General Topology Research Articles

A Novel Unequal Power Divider With General Isolation Topology: Design and Verification

In this letter, a novel unequal power divider (PD) with three standard 50- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> ports is presented. It consists of two transmission line (TL) sections, two resistors, and a general isolation topology (GIT). Through analyzing voltages and currents of each branch, the constraint conditions of such a GIT are newly established. Considering realization of GIT, two types of topologies, i.e., asymmetrical coupled line and cascaded TL, are selected for verification. From the design charts and several design examples, the proposed PD could not only provide high power ratio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k^{2}$ </tex-math></inline-formula> with compact size but also independently adjust their fractional bandwidths ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{11}$ </tex-math></inline-formula> or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{32}$ </tex-math></inline-formula> ) with the same power ratio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k^{2}$ </tex-math></inline-formula> . Finally, an unequal PD with the power ratio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k^{2} =8$ </tex-math></inline-formula> is fabricated, and the measured results meet the simulated results very well.

Multipath Congestion Control: Measurement, Analysis, and Optimization From the Energy Perspective

Multipath TCP (MPTCP) is a promising TCP extension that exploits different Internet paths between a pair of hosts to obtain high aggregate throughput, while it also brings the concern of energy consumption. There has been a lively interest in the design of energy-efficient MPTCP. The research community, however, lacks a comprehensive understanding of which components in an MPTCP congestion control algorithm play the fundamental role in energy efficiency, how various algorithms compare against each other from energy-consuming perspective, or whether there exist potentially better solutions for energy saving. This paper takes the first step towards answering these questions. Through realworld MPTCP Linux kernel experiments, we show that the energy consumption is related to three major aspects: average throughput, path delay and different network scenarios. In order to bridge congestion control to the three aspects, we analyze the existing algorithms and capture the essential parameters of multipath congestion control model related to energy efficiency. Then we propose a window increase factor to shift traffic to low-delay energy-efficient paths. To further extend this design, we apply an energy-aware compensative parameter to fit the general hierarchical Internet topology. Our evaluation indicates that the enhanced congestion control module can successfully improve MPTCP energy efficiency without affecting its transmission performance.

DIRECTIONS OF OPTIMIZATION OF CORPORATE MULTISERVICE COMMUNICATION NETWORK PROTECTION COMPLEXES

The article considers a comprehensive approach to the protection of information of a corporate multi-service communication network, which consists in the use of technical, hardware- program, and organizational-legal measures of protection. It was determined that the protection of information from unauthorized access and its leakage through technical channels is more effectively achieved by the use of technical means. In order to determine the direction of optimization of the corporate multi-service network protection complexes and general approaches to its implementation, a model of the communication network built according to the hierarchical principle is considered. The place of the corporate network in the communication network is determined. It is noted that a more rational approach to ensuring information protection should be considered the design stage, when it is possible to predict and implement a given level of protection. A general algorithm for designing a corporate network is proposed, which consists of the stages listed in the article. At the first stage, the selection and justification of the general topology of the protected corporate network adapted to the requirements of its users was carried out. The directions of the communication traffic between the sender and the recipient of information through the network are determined. Evaluation and calculation of information flows taking into account the scaling of the network, increasing the intensity and volume of traffic, the systematization of protection functions with the possibility of both generalization and localization of them are the subject of further research. When choosing the types of physical equipment for the provision and implementation of the specified classes and functions, protection is considered for three levels of the network: the hardware part of servers and workstations; communication equipment and communication channels; gateways, bridges and tunnels of the entire diameter of the network, including segments and domains. Identified directions for improving information protection at the hardware, channel, and network support levels. Based on the results of the research, it was concluded that the complexity of solutions to increase information protection is achieved in addition to the technical direction by hardware- software and organizational-legal ones.

New Approach of Multi-Cell Stacked Cell Inverter for Solar Photovoltaic System

In this paper, a new inverter topology dedicated to isolated or grid-connected PV systems is proposed. This inverter is based on the structures of a stacked multi-cell converter (SMC) and an H-bridge. This new topology has allowed the voltage stresses of the converter to be distributed among several switching cells. Secondly, divide the input voltage into several fractions to reduce the number of power semiconductors to be switched. In this contribution, the general topology of this micro-inverter has been described and the simulation tests developed to validate its operation have been presented. Finally, we discussed the simulation results, the efficiency of this topology and the feasibility of its use in a grid-connected photovoltaic production system.

