Properties Of Operators Research Articles

Study of the structure and operational properties of the surface layer of 60S2A steel subjected to combined EMT + SPD hardening

Study of the structure and operational properties of the surface layer of 60S2A steel subjected to combined EMT + SPD hardening

Operators on anti-dual pairs: Supremum and infimum of positive operators

Our purpose in this note is to investigate the order properties of positive operators from a locally convex space into its conjugate dual. We introduce a natural generalization of the Busch-Gudder strength function and we prove Kadison's anti-lattice theorem and Ando's result on the infimum of positive operators in that context.

COMPLEX INTUITIONISTIC FUZZY DOMBI PRIORITIZED AGGREGATION OPERATORS AND THEIR APPLICATION FOR RESILIENT GREEN SUPPLIER SELECTION

One of the main problems faced by resilient supply chain management is how to solve the problem of supplier selection, which is a typical multi-attribute decision-making (MADM) problem. Given the complexity of the current decision-making environment, the primary influence of this paper is to propose the theory of Dombi operational laws based on complex intuitionistic fuzzy (CIF) information. Moreover, we examined the theory of CIF Dombi prioritized averaging (CIFDPA) and CIF weighted Dombi prioritized averaging (CIFWDPA), where these operators are the modified version of the prioritized aggregation operators and Dombi aggregation operators for fuzzy, intuitionistic fuzzy, complex fuzzy and complex intuitionistic fuzzy information. Some reliable properties for the above operators are also established. Furthermore, to state the art of the proposed operators, an application example in the presence of the invented operators is evaluated for managing resilient green supplier selection problems. Finally, through comparative analysis with mainstream technologies, we provide some mechanism explanations for the proposed method to show the supremacy and worth of the invented theory.

Pseudo-differential calculi and entropy estimates with Orlicz modulation spaces

We deduce continuity properties for pseudo-differential operators with symbols in Orlicz modulation spaces when acting on other Orlicz modulation spaces. In particular we extend well-known results in the literature. For example we generalize the classical result by Cordero and Nicola that if1p′+1q′⩽1p1+1p2,1p′+1q′⩽1q1+1q2,pj,qj⩽q′,q⩽p and a∈Mp,q, then the pseudo-differential operator Op(a) is continuous from Mp1,q1 to Mp2′,q2′.We also show that the entropy functional Eϕ possess suitable continuity properties on a suitable Orlicz modulation space MΦ satisfying Mp⊆MΦ⊆M2, though Eϕ is discontinuous on M2=L2.

Some Properties of Operations in the Collection of Intuitionistic Fuzzy Sets : A Novel Approach

In this paper, we introduce collection of intuitionistic fuzzy sets as a new concept of intuitionistic fuzzy sets. In ordinary, universal set in intuitionistic fuzzy sets is classical set. So in this paper, we generalize the universal set as a collection or family of intuitionistic fuzzy sets. We also present intersection and union operation on collection of of intuitionistic fuzzy sets and show that the operations hold commutative, assosiative, idempotent, and De Morgan’s laws properties.

Fuzzy preorders and generalized distances: The aggregation problem revisited

Transitive fuzzy relations play a central role in fuzzy research activity. A special type of this class of fuzzy relations is known as indistinguishability operators. Many works have focused their efforts on the study of the properties of such operators. One celebrated problem is to find out the class of functions that allows to aggregate a collection of indistinguishability operators into a new single one. Characterizations of this class of functions have been obtained and the relationship with those functions that aggregate a collection of extended pseudo-metrics into a single one has been revealed in the literature. Moreover, fuzzy preorders are a class of fuzzy transitive relations that extend the notion of indistinguishability operators to the asymmetric context. In this paper we show that there is an equivalence between functions that aggregate fuzzy preorders and those functions that merge extended quasi-pseudo-metrics. The new provided characterizations reveal that, in essence, such functions must be monotone and subadditive. Special attention is paid to the case of fuzzy partial orders (a special case of fuzzy preorder) showing that there is a correspondence between those functions aggregating fuzzy partial orders and those that aggregate extended quasi-metrics. Since all the aforesaid fuzzy relations are transitive we also provide new information about those functions that preserve the class of transitive fuzzy relations in terms of those that preserve the so-called ordinary triangular triplets and those that preserve the triangle inequality. The potential applicability of the exposed theory to multi-criteria decision making problems has been discussed.

