Conditions For Existence Research Articles

The algorithms for the Eulerian cycle and Eulerian trail problems for a multiple graph

In this paper, we study undirected multiple graphs of any natural multiplicity $k>1$. There are edges of three types: ordinary edges, multiple edges and multi-edges. Each edge of the last two types is a union of $k$ linked edges, which connect 2 or $(k+1)$ vertices, correspondingly. The linked edges should be used simultaneously. If a vertex is incident to a multiple edge, it can be also incident to other multiple edges and it can be the common end of $k$ linked edges of some multi-edge. If a vertex is the common end of some multi-edge, it cannot be the common end of another multi-edge. We set the problem of finding the eulerian walk (the cycle or the trail) in a multiple graph, which generalizes the classical problem for an ordinary graph. We formulate the necessary conditions for existence of an eulerian walk in a multiple graph and show that these conditions are not sufficient. Besides that, we show that the necessary conditions of existence of an eulerian cycle and eulerian trail are not mutually exclusive for an arbitrary multiple graph, that is why it is possible to construct a multiple graph where two types of eulerian walks exist simultaneously. Any multiple graph can be juxtaposed to the ordinary graph with quasi-vertices, which represents the structure of the initial graph in a simpler form. In particular, each eulerian walk in the multiple graph corresponds to the eulerian walk in the graph with quasi-vertices. The algorithm for getting such a graph is formulated. Also, the auxiliary problem of finding the covering trails with given endpoints in an ordinary graph is studied. Two algorithms are obtained for this problem. We elaborate the algorithm for finding the eulerian walk in a multiple graph, which has the exponential complexity. We suggest the polynomial algorithm for the special case of a multiple graph and show that the necessary conditions are sufficient for existence of an eulerian walk in this special case.

Infinity augmented state Kalman filter and its application in unknown input and state estimation

This paper investigates the infinity augmented state Kalman filter (IASKF) to obtain the unknown input and state estimation for systems with the rank-deficient matrix. With the aid of input model, which is described as the random walk process with finite covariance, the augmented state Kalman filter (ASKF) is established. Then in light of matrix limiting, the IASKF is deduced from the ASKF as the covariance of the input signal tends to infinity. It is shown that the previous unbiased minimum-variance (UMV) algorithm and recursive three-step filter (RTSF) are the special cases of the proposed IASKF algorithm. Moreover, the condition of existence of the IASKF is given. The present work gives a new insight into unknown input and state estimation. It indicates that the ASKF can also be used to estimate the unknown input and state by only choosing a proper covariance matrix of the input signal. A simulation example is given to illustrate the effectiveness of the proposed results.

Theory of linear focusing in chromatographic columns with exponential retention. Part 2: Analysis of special cases

The unified approach to studies of different separation techniques (GC, LC, etc.) adopted in Part 1 continued herein. As before, the column temperature in GC, the solvent composition in LC, etc., are represented by the concept of solute mobilization (y). General equations for dynamic (moving) linear y-gradients (gradients in y) in non-uniform columns developed in Part 1 are reduced herein to special cases of uniform columns. Only the uniform columns, the ideal sample introduction, the positive y-rates, the negative y-gradients, and the eluting solutes are considered. Equations for solute band compression, peak width, peak focusing, peak separation and others derived. All equations are expressed via dimensionless parameters eliminating unessential factors like the mobile phase type, column type and dimensions, etc. The conventional gradient elution LC is treated as a special case of the separations with y-gradients. Effects of the y-gradients on solute retention time, on band compression, on peak focusing and on peak separation are analyzed.The equations developed herein, while describing simple and familiar concepts (retention time, peak width, etc.), are, unfortunately, cumbersome in many cases. The good news is that the equations are exact and the conditions of existence of the equations are explicitly formulated so that there is no question where the equations can and where thy cannot be used.

