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The purpose of this paper is to design an on-chip inductor with high inductance, high-quality factor and high self-resonance frequency for the equivalent on-chip area using fractal curves.

A novel hybrid series stacked differential fractal inductor using Hilbert and Sierpinski fractal curves is proposed with two different layers connected in series using vias. The inductor is implemented in Sonnet EM simulator using 180 nm CMOS standard process technology.

The proposed inductor reduces the parasitic capacitance and negative mutual inductance between the adjacent layers with significant improvement in overall inductance, quality factor and self-resonance frequency when compared with conventional series stacked fractal inductors.

The fractal inductor is used to create high inductance in the single-layer process, but access to multilayers is restricted owing to unusual and expensive fabrication processes.

The proposed inductor can be used in implementation of low noise amplifier, voltage controlled oscillators and power amplifiers.

This paper introduces a combination of two fractal curves to implement a hybrid fractal inductor that enhances the performance of the inductor.

This paper aims to propose a single element, dual feed, polarisation diversity antenna. The proposed antenna operates from 2.9 to 10.6 GHz for covering the entire ultra-wideband (UWB) frequency range. The antenna is designed for usage in massive multiple input multiple output (MIMO) and closed packaging applications.

The size of the antenna is 24 × 24 × 1.6 mm³. The radiating element of the antenna is derived from the Sierpinski–Knopp (SK) fractal geometry for miniaturization of the antenna size. The antenna has a single reflecting stub placed between the two orthogonal feeds, to improve isolation.

The proposed antenna system exhibits S₁₁ < −10 dB, S₂₁ < −15 dB and stable radiation characteristics in the entire operating region. It also offers an envelope correlation coefficient < 0.01, a diversity gain > 9.9 dB and a capacity loss < 0.4 bps/Hz. The simulated and measured outputs were compared and results were found to be in similarity.

The proposed UWB-MIMO antenna has significant size reduction through usage of SK fractal geometry for radiating element. The antenna uses a single radiating element with dual feed. The stub is between the antenna elements which provide a compact and miniaturized MIMO solution for high density packaging applications. The UWB-MIMO antenna provides an isolation better than −20 dB in the entire UWB operating band.

This paper aims at multi-attribute and multi-program group decision making when the attribute weights are completely unknown and the attribute value information is in the form of the interval number.

This is an artificial intelligence algorithm for designing information gathering in group decision making. The authors propose the nonlinear programming model to gather information based on plant growth simulation algorithm (PGSA). The authors collect each program on each attribute group decision preference ordering interval and then use them to find the preference vector and the preference matrix. The entropy method is used to determine the weight of each attribute by the constructed preference matrix. According to the possibility degree matrix of each attribute, the combined effect vector is established by the priority weight vector method, which sorts and selects the best decision making program.

To the authors' knowledge, the application of PGSA in the field of management decisions to collect program on each attribute group decision making preference interval number is the first trial in literature. It has retained more valuable decision making information from all experts without distortion.

In practice, a real number may not be an accurate representation, but only gives a range of values to describe the attributes. This study provides a useful measurement of interval number information for managers to evaluate military science, venture capital, and environmental assessment, etc.

The methodology considers the complete information to ensure no information distortion even with large and complex systems. The authors adopt computer artificial intelligence algorithms to obtain the objective evaluation, which is meaningful for both research studies and practical use.

Antenna miniaturization, multiband operation and wider operational bandwidth are vital to achieve optimal design for modern wireless communication devices. Using fractal geometries is recognized as one of the most promising solutions to attain these characteristics. The purpose of this paper is to present a unique structure of patch antenna using hybrid fractal technique to enhance the performance characteristics for various wireless applications and to achieve better miniaturization.

In this paper, the authors propose a novel hybrid fractal antenna by combining Koch and Minkowski (K-M) fractal geometries. A microstrip patch antenna (MPA) operating at 1.8 GHz is incorporated with a novel K-M hybrid fractal geometry. The proposed fractal antenna is designed and simulated in CST Microwave studio and compared with existing Koch fractal geometry. The prototype for the third iteration of the K-M fractal antenna is then fabricated on FR-4 substrate and tested through vector network analyzer for operating band/voltage standing wave ratio.

The third iteration of the proposed K-M fractal geometry results in achieving a 20% size reduction as compared to an ordinary MPA for the same resonant frequency with impedance bandwidth of 16.25 MHz and a directional gain of 6.48 dB, respectively. The operating frequency of MPA also lowers down to 1.44 GHz.