Continuity and separation axioms via infra-topological spaces

In order to investigate a particular topic in mathematics, more specifically, general topology, it is always desirable to find a weaker condition. This work is planned to study a weak (topological) structure named infra-topological space. An infra-topological space is the collection of subsets of a universe that includes the empty set and is closed under finite intersections. The continuity, openness, and homeomorphism of mappings between infra-topological spaces are explored. Through the use of some examples, analogous properties and characterizations of ordinary mappings cannot be hopped on infra-topological structures. Then, the concepts of product and coproduct of infra-topological spaces are analyzed. Furthermore, the notion of infra-quotient topologies, which are inspired by infra-continuity, is introduced. The essential properties indicate that infra-quotient topologies and ordinary quotient topologies act in parallel. The final part of this paper is devoted to the investigation of infra separation axioms (infra \(T_i\)-spaces, \(i=0,1,\ldots, 4\)). The behaviour of ordinary separation axioms cannot be translated to an infra-topological structure. More precisely, infra-\(T_3\) and infra-\(T_4\)-spaces are independent, and singletons need not be infra-closed in infra-\(T_1\)-spaces.

Ultraproducts and Related Constructions

In this work, we survey some research directions in which the ultraproduct construction and methods based on ultrafilters play significant roles. Rather different areas of mathematics have been considered: topics we are reviewing here include some aspects of the model theory of first-order and second-order existential logics, finite Ramsey theory and general topology. Special emphasis has been made for producing a uniform treatment and for highlighting interconnections between these different subjects.

Motion Magnification Applications for the Protection of Italian Cultural Heritage Assets

In recent years, the ENEA has introduced a novel methodology based on motion magnification (MM) into the Italian cultural heritage protection and monitoring field. It consists of a digital video signal processing technique able to amplify enormously the tiny movements recorded in conventional videos, while preserving the general topology of the acquired frames. Though the idea of such a methodology is not new, it has recently been provided with an efficient algorithm that makes possible a viable and low-cost magnification. Applications are extremely varied in almost every field of science and technology; however, we are interested in its application to the safeguarding of architectural heritage, a sector of the utmost importance for Italy. As ancient buildings can be extremely sensitive to even minimally invasive instrumentation, most common monitoring sensors can be replaced by contactless tools and methods, such as video-based techniques like MM. It offers many advantages: easy to use, contactless devices, virtual sensors, reusability of the videos, practicality, intuitive graphical results, quantitative analyses capability and low costs. These characteristics are well suited to the monitoring of large ancient monuments; on the other hand, historical sites have peculiarities of their own, requiring careful approaches, proper tools and trained personnel. Moreover, outdoor applications of MM present quite notable difficulties from a practical point of view, e.g., the dimensions of the studied objects, uncontrolled environmental conditions, spurious vibrations, lighting change/instability, etc. Here we give a general idea of the potential of MM and related issues, using some relevant in-the-field case studies in Italian heritage protection.

Soft ideal topological spaces

The article deals with the correspondence between soft ideal topological spaces and ideal topological ones. Investigation of soft ideal topological spaces is based on methods of general topology, and the application of results for soft omega open and strongly soft omega open sets is given.

Comparative Performance Analysis of the DC-AC Converter Control System Based on Linear Robust or Nonlinear PCH Controllers and Reinforcement Learning Agent

Starting from the general topology and the main elements that connect a microgrid represented by a DC power source to the main grid, this article presents the performance of the control system of a DC-AC converter. The main elements of this topology are the voltage source inverter represented by a DC-AC converter and the network filters. The active Insulated Gate Bipolar Transistor (IGBT) or Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) elements of the DC-AC converter are controlled by robust linear or nonlinear Port Controlled Hamiltonian (PCH) controllers. The outputs of these controllers are modulation indices which are inputs to a Pulse-Width Modulation (PWM) system that provides the switching signals for the active elements of the DC-AC converter. The purpose of the DC-AC converter control system is to maintain ud and uq voltages to the prescribed reference values where there is a variation of the three-phase load, which may be of balanced/unbalanced or nonlinear type. The controllers are classic PI, robust or nonlinear PCH, and their performance is improved by the use of a properly trained Reinforcement Learning-Twin Delayed Deep Deterministic Policy Gradient (RL-TD3) agent. The performance of the DC-AC converter control systems is compared using performance indices such as steady-state error, error ripple and Total Harmonic Distortion (THD) current value. Numerical simulations are performed in Matlab/Simulink and conclude the superior performance of the nonlinear PCH controller and the improvement of the performance of each controller presented by using an RL-TD3 agent, which provides correction signals to improve the performance of the DC-AC converter control systems when it is properly trained.

Esakia Duality for Heyting Small Spaces

We continue our research plan of developing the theory of small and locally small spaces, proposing this theory as a realisation of Grothendieck’s idea of tame topology on the level of general topology. In this paper, we develop the theory of Heyting small spaces and prove a new version of Esakia Duality for such spaces. To do this, we notice that spectral spaces may be seen as sober small spaces with all smops compact and introduce the method of the standard spectralification. This helps to understand open continuous definable mappings between definable spaces over o-minimal structures.

