Inequality Principle Research Articles

A Closed-Form Solution to Observer Design Problem for Ostensible Metzler Takagi-Sugeno Systems

This paper addresses the state estimation problems related to the generalized fuzzy observer design for ostensible Metzler Takagi-Sugeno (T-S) systems. Attention is focused on design constraints for the concept of diagonal stabilization and positivity of observer gain matrices. On the basis of some new interpretations, the parameterizations of ostensible Metzler T-S fuzzy systems is presented, which opens the way to the solution of the design problem using only the principle of linear matrix inequalities. The same approach is intended to ensure the stability of the dynamics of the estimation error. The presented method extends and generalizes the results that have been presented in the literature so far.

Estimations of global Mittag–Leffler bounds and synchronization for fractional-order permanent magnet synchronous motor systems

This article investigates the global Mittag-Leffler bounds (GM-LBs) and synchronization of fractional-order permanent magnet synchronous motors (FOPMSMs). To begin with, by using some appropriate generalized Lyapunov functions, the extremum principle of function and fractional differential inequalities, a few new bounds for the three-dimensional cylindrical and ellipsoidal domains and a rotatory parabolic body of FOPMSMs are estimated by utilizing the parameters in the systems, which improves the earlier studies and may conclude some new estimates. Moreover, linear feedback control strategies owning one or two inputs and fractional adaptive control owning both single input and single state are accepted to come true the global Mittag-Leffler synchronization (GM-LS) and global asymptotic synchronization (GAS) of two FOPMSMs. Some new criteria for the synchronization are acquired by utilizing some inequality approaches. Finally, the feasibility of the proposed control schemes is verified by numerical simulations.

GVP-RRT: a grid based variable probability Rapidly-exploring Random Tree algorithm for AGV path planning

In response to the issues of low solution efficiency, poor path planning quality, and limited search completeness in narrow passage environments associated with Rapidly-exploring Random Tree (RRT), this paper proposes a Grid-based Variable Probability Rapidly-exploring Random Tree algorithm (GVP-RRT) for narrow passages. The algorithm introduced in this paper preprocesses the map through gridization to extract features of different path regions. Subsequently, it employs random growth with variable probability density based on the features of path regions using various strategies based on grid, probability, and guidance to enhance the probability of growth in narrow passages, thereby improving the completeness of the algorithm. Finally, the planned route is subjected to path re-optimization based on the triangle inequality principle. The simulation results demonstrate that the planning success rate of GVP-RRT in complex narrow channels is increased by 11.5–69.5% compared with other comparative algorithms, the average planning time is reduced by more than 50%, and the GVP-RRT has a shorter average planning path length.

More Quickly-RRT*: Improved Quick Rapidly-exploring Random Tree Star algorithm based on optimized sampling point with better initial solution and convergence rate

RRT* (Rapidly-exploring Random Tree Star), as a variant of RRT (Rapidly-exploring Random Tree), is widely used to solve path planning problems because of its asymptotic optimality. However, the algorithm is inefficient due to the high initial path cost and the slow convergence rate. In this paper, we propose a More Quickly-RRT* (MQ-RRT*) path planning algorithm based on optimized sampling points to solve the problems. A sparse sampling mechanism is proposed in MQ-RRT* to improve the global search efficiency by reducing repetitive sampling. To make the random tree oriented when expanding, a dynamic goal-biased strategy is proposed, which can reduce the sampling time. Like Q-RRT* (Quick-RRT*), MQ-RRT* expands the set of possible parent nodes in the ChooseParent and Rewire phases, which reduces the path cost. On this basis, a method for creating a new parent node close to the obstacle is proposed. The creation process can be divided into two steps: Remove-tips and CreateNodes, which further reduces the cost of path generation and makes the path smoother by using the triangle inequality principle. Finally, numerical simulations are used to compare the proposed algorithm with RRT*, Q-RRT*, GuILD (Guided Incremental Local Densification), and F-RRT* (Fast-RRT*), which verifies that the proposed algorithm has certain advantages in path cost, convergence rate, and path smoothness.