Further testing for the radiation patterns in an anechoic chamber shows good agreement to those of simulated results.

The objective of the present work is to find an alternative approach for gearbox condition monitoring using wear particle characterization incorporated with image vision systems.

It is a quite well‐known phenomenon that wear generates whenever two metallic bodies have contact with each; other hence the present work tries to investigate the effect of improper lubrication in the gearbox due to wear particle generation between gear wheels. Since the identification of wear for machine condition monitoring needs much expertise knowledge and is time‐consuming using the conventional process, fractal mathematics with image morphological analysis has been utilized to overcome this situation in the present work.

The type of wear has been found for the present method by utilizing the lubricant used in the system ferrographically and a great deal of image processing has been done to characterize the type of particle so that the proper maintenance strategy can be undertaken.

Wear particle characterization is a quite common method in maintenance engineering, especially when fault diagnosis of any equipment is concerned. In the present work, the CCD acquisition of the images has been done for different particles, but one analysis amongst them has been shown in this paper. Among all other methodologies, the new technique of fractal mathematics has been used in the present work to minimize the imaging hazards and to make the system more user‐friendly.

Presents the most recent work carried out in the wider context of IST‐Adrenalin project, dealing with the facilitation, formation and lifecycle management of networked enterprises and organisations. In this respect, how information supply chains and routes can be organised and navigated across networked enterprise activities is specified, designed and realised in a conceptual way within the context of a branch independent model that builds on the fractal idea by supporting self‐similarity, self‐organisation, self‐optimisation and dynamic organisational behavior. The approach described places heavy emphasis on the need for interoperable, integrated, and cost‐effective business practices and capabilities within each individual organisation and across the supply as well as the value chains with respect to information technology. A reflection of the above approach will be realized by the efficient optimisation of the information supply chain and fractal company concepts which will in turn significantly affect the design and performance of the industry concerned (and particularly networked organisations).

The distribution of natural numbers in the Ulam spiral manifests a series of unexpected regularities of the elusive prime numbers. Their sequencing remains a topic of research interest, with many ramifications in different branches of Mathematics, especially in number theory and the prime factorisation problem. Accordingly, the focus of the research is on the most known and widespread asymmetric cryptographic system, that is, the RSA encryption.

This paper presents the presence of one, two, three or four adjacencies for the diverse primes that appear in a spiral, considering the Hardy–Littlewood twin prime conjecture and the constellations of primes.

Through equations, the calculation formulas of primes inside a spiral that have one to four primes in their adjacent places is offered, with approximate expressions that facilitate the operations, showing that the adjacencies decrease very rapidly as the spiral progresses, although without disappearing.

A generalisation to cases in which the distances to the prime values change in an ascending way in accordance with the step of the Ulam spiral is offered.

In particular, this paper aims to systematically analyze a few prominent wireless sensor network (WSN) clustering routing protocols and compare these different approaches according to the taxonomy and several significant metrics.

In this paper, the authors have summarized recent research results on data routing in sensor networks and classified the approaches into four main categories, namely, data-centric, hierarchical, location-based and quality of service (QoS)-aware, and the authors have discussed the effect of node placement strategies on the operation and performance of WSNs.

Performance-controlled planned networks, where placement and routing must be intertwined and everything from delays to throughput to energy requirements is well-defined and relevant, is an interesting subject of current and future research. Real-time, deadline guarantees and their relationship with routing, mac-layer, duty-cycles and other protocol stack issues are interesting issues that would benefit from further research.

A least‐squares finite element analysis of viscous fluid flow together with a trajectory integration technique for tracers is formulated and provides a mechanism for investigating mixing. Tracer integration is carried out using an improved Heun predictor‐corrector. Results from our supporting numerical studies on the CRAY and Connection Machine (CM) closely resemble the patterns of mixing observed in experiments. A “box‐counting” scheme and other measures to characterize the level of mixing are developed and investigated. This measure is utilized in numerical experiments to determine an optimal forcing frequency for mixing by periodic boundary motion in a rectangular enclosure. Some details concerning the numerical schemes and vector‐parallel implementation are also included.

Seeks to integrate the complete design process beginning with a design created with the mathematical perception of fractal geometry, followed by the introduction of these images into CAD systems and its adjustment to the technical and aesthetic limitations of the printing industry. The result is an artwork created on a pure mathematical basis using the most recent techniques of computer‐aided textile design.