The paper presents an error model of a measurement chain containing link performing discrete wavelet transform algorithm which is most often the last stage of measurement signal processing. The goal is to determine the uncertainty budget of the input quantities of the wavelet transform algorithm. The error model takes into account parts of analog, analog-to-digital and digital processing, describing the properties of subsequent fragments of the chain using their transmittance and processing functions. The proposed model enables the description of both deterministic and non-deterministic properties of signal errors. The proposed model was validated using an example measurement chain created for this purpose.

This algorithm is designed to perform Discrete Fourier Transforms (DFT) to convert temporal data into spectral data. This algorithm obtains the Fourier Transforms by studying the Coefficient of Determination of a series of artificial sinusoidal functions with the temporal data, and normalizing the variance data into a high-resolution spectral representation of the time-domain data with a finite sampling rate. What is especially beneficial about this DFT algorithm is that it can produce spectral data at any user-defined resolution.

Discrete Double Hilbert Exponential sums along polynomials. This is preprint version (not peer reviewed) And we now check the proof of (ii) of Lemma 3.2 whether it is really true.

High Efficiency Video Coding (HEVC) uses an 8-point filter and a 7-point filter, which are based on the discrete cosine transform (DCT), for the 1/2-pixel and 1/4-pixel interpolations, respectively. In this paper, discrete sine transform (DST)-based interpolation filters (IF) are proposed. The first proposed DST-based IFs (DST-IFs) use 8-point and 7-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. The final proposed DST-IFs use 12-point and 11-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. These DST-IF methods are proposed to improve the motion-compensated prediction in HEVC. The 8-point and 7-point DST-IF methods showed average BD-rate reductions of 0.7% and 0.3% in the random access (RA) and low delay B (LDB) configurations, respectively. The 12-point and 11-point DST-IF methods showed average BD-rate reductions of 1.4% and 1.2% in the RA and LDB configurations for the Luma component, respectively.

In this paper, we proposed the fusion of two projection based face recognition algorithms: local binary Patterns in DCT domain and singular value decomposition (SVD) characterized by its simplicity and efficiently. Standard databases ORL are used to test the experimental results which prove that proposed system achieves more accurate face recognition as compared to individual method.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform (DHT) and inverse DFT sequence can be exploited for efficient code. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.

Medical image segmentation is a critical step in various healthcare applications, aiding in diagnosis, treatment planning, and disease monitoring. In this study, we investigate the efficacy of a segmentation approach based on the 2D wavelet transform. Leveraging a dataset comprising 10 diverse medical images, we evaluate the performance of our segmentation method using three key metrics: accuracy, precision, and recall. Our findings demonstrate that the proposed approach enhances segmentation accuracy, offering promising results compared to existing methods. By harnessing the multi-resolution feature extraction capabilities of the 2D wavelet transform, our method achieves improved delineation of medical image structures, paving the way for more accurate and efficient healthcare interventions.

This addendum contains clarifications and a sharpening of some of the results on the VIT transform framework developed in [1]. The focus is on the right-coefficient and left- coefficient forms of the transform, the extraction of a first-order term from a left polynomial fraction, and the application to linear time-varying systems.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In this paper, we propose and evaluate the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. This discrete theory is shown to arise from discretization schemes that have been previously employed with the 1D DFT and the discrete Hankel Transform (DHT). The proposed transform possesses orthogonality properties, which leads to invertibility of the transform. In the first part of this two-part paper, the theory of the actual manipulated quantities is shown, including the standard set of shift, modulation, multiplication, and convolution rules. Parseval and modified Parseval relationships are shown, depending on which choice of kernel is used. Similar to its continuous counterpart, the 2D DFT in polar coordinates is shown to consist of a 1D DFT, DHT and 1D inverse DFT.

