Type Operators Research Articles

The integro‐differential operators of infinite order on the half line related to the Legendre operator

In this paper, we introduce certain integro‐differential operators of Legendre type of infinite order. Some properties of these operators are obtained. Moreover, we establish the necessary and sufficient conditions for a class of integro‐differential operators of infinite order being unitary on . Some classes of related integro‐differential equations are also considered.

Generalized Stević-Sharma type operators from derivative Hardy spaces into Zygmund-type spaces

<abstract><p>Let $ u, v $ be two analytic functions on the open unit disk $ {\mathbb D} $ in the complex plane, $ \varphi $ an analytic self-map of $ {\mathbb D} $, and $ m, n $ nonnegative integers such that $ m < n $. In this paper, we consider the generalized Stević-Sharma type operator $ T_{u, v, \varphi}^{m, n}f(z) = u(z)f^{(m)}(\varphi(z))+v(z)f^{(n)}(\varphi(z)) $ acting from the derivative Hardy spaces into Zygmund-type spaces, and investigate its boundedness, essential norm and compactness.</p></abstract>

SPECTRUM CHARACTERISTICS IN TELEVISION SYSTEMS OBJECTS WITH QUASI-PERIODIC PHASE-TIME CONVERSIONS OF VIDEO INFORMATION

Quasiperiodic phase-time transformations of video information can be car-ried out both due to the objects corresponding displacements themselves, and through the necessary displacements organization, for example, in the signal sensor of television systems. The essence of this transformation type is rel-ative, time-periodic displacements of controlled objects in raster space on the photosensitive surface of the signal sensor, accompanied by changes in the position of the object relative to the optical axis. In this case, large-scale changes in coordinates also affect the angle of each element of the object image. Consequently, the action of the operator of “periodic circular dis-placements” is associated with the occurrence of the effect of relative sup-pression of the upper spatial frequencies of the initial influence. The article shows that in terms of the effect on the spatio-temporal spectrum of the initial impact, it is advisable to classify the operator of “periodic linear displace-ments” as operators of the differential type, and the operator of “periodic circular displacements” as operators of the integral type. Any operator of integral type can be reduced to differential type and vice versa. An example is considered where the operator of periodic circular displacements is easily converted to a differential type when introducing a return circular displace-ment along the same trajectory.

Α-Baskakov-Durrmeyer type operators and their approximation properties

In the present research article, we construct a new family of summation-integral type hybrid operators in terms of shape parameter ? ? [0, 1]. Further, basic estimates, rate of convergence and the order of approximation with the aid of Korovkin theorem and modulus of smoothness are investigated. Moreover, numerical simulation and graphical approximations are studied. For these sequences of positive linear operators, we study the local approximation results using Peetre?s K-functional, Lipschitz class and modulus of smoothness of second order. Next, we obtain the approximation results in weighted space. Lastly, A-statistical-approximation results are presented.

On a Stević-Sharma type operator from weighted-type spaces into Bloch-type spaces

On a Stević-Sharma type operator from weighted-type spaces into Bloch-type spaces

Generalized Stević-Sharma type operators from H^∞ space into Bloch-type spaces

Generalized Stević-Sharma type operators from H^∞ space into Bloch-type spaces

Convergence on sequences of Szász-Jakimovski-Leviatan type operators and related results

<p style='text-indent:20px;'>In the present article, we construct the Szász-Jakimovski-Leviatan operators in parametric form by including the sequences of continuous functions and then investigate the approximation properties. We have successfully estimated the convergence by use of modulus of continuity in the spaces of Lipschitz functions, Peetres <inline-formula><tex-math id="M1">\begin{document}$ K $\end{document}</tex-math></inline-formula>-functional and weighted functions.</p>

Approximation by a modification of operators of exponential type associated with the Baskakov operators

In the current article, we modify the operators of exponential type associated with the Baskakov operators so as to preserve the linear functions. Initially, we obtain the moments and central moments for the modified form. Further, we derive few convergence results including Voronovskaja type asymptotic formula and validate our results through graphical illustration. In the end, we obtain the difference estimate between the exponential type operators associated with the Baskakov operators and its modified form.

Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent

Abstract We consider the nonlinear elliptic–parabolic boundary value problem involving the Dirichlet-to-Neumann operator of p-Laplace type at the critical Sobolev exponent. We first obtain the existence and asymptotic estimates of the global solution, and the sufficient conditions of finite time blowup of the solution by using the energy method. Second, we improve the regularity of solution by Moser-type iteration. Finally, we analyze the long-time asymptotic behavior of the global solution. Moreover, with the help of the concentration compactness principle, we present a precise description of the concentration phenomenon of the solution in the forward time infinity.

