Modular Design for Symmetric Functions Using Quantum Quaternary Logic

Abstract In this paper, we developed a new navigation system, called ATCM, which detects obstacles in a sliding window with an adaptive threshold clustering algorithm, classifies the detected obstacles with a decision tree, heuristically predicts potential collision and finds optimal path with a simplified Morphin algorithm. This system has the merits of optimal free-collision path, small memory size and less computing complexity, compared with the state of the arts in robot navigation. The modular design of 6-steps navigation provides a holistic methodology to implement and verify the performance of a robot’s navigation system. The experiments on simulation and a physical robot for the eight scenarios demonstrate that the robot can effectively and efficiently avoid potential collisions with any static or dynamic obstacles in its surrounding environment. Compared with the particle swarm optimisation, the dynamic window approach and the traditional Morphin algorithm for the autonomous navigation of a mobile robot in a static environment, ATCM achieved the shortest path with higher efficiency.

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Applying Ateb–Gabor Filters to Biometric Imaging Problems

Symmetry ◽

10.3390/sym13040717 ◽

2021 ◽

Vol 13 (4) ◽

pp. 717

Author(s):

Mariia Nazarkevych ◽

Natalia Kryvinska ◽

Yaroslav Voznyi

Keyword(s):

Wavelet Transformation ◽

Symmetric Functions ◽

Gabor Filter ◽

Signal To Noise Ratio ◽

The Other ◽

Mean Square ◽

Image Transformation ◽

Gabor Filtering ◽

Signal To Noise ◽

Filtration Method

This article presents a new method of image filtering based on a new kind of image processing transformation, particularly the wavelet-Ateb–Gabor transformation, that is a wider basis for Gabor functions. Ateb functions are symmetric functions. The developed type of filtering makes it possible to perform image transformation and to obtain better biometric image recognition results than traditional filters allow. These results are possible due to the construction of various forms and sizes of the curves of the developed functions. Further, the wavelet transformation of Gabor filtering is investigated, and the time spent by the system on the operation is substantiated. The filtration is based on the images taken from NIST Special Database 302, that is publicly available. The reliability of the proposed method of wavelet-Ateb–Gabor filtering is proved by calculating and comparing the values of peak signal-to-noise ratio (PSNR) and mean square error (MSE) between two biometric images, one of which is filtered by the developed filtration method, and the other by the Gabor filter. The time characteristics of this filtering process are studied as well.

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Engineered Modular Design of a Nanoscale CoNP/Aunano Hybrid Assembly for High-Performance Overall Water Splitting

ACS Applied Energy Materials ◽

10.1021/acsaem.1c01221 ◽

2021 ◽

Author(s):

Noor-Ul-Ain Babar ◽

Fayyaz Hussain ◽

Muhammad Naeem Ashiq ◽

Khurram Saleem Joya

Keyword(s):

Water Splitting ◽

High Performance ◽

Modular Design ◽

Hybrid Assembly ◽

Overall Water Splitting

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The Modular Design of M-SIW Wideband Band-stop Filter

2020 IEEE Ukrainian Microwave Week (UkrMW) ◽

10.1109/ukrmw49653.2020.9252676 ◽

2020 ◽

Author(s):

Kemal Guvenli ◽

Sibel Yenikaya ◽

Mustafa Secmen ◽

Ceyhan Turkmen

Keyword(s):

Modular Design ◽

Band Stop Filter

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A symmetric Bloch–Okounkov theorem

Research in the Mathematical Sciences ◽

10.1007/s40687-021-00253-8 ◽

2021 ◽

Vol 8 (2) ◽

Author(s):

Jan-Willem M. van Ittersum

Keyword(s):

Symmetric Functions ◽

Graded Algebra ◽

Symmetric Polynomials ◽

Generating Series

AbstractThe algebra of so-called shifted symmetric functions on partitions has the property that for all elements a certain generating series, called the q-bracket, is a quasimodular form. More generally, if a graded algebra A of functions on partitions has the property that the q-bracket of every element is a quasimodular form of the same weight, we call A a quasimodular algebra. We introduce a new quasimodular algebra $$\mathcal {T}$$ T consisting of symmetric polynomials in the part sizes and multiplicities.

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