Robust stabilization of fractional-order hybrid optical system using a single-input TS-fuzzy sliding mode control strategy with input nonlinearities

<p>Hybrid optical systems with integrated control mechanisms enable a dynamic adjustment of optical components, ensuring real-time optimization, adaptability to changing conditions, and precise functionality. This control requirement enhances their performance in applications demanding responsiveness, such as autonomous systems, adaptive optics, and advanced imaging technologies. This research introduces a novel approach, employing a dynamic-free Takagi-Sugeno fuzzy sliding mode control (TS-fuzzy SMC) technique, to regulate and stabilize a specific category of chaotic fractional-order modified hybrid optical systems. The method addresses uncertainties and input-saturation challenges within the system. Leveraging a novel fractional calculus definition along with the non-integer type of the Lyapunov stability theorem and linear matrix inequality principle, the TS-fuzzy SMC approach was applied to effectively mitigate and regulate the undesired behavior of the fractional-order chaotic-modified hybrid optical system. Notably, this scheme achieved control without experiencing undesirable chattering phenomena. The paper concludes by offering concrete examples and comparisons, demonstrating how the theoretical findings are applied in real-world scenarios. This provides practical insights into the effectiveness of the proposed approach in diverse applications.</p>

Bounding Formulae for the Capacitance of a Cylindrical Two-dimensional Capacitor with Cartesian Orthotropic Dielectric Material

This paper addresses the evaluation of a two-dimensional cylindrical capacitor featuring homogeneous Cartesian anisotropic dielectric material. The development of a bounding formula forms the crux of the investigation and is grounded in the principles of the Cauchy-Schwarz inequality, a mathematical concept widely acknowledged for establishing relationships between different mathematical entities. In the course of this study, a dual-sided bound is systematically derived for the circular cylindrical two-dimensional capacitor through the application of well-established inequality relations. These bounds play a pivotal role in setting limits on the capacitance of the system, providing valuable insights into its electrical behavior.

Variational principles for monotone variational inequalities: The single-valued case

We consider a parameterized variational inequality \((A,Y)\) in a Banach space \(E\) defined on a closed, convex and bounded subset \(Y\) of \(E\) by a monotone operator \(A\) depending on a parameter. We prove that under suitable conditions, there exists an arbitrarily small monotone perturbation of \(A\) such that the perturbed variational inequality has a solution which is a continuous function of the parameter, and is near to a given approximate solution. In the nonparametric case this can be considered as a variational principle for variational inequalities, an analogue of the Borwein-Preiss smooth variational principle.
 Some applications are given: an analogue of the Nash equilibrium problem, defined by a partially monotone operator, and a variant of the parametric Borwein-Preiss variational principle for Gâteaux differentiable convex functions under relaxed assumtions.
 The tool for proving the main result is a useful lemma about existence of continuous \(\varepsilon\)-solutions of a variational inequality depending on a parameter. It has an independent interest and allows a direct proof of an analogue of Ky Fan's inequality for monotone operators, introduced here, which leads to a new proof of the Schauder fixed point theorem in Gâteaux smooth Banach spaces.

Understanding the Importance and Profitability Impact of Debt to Equity Ratio on Companies

The progressive debate on the capitalist system of capitalism has been one of the most important institutional topics in the literature since Modigliani and Miller (M-M theorem 1958 and 1963) incorporated it into origin and education. Financial impact on company value. To address this issue, it relied on an international agency that has evaluated the performance of large and low-debt companies since 2004. December. until 2018 The findings showed the performance of large debt capital companies. significantly lower than the low debt-to-equity ratio. We noticed tall companies. Businesses are designed to be financially stable and therefore cheaper than their peers, as higher debt leads to less bankruptcy losses. Interestingly, our research focuses on specific areas: cross-border, cross-sectoral, added value and long-term analysis. These empirical data later contradicted M. M.'s recommendations on the principle of inequality in the capital system (1958; 1963).

Sharp constants in inequalities admitting the Calderón transference principle

AbstractThe aim of this note is twofold. First, we prove an abstract version of the Calderón transference principle for inequalities of admissible type in the general commutative multilinear and multiparameter setting. Such an operation does not increase the constants in the transferred inequalities. Second, we use the last information to study a certain dichotomy arising in problems of finding the best constants in the weak type $(1,1)$ and strong type $(p,p)$ inequalities for one-parameter ergodic maximal operators.