Operator ranges in Banach spaces with weak star separable dual

We provide several extensions for Banach spaces with weak⁎-separable dual of a theorem of Schevchik ensuring that for every proper dense operator range R in a separable Banach space E, there exists a one-to-one and dense-range operator such that T(E)∩R={0}. These results lead to several characterizations of Banach spaces with weak⁎-separable dual in terms of disjointness properties of operator ranges, which yield a refinement of a theorem of Plichko concerning the spaceability of the complementary set of a proper dense operator range, and an affirmative solution to a problem of Borwein and Tingley for the class of Banach spaces with a separable quotient and weak⁎-separable dual. We also provide an extension to these spaces of a theorem of Cross and Shevchik, which guarantees that for every proper dense operator range R in a separable Banach space E there exist two closed quasicomplementary subspaces X and Y of E such that R∩(X+Y)={0}. Finally, we prove that some weak forms of the theorems of Shevchik and Cross and Shevchik do not hold in any nonseparable weakly Lindelöf determined Banach space.

Operational properties involving functions with generalized continuity

In the work [11], Vieira introduced a new perspective about continuity of functions, which involves the idea of a suitable type of continuity of a function with respect to another function. The inspiration for this notion of generalized continuity arises naturally from the concept of generalized limit of a function with respect to another function, thus expanding the field of mathematical knowledge about continuity of functions. Initially presented by Vieira and Braz in [1], the concept of generalized limit is relevant, since a Riemann integral is a case of a generalized limit, as can be seen in [11]. This article proposes to further explore this notion of generalized continuity and its main focus is to investigate and present operational properties that arise when we deal with functions that exhibit this generalized continuity, operational properties such as composition, concatenation, among others. Through this study, it is hoped to shed light on the meaning and implications of these properties in this context of generalized continuity, allowing a broader understanding of this notion of continuity.

Probing the kinetic sensitization effect of NO2 on ethylene oxidation

Exhaust gas recirculation (EGR) has been widely equipped in modern engines for pollutant emission abatement. NOx present in EGR can greatly influence fuel combustion properties in engine operation. Ethylene (C2H4) is well-known a critical intermediate formed via β-scission reactions of alkyl radicals in the pyrolysis and oxidation of hydrocarbons, thus investigating the mutual effects of C2H4 and NOx is beneficial to engine design as well as hierarchically developed strategy of the chemical kinetic model. This study investigated the auto-ignition behavior of C2H4/air mixtures containing different levels of NO2 (0 ppm, 200 ppm, 500 ppm, 3000 ppm) in a high-pressure shock tube at pressures of 1 atm and 24 atm, temperatures of 820–1300 K and different equivalence ratios of 0.5, 1.0 and 2.0. The results showed that the addition of NO2 significantly promoted auto-ignition at high pressure, while only limited effects at low pressure. A detailed kinetic mechanism was proposed based on a hierarchically developed strategy, and it successfully reproduced the experimental data over the entire test conditions. Flux and sensitivity analyses were implemented to explore the sensitization effect of NO2 addition on the ignition kinetics of C2H4. The analysis revealed that NO2 mainly affects the reaction pathway of ĊH2CHO radical, leading to the formation of HONO. The additional generation of ȮH radicals through HONO = NO + ȮH and NO + HȮ2 = NO2 + ȮH accelerate the auto-ignition of C2H4. At low pressure, the decrease in the rate constant of HONO decomposition weakens the role of NO2.

Overview of Promising Solutions in Subsurface Sounding Equipment.

This overview analyzes current advances in the equipment for detecting various subsurface metal and metal-containing objects. Various metal detector types are discussed alongside their operation principles, properties, and capabilities. Following the analysis of conventional metal detectors, promising design and technical solutions are explored, implementing new physical metal detector operation principles that have not been used before for this equipment class. The information provided allows for evaluating new metal detector concepts developed to improve the sensitivity and accuracy of detecting equipment.

Wavelet-based Edge Multiscale Parareal Algorithm for subdiffusion equations with heterogeneous coefficients in a large time domain

We present the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm, recently proposed in Li and Hu (2021), for efficiently solving subdiffusion equations with heterogeneous coefficients in long time. This algorithm combines the benefits of multiscale methods, which can handle heterogeneity in the spatial domain, and the strength of parareal algorithms for speeding up time evolution problems when sufficient processors are available. Our algorithm overcomes the challenge posed by the nonlocality of the fractional derivative in previous parabolic problem work by constructing an auxiliary problem on each coarse temporal subdomain to completely uncouple the temporal variable. We prove the approximation properties of the correction operator and derive a new summation of exponential to generate a single-step time stepping scheme, with the number of terms of O(|logτf|2) independent of the final time, where τf is the fine-scale time step size. We establish the convergence rate of our algorithm in terms of the mesh size in the spatial domain, the level parameter used in the multiscale method, the coarse-scale time step size, and the fine-scale time step size. Finally, we present several numerical tests that demonstrate the effectiveness of our algorithm and validate our theoretical results.