Interior topology: A new approach in topology

&lt;span&gt;This paper defined a new type of topology known as Interior topology. This work falls among the types of topology (such as general topology, supra topology, generalized topology, and filter) that are motivated by real-world concepts such as the orbits of planets around the sun, electron orbits around the nucleus, and so on. This form of topology is self-contained. The primary objective of this study is to respond to the question “Is general topology capable of producing Interior topology?”. Finally, we define the base for Interior topology which is called i-base.&lt;/span&gt;

A Low-Voltage Low-Loss Active Reflected Wave Canceller for a Medium-Voltage SiC Motor Drive Based on a Generalized Multilevel Inverter Topology

Multilevel topologies with SiC devices for medium-voltage (MV) motor drive have advantages to reduce the harmonics and device voltage stress and increase efficiency. However, with the application of SiC devices, the reflected wave phenomenon still happens in multilevel motor drives due to its high dv/dt, resulting in overvoltage at motor terminals. This article proposed a T-type circuit-based active reflected wave canceller (ARWC) to suppress the overvoltage of an M-level motor drive with a reduced voltage rating of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm {dc}}$ </tex-math></inline-formula> /( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M-1$ </tex-math></inline-formula> ). A coupled inductor is applied to isolate the ARWC output and the main inverter. In addition, the coupled inductor is designed with a small resistor to allow low current flow into ARWC. The proposed ARWC configuration can be applied for general multilevel topologies. A three-level ANPC converter with a 3.3-kV SiC device is built in the laboratory. A 1.2-kV SiC module is applied in the proposed ARWC. The experimental results at 1.6-kV <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm {dc}}$ </tex-math></inline-formula> and 16-A (rms) load current with and without proposed ARWC are provided and compared to verify the validity of the proposed method.

Topological Sensitivity on Hyperspaces

We introduce and study topological asymptotic sensitivity, Li-Yorke topological sensitivity, pointwise topological sensitivity for general topological spaces. We study relations among these variants of topological sensitivities and $\mathcal F$ topological sensitivity, strong topological sensitivity and multi topological sensitivity. We prove that strong topological sensitivity (respectively multi topological sensitivity) on the hyperspace dynamical system is equivalent to strong topological sensitivity (respectively multi topological sensitivity) of a dynamical system for uniform compact spaces. It is shown that Li-Yorke sensitivity and Li-Yorke topological sensitivity are equivalent on compact metric spaces. We also show that on compact Hausdorff topological spaces topological sensitivity implies topological asymptotic sensitivity. Moreover, we provide necessary examples and counterexamples.

METHOD OF TEACHING CONTINUOUS MAPPING OF TOPOLOGICAL SPACE AND ITS APPLICATION BY THE CONCEPT OF SOCIETY AND EDUCATION

In this paper, we will show how to teach general topology by using traditional methods with examples and show some applications of the rules of topology, especially in the concept of continuity between topological spaces. The application will be given as a definition of society and education through the continuity of topological spaces.

물리적 인간-로봇 상호작용을 위한 수동적 제어기의 설계

In this paper, we study the problem of control design for physical human–robot interactions. By exploring the general topology of the given control problem, we propose a generic control architecture (TDA) based on 2DOF Youla-based control. Compared to the inherent properties and tradeoffs of classical admittance control, the proposed TDA enhances nominal performance while guaranteeing coupled-stability conditions. The proposed control design method is demonstrated with numerical simulations and experiments.

The Value of the Early-Time Lieb-Robinson Correlation Function for Qubit Arrays

The Lieb-Robinson correlation function is one way to capture the propagation of quantum entanglement and correlations in many-body systems. We consider arrays of qubits described by the tranverse-field Ising model and examine correlations as the expanding front of entanglement first reaches a particular qubit. Rather than a new bound for the correlation function, we calculate its value, both numerically and analytically. A general analytical result is obtained that enables us to analyze very large arrays of qubits. The velocity of the entanglement front saturates to a constant value, for which an analytic expression is derived. At the leading edge of entanglement, the correlation function is well-described by an exponential reduced by the square root of the distance. This analysis is extended to arbitrary arrays with general coupling and topologies. For regular two and three dimensional qubit arrays with near-neighbor coupling we find the saturation values for the direction-dependent Lieb-Robinson velocity. The symmetry of the underlying 2D or 3D lattice is evident in the shape of surfaces of constant entanglement, even as the correlations front expands over hundreds of qubits.

