Compact Topology Research Articles

Compact complement topologies and k-spaces

Let (X,?) be a Hausdorff space, where X is an infinite set. The compact complement topology ?* on X is defined by: ?* = {0}?{X\M:M is compact in (X,?)}. In this paper, properties of the space (X,?*) are studied in ZF and applied to a characterization of k-spaces, to the Sorgenfrey line, to some statements independent of ZF, as well as to partial topologies that are among Delfs-Knebusch generalized topologies. Between other results, it is proved that the axiom of countable multiple choice (CMC) is equivalent with each of the following two sentences: (i) every Hausdorff first-countable space is a k-space, (ii) every metrizable space is a k-space. A ZF-example of a countable metrizable space whose compact complement topology is not first-countable is given.

Separation Axioms in Intuitionistic Fuzzy Compact Topological Spaces

Separation Axioms in Intuitionistic Fuzzy Compact Topological Spaces

Locally compact groups with totally disconnected space of subgroups

Abstract The closed subsets ℱ ⁢ ( X ) {\mathcal{F}(X)} of any topological space can be given a topology, called the Chabauty–Fell topology, in which ℱ ⁢ ( X ) {\mathcal{F}(X)} is quasi-compact. If X is a locally compact space, then ℱ ⁢ ( X ) {\mathcal{F}(X)} is Hausdorff. If X = G {X=G} is a locally compact group, then the subset 𝒮 ⁢ 𝒰 ⁢ ℬ ⁢ ( G ) {\mathcal{S\kern-0.853583ptU\kern-0.569055ptB}(G)} of closed subgroups is closed in ℱ ⁢ ( G ) {\mathcal{F}(G)} , and the set of closed subgroups inherits its own compact topology, called the Chabauty topology. We develop some of the important properties of this topology. More precisely, the results contained in this paper deal with the following question: Given a locally compact topological group, when is ℱ ⁢ ( G ) {\mathcal{F}(G)} (resp. 𝒮 ⁢ 𝒰 ⁢ ℬ ⁢ ( G ) {\mathcal{S\kern-0.853583ptU\kern-0.569055ptB}(G)} ) a totally disconnected space?

Completely simple endomorphism rings of modules

<p>It is proved that if A<sub>p</sub> is a countable elementary abelian p-group, then: (i) The ring End (A<sub>p</sub>) does not admit a nondiscrete locally compact ring topology. (ii) Under (CH) the simple ring End (A<sub>p</sub>)/I, where I is the ideal of End (A<sub>p</sub>) consisting of all endomorphisms with finite images, does not admit a nondiscrete locally compact ring topology. (iii) The finite topology on End (A<sub>p</sub>) is the only second metrizable ring topology on it. Moreover, a characterization of completely simple endomorphism rings of modules over commutative rings is obtained.</p>

A $G$ -Band Broadband Balanced Power Amplifier Module Based on Cascode mHEMTs

The first full $G$ -band power amplifier module demonstrated in GaAs metamorphic high electron mobility transistor (mHEMT) technology has been developed for use as a driver amplifier in instrumentation. The circuit integrated in this module uses a compact balanced cascode topology and is based on a 35-nm mHEMT technology in a grounded coplanar waveguide environment. High compactness is achieved due to the use of a small ground-to-ground spacing of $14~\mu {\mathrm{ m}}$ and an advanced process with three metallization layers. The millimeter-wave integrated circuit exhibits a linear gain higher than 15.3 dB and return losses better than 10 dB from 118 to 236 GHz, which represents an ultrabroad relative bandwidth (RBW) of 67%. A peak output power of 10 dBm is achieved at 200 GHz. The WR-5 module uses broadband transitions, which show insertion losses of less than 1.5 dB. It demonstrates a small-signal gain that exceeds 13.4 dB in the whole $G$ -band (RBW ≥ 54%). Large-signal characterization exhibits power levels higher than 3.6 dBm from 130 to 210 GHz (RBW = 47%). This module achieves the highest bandwidth in $G$ -band and the highest output power when comparing it with modules based on similar technologies.