Organizational normativity and teleology: a critique

In recent years, so-called organizational accounts (OA) have emerged in theoretical biology as a powerful, viable strategy for naturalizing teleology and normativity. In the wake of the theoretical tradition of autopoiesis and biological autonomy, OA notably propose a new meaning for the notion of “organization,” which they claim to be capable, among other things, of grounding objective and observer-independent normative teleological ascriptions. In this paper, I focus on this last claim, asking “How are ‘organization’ and ‘normativity’ conceptually connected?” The basic insight mobilized by the OA framework to answer this question is most often expressed as a counterfactual argument regarding the “conditions of existence” of organized entities. In this paper, I show that careful scrutiny of this core OA argument reveals a substantial shortcoming. To make this point, I first analyze how the OA framework positions the idea of “conditions of existence” via the notions of “dependence”, “constraint,” and “closure.” Second, I consider various possible interpretations of the OA counterfactual argument grounding norms. I conclude that the implications of this argument do not enable OA to deliver what they promise, i.e., a straightforward link between organization and norms. I argue that a different strategy is needed to capture the basic organizational intuition about biological normativitiy and suggest that a stipulative route might be better suitable to that end.

Modern services led growth and development in a structuralist dual economy: Long‐run implications of skilled labor constraint

AbstractMotivated by the South Asian experience, this paper examines the role of expansion of skilled labor force for modern services led growth and development in economies with low average educational attainment. The model economy consists of two capital‐using sectors—a service sector that employs only skilled labor and an industry sector that does not require skilled labor. The service sector represents modern skilled‐labor intensive services whereas the industry sector represents a typical South Asian industry. Supply of unskilled labor is unlimited but skilled labor is relatively scarce and grows at a finite rate. Increase in the skill premium only partially explains growth of skilled‐labor supply while the rest depends on autonomous factors, which may be influenced by education policies of the government. The main result specifies a set of necessary and sufficient conditions for existence of a unique steady state characterized by balanced sectoral growth at a rate determined by the autonomous part of skilled labor growth. A low wage share and stagnant investment conditions in the industry sector are conducive for both existence and local stability of this steady state. The model shows that supply‐side factors may completely determine steady state growth rates in structuralist models despite presence of unemployed resources.

Fuzzy optimal tracking control for nonlinear underactuated unmanned surface vehicles

In this paper, a reinforcement Q-learning fuzzy optimal tracking control method is investigated for nonlinear underactuated unmanned surface vehicles (USVs) with external disturbances. Firstly, the motion dynamics of USVs are described by the Takagi–Sugeno (T–S) fuzzy discrete-time systems. Secondly, by applying parallel distributed compensation (PDC) method and constructing cost function, the existence condition of optimal solutions is derived and reduced to the algebraic Riccati equations (AREs). To solve the solutions of the GAREs, a Q-learning value iteration (VI) algorithm is further developed, which can be implemented by eliminating the demand of initial allowable control policy and system information. The developed strategy has the advantage that the optimal control policy can ensure the USV to be stable and the desired reference signal can also be well tracked by the USV output. Finally, the proposed fuzzy optimal control algorithm is applied to control the USV, the simulation results verify the feasibility of the proposed optimal control algorithm.

On the Functional Observer Design With Sampled Measurement

In this paper, a functional observer for continuous systems with sampled measurement is designed for a class of nonlinear systems, operating under unknown inputs, and the existence conditions are derived. The nonlinear function, as a function of full states, is decomposed to Lipschitz term and an unknown one. The stability and boundedness of the estimation dynamics are analyzed and accordingly, the design procedure is formulated as a Linear Matrix Inequality (LMI) problem. Moreover, the design algorithm for some special cases is obtained. The numerical simulations are performed to evaluate the effectiveness of the proposed approach.

Finite Frequency H∞ Control of Fractional-Order Continuous–Discrete 2-D Roesser Models

The H∞ control problem of fractional-order continuous-discrete 2D Roesser models in the finite frequency is investigated in this paper. Firstly, based on the frequency-partitioning method and generalized Kalman–Yakubovič–Popov lemma, the finite frequency bounded real lemmas in form of linear matrix inequalities (LMIs) are proposed, which can be solved by LMI solvers immediately. Then, the H∞ state feedback controller is designed, and the existence conditions are established in form of bilinear matrix inequalities (BMIs). Moreover, by the provided iterative algorithm, these BMI-based conditions can be solved based on LMIs. Finally, the numerical examples are provided verify the validity of our results.

