Explosive Behaviors on Coupled Fractional-Order System

Fractional derivatives provide a prominent platform for various chemical and physical system with memory and hereditary properties, while most of the previous differential systems used to describe dynamic phenomena including oscillation quenching are integer order. Here, effects of fractional derivative on the transition process from oscillatory state to stationary state are illustrated for the first time on mean-filed coupled oscillators. It is found the fractional derivative could induce the emergence of a first-order discrete transition with hysteresis between oscillatory and stationary state. However, if the fractional derivative is smaller than the critical value, the transition will be invertible. Besides, the theoretical conditions for the steady state are calculated via Lyapunov indirect method which probe that, the backward transition point is unrelated to mean-field density. Our result is a step forward in enlightening the control mechanism of explosive phenomenon, which is of great importance to highlight the function of fractional-order derivative in the emergence of collective behaviors on coupled nonlinear model.

Influence of different hard-facing procedures on quality of surfaces of regenerated gears

During the process of regeneration of machine parts, certain phenomena occur that have a significant impact on the loss of their working ability. Hereditary properties are expressed by the interdependence of geometric and physical-mechanical-metallurgical parameters of gear teeth created during the technological operations of regeneration of worn teeth by hard-facing. The influence of the type of additional material (electrodes and their combinations) on the tribological characteristics of welded gear teeth was considered, whereby the so-called hard additional materials were applied. Those are the additional materials that give the required surface hardness of the teeth without subsequent thermal or thermochemical treatment. This research did not involve the regeneration of specific worn gears removed from machine systems, but the new gears were made, which were then damaged and then regenerated by hard-facing using the shielded metal arc welding (SMAW) procedure. Thus, all the tested gears were made of the same material, belonged to one batch and were machined on the same machines with the same machining regimes. The tests were performed on samples made of 20MnCr5 steel for cementation, on a tribometer by the “block on disc” method, which was designed to simulate the operating conditions of coupled teeth of concrete gears in the exploitation conditions. Based on the conducted tribological tests, the average coefficients of friction and topography of the surfaces were determined by measuring the wear trace and it was defined which additional materials give the best tribological characteristics of the surfaces of gears regenerated by hard-facing.

Two Classes of Infrasoft Separation Axioms

One of the considerable topics in the soft setting is the study of soft topology which has enticed the attention of many researchers. To contribute to this scope, we devote this work to investigate two classes of separation axioms with respect to the distinct ordinary elements through one of the generalizations of soft topology called infrasoft topology. We first formulate the concepts of infra- t p -soft T j using total belong and partial nonbelong relations and then introduce the concepts of infra- t t -soft T j -spaces using total belong and partial nonbelong relations. To illustrate the relationships between them, we provide some examples. We discuss their fundamental properties and study their behaviors under some special types of infrasoft topologies. An extensive discussion is given for the transmission of these two classes between infrasoft topology and its parametric infratopologies. In the end, we demonstrate which ones have topological and hereditary properties, and we show their behaviors under the finite product of soft spaces.

Property Testing on Graphs and Games

Constant-time algorithms are powerful tools, since they run by reading only a constant-sized part of each input. Property testing is the most popular research framework for constant-time algorithms. In property testing, an algorithm determines whether a given instance satisfies some predetermined property or is far from satisfying the property with high probability by reading a constant-sized part of the input. A property is said to be testable if there is a constant-time testing algorithm for the property. This chapter covers property testing on graphs and games. The fields of graph algorithms and property testing are two of the main streams of research on discrete algorithms and computational complexity. In the section on graphs in this chapter, we present some important results, particularly on the characterization of testable graph properties. At the end of the section, we show results that we published in 2020 on a complete characterization (necessary and sufficient condition) of testable monotone or hereditary properties in the bounded-degree digraphs. In the section on games, we present results that we published in 2019 showing that the generalized chess, Shogi (Japanese chess), and Xiangqi (Chinese chess) are all testable. We believe that this is the first results for testable EXPTIME-complete problems.