$ W^{1, \infty} $-seminorm superconvergence of the block finite element method for the five-dimensional Poisson equation

<abstract><p>This study focused on the superconvergence of the finite element method for the five-dimensional Poisson equation in the $ W^{1, \infty} $-seminorm. Specifically, we investigated the block finite element method, which is a tensor-product finite element approach applied to regular rectangular partitions of the domain. First, we introduced the finite element scheme for the equation and discussed various functions related to it, along with their properties. Next, we proposed a weight function and established its important properties, which play a crucial role in the theoretical analysis. By utilizing the properties of the weight function and employing weighted-norm analysis techniques, we derived an optimal order estimate in the $ W^{2, 1} $-seminorm for the discrete derivative Green's function (DDGF). Furthermore, we provided an interpolation fundamental estimate of the second type, also known as the weak estimate of the second type, for the block finite element. This weak estimate is based on a five-dimensional interpolation operator of the projection type. Finally, by combining the derived $ W^{2, 1} $-seminorm estimate for the DDGF and the weak estimate for the block finite element, we obtained a superconvergence estimate for the block finite element approximation in the pointwise sense of the $ W^{1, \infty} $-seminorm. The correctness of the theoretical results was demonstrated through a numerical example.</p></abstract>

A simple proof of the real Riesz–Thorin interpolation theorem in the lower triangle

A simple proof of the real Riesz–Thorin interpolation theorem for operators of strong types $(p_0, q_0)$ and $(\infty , \infty )$ in the lower triangle, that is, if $0 \lt p_0 \leq q_0 \lt \infty $ with the best estimate of the norms is presented.

On the weighted maximal operators of Marcinkiewicz type Cesàro means of two-dimensional Walsh-Fourier series

In this paper we investigate the behaviour of the weighted maximal operators of Marcinkiewicz type (C,?)-means ??,* p (f) := supn?P |??n(f)|/ n2/p?(2+?) in the Hardy space Hp(G2) (0 < ? < 1 and p < 2/(2 + ?)). It is showed that the maximal operators ??,* p (f) are bounded from the dyadic Hardy space Hp(G2) to the Lebesgue space Lp(G2), and that this is in a sense sharp. It was also proved a strong convergence theorem for the Marcinkiewicz type (C, ?) means of Walsh-Fourier series in Hp(G2).

Design of a container grabbing and lifting mechanism for equipping a robotic wheeled chassis

This article presents the results of designing a mechanism for grabbing, lifting and holding a container with which it is supposed to equip a robotic wheeled chassis with an apple harvesting module in an industrial garden. The technical solutions used in agricultural engineering for lifting and holding operations of various types of loads weighing from 300 kg were analyzed, their design and technical features were considered. As a result of the analysis, based on the criteria of compactness and metal consumption, the most preferred variant of the lifting mechanism was selected - a parallelogram lifting mechanism driven by electric cylinders. In order to fulfill the conditions of structural strength of the mechanism for gripping and lifting the container, a strength calculation of the structure was carried out, and also the necessary characteristics of the electric cylinder for the mechanism for lifting the container and the paws for the mechanism for lifting the paws were determined. The main load in the structure is carried by the upper horizontal guides, vertical racks and lower grips. As a result of the analysis, zones of maximum stress and strain concentration were established. The loading of the lower gripper parts occurs with a force directed vertically downward with a force of 1750 H. The highest voltage was about 169 MPa, which ensures sufficient strength of the part with a margin of 3 times, the maximum movements of the guides are 1.6 mm.

Evaluation of Current Farm Machinery Selection Practices of Wonji Shoa Sugar Factory

The Government of Ethiopia is trying to improve sugar industry sector by establishing new factories, expansion projects and rehabilitation of existing ones. The main input in this process is agricultural mechanization; however it has been resulted in a huge number of farm machinery of various types and sizes, without consideration of proper selection and matching between tractors and their attachments (implements). This approach had led to high cost of agricultural operation, resulted in an unbalanced distribution of machinery and the agricultural operations throughout the years. Wonji Shoa Sugar factory is one of the victims of the aforementioned problem. The present study was conducted to evaluate the current farm machinery selection practices of Wonji Shoa Sugar Factory. Three soil types namely; heavy clay, vertisol and sandy loam were selected with four field activities (subsoiling, ploughing, harrowing and furrowing). For subsoiling, ploughing and harrowing, 9410-R John Deer tractor with implements of 5 shank and 3.2 m wide mounted subsoiler, 2.8 m wide double gang offset disc plough, and 3.5 m wide semi mounted four gangs double offset were used respectively. For furrowing YTO-1804 tractor and a four bottom fully mounted 4.5 m wide rider was used. For each experiment, the draft force requirement of the implements, the drawbar power, fuel consumption, overall energy efficiency and power utilization ratio were determined at different tractor travel speeds. Subsoiling, ploughing and harrowing were activities were evaluated at the travel speed of w 3, 4, 5 and 6 km/hr. And a travel speed of 4, 5, 6 and 7 km/hr were used for furrowing operation. Linear regression tests were run to examine the interactions between the factors and determine their significant impact. The results of this study noted for furrowing operation as lowest draft force, drawbar power, fuel consumption and energy efficiency of 14 kN, 12.65kW, 13 lit/hr and 8.7 % respectively in sandy loam soil type. The maximum Draft force of 79.8 kW and drawbar power of 131 kW was noted for subsoiling operation in Heavy clay soil. Moreover the results of all operation in all soil type, as indicated by both overall energy efficiency and power utilization factor shows the mismatch between the tractor and implements, as the tractors were overpowered. That means a less amount of the available power from the tractor is being used to operate the implement. If the tractor had been matched with a bigger and compatible implement a better efficiency and higher productivity of the tractor implement combination could have been achieved.