Image Restoration with Fractional-Order Total Variation Regularization and Group Sparsity

In this paper, we present a novel image denoising algorithm, specifically designed to effectively restore both the edges and texture of images. This is achieved through the use of an innovative model known as the overlapping group sparse fractional-order total variation regularization model (OGS-FOTVR). The OGS-FOTVR model ingeniously combines the benefits of the fractional-order (FO) variation domain with an overlapping group sparsity measure, which acts as its regularization component. This is further enhanced by the inclusion of the well-established L2-norm, which serves as the fidelity term. To simplify the model, we employ the alternating direction method of multipliers (ADMM), which breaks down the model into a series of more manageable sub-problems. Each of these sub-problems can then be addressed individually. However, the sub-problem involving the overlapping group sparse FO regularization presents a high level of complexity. To address this, we construct an alternative function for this sub-problem, utilizing the mean inequality principle. Subsequently, we employ the majorize-minimization (MM) algorithm to solve it. Empirical results strongly support the effectiveness of the OGS-FOTVR model, demonstrating its ability to accurately recover texture and edge information in images. Notably, the model performs better than several advanced variational alternatives, as indicated by superior performance metrics across three image datasets, PSNR, and SSIM.

Application of Ant Colony Optimization Algorithm Based on Triangle Inequality Principle and Partition Method Strategy in Robot Path Planning

Path planning is an important area of mobile robot research, and the ant colony optimization algorithm is essential for analyzing path planning. However, the current ant colony optimization algorithm applied to the path planning of mobile robots still has some limitations, including early blind search, slow convergence speed, and more turns. To overcome these problems, an improved ant colony optimization algorithm is proposed in this paper. In the improved algorithm, we introduce the idea of triangle inequality and a pseudo-random state transfer strategy to enhance the guidance of target points and improve the search efficiency and quality of the algorithm. In addition, we propose a pheromone update strategy based on the partition method with upper and lower limits on the pheromone concentration. This can not only improve the global search capability and convergence speed of the algorithm but also avoid the premature and stagnation phenomenon of the algorithm during the search. To prevent the ants from getting into a deadlock state, we introduce a backtracking mechanism to enable the ants to explore the solution space better. Finally, to verify the effectiveness of the proposed algorithm, the algorithm is compared with 11 existing methods for solving the robot path planning problem, including several ACO variants and two commonly used algorithms (A* algorithm and Dijkstra algorithm), and the experimental results show that the improved ACO algorithm can plan paths with faster convergence, shorter path lengths, and higher smoothness. Specifically, the algorithm produces the shortest path length with a standard deviation of zero while ensuring the most rapid convergence and the highest smoothness in the case of the shortest path in four different grid environments. These experimental results demonstrate the effectiveness of the proposed algorithm in path planning.

Potential-Field-RRT: A Path-Planning Algorithm for UAVs Based on Potential-Field-Oriented Greedy Strategy to Extend Random Tree

This paper proposes a random tree algorithm based on a potential field oriented greedy strategy for the path planning of unmanned aerial vehicles (UAVs). Potential-field-RRT (PF-RRT) discards the defect of traditional artificial potential field (APF) algorithms that are prone to fall into local errors, and introduces potential fields as an aid to the expansion process of random trees. It reasonably triggers a greedy strategy based on the principle of field strength descending gradient optimization, accelerating the process of random tree expansion to a better region and reducing path search time. Compared with other optimization algorithms that improve the sampling method to reduce the search time of the random tree, PF-RRT takes full advantage of the potential field without limiting the arbitrariness of random tree expansion. Secondly, the path construction process is based on the principle of triangle inequality for the root node of the new node to improve the quality of the path in one iteration. Simulation experiments of the algorithm comparison show that the algorithm has the advantages of fast acquisition of high-quality initial path solutions and fast optimal convergence in the path search process. Compared with the original algorithm, obtaining the initial solution using PF-RRT can reduce the time loss by 20% to 70% and improve the path quality by about 25%. In addition, the feasibility of PF-RRT for UAV path planning is demonstrated by actual flight test experiments at the end of the experiment.