Plant genome modification technologies and some aspects of their practical use

Aim. To analyze modern methods of plant genome modification on the example of cereals and to evaluate the prospects of their use and practical significance. Methods. A review of available scientific sources and electronic resources containing data on existing and promising methods of genetic modification of cereals was conducted. Results. During the entire time of its development, mankind solved the issue of creating more productive agricultural crops that were adapted to the climatic conditions of existence. For this, domestication and selection based on spontaneous mutations were traditionally used. New technologies of genetic recombination, which have been developed in recent decades, make it possible to change the genome of plants in certain sites determined by the researcher. This has opened up unprecedented opportunities both in fundamental terms and in a whole range of applied aspects for elucidating the functions of specific genes and targeted improvement of the productivity of plants and some of them properties. Conclusions. Some modern new technologies of plant genome modifications are of significant scientific interest and practical importance. The use of these technologies is extremely important in many practical areas, especially for wheat and barley as the most agronomically important cereal crops in the world. Genome modifications agricultural crops require significant attention in terms of their safety and legal regulation of practical use. Information about modern methods of plant genome modification and directions for their use should be a mandatory element in educational courses on modern biotechnology in specialized educational institutions.

Combined Fault Diagnosis Scheme Based on Recurrent Neural Network and H− Observer for Satellite Attitude Control System

This study proposes a combined fault diagnosis scheme based on a recurrent neural network (RNN) and an H− observer for satellite attitude control systems (ACSs) in the presence of model uncertainties, external disturbances, and measurement noise. The ACS is decoupled into multiple independent channels, such that the residuals generated by the observers respond to the corresponding faults. A novel multilayer adaptive Gaussian recurrent neural network (MAGRNN) structure is developed as an approximator to estimate the lumped disturbance; a robust term is introduced to improve accuracy. Considering the actuator fault in the finite frequency domain and the fault-sensitive index, a set of H− unknown input observers (UIOs) is designed using the output of the MAGRNN-based approximator as compensation. The existence conditions of the approximator and observer are proposed and proved. The fault diagnosis results for three cases verify that the proposed method can be used for small fault detection and isolation.

Study of fractional diabetes model with and without complication class

This study investigates Diabetes Mellitus, focusing on global variations and complications for human health. We employ the ABC fractional derivative to develop a fractional-ordered diabetes model that incorporates complications for deeper understanding. This study is crucial for identifying patterns and trends by examining Diabetes Mellitus region-wise, aiding in targeted interventions and healthcare strategies, and using the ABC fractional derivative for a more accurate representation of the complexities associated with the disease, leading to more effective modeling and analysis. Our research yields important results that distinguish it from previous studies. Specifically, we investigate the stability and existence conditions of the proposed fractional-ordered diabetes model. Additionally, we employ the Adomian decomposition Laplace transform method to obtain solutions, enabling us to analyze the dynamics of the system comprehensively. Through graphical interpretations, we compare the recovery rates of diabetes in susceptible patients, both with and without complications. Regional analysis reveals varying prevalences and characteristics of Diabetes Mellitus, requiring tailored healthcare approaches. By incorporating complications into the fractional-ordered model, we enhance our understanding of the disease’s progression and its impact on recovery rates. These insights contribute to the broader field of diabetes research and offer valuable implications for clinical practice and public health policy.

Role of the whitefly maturation period on mosaic disease propagation in Jatropha curcas plant

Mosaic disease in Jatropha curcas plants is caused by begomoviruses carried by whitefly vectors, and only mature vectors can transmit the virus. In this study, a mathematical model is developed for the dynamic analysis of the spread of mosaic disease in the J. curcas plantation, accounting for the whitefly maturation period as a time delay factor. The existence conditions and stability of the equilibrium points have been studied with qualitative theory. The basic reproduction number, R0, is determined to study the stability of the disease-free equilibrium with respect to it. Transcritical bifurcation of the disease-free equilibrium and Hopf bifurcation of the endemic equilibrium are also analyzed. Using numerical simulations, the analytical findings are verified and discussed the different dynamical behaviors of the system. In this research, the stabilizing role of maturation delay has been established. That means when maturation time is large, disease will be transmitted when the infection rate is high.

