This monograph introduces an investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson's type before ...turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations.
This paper introduces a cryptanalysis of image encryption techniques that are using chaotic scrambling and logic gates/circuits. Chaotic scrambling, as well as general permutations are considered ...together with reversible and irreversible gates, including XOR, Toffoli and Fredkin gates. We also investigate ciphers based on chaotic permutations and balanced logic circuits. Except for the implementation of Fredkin’s gate, these ciphers are insecure against chosen-plaintext attacks, no matter whether a permutation is applied globally on the image or via a block-by-block basis. We introduce a new cipher based on chaotic permutations, logic circuits and randomized Fourier-type transforms. The strength of the new cipher is statistically verified with standard statistical encryption measures.
Melanoma is the most fatal type of skin cancer. Detection of melanoma from dermoscopic images in an early stage is critical for improving survival rates. Numerous image processing methods have been ...devised to discriminate between melanoma and benign skin lesions. Previous studies show that the detection performance depends significantly on the skin lesion image representations and features. In this work, we propose a melanoma detection approach that combines graph-theoretic representations with conventional dermoscopic image features to enhance the detection performance. Instead of using individual pixels of skin lesion images as nodes for complex graph representations, superpixels are generated from the skin lesion images and are then used as graph nodes in a superpixel graph. An edge of such a graph connects two adjacent superpixels where the edge weight is a function of the distance between feature descriptors of these superpixels. A graph signal can be defined by assigning to each graph node the output of some single-valued function of the associated superpixel descriptor. Features are extracted from weighted and unweighted graph models in the vertex domain at both local and global scales and in the spectral domain using the graph Fourier transform (GFT). Other features based on color, geometry and texture are extracted from the skin lesion images. Several conventional and ensemble classifiers have been trained and tested on different combinations from those features using two datasets of dermoscopic images from the International Skin Imaging Collaboration (ISIC) archive. The proposed system achieved an AUC of
99.91
%
, an accuracy of
97.40
%
, a specificity of
95.16
%
and a sensitivity of
100
%
.
•Two automated defect detection algorithms are established, based on the correlation coefficient and Boolean functions.•Both algorithms are efficiently implemented to detect defects in printed ...circuit boards.•Detailed performance and comparisons with recent relevant techniques are carried out in normal and presence of noise situations.
We establish two automated defect detection (ADD) algorithms and apply them to detect faults in printed circuit boards (PCBs). Both techniques are referential and are implemented on the binary bit-plane images of the PCBs. In the first algorithm we measure the association between reference and inspected images via the φ-correlation coefficient of percentage statistics, while in the second approach we apply a carefully selected boolean function, as well as a smoothing median filter. Both techniques show a high accuracy, which is comparable to the state-of-the-art techniques, but in a notably faster time. For instance, the boolean function approach is faster than the use of the normalized cross correlation (NCC) by 1700% and it is faster than the use of a fast form of the NCC by 700%, while the use of the φ-correlation coefficient accelerates the procedure by 500% and 200% for the use of the NCC and some of its fast forms respectively.
We establish a new method to compute the eigenvalues of Sturm–Liouville problems by the use of Hermite interpolations at equidistant nodes. We rigorously give estimates for the error by considering ...both truncation and amplitude errors. We compare the results of the new technique with those involving the classical sinc method as well as a SLEIGN2-based method. We also introduce curves that illustrate the enclosure intervals.
Other q-Fractional Calculi Annaby, Mahmoud H; Mansour, Zeinab S
Q-Fractional Calculus and Equations,
2012, 20120711, Volume:
2056
Book Chapter
Peer reviewed
In this chapter we investigate q-analogues of some known fractional operators. This chapter includes as well the fractional generalization of the Askey–Wilson operator introduced in (Ismail and ...Rahman, J. Approx. Theor. 114(2), 269–307, 2002). At the end of this chapter we introduce a fractional generalization of the q-difference operator introduced in (Rubin, J. Math. Anal. Appl. 212(2), 571–582, 1997).
Riemann–Liouville q-Fractional Calculi Annaby, Mahmoud H; Mansour, Zeinab S
Q-Fractional Calculus and Equations,
2012, 20120711, Volume:
2056
Book Chapter
Peer reviewed
In this chapter we investigate q-analogues of the classical fractional calculi. We study the q-Riemann–Liouville fractional integral operator introduced by Al-Salam (Proc. Am. Math. Soc. 17, 616–621, ...1966; Proc. Edinb. Math. Soc. 2(15), 135–140, 1966/1967) and by Agarwal (Proc. Camb. Phil. Soc. 66, 365–370, 1969). We give rigorous proofs of existence of the fractional q-integral and q-derivative. Therefore we establish a q-analogue of Abel’s integral equation and its solutions.
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