HUMAN RIGHTS RELATIONSHIPS ON THOSE CHILDREN STUDIED IN A SCHOOL UNDER ARTICLE 31 OF EDUCATION OF THE CONSTITUTION OF THE REPUBLIC OF INDONESIA 1945 (at Tunas Mulia Elementary School Gading Serpong)

The study aims to identify obstacles - obstacles faced in fulfilling a child's basic human rights (human rights) in education article 31. The protection of human rights became an element of legal sovereignty. A legal requirement is good if it produces a good application. The theory supporting this study is the concept of legal sovereignty, where the theory of justice lies in the two principal principles used in creating justice. Same freedom, as long as it benefits all parties, the principle of inequality used to profit the weakest. The research method used is a correlation description analysis with data collection techniques in-depth interviews, observation, and documentation. Studies show that human rights in children have a correlation value of 0.145. Basically, human rights enforcement efforts in basic have a significantly low correlation with Article 31 Education guarantee freedom in self-development in accordance with a nine-year government program.

Linear Matrix Inequality-Based Multivariable Controller Design for Boost Cascaded Charge-Pump-Based Double-Input DC–DC Converter

An analysis and controller design of double-input dc–dc converter (DIDDC) is introduced in this article. This converter is integrated with buck and boost converters at the front-end and a charge pump on the back-end. Salient features of this topology are as follows: (i) ripple content is low in source currents, (ii) both the dc sources are connected through an inductor, which gives rise to a smooth source current waveform, (iii) both the sources supply power to load either in standalone or simultaneously together, and (iv) two control–loops (one for source current regulation, while the second one for load voltage regulation) are sufficient enough to ensure power transfer/management from dc sources to load. To ensure power management on the input dc sources while keeping a stable closed-loop converter system, a multivariable diagonal controller is designed. The first diagonal controller performs the load voltage regulation task, while the second controller regulates input of source-2 dc current. From the control point of view, the double-input single-output converter becomes a two-input two-output control problem and exhibits control–loop interactions due to the power flow from two different sources to load through common elements. The impact of off-diagonal elements’ interactions is accounted by using decouplers. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust control theory and linear matrix inequality (LMI) principles are adopted to design reliable controllers. The structured controller of fixed order (PID) is designed by enforcing the necessary type LMIs. To demonstrate the feasibility and effectiveness of multivariable controllers of the DIDDC, a 60/24 V to 48 V, 150 W, 50 kHz topology prototype is constructed, and the power management aspects are investigated experimentally. Load voltage regulation, source current regulation, load sharing on the input dc sources, and power management aspects of LMI-based controllers were tested extensively for all possible disturbances. In all these test cases, the closed-loop double-input converter system is stable and robust in rejecting a variety of disturbances created.

ФОРМУВАННЯ ВІДНОСИН МІЖ РСФРР І УСРР НА ПОЧАТКУ 1920-Х РР.: ШЛЯХ ДО УНІТАРИЗМУ

The article examines the process of formation of a unitary Soviet state, features of relations between the RSFSR and the USSR in 1919–1923, elements of their interstate status, circumstances of the political motivation of unitarism in relations are revealed. The formation and functioning of relations between the RSFSR and the USSR, their institutionalization, are revealed. The factors that influenced the fragmentation of the interstate status during the researched period, its unification in the conditions of systemic unitization with their implementation in political-economic and administrative-territorial relations were established. It was established that the measures aimed at the political mastery of Ukraine by Soviet Russia went beyond the scope of the legal registration of state relations between Russia and Ukraine. In the relations between the RSFSR and the USSR in the first third of the 1920s, a combination of tactics of incorporation by means of forceful expansion was observed with an emphasized declaration of Ukraine's independence and the adoption of decisions that transformed the latter into autonomy. The interstate relations of the RSFSR and the USSR were based on the Bolshevik doctrine, the commonality of ideological and political tasks, the state system and socio-economic system, which was equally organized and built on common foundations. The relations formed between the RSFSR and the USSR in the early 1920s had significant flaws. They were immediately based on the principle of inequality of their subjects. The RSFSR had serious advantages in relations with Ukraine, appropriating the rights of the union center.