RESEARCH OF PHYSICAL AND MECHANICAL PARAMETERS OF RAILWAY BRAKE PADS

The article presents the results of tests of the installation batch of railway brake pads, taking into account the modern requirements of railway transport for safety in conditions of increased speeds and increased load capacity. The value of the friction coefficient of the pad on the wheel steel was used as the main criterion in the analysis for the development of solutions. The main indicators characterizing the operational properties of the pads are the speed of movement of the rolling stock and the force of pressing the pads on the wheel steel. Experimental dependences of the value of the coefficient of friction on the production parameters of the rolling stock with a change in the compressive strength of the composite layer are established. A nomogram has been developed to determine operational indicators, which allows solving two tasks: – operational, allowing for a given value of the maximum speed of the rolling stock and the strength properties of the pad to set the force of normal pressure on the wheel and the corresponding value of the coefficient of friction. – technical, which consists in setting the maximum pressure velocity of the rolling stock depending on the value of the normal pressure on the block and its strength properties.

An information model concept for a thermomechanical process in grinding

The purpose of the work is to present the concept of an information modelof the thermomechanical process in grinding of products from materials prone to defect formation due to the fact that their surface layer has hereditary defects of structural or technological origin.The products' strength and functionality depend on the inhomogeneity and defectiveness of the structure of the materials from which they are made. Such materials have many different micro defects formed in the surface layer of parts during the technological operations of their production. Reducing number of defectsin the finishing operations of these materials and increasing the operational properties of products made of these materials is an essential national and economical task, the solution of which leads to a significant saving of material resources, labour intensity and cost of manufacturing parts. The currently available information on the thermal processes of diamond abrasive processing is obtained on the assumption of the homogeneity of the materials being polished and needs to consider the presence of defects in the technological heredity of the products. The phenomenological approach in studying the causes of cracking of materials prone to this type of defect does not allow to revealthe mechanism of genesis and development of grinding cracks. The choice of the method of investigation of the mechanism of crack formation is based on micro-research related to inhomogeneities, which are formed in the surface layer of parts during previous technological operations. A mathematical model has been developed that describes thermomechanical processes in the surface layer during grinding of parts made of materials and alloys, taking into account their inhomogeneities, which affect the intensity of the formation of grinding cracks. Calculated dependences between the crack resistance criterion and the main controlling technological parameters were obtained. According to the known characteristics of hereditary defects, the limit values of thermomechanical criteria, which ensure the necessary quality of the surfaces of the processed products, are determined. Based on the obtained criterion ratios, an algorithm for selecting technological possibilities for defect-free processing of products from materials prone to loss of quality of the surface layer of parts was built. A decision support system has been developed to increase the efficiency of the finishing process management.

Experimental and Theoretical Justification of the Foam Fiber-Reinforced Concrete Application Expediency in Earthquake-Resistant Construction

Introduction. Based on the evolutionary approach to the analysis of the lightweight concrete application expediency in earthquake-resistant construction it has been revealed that development of the above mentioned technologies fosters the reduced material consumption in construction and the increased durability of buildings under the seismic loads. The efficient solutions for constructing the earthquake-resistant buildings are constantly searched for, and the reasons for reducing the range of energy-efficient products made of the autoclaved aerated concrete are noticed. The research is aimed at compiling an inventory of modern technological methods of increasing the buildings seismic resistance.Materials and Methods. The list and properties of raw materials used for single-stage technology manufacture of the foam concrete mixtures have been provided. The list of equipment used for assessing the studied materials’ mechanical properties has been defined.Results. The new experimental data confirming the significant influence of the individual properties of fiber on the value of the dispersedly reinforced foam concrete ultimate deformability and bending tensile strength has been obtained. The positive effect of the length of fiber on the foam concrete mechanical properties has been confirmed. The considerably positive effect of the dispersed reinforcement on the homogeneity of mechanical properties observed in the foam concrete mass has been distinguished.Discussion and Conclusions. The work performed has elucidated the importance of the individual properties of fiber as a tool for managing the operational properties of foam concrete. The ultimate properties of the aerated rock material are influenced by the length of fibers and their ultimate deformability. The length of fiber is important for the bending tensile strength, whereas the values of this parameter in the composite material are regulated by the ultimate extensibility.

Design and Technological Engineering of Gear Wheel Working Surfaces in a Gas Turbine Engine

The design and production of gear wheels includes a number of specialized principles and disciplines aimed to practical application of scientific and practical knowledge. The proposed design method for the subsequent production of the gear configuration together with the technology of virtual life cycle modeling allows predicting its behavior in certain operating modes taking into account the capabilities of an existing production at the design stage. Ensuring the functional properties of the gearing is a complex task, which is solved at all stages of the mechanism life cycle. The solution requires a model of design and technological control of operability, covering the whole life cycle, based on the management of the gearing configuration and the way of objective assessment of the operational properties, based on ensuring the functionality and acceptability. A model of design engineering based on the analysis of the gear acceptability, particularly of the tooth working surface damage classification, based on the reliability of strength calculations, knowledge of materials and precision machining inherent in serial production, with the analysis of the serviceability by functional parameters is proposed. This model allows considering the inconsistencies as acceptable, which often appear, but are not significant. The possibility of making optimal design decisions at the design stage of developing the mechanism configuration in the conditions of using information on serial technological capabilities based on the concept of a “digital twin” when performing feedback between the technological and design directions of gear wheel creating is considered. This creates the groundwork for the development of a new organizational approach to the engineering development of the configuration of assemblies with a tight advantageous cooperation of the designer and technologist.