“TERRORISM”: REALITY AND CONCEPTUAL FRAMEWORK

The purpose of the article is to embed the modern representation of terrorism into the conceptual framework defined in the horizon of the fundamentals of the dominant liberal version of the economic paradigm of the political (“managerial paradigm”). The political is presented as a balance of interests, fixed at the moment as the result of endless public discussion; politics in this case is management, whose task is to harmonize interests and ensure conditions for peaceful existence - based on a liberal consensus on basic rights. The reality of the political arises in the process of aesthetic/historical representation, for which perspectivism is constitutive; such reality is fragmented and centered relative to an empty place (the exclusion of the sovereign and the sovereign decision), has the properties of hyperreality, the phenomena of which are simulacra of the third level. The absence of the possibility of drawing a border (the exclusive prerogative of a sovereign decision) leads to the non-distinction of “internal” and “external”, the area of “order” and “anomie”. In this situation, war becomes a permanent mechanism for the biopolitical production of life; an unrecognized enemy is a party to the war; the war is presented as fair, the goal is declared to restore the disturbed order. An unrecognized enemy is called a terrorist; the conceptual horizon for defining the concept of “terrorism” is the anti-terrorist war in the nearest way. Thus, the philosophical approach differs from the disciplinary scientific one; the philosophical concept of terrorism has other grounds than its ideal-typical concepts, which are operated by the disciplinarily organized sciences; the evidence of paradigmatic principles makes philosophical conceptualization difficult.

FEATURES OF THE INFLUENCE OF SOCIAL MEDIA ON THE POLITICAL IDENTIFICATION OF YOUTH

The relevance of the research topic lies in the development of technical instruments that change the conditions of social existence in general and political interaction in particular. The use of such instruments has an impact on all forms of collective existence, which means that it requires different forms of identification from a person, including young people. The aim of the article is to determine the features of the influence of social media on the collective identification of young people in the political environment. To achieve this goal, it is necessary to solve a number of tasks: 1) to formulate an understanding of the essence of social media; 2) to determine the content of the concepts of “identity” and “identification”, to link them with the phenomenon of imaginary communities; 3) to identify some features of the influence of social media on the process of achieving political identity among young people. A logical method is used in this article. It allows to form a holistic view of the content of the concepts of “social media” and “identification”. A critical method is also used, which is expressed in identifying the influence of social media on the political identification of young people. The results obtained and the main conclusions of the study are that the interactive nature of social media, an unlimited range of content broadcast in them, the formation of digital identity of young people, as well as the simplified possibility of organizing civil society through the formation of imaginary Internet communities - all these aspects affect political identification of youth and have a positive impact on the course of political processes in the state.

Existence and uniqueness of limits at infinity for homogeneous Sobolev functions

We establish the existence and uniqueness of limits at infinity along infinite curves outside a zero modulus family for functions in a homogeneous Sobolev space under the assumption that the underlying space is equipped with a doubling measure which supports a Poincaré inequality. We also characterize the settings where this conclusion is nontrivial. Secondly, we introduce notions of weak polar coordinate systems and radial curves on metric measure spaces. Then sufficient and necessary conditions for existence of radial limits are given. As a consequence, we characterize the existence of radial limits in certain concrete settings.

Ahlussunnah Wal Jama'ah (ASWAJA) as a Basic Value Base for the Movement and Thought of the Indonesian Islamic Student Movement (PMII)

The Islamic Students Movement of Indonesia is an organization aimed at the formation of Indonesian Muslims who are afraid of Allah SWT, righteous, knowledgeable, competent, and responsible in practicing their knowledge and commitment to the realization of the ideals of Indonesia's independence. The purpose of this research is to know and analyze the values contained in the Ahlussunnah Wal Jama’ah (ASWAJA), which is made PMII, as the basis of the value of thought and the theological foundation. The method used in this research is the qualitative descriptive approach, which is a way to find new meanings, explain a condition of existence, determine the frequency of occurrence of something, and categorize information. In this study, there are four principles of values that can be transformed into the direction of the PMII movement, which is a framework of thinking to be able to formulate concrete solutions to the problems that exist in the current reality. There are four kinds of worshippers in the Qur’an: al-Tawassuth, Al-Tawazun, al-Asamuh, and al-I’tidal.