High step‐up DC–DC converter using coupled inductor voltage multiplier cell and differential connection method

This paper proposes a high step-up DC–DC converter using coupled inductor voltage multiplier cell and differential connection method. The proposed converter is obtained by differentially connecting a Cuk converter and a Buck-Boost converter and integrating a coupled inductor voltage multiplier cell. The control mode of the two switches adopts interleaved control and the proposed converter has higher voltage gain. The diode-capacitor branch in the shared topology is used as a passive clamping branch to reduce the maximum voltage stress of switches. The working principle of the proposed converter is analyzed and its performance parameters and boundary conditions are given. The voltage gain of the converter can be improved by adding different voltage doubling structures and the general topology of the proposed converter is given. The effect of leakage inductance on the performance of the proposed converter is analyzed. Finally, a 300-W prototype was built and verified the theoretical analysis.

ω1-strongly compact cardinals and normality

We present more applications of the recently introduced ω1-strongly compact cardinals in the context of either consistency or reflection results in General Topology, focusing on issues related to normality. In particular, we show that such large cardinal notion provides a new upper bound for the consistency strength of the statement “All normal Moore spaces are metrizable” (NMSC). The proof uses random forcing, as in the original consistency proof of NMSC due to Nykos-Kunen-Solovay (see Fleissner [10]). We establish a compactness theorem for normality (i.e., reflection of non-normality) in the realm of first countable spaces, using the least ω1-strongly compact cardinal, as well as two more similar compactness results on related topological properties. We finish the paper by combining the techniques of reflection and forcing to show that our new upper bound for the consistency strength of NMSC can be also obtained via Cohen forcing, using some arguments from Dow-Tall-Weiss [6].

Application of artificial neural network with metaheuristic optimization for improving the nutritive value of fried fish

AbstractNutritional quality indices of fish deteriorate drastically during frying. In this study, using Catla catla fish and mustard oil (culinary media), extensive experiments are carried out varying the temperature, time, and oil amount to attain the best nutritional quality indices of fried fish with a tuned combination of cooking parameters. An artificial neural network (ANN) is developed to select the best model to find a nonlinear correlation between the frying conditions and nutritional quality indices. ANN‐based metaheuristic optimization methodologies, namely genetic algorithm (GA), differential evolution, firefly optimization, and gray wolf optimization (GWO), are applied to optimize the best cooking conditions. Among these, GWO is most promising for optimizing favorable inputs, practical optimal solutions, and reasonable execution time. As outputs are conflicting, multi‐objective genetic algorithm (MOGA) is implemented for their simultaneous optimization with optimum values of process variables for health benefit, reducing frying time, and minimizing the wastage of culinary media. The MOGA successfully improves the ω‐3/ω‐6 fatty acids, polyunsaturated fatty acids/saturated fatty acids, cis/trans fatty acids ratio, and index of atherogenicity values up to 40.43%, 65.35%, 137%, and 83.84%, respectively, satisfying the multi‐objective criteria.Practical applicationsThe conventional frying process of fish is successfully optimized by the developed hybrid “model‐optimization” topology that improves the nutrient value of fried fish significantly. The developed neural model automatically searches all available algorithms and activation functions exhaustively to select the best model. All single‐objective and multi‐objective genetic algorithms integrated with an artificial neural network can attain the optimum successfully for all outputs by a unique tuned cooking condition. Operators can choose the preferred solution among many Pareto optimal combinations as per their needs. Furthermore, this developed, generic topology provides a tool for process modification and optimization of other food process engineering methods.

A mathematical perspective of ultrasound image representations and image quality criteria

What is an ultrasound “image”? Where an engineer or physicist may see a quantitative map of physical properties, a physician may see qualitative anatomical features and pathologies. In the past, each image type was evaluated appropriately within its respective context: quantitative image quality was measured with criteria like the contrast-to-noise ratio (CNR), and qualitative images underwent dynamic range transformations to optimize human perception of contrast. Recent non-linear beamforming methods have blurred this line: the produced images are transformed like qualitative images but evaluated with quantitative criteria like CNR. Here, we identify the mathematical flaws in reasoning and suggest rigorous alternatives.An image assigns values to spatial coordinates. Let X denote the set of all possible image values. The mathematical structure endowed on X determines the set of equivalence-preserving transformations. For instance, qualitative images treat X as a general topological space, where images are equivalent under homeomorphisms of X (dynamic range transformations). Quantitative images treat X as a metric space and have fewer equivalence-preserving transformations. These structures determine when criteria like contrast, CNR, generalized CNR, and spatial resolution can be used. To extrapolate these criteria to other contexts, one must use relevant structure-preserving isomorphisms (e.g., histogram matching to preserve information content).