Nanostructured-microfibrillar polypyrrole coated NiTi current collectors for high power and shape memory LiFePO4 cathodes for Li-ion batteries

Powering the shape-memory alloy-based actuators and wearables needs flexible and compatible energy sources. Lithium iron phosphates are also attractive for their unique properties for safe operation. This study used NiTi thin film as the shape memory current collector coated with one-dimensional (1D) polypyrrole microfibrils for flexible and high-power lithium-ion batteries. The PPy microfibrils facilitated the electron pathway and improved the rate capability of the LiFePO4 cathode significantly. While the pure LiFePO4 showed a 108 mAh/g capacity at 0.1 C, the nanocomposite with microfibril PPy had 136 mAh/g. Discharging at 10 C was associated with a significant loss of capacity for pure cathode (15 mAh/g), whereas 75 mAh/g for nanocomposite with PPy. The rate capability of the LiFePO4 cathode was also improved significantly using PPy microfibrils. For a single-layer pouch battery, the capacity of the flat cell was retained at about 20 mAh. In contrast, the capacity of the nanocomposite decreased to about 18 mAh after curving the cell and recovered to about 19 mAh once relieving at 1 C.

Some Properties of ?-supercyclic operators

In this paper, we define Γ-transitive operators to study some further properties of Γ-supercyclic operators. In particular, we study Γ-supercyclic criterion which is a set of some sufficient conditions for an operator to be Γ-supercyclic. We use these conditions to partially answer an open problem in the literature. In particular, we show that if Γ = ?? and ? satisfies Γ-criterion, then ? is supercyclic.

Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects

Demicontractive operators form an important class of nonexpansive type mappings whose study led researchers to the creation of some beautiful results in the framework of metric fixed-point theory. This article aims to provide an overview of the most relevant results on the approximation of fixed points of single-valued demicontractive mappings in Hilbert spaces. Subsequently, we exhibit the role of additional properties of demicontractive operators, as well as the main features of the employed iterative algorithms to ensure weak convergence or strong convergence. We also include commentaries on the use of demicontractive mappings to solve some important nonlinear problems with the aim of providing a comprehensive starting point to readers who are attempting to apply demicontractive mappings to concrete applications. We conclude with some brief statements on our view on relevant and promising directions of research on demicontractive mappings in nonlinear settings (metric spaces) and some application challenges.

A “Polymer‐in‐Salt” Solid Electrolyte Enabled by Fast Phase Transition Route for Stable Zn Batteries

AbstractSolid polymer electrolyte‐based batteries show great promise because of their safe operating properties, wide voltage window and suitable flexibility. However, low ionic conductivity, low cation transfer number, weak oxidation/reduction resistance and low mechanical strength limit their implementation in Zn ion batteries. Here, w e developed a “polymer‐in‐salt” Zn2+‐conductive solid electrolyte (denoted as 70% salt‐SPE) constructed by a simple and fast phase transition method. The room‐temperature ionic conductivity and the transfer number of the 70% salt‐SPE reaches 1.6 mS cm−1 and 0.78, respectively. Meanwhile, the ZnF2‐rich inorganic/organic hybrid solid electrolyte interface is formed, and the stable voltage window reaches 9.35 V. In consequence, the Zn||Zn symmetric cell continuously cycles over 700 hours at current density of 2 mA cm−2 and the Zn||Cu symmetric battery runs with Coulombic efficiency of >99%. The Zn||MnPBA full battery delivers a discharge specific capacity of 109 mAh g−1 at room temperature and 190 mAh g−1 at 60 °C. Meanwhile, impressive cyclic stability of 6000 cycles with capacity retention of 80% is achieved, which originates from the effectively optimized ion transport action and dendrite‐free Zn plating/stripping.

Composition operators on de Branges–Rovnyak spaces associated to a rational (not inner) function

In this paper, we characterize the boundedness, the compactness and the Hilbert–Schmidt property for composition operators acting from a de Branges–Rovnyak space H(b) into itself, when b is a rational function in the closed unit ball of H∞ (but not a finite Blaschke product). In particular, we extend some of the results obtained by D. Sarason and J.N. Silva in the context of local Dirichlet spaces.