39 research outputs found
Constructions for orthogonal designs using signed group orthogonal designs
Craigen introduced and studied signed group Hadamard matrices extensively and
eventually provided an asymptotic existence result for Hadamard matrices.
Following his lead, Ghaderpour introduced signed group orthogonal designs and
showed an asymptotic existence result for orthogonal designs and consequently
Hadamard matrices. In this paper, we construct some interesting families of
orthogonal designs using signed group orthogonal designs to show the capability
of signed group orthogonal designs in generation of different types of
orthogonal designs.Comment: To appear in Discrete Mathematics (Elsevier). No figure
Some Constructions for Amicable Orthogonal Designs
Hadamard matrices, orthogonal designs and amicable orthogonal designs have a
number of applications in coding theory, cryptography, wireless network
communication and so on. Product designs were introduced by Robinson in order
to construct orthogonal designs especially full orthogonal designs (no zero
entries) with maximum number of variables for some orders. He constructed
product designs of orders , and and types and ,
respectively. In this paper, we first show that there does not exist any
product design of order , , and type where the notation is used to show that repeats
times. Then, following the Holzmann and Kharaghani's methods, we construct some
classes of disjoint and some classes of full amicable orthogonal designs, and
we obtain an infinite class of full amicable orthogonal designs. Moreover, a
full amicable orthogonal design of order and type is constructed.Comment: 12 pages, To appear in the Australasian Journal of Combinatoric
Some non-existence and asymptotic existence results for weighing matrices
Orthogonal designs and weighing matrices have many applications in areas such
as coding theory, cryptography, wireless networking and communication. In this
paper, we first show that if positive integer cannot be written as the sum
of three integer squares, then there does not exist any skew-symmetric weighing
matrix of order and weight , where is an odd positive integer. Then
we show that for any square , there is an integer such that for each
, there is a symmetric weighing matrix of order and weight .
Moreover, we improve some of the asymptotic existence results for weighing
matrices obtained by Eades, Geramita and Seberry.Comment: To appear in International Journal of Combinatorics (Hindawi). in
Int. J. Combin. (Feb 2016
Least-Squares Wavelet Analysis and Its Applications in Geodesy and Geophysics
The Least-Squares Spectral Analysis (LSSA) is a robust method of analyzing unequally spaced and non-stationary data/time series. Although this method takes into account the correlation among the sinusoidal basis functions of irregularly spaced series, its spectrum still shows spectral leakage: power/energy leaks from one spectral peak into another. An iterative method called AntiLeakage Least-Squares Spectral Analysis (ALLSSA) is developed to attenuate the spectral leakages in the spectrum and consequently is used to regularize data series. In this study, the ALLSSA is applied to regularize and attenuate random noise in seismic data down to a certain desired level. The ALLSSA is subsequently extended to multichannel, heterogeneous and coarsely sampled seismic and related gradient measurements intended for geophysical exploration applications that require regularized (equally spaced) data free from aliasing effects.
A new and robust method of analyzing unequally spaced and non-stationary time/data series is rigorously developed. This method, namely, the Least-Squares Wavelet Analysis (LSWA), is a natural extension of the LSSA that decomposes a time series into the time-frequency domain and obtains its spectrogram. It is shown through many synthetic and experimental time/data series that the LSWA supersedes all state-of-the-art spectral analyses methods currently available, without making any assumptions about or preprocessing (editing) the time series, or even applying any empirical methods that aim to adapt a time series to the analysis method. The LSWA can analyze any non-stationary and unequally spaced time series with components of low or high amplitude and frequency variability over time, including datum shifts (offsets), trends, and constituents of known forms, and by taking into account the covariance matrix associated with the time series. The stochastic confidence level surface for the spectrogram is rigorously derived that identifies statistically significant peaks in the spectrogram at a certain confidence level;
this supersedes the empirical cone of influence used in the most popular continuous wavelet transform.
All current state-of-the-art cross-wavelet transforms and wavelet coherence analyses methods impose many stringent constraints on the properties of the time series under investigation, requiring, more often than not, preprocessing of the raw measurements that may distort their content. These methods cannot generally be used to analyze unequally spaced and non-stationary time series or even two equally spaced time series of different sampling rates, with trends and/or datum shifts, and with associated covariance matrices. To overcome the stringent requirements of these methods, a new method is developed, namely, the Least-Squares Cross-Wavelet Analysis (LSCWA), along with its statistical distribution that requires no assumptions on the series under investigation. Numerous synthetic and geoscience examples establish the LSCWA as the method of methods for rigorous coherence analysis of any experimental series
Cayley graphs of order 27p are hamiltonian
Suppose G is a finite group, such that |G| = 27p, where p is prime. We show
that if S is any generating set of G, then there is a hamiltonian cycle in the
corresponding Cayley graph Cay(G;S).Comment: 13 pages, no figures; minor revisions, including suggestions from a
referee; this version is to appear in the International Journal of
Combinatoric
An observer-based type-3 fuzzy control for non-holonomic wheeled robots
Non-holonomic wheeled robots (NWR) comprise a type of robotic system; they use wheels
for movement and offer several advantages over other types. They are efficient, highly, and maneuverable, making them ideal for factory automation, logistics, transportation, and healthcare. The control of this type of robot is complicated, due to the complexity of modeling, asymmetrical non-holonomic constraints, and unknown perturbations in various applications. Therefore, in this study, a novel type-3 (T3) fuzzy logic system (FLS)-based controller is developed for NWRs. T3-FLSs are employed for modeling, and the modeling errors are considered in stability analysis based on the symmetric Lyapunov function. An observer is designed to detect the error, and its effect is eliminated by a developed terminal sliding mode controller (SMC). The designed technique is used to control a case-study NWR, and the results demonstrate the good accuracy of the developed scheme under non-holonomic constraints, unknown dynamics, and nonlinear disturbances
Coherency and phase delay analyses between land cover and climate across Italy via the least-squares wavelet software
Land cover and climate monitoring is a crucial task in agriculture, forestry, hazard management, and ecosystems assessment. In this paper, normalized difference vegetation index (NDVI), land surface temperature (LST), and land cover products by the moderate resolution imaging spectroradiometer (MODIS) as well as precipitation were utilized to monitor the spatiotemporal dynamics of vegetation and climate along with their correlation and coherency across Italy during 2000–2021. The analyses were performed on both pixel and ecoregion levels via the least-squares wavelet software (LSWAVE). It was found that relatively more areas in all ecoregions had positive NDVI gradients than negative for each month since 2000. It was estimated that the average NDVI has increased by 0.07 since 2000 for all ecoregions. Except the southern ecoregion which showed an insignificant daytime cooling, other ecoregions have been warming by less than 0.05 °C/year since 2000. Furthermore, precipitation had an insignificant decreasing trend for almost all ecoregions over the past two decades. The annual coherency between NDVI and LST was found much stronger than the annual coherency between NDVI and precipitation. The annual cycles of NDVI and LST were out-of-phase for the southern ecoregion while the annual cycle of precipitation led the one in NDVI by about one month for this ecoregion, the only ecoregion showing the highest Pearson correlation (53%) and annual coherency (39%) between NDVI and precipitation. For other ecoregions, the annual cycles of NDVI and LST were approximately in-phase, i.e., less than a month phase delay