Approximation by nonlinear Bernstein-Chlodowsky operators of Kantorovich type

In this study, we give the monotonicity of the Bernstein-Chlodowsky max product operator. Then, we introduce Bernstein-Chlodowsky-Kantorovich operators of max-product type and obtain this operator preserves quasi-concavity. Also, we give some approximation properties of Lipschitz functions by max-product kind of Bernstein-Chlodowsky-Kantorovich operators.

Justification of the parameters and efficiency indicators of the technological process TO-1 of MAN TGL trucks

Purpose. Justification of the parameters and efficiency indicators of the MAN TGL truck MAINTENANCE-1 technological process to achieve its specified productivity at the expense of three types of resources, namely: changes in the number of workers, equipment and posts. Methods. The study is based on the modeling of maintenance technological processes using the basic principles of graph theory and schedules, a heuristic algorithm for the distribution of the entire set of maintenance operations of a certain type, among workers at the maintenance point posts, taking into account the amount of equipment, with the aim of obtaining a schedule of operations that minimized cycle duration. Results. The results of the simulation are the dependence of the duration of the technological process of maintenance of MAN TGL vehicles on the number of involved workers, equipment and posts, as well as the dependence between the number of different resources involved and the efficiency indicators of their use. Conclusions. The analysis of the research results showed that the increase in the number of workers slightly shortens the duration of technological processes of maintenance of MAN TGL vehicles, and also increases the utilization rates of workers' time funds and equipment. Keywords: MAN TGL vehicle, maintenance, technological process, modeling, parameters and performance indicators.

Uniportal video-assisted thoracoscopy in pediatrics-initial experience.

It has become apparent that the endoscopic surgeries are rapidly developing, and they have become an essential part of every specialty of surgery. Single port thoracoscopic surgery is developing, enhancing the advantages of muti-portal video-assisted thoracoscopic surgery (VATS). Although becoming a well-recognised approach for adult patients, extremely limited literature exists concerning uniportal VATS among pediatric cases. This study aims to present our initial experience with this approach in a single tertiary hospital and extrapolate its feasibility and safety in this specific context. Perioperative parameters and surgical outcomes for all pediatric patients who underwent an intercostal or subxiphoid uniportal VATS surgery in our department in 2 years retrospectively reviewed. The median length of follow-up was 8 months. Sixty-eight pediatric patients underwent different uniportal VATS operation for different types of pathology. The median age was (3.5 years). Median operating time was 116 minutes. Three cases converted to open. The mortality rate was zero. The median length of stay was 5 days. Three patients presented complications. Three patients lost from follow-up. Despite literature data heterogeneity, these results provide support to the feasibility and applicability of uniportal VATS in the pediatric population. Further studies are required to explore the benefit of uniportal over multi-portal VATS (including chest wall deformities, cosmesis and quality of life).

Spectral properties of the finite system of Klein-Gordon S-wave equations with general boundary condition

The spectral characteristics of the operator L is studied where L is defined within the Hilbert space L2(R+, CV) given by a finite system of Klein-Gordon type differential equations and boundary condition at general form. The research of the Klein-Gordon type operator continues to be an important topic for researchers due to the range of applicability of them in numerous branches of mathematics and quantum physics. Contrary to the previous works, we take the potential as complex valued and generalize the problem to the matrix Klein-Gordon operator case. The spectrum is derived by determining the Jost function and resolvent operator of the prescribed operator. Further, we provide the conditions that must be met for the certain quantitative properties of the spectrum.

Integral Baskakov type operator with quadratic order of approximation

Integral Baskakov type operator with quadratic order of approximation

Lewy-Stampacchia inequality for noncoercive parabolic obstacle problems

<abstract><p>We investigate the obstacle problem for a class of nonlinear and noncoercive parabolic variational inequalities whose model is a Leray–Lions type operator having singularities in the coefficients of the lower order terms. We prove the existence of a solution to the obstacle problem satisfying a Lewy-Stampacchia type inequality.</p></abstract>