Locally Starplus-Compactness in L-Topological Spaces

ABSTRACTThe notion of local starplus-compactness on an L-fuzzy topological space, which is an extension of the notion of local compactness in general topology, is introduced. It turns out that local starplus-compactness is finitely productive, closed hereditary and invariant under fuzzy continuous open surjections. Moreover, local starplus-compactness is a good extension of the notion of local compactness in general topology. Examples are included to show that local starplus-compactness is neither hereditary nor expansive, nor contractive.

A Symmetrical Cascaded Compact-Module Multilevel Inverter (CCM-MLI) With Pulsewidth Modulation

Cascaded H-bridge (CHB) multilevel inverters (MLIs) have been widely used for power electronics systems. While high-voltage blocking across power switches is not a constraint for low voltage applications, the research trend has been oriented to the design of more compact module topologies as an alternative for CHB. Despite the generation of more voltage levels with reduced switch count, the existing module topologies in recent literature take no account of the freewheeling current path during dead-time, thus, inducing multistep jumps in voltage levels and giving rise to undesirable voltage spikes. Addressing this concern, this paper proposes two symmetrical compact-module topologies for cascaded MLI, where freewheeling current path during dead-time is provided for smooth transition between voltage levels to prevent voltage spikes. The proposed 7-level and 13-level compact-modules demonstrated low number of conducting switches for all voltage levels. Comprehensive analysis and comparison with the latest module topologies are conducted. To validate the operation of the proposed compact-module topologies, simulation and experimental results are presented.

A 0.18 μm CMOS LDO Regulator for an On-Chip Sensor Array Impedance Measurement System.

This paper presents a fully integrated 0.18 μm CMOS Low-Dropout (LDO) Voltage Regulator specifically designed to meet the stringent requirements of a battery-operated impedance spectrometry multichannel CMOS micro-instrument. The proposed LDO provides a regulated 1.8 V voltage from a 3.6 V to 1.94 V battery voltage over a −40 °C to 100 °C temperature range, with a compact topology (<0.10 mm2 area) and a constant quiescent current of only 7.45 μA with 99.985% current efficiency, achieving remarkable state-of-art Figures of Merit (FoMs) for the regulating–transient performance. Experimental measurements validate its suitability for the target application, paving the way towards the future achievement of a truly portable System on Chip (SoC) platform for impedance sensors.

Design and Manufacturing of the SiC-Based Power Supply System for Resistive-Wall-Mode Control in JT-60SA

In JT-60SA, the control of resistive-wall-mode (RWM) instabilities will also be realized with a dedicated active control system based on 18 in-vessel sector coils. Each coil will be fed independently by a dedicated fast inverter. Due to the outstanding dynamic performance required, new insulated-gate bipolar transistor modules based on silicon carbide (SiC) have been adopted. Being capable to switch at 30 kHz, these components, together with a very fast control system, allow reaching the required high dynamic performance with the simple and compact H-bridge topology. The RWM-PS will be the first power supply system for fast control of plasma instabilities in fusion experiments adopting SiC semiconductors. This paper gives an overview of the final design of the RWM-PS, with particular emphasis on its special features and the solutions implemented to satisfy the critical requirements. The issues related with the high switching frequency and the peculiar nature of the load will be treated in detail.

On locally compact shift-continuous topologies on the α-bicyclic monoid

Abstract A topology τ on a monoid S is called shift-continuous if for every a, b ∈ S the two-sided shift S → S, x ↦ axb, is continuous. For every ordinal α ≤ ω, we describe all shift-continuous locally compact Hausdorff topologies on the α-bicyclic monoid Bα. More precisely, we prove that the lattice of shift-continuous locally compact Hausdorff topologies on Bα is anti-isomorphic to the segment of [1, α] of ordinals, endowed with the natural well-order. Also we prove that for each ordinal α the α + 1-bicyclic monoid Bα+1 is isomorphic to the Bruck extension of the α-bicyclic monoid Bα.

The nonvacuum Einstein flow on surfaces of nonnegative curvature

ABSTRACTWe prove future nonlinear stability of homogeneous solutions to the Einstein–Vlasov system with massive particles on manifolds with topology M = ℝ×Σ, where Σ is either 𝕊2 or 𝕋2. For the sphere this implies the existence of an open subset of the initial data manifold with elements of strictly positive scalar curvature, whose developments are future geodesically complete. In combination with an earlier result for hyperbolic surfaces we conclude future completeness for the Einstein–Vlasov system in 2+1 dimensions independent of the compact spatial topology for an open set of initial data.