Exploitation Characteristics of Teeth Flanks of Gears Regenerated by Three Hard-Facing Procedures

Numerous phenomena that occur during the process of machine parts’ regeneration have a significant impact on the loss of their working ability. Therefore, the properties of the working surfaces of the teeth flanks of repaired gears were analyzed in this research. The hereditary properties of the gear teeth are expressed by the interdependence of their geometric and physical-mechanical-metallurgical parameters created during the technological operations of regeneration of worn teeth by welding/hard-facing. The hard-facing was executed with three filler metal types, namely: combination Inox 18/8/6 + EDur 600, Castolin 2 and UTP 670. The tested properties included geometrical accuracy, microstructure and microhardness. Evaluation of the executed regeneration procedures was done by comparing the mentioned parameters of the regenerated gears and the new ones. The tested gears were not withdrawn from production due to damage, but they were newly manufactured and intentionally damaged gears, made of the same materials, subjected to the same manufacturing process. In this way, all influences except for the considered filler metal type were eliminated. Based on results of the conducted experiments, it was possible to establish the influence of the filler metal type on the surface characteristics of the regenerated gears’ teeth flanks.

SELECTION OAK SEEDLING FOR THE RAPID GROWTH BASED ON MORPHOLOGICAL AND CYTOGENETIC INDICATORS

The plantations of the pedunculate oak (Quercus robur L) are the most valuable forestry, ecological, economic and environmental resource. To implement measures for the reproduction of forests, it is necessary to create artificial plantations with planting material with improved hereditary properties. In this regard, the selection of high-quality seeds and fast-growing seedlings of Quercus robur is an extremely topical issue. For the study, we selected objects of oak forests, which have a different degree of recreational load, but are located in identical forest conditions. When collecting experimental material and analyzing the data obtained, generally accepted breeding approaches and methods of statistical processing of results were used. The method of selection by phenotype and fixation of a trait in the offspring justifies itself, but requires acceleration and deepening of knowledge in this direction with the use of modern methods of marker selection. In this connection, the purpose of the work on identifying additional selection criteria that allows for the selection assessment of seedlings is relevant. A close correlation has been established between the height of seedlings and the mitotic index; the height of the seedlings and the pathology of mitosis. It is proposed to use the mitotic index without taking into account cells at the stage of prophase and pathology of mitosis as additional criteria for selecting seedlings for growth rate. On the basis of a comprehensive assessment of the above morphological and cytogenetic characteristics, it is recommended to select highly adaptive and fast-growing seedlings to create forest cultures of Quercus robur

Online Node- and Edge-Deletion Problems with Advice

In online edge- and node-deletion problems the input arrives node by node and an algorithm has to delete nodes or edges in order to keep the input graph in a given graph class $$\Pi $$ Π at all times. We consider only hereditary properties $$\Pi $$ Π , for which optimal online algorithms exist and which can be characterized by a set of forbidden subgraphs $${{\mathcal{F}}}$$ F and analyze the advice complexity of getting an optimal solution. We give almost tight bounds on the Delayed Connected$${{\mathcal{F}}}$$ F -Node-Deletion Problem, where all graphs of the family $${\mathcal{F}}$$ F have to be connected and almost tight lower and upper bounds for the Delayed$$H$$ H -Node-Deletion Problem, where there is one forbidden induced subgraph H that may be connected or not. For the Delayed$$H$$ H -Node-Deletion Problem the advice complexity is basically an easy function of the size of the biggest component in H. Additionally, we give tight bounds on the Delayed Connected$${\mathcal{F}}$$ F -Edge-Deletion Problem, where we have an arbitrary number of forbidden connected graphs. For the latter result we present an algorithm that computes the advice complexity directly from $${\mathcal{F}}$$ F . We give a separate analysis for the Delayed Connected$$H$$ H -Edge-Deletion Problem, which is less general but admits a bound that is easier to compute.

SOME PROPERLY HEREDITARY BITOPOLOGICAL PROPERTIES

In this paper we discuss some pairwise properly hereditary properties concerning pairwise separation axiom, and obtain several results related to these properties.

Functionally Separation Axioms on General Topology

In this paper, we define a new family of separation axioms in the classical topology called functionally T i spaces for i = 0,1,2 . With the assistant of illustrative examples, we reveal the relationships between them as well as their relationship with T i spaces for i = 0,1,2 . We demonstrate that functionally T i spaces are preserved under product spaces, and they are topological and hereditary properties. Moreover, we show that the class of each one of them represents a transitive relation and obtain some interesting results under some conditions such as discrete and Sierpinski spaces.