Diabetic retinopathy (DR) is the primary factor leading to vision impairment and blindness in diabetic people. Uncontrolled diabetes can damage the retinal blood vessels. Initial detection and prompt medical intervention are vital in preventing progressive vision impairment. Today's growing medical field poses more significant workload and diagnostic demands on medical professionals. In the proposed study, a convolutional neural network (CNN) is employed to detect the stages of DR. This research is crucial for studying DR because of its innovative methodology incorporating two different public datasets. This strategy enhances the model's capacity to generalize unseen DR images, as each dataset encompasses unique demographics and clinical circumstances. The network can learn and capture complicated hierarchical image features with asymmetric weights. Each image undergoes preprocessing using contrast-limited adaptive histogram equalization (CLAHE) and the discrete wavelet transform (DWT). The model is trained and validated using the combined datasets of Dataset for Diabetic Retinopathy (DDR) and the Asia Pacific Tele-Ophthalmology Society (APTOS). The CNN model is tuned with different learning rates and optimizers. The CNN model with Adam optimizer achieved 70% accuracy and an area under curve (AUC) score of 0.82. The recommended study results may reduce diabetes-related vision impairment by early DR severity identification.

This paper presents the methodology to detect and identify the type of fault that occurs in shunt connected static synchronous compensator (STATCOM) transmission line using a combination of Discrete Wavelet Transform (DWT) and Naive Bayes classifier. To study this, the network model is designed using Mat-lab/Simulink. The different faults such as Line to Ground (LG), Line to Line (LL), Double Line to Ground (LLG) and three-phase (LLLG) fault are applied at different zones of system with and without STATCOM considering the effect of varying fault resistance. The three-phase fault current waveforms obtained are decomposed into several levels using daubechies mother wavelet of db4 to extract the features such as standard deviation and Energy values. The extracted features are used to train the classifiers such as Multi-Layer Perceptron Neural Network (MLP), Bayes and Naive Bayes (NB) classifier to classify the type of fault that occurs in the system. The results reveal that the proposed NB classifier outperforms in terms of accuracy rate, misclassification rate, kappa statistics, mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE) and root-relative square error (RRSE) than MLP and Bayes classifier.

The diagnosis of Cardio-Vascular diseases (CVD) is highly dependent on analysis of ECG signals. ECG analysis can be helpful in estimating the underlying cause and condition of heart in cardiac abnormality. The effectiveness of ECG signal analysis in detection of CVDs is widely accepted by professional healthcare service provider. Many algorithms have been proposed but almost all of them have some kind of limitations, and these limitations largely influence the effectiveness of ECG analysis. The performed research work is dedicated for design of unique self-organizing maps (SOMs) based neural network for classification of arrhythmia according to a particular ECG signal, the generation of SOMs is based on the certain unique signatures of ECG signals and have potential to classify different cardiac conditions. For extraction of unique features from ECG signals, we have proposed to use Fast Discrete Stockwell Transform (FDST). Since the proposed technique is a result of combining two different techniques hence called as hybrid technology. The purpose of using FDST is to identify unique signatures of ECG signals in a more improved manner than existing one, the term improved is used because it has several advantages over existing techniques such as wavelet and Fourier Transform based methods. Results obtained from the implementation of the technique are capable in visualizing the ECG sinus rhythm and arrhythmia conditions in form of unique SOM for each associated arrhythmia condition. This unique SOM based classification makes them ideal for being used as a diagnostic tool. This ability of arrhythmia classification using FDST and SOMs makes the technique unique and useful providing valuable information about patient condition. Using proposed technology a portable diagnosis tool for monitoring of patient at their site may be facilitated later, that will improve the quality of life of the patient by diagnosing cardiac condition.

The electroencephalogram (EEG) is a record of brain activity. Brain Computer Interface (BCI) technology formed by the EEG signal has become one of the hotspots at present. How to extract the feature signal of EEG is the most basic research of BCI technology. In this paper, A new method of recognizing fatigue, conscious, concentrated state of human brain is proposed by the combination of discrete wavelet transform and the neural network based on EEG signal. First of all, the law signal is preprocessed by the wavelet denoising method because the law EEG signal contains a large number of high frequency noise, which is decomposed into multi-layer high frequency signal and low frequency signal. thus, δ wave, θ wave, α wave, β wave are obtained by the wavelet transform. And then, frequency band energy of the different wave is regards as the feature signal of EEG. In the experiment, the feature signal is classified by radial basic function (RBF) and annealed chaotic competitive learning network (ACCLN). RBF and ACCLN networks are trained with 500 sets of sample data and are tested by 100 sets of samples in different mental states. The experimental results show that the average accuracy of RBF network under three conditions are 88.75%, 88.25%, 88.5%, respectively, and the correct rate of ACCLN network is 97%, 98%, 98%, respectively.