On-Chip AC–DC Multiple-Power-Supplies Module for Transcutaneously Powered Wearable Medical Devices

Replacing the batteries of wearable medical devices is an inconvenience to the user. Wireless power transfer (WPT) could be a solution for this problem. However, the structure should be compact to satisfy the wearable device requirements and the power efficiency should be as high as possible for prolonging the user experience. Besides, as algorithms embedded in these devices become more complex, the device power consumption also increases. Fulfilling these specifications in a compact structure with better efficiency is the aim of this research paper. This paper proposes a power processing module for WPT applications. This module is embedded within the WPT path to convert receiving end ac power to dc power, and to simultaneously provide multiple dc–dc power conversion for wearable medical devices. The ac–dc circuit is specifically designed using a compact topology to convert wireless ac power to stable dc power. The dc power is further regulated by different mode controls either to perform battery charging or to provide independent voltage supplies to dc loads. The integrated circuit occupies an area of 1.9 × 2.3 mm when implemented on a 0.25 μm high voltage CMOS process.

Compact cell topology selection for size-reduction-oriented design of microstrip rat-race couplers

Compact cell topology selection for size-reduction-oriented design of microstrip rat-race couplers

Semigroup extensions of Abelian topological groups

We show that an Abelian topological group G is absolutely closed in the class of topological semigroups if and only if G is complete and there is $$n\in \mathbb {N}$$ such that the subgroup $$nG=\{nx:x\in G\}$$ is totally bounded. If for every $$n\in \mathbb {N}$$ , the subgroup nG is not totally bounded, then the topology of G can be extended to a semigroup topology $$\mathcal {T}$$ on $$G\times \mathbb {Z}^+$$ in which G is open and dense, and if G is locally compact, so can be chosen $$\mathcal {T}$$ . In particular, the topology of $$\mathbb {R}$$ can be extended to a locally compact semigroup topology on $$\mathbb {R}\times \mathbb {Z}^+$$ in which $$\mathbb {R}$$ is dense. We also show that the topology of G can be extended to a regular (equivalently, Tychonoff) semigroup topology on $$G\times \mathbb {Z}^+$$ in which G is open and dense if and only if there is a neighborhood U of $$0\in G$$ such that for every $$n\in \mathbb {N}$$ , the subgroup nG is U-unbounded.

Divergent assemblage patterns and driving forces for bacterial and fungal communities along a glacier forefield chronosequence

Despite the ubiquitous distributions and critical ecological functions of microorganisms in pedogenesis and ecosystem development in recently deglaciated areas, there are contrasting successional trajectories among bacteria and fungi, but the driving forces of community assembly still remain poorly resolved. In this study, we analyzed both bacterial and fungal lineages associated with seven different stages in the Hailuogou Glacier Chronosequence, to quantify their taxonomic composition and successional dynamics, and to decipher the relative contribution from the bottom-up control of soil nutrients and altered vegetation as well as top-down pressures from nematode grazers. Co-occurrence networks showed that the community complexity for both bacteria and fungi typically peaked at the middle chronosequence stages. The overlapping nodes mainly belonged to Proteobacteria and Acidobacteria in bacteria, and Ascomycota and Basidiomycota in fungi, which was further supported by the indicator species analysis. Variation in partitioning and structural equation modeling suggested that edaphic properties were the primary agents shaping microbial community structures, especially at the early stages. The importance of biotic factors, including plant richness and nematode feeding, increased during the last two stages along with the establishment of a coniferous forest, eventually governing the turnover of fungal communities. Moreover, bacterial communities exhibited a more compact network topology during assembly, thus supporting determinism, whereas the looser clustering of fungal communities illustrated that they were determined more by stochastic processes. These pieces of evidence collectively reveal divergent successional trajectories and driving forces for soil bacterial and fungal communities along a glacier forefield chronosequence.

