model and prototype, scale effect which derived from similarity law was picked up to investigate the hydraulic performance and operating properties. Through comparison and analysis, it’s concluded that distinct from high-head application similarity conversion turns out to be more complicated for bulb turbines in case of flow characteristics, and it’s recommended that this conversion be further modified considering different boundary conditions. Such achievements will be of great help to look into the mechanism of ratio effect and accelerate research progress.

Endoscopic scoring indices for assessing disease severity in familial adenomatous polyposis: Systematic review.

Background and study aims There is limited consensus on the optimal method for measuring disease severity in familial adenomatous polyposis (FAP). We aimed to systematically review the operating properties of existing endoscopic severity indices for FAP. Methods We searched MEDLINE, EMBASE, and the Cochrane Library from inception to February 2023 to identify randomized controlled trials (RCTs) that utilized endoscopic outcomes or studies that evaluated the operating properties of endoscopic disease severity indices in FAP. Results A total of 134 studies were included. We evaluated scoring indices and component items of scoring indices, such as polyp count, polyp size, and histology. Partial validation was observed for polyp count and size. The most commonly reported scoring index was the Spigelman classification system, which was used for assessing the severity of duodenal involvement. A single study reported almost perfect interobserver and intra-observer agreement for this system. The InSIGHT polyposis staging system, which was used for assessing colorectal polyp burden, has been partially validated. It showed substantial interobserver reliability; however, the intra-observer reliability was not assessed. Novel criteria for high-risk gastric polyps have been developed and assessed for interobserver reliability. However, these criteria showed a poor level of agreement. Other scoring indices assessing the anal transition zone, duodenal, and colorectal polyps have not undergone validation. Conclusions There are no fully validated endoscopic disease severity indices for FAP. Development and validation of a reliable and responsive endoscopic disease severity instrument will be informative for clinical care and RCTs of pharmacological therapies for FAP.

Оценка нестабильности последовательных впрыскиваний топливной аппаратуры дизелей

The issues of uneven cyclic feed in sequential injections by diesel fuel equipment are considered, which is directly related to solving the problem of ensuring the quality of operation of engines of various types and purposes when operating at low loads and rotational speeds. The special importance of solving these problems from the standpoint of ensuring fuel efficiency, environmental pollution, solving issues of engine reliability and improving their operational properties was noted. The features of the formation of residual fuel pressure in the high-pressure pipeline are revealed. The periodic fluctuations of the cyclic feed and injection parameters from cycle to cycle are estimated. A study of possible options for the operation of fuel equipment in low fuel supply modes has been carried out. Based on the analysis, a criterion for evaluating the instability of successive injection cycles for diesel fuel equipment during its operation in various modes has been introduced. By studying numerical examples, the conditions of unstable fuel supply processes in successive injections of various characteristic modes are determined. The criterion determines the quality of the fuel equipment of marine diesel engines and diesel generators in terms of ensuring a minimum stable idle speed and the possibility of ensuring stable reduced fuel supplies. The variability of fuel supply processes in sequential feeds is the cause of increased exchange processes of electric power flow during parallel operation of diesel alternators and reduces the performance characteristics of diesels for various purposes when operating in partial modes. In the process of carrying out development work, scientific research and during the refinement of diesels, the instability criterion allows us to assess the quality of the fuel equipment precisely in partial modes. This is of particular importance for diesel engines of fishing vessels operating for a long time at shared loading modes and low idle speeds, as well as for engines of the tugboat fleet and auxiliary diesel generator sets of all types of facilities used.

Технологическое обеспечение эксплуатационных свойств сопрягаемых поверхностей элементов сборной формообразующей оснастки с учетом установленной долговечности пресс-форм

Design and technological concepts are viewed at the stages of designing, manufacturing and joining process providing for the required reliability (durability) of mold elements. Recommendations are given for rationing and achieving the parameters of accuracy and quality of mating surfaces, taking into account the formation of the necessary operational properties at the main stages of the product life cycle. The factors that have the greatest impact on ensuring the correct and accurate location of forming tool elements have been elicited. The concept of determining the actual contact area and calculating the scale parameter, which provides a contact interface degree specification for conjugated surfaces, is presented. The hypothesis of the formation of reliability indicators is found, taking into account the manufacturing capability and technical capacity of production with the introduction of correction of the upper and lower dimensional deviations included in the dimension chains and ensuring the pre-set accuracy parameters of the master link. The analysis of the operating conditions of the studied type of pressmold elements is carried out. The main operational properties that provide the required operating time for shaping part failures are identified and analyzed. Special attention is paid to the study of the structural features of such parts, a comparison of the integral and prefabricated structures is made, and also, contact stresses under the joining operation for the most promising of the latter are calculated for contact interface degree simulation. This will allow developing practical recommendations for any type of compound forming tool for the benefit of basic mechanical properties rate making, accuracy indicators, including deviation allowances in the correct geometric shape, including quality parameters of the surface layer at the designing stage,processing methods dispatch and modes setting at the manufacturing and testing stages and also suggesting the amount of static loading when assembling.

Perturbed Dirac Operators and Boundary Value Problems

In this paper, the time-independent Klein-Gordon equation in R3 is treated with a decomposition of the operator Δ−γ2I by the Clifford algebra Cl(V3,3). Some properties of integral operators associated the kind of equations and some Riemann-Hilbert boundary value problems for perturbed Dirac operators are investigated.

Dunford property for composition operators on $H^p$-spaces

Dunford property for composition operators on $H^p$-spaces

Sufficient Conditions for Linear Operators Related to Confluent Hypergeometric Function and Generalized Bessel Function of the First Kind to Belong to a Certain Class of Analytic Functions

Geometric function theory has extensively explored the geometric characteristics of analytic functions within symmetric domains. This study analyzes the geometric properties of a specific class of analytic functions employing confluent hypergeometric functions and generalized Bessel functions of the first kind. Specific constraints are imposed on the parameters to ensure the inclusion of the confluent hypergeometric function within the analytic function class. The coefficient bound of the class is used to determine the inclusion properties of integral operators involving generalized Bessel functions of the first kind. Different results are observed for these operators, depending on the specific values of the parameters. The results presented here include some previously published findings as special cases.

Dunford property for composition operators on $H^p$-spaces

Dunford property for composition operators on $H^p$-spaces