Curriculum Proposal for Social Justice Education: A Case Study within High School and College in Japan

During the COVID-19 pandemic, the socially vulnerable were placed in an even more difficult position. High school and college liberal arts education on social justice is needed to address the possible emerging and re-emerging infectious disease pandemics. A desirable educational curriculum to actualize this should include (1) Basic Theory of Ethics and Social Justice—justice and goodness, justice in Ancient Greece, deontology, utilitarianism, and the principle of inequality—, (2) Social Justice Theories—liberal egalitarianism, communitarianism, and social structural approach, (3) Psychology and Behavioral Economics—social intuitionist model, implicit association test, and nudge—, and (4) Advocacy—racism and xenophobia, elderly, disabilities, women, gender and justice—. The curriculum on social justice aims to help students understand the value of social justice, recognize inequality and disparity in society, and acquire the ability to address the widening social gap and inequality. The concept of justice is internationally diverse. Thus, extracting “social justice” in the context of each country’s culture and adding it to the social justice education curriculum is important.

Design and Implementation of an Improved K-Means Clustering Algorithm

Aiming at the problems of the traditional K-means clustering algorithm, such as the local optimal solution and the slow clustering speed caused by the uncertainty of k value and the randomness of the initial cluster center selection, this paper proposes an improved KMeans clustering method. The algorithm first uses the idea of the elbow rule based on the sum of squares of errors to obtain the appropriate number of clusters k, then uses the variance as a measure of the degree of dispersion of the samples, and selects k data points with the smallest variance and the distance greater than the average distance of the samples as the initial clustering center of the data set. Finally, combined with the “triangular inequality principle,” the unnecessary distance calculation of the KMeans algorithm in the iterative process is reduced, and the algorithm operation efficiency is improved. The results show that the improved KMeans clustering algorithm is tested on the UCI data set. Compared with the traditional k-means algorithm and Canopy-KMeans algorithm, the accuracy and speedup ratio of the improved KMeans clustering algorithm are significantly improved, and the clustering quality is improved.

Periyar's ideas of Social Justice in Dravidianism

It was Thanthai Periyar who taught the definition of human life that a life of self-respect is a healthy life. Thanthai Periyar was a self-thinker who fought vigorously for the abolition of caste. He was involved in the struggles to eradicate the inherent discrimination caused by God, religion, and caste, and to create equality for all. One such struggle was the reservation struggle, also called communal rights. It can be seen through this that awareness is given to the Tamils to maintain the victory achieved in the struggle for communal rights. The purpose of this article is to bring out economic discrimination, social differences, the discrimination of man, the one society without caste, which made me a rationalist, the one who advocated a religion other than caste, the principle of inequality, no discrimination, the principle of self-respect, and the countless castes in the same nation.

War as a Phenomenon and Reality: 02.24.2022

The military aggression of Russia (RF) against Ukraine, which began in 2014 and received the status of a full-scale war on February 24, 2022, became a watershed in the history of modern Europe and the world, breaking the world order that existed for almost 70 years after World War II. An analysis of the causes of what happened today should be carried out not with a theoretical, but with an instrumental goal: its results should provide a clear understanding and specific tools of influence – «here and now» – on what is happening, since the war is relevant, it unfolds in real time and space, taking real lives and destroying real cities of a real country - Ukraine. The article analyzes war as a Phenomenon and a terrible Reality that occurs and unfolds «here and now»... An ontological analysis of the principle of inequality is undertaken – as a deep mechanism for the coexistence and interaction of states, whose value, discursive, existential and other differences inevitably lead to wars, if systemic “instruments of deterrence” are not purposefully and methodically introduced. Аnd the rules of mutual observance of common values in the process of their existence and life. The attitudes to the Past (History), Truth and the Other are analyzed as ontological foundations of the subjectivity of the state, dysfunctions within which lead to tragic crises, including war. Antinomic (opposite and invariably accompanying each other) traitssigns of societies-cultures are presented, which lead to antagonism and the impossibility of peaceful coexistence, since they reveal an essential, ontological contradiction – the inequality of values. The phenomenon of “subjectivity of the state” is characterized as a key instrument of sovereignty.

A Liouville comparison principle for semilinear elliptic second-order inequalities

We consider semilinear elliptic second-order partial differential inequalities of the form (*) in the whole space , where , q>0 and L is a linear elliptic second-order partial differential operator in divergence form. We assume that the coefficients of the operator L are measurable and locally bounded such that the quadratic form associated with the operator L is symmetric and non-negative definite. We obtain a Liouville comparison principle in terms of capacities associated with the operator L for solutions of (*) which are measurable and belong locally in to a Sobolev-type function space also associated with the operator L.