COMPACT FLAT DIPOLE RECTENNA FOR IOT APPLICATIONS

A new compact topology of rectenna, which combines a miniaturized wideband printed antenna and a rectifier integrated on the radiating surface, is reported in this paper. The rectenna is designed for ISM 900 MHz band and applied to wireless power transmission and energy harvesting to supply Ultra-Wideband tags for 3D indoor localization. The rectenna allows activating a DC-DC boost converter that supplies power to the tags. It exhibits a minimum conversion efficiency of 25% for very low microwave power densities (> 0.18 µW/cm 2) on the non-optimal loading impedance (of about 10 kΩ) of a commercial DC-to-DC boost converter and power management unit. The harvested DC voltage obtained from this novel rectenna exceeds 330 mV for microwave power density of 0.22 µW/cm 2. This measured DC voltage is in the range of the cold turn-on/start-up voltage of nowadays commercial off-the-shelf DC-to-DC boost converters and power management units. The proposed rectenna is also very compact, as its surface (11 × 6 cm 2) is of 0.05λ 2 at the operating frequency (860 MHz).

On the Connection between the Dynamical System and the Ellis Compactification with Transitive Pointed System

In this paper, some relations between the flows and the Enveloping Semi-group were studied. It allows to associate some properties on the topological compactification to any pointed flows. These relations enable us to study a number of the properties of the principles of flows corresponding with using algebric properties. Also in this paper proofs to some theorems of these relations are given.

Multiple String LED Driver With Flexible and High-Performance PWM Dimming Control

The main objectives in driving multiple LED strings include achieving uniform current control and high performance PWM dimming for all strings. This work proposes a new multiple string LED driver to achieve not only current balance, but also flexible and wide range PWM dimming ratio for each string. A compact single-inductor multiple-output topology is adopted in the driver, accompanied by synchronous integrators and variable dimming frequency, to achieve both high efficiency and high performance dimming. By using the proposed variable dimming frequency scheme, high dimming frequency is applied to a string with high dimming ratio, which helps to maintain the deviation of LED string current in an acceptable range, while low dimming frequency is applied to a string with low dimming ratio, which helps to achieve rectangular LED current waveform. Meanwhile, the new time multiplexing control scheme automatically optimizes the LED string's bus voltages, thus minimizes each string's power loss. A three string LED driver prototype is constructed to validate the effectiveness of the peoposed control scheme, where the three strings can have different dimming ratios between 4% and 100%.

Design and Fabrication of Tri-Stopband Bandstop Filters Using Cascaded and Multi-Armed Methods

In this paper, we proposed a compact C-open-loop ring resonator and its equivalent circuit. The second cascaded BSF are designed using this simple C-ring resonator. The double ring BPF consists of two cascaded C-ring resonators, which are placed on the RO4003 substrate, while the other triple BSF structure consists of tree cascaded C-ring resonators, which are connected with input and output through microstrip feed lines. The both filters are simulated, optimized and partially realized using MWR simulator and Anritsu E5072A vector network analyzer VNA. In order to reduce the size and to improve the filter characteristics, novel compact filter topologies are designed basing on the previous structures. The proposed multi-band bandstop filters consist of several open-loop ring resonators placed vertically overlapping (coupled multi-armed ring resonator). Using this idea, the filter topologies with design flexibility, close size and excellent results are reached. The novel compact multi-band bandstop filters produce several stopband along a frequency range from DC to 9 GHz, in which each separate band exhibits an acceptable and useful bandwidth. Each stopband has regenerated two reflexion zeros, what leads to a good sharpness factors in the transition domains. Good agreement between the experimental results, full-wave simulation has been achieved. This new filter idea can be very attractive for the nowadays multilayer and compact radio frequency integrated circuit design.

Design of inverse Class‐F power amplifier based on dual transmission line with 87.4% drain efficiency

AbstractIn this paper, an inverse Class‐F power amplifier (PA) based on dual transmission line (DTL) is presented. The output matching network (OMN) with DTL has a simple and compact circuit topology compared with other harmonic‐tuned OMNs with open/short shunt stubs and provides up to 6th harmonic suppression. In addition, the DTL structure is equivalent to a quarter wavelength transformer for fundamental matching. A GaN HEMT is adopted to achieve high output power and high drain efficiency in the proposed inverse Class‐F PA. Finally, a 2.4 GHz inverse Class‐F PA is designed and fabricated. The experimental results show the highest drain efficiency of 87.4% in the operating frequency with the corresponding output power of 44.5 dBm, and adjacent channel power ratio (ACPR) of −50.8/‐51.6 dBc with digital predistortion technique (DPD) at 2.4 GHz.