Multiple structures and transition mechanisms of laminar fuel-rich ethanol/air counterflowing spray flames

Structures of laminar non-premixed ethanol/air spray flames in the axisymmetric counterflow configuration are studied under fuel-rich conditions by means of numerical simulations. The monodisperse ethanol spray is carried by air and directed against an air stream. Both streams enter at 300 K, and the system is at atmospheric pressure. Up to three different structures of these flames for identical boundary and initial conditions are identified, and regime diagrams are presented that show their conditions of existence in terms of the gas strain rate on the spray side of the configuration, [Formula: see text], starting from 55/s at an initial spray velocity of 0.44 m/s. The equivalence ratio on the spray side, [Formula: see text], is varied between 1.1 and 1.6, and initial droplet radii, [Formula: see text], from 10 to 50 [Formula: see text]m are considered. The most stable spray flame structure is characterized by two chemical reaction zones. For some conditions, single chemical reaction zones on either side of the counterflow configuration are found. Conditions under which these different flame structures exist are analyzed. Previous studies identified only two different structures for non-identical boundary conditions, and in this study, three different structures are presented for the first time. Moreover, the transition mechanisms of one structure to another are analyzed. The competition between the energy-consuming spray evaporation and the exothermic chemical reaction rates as well as the location of the spray determines the existence of the different flame structures. This transition of the different flame structures may explain spray flame characteristics such as flame pulsation or flame instabilities.

Emergence and highly directed output of long-lived resonances in photonic step ladder structure

A bound state eigenfunction is defined here to be strictly localized within a subspace of a system and has no decreasing behavior. Its eigenvalue can be within state continua. Bound states in the continuum (BICs) and long-lived resonances have become a unique way to produce the extreme localization of light waves. In this communication, we present a theoretical and numerical demonstration of infinite bound states in the continuum (IBIC) and long-lived resonances in photonic ladder-like structures with four semi-infinite leads, together with their existence conditions. IBIC states are localized in an infinite subspace domain. Some of these states are inactive in the scattering and induce output zeros. Other are scattering active and induce output ones in the middle of long-lived resonances. Several continua of IBIC states remain hidden. They are bound in one of two infinite guides and some of them also in the closed loop. These discoveries are reported here for the first time to our knowledge. The ladder reference structure is composed of connected open loops of lengths L1 and L2 and four semi-infinite leads. The obtained results take due account of the state number conservation between the final system and the reference one. This conservation rule enables to find all the states of the final system and among them the bound in the continuum ones. In addition, we show the existence of long-lived resonances in each of two parallel output lines and long-lived anti-resonances in each of the two other output lines, when one uses two identical parallel simultaneous inputs. The analytical results are obtained by means of the Green’s function technique. The structures and the long-lived resonances presented in this work may have potential applications, in particular in sensing, filtering and communications.

CRITICAL BUCKLING LOAD SOLUTION OF THIN BEAM ON WINKLER FOUNDATION VIA POLYNOMIAL SHAPE FUNCTION IN STODOLA-VIANELLO ITERATION METHOD

The critical buckling load analysis of thin beam on Winkler foundation (BoWF) is crucial for BoWF subjected to in-plane compressive load. This paper presents the Stodola-Vianello method for the approximate solution of the governing ordinary differential equation (ODE). The Stodola-Vianello method expresses the ODE in iteration form after four successive integrations have been used in reformulating the equation. The problem then reduces to iteration in algebra. By deriving algebraic buckling shape functions that satisfy the boundary conditions, and substitution into the Stodola-Vianello iteration formula derived successive iterations of the buckling shape function would yield better approximations of the buckling shape. The existence condition for convergence which is the identity of the nth and (n +1) iterations are used to find the eigenvalue from which the buckling load is determined. The candidate problem solved is a BoWF with Dirichlet boundary conditions. It is found that one iteration yields sufficiently accurate buckling loads which differs from the exact solution by 0.129% for 0.0807% for and 0.0567% for where bl4 is a parameter measuring the beam structure – Winkler foundation interaction. The negligible difference in the critical buckling load found is because an approximate algebraic one-parameter shape function was used in the iteration. The paper has demonstrated the effectiveness of the Stodola-Vianello iteration for solving the stability of thin beam on Winkler foundation.

Bacterial Competition in the Presence of a Virus in a Chemostat

We derive a mathematical model that describes the competition of two populations in a chemostat in the presence of a virus. We suppose that only one population is affected by the virus. We also suppose that the substrate is continuously added to the bioreactor. We obtain a model taking the form of an “SI” epidemic model using general increasing growth rates of bacteria on the substrate and a general increasing incidence rate for the viral infection. The stability of the steady states was carried out. The system can have multiple steady states with which we can determine the necessary and sufficient conditions for both existence and local stability. We exclude the possibility of periodic orbits and we prove the uniform persistence of both species. Finally, we give some numerical simulations that validate the obtained results.