Lamb wave-based structural health monitoring is widely acknowledged as a reliable 11 method for damage identification, classification, localization and quantification. However, due to 12 the complexity of Lamb wave signals, especially after interacting with structural components and 13 defects, interpreting these waves and extracting useful information about the structure's health is 14 still a major challenge. However, deep learning-based strategy offers a great opportunity to address 15 such challenges as the algorithm can operate directly on raw discrete time-domain signals. Unlike 16 traditional methods, which often require careful feature engineering and preprocessing, deep learn-17 ing can automatically extract relevant features from the raw data. This paper proposes an autoen-18 coder based on a bidirectional long short-term memory network with maximal overlap discrete 19 wavelet transform layer to detect the signal anomaly and determine the location of the damage in 20 the composite structure. This approach has the potential to greatly enhance our ability to detect and 21 locate structural damage in composite structures, thereby increasing safety and efficiency.

This paper presents a method to detect and classify the high impedance fault that occur in the medium voltage distribution network using discrete wavelet transform (DWT) and adaptive neuro-fuzzy inference system (ANFIS). The network is designed using Matlab software and various faults such as high impedance, symmetrical and unsymmetrical fault have been applied to study the effectiveness of the proposed ANFIS classifier method. This is achieved by training the ANFIS classifier using the features (standard deviation values) extracted from the three phase fault current signal by DWT technique for various cases of fault with different values of fault resistance in the system. The success and discrimination rate obtained for identifying and classifying the high impedance fault from the proffered method is 100% whereas the values are 66.7% and 85% respectively for conventional fuzzy based approach. The results indicate that the proposed method is more efficient to identify and discriminate the high impedance fault accurately from other power system faults in the system.

The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

The paper delves into the critical issue of damage detection within the guy cable of a truss steel mast, a pivotal component in structural integrity. It introduces a model wherein damage manifests as a localized cross-section reduction in a single element of the cable. Employing Discrete Wavelet Transform (DWT), a pioneering methodology, the study scrutinizes the behavior of the affected elements through static structural analyses. Signal decomposition via the Mallat pyramid algorithm facilitates comprehensive examination. Static displacements at the connection point between the cable and the truss mast serve as the measured variables. Through systematic investigation, the paper evaluates the impact of damage size and location, external loading force, and cable tension force on the efficacy of the proposed approach. Utilizing data derived from Finite Element Method (FEM) computations for wavelet analysis the authors substantiate the findings with numerical examples, thus offering valuable insights into damage detection strategies for structural health monitoring and engineering applications.

Teaching kinematic rotations is a daunting task for even some of the most advanced mathematical minds. However, envisioning and explaining the three-dimensional rotations can be highly simplified by changing the paradigm. This paradigm change allows for a high school student with a understanding of geometry to be able to not only develop the matrix but also explain the rotations at a collegiate level. The proposed method includes the assumption of a point (P) within the initial three-dimensional frame with axes (x ̂_i, y ̂_i, z ̂_i). It then utilizes a two-dimensional rotation view (2DRV) to measure how the coordinates of point P translate after the initial axis is rotated instead of using the established Euler's formula. The equations are used in matrix notation to develop a direction cosine matrix (DCM) for future equations. This method provides a high school student with an elementary and repeatable process to compose and explain kinematic rotations.

Recently, significant progress has been made in developing computer-aided diagnosis (CAD) systems for identifying glaucoma abnormalities using fundus images. Despite their drawbacks, methods for extracting features such as wavelets and their variations, along with classifier like support vector machines (SVM), are frequently employed in such systems. This paper introduces a practical and enhanced system for detecting glaucoma in fundus images. This system adresses the chanallages encountered by other existing models in recent litrature. Initially, we have employed contrast limited adaputive histogram equalization (CLAHE) to enhanced the visualization of input fundus inmages. Then, the discrete ripplet-II transform (DR2T) employing a degree of 2 for feature extraction. Subsequently, a golden jackal optimization algorithm (GJO) employed to select the optimal features to reduce the dimension of the extracted feature vector. During the classification stage the least square support vector machine (LS-SVM) with three kernels called as linear, polynomial and radial basis function(RBF), for classifying of fundus images as glaucoma or healthy. The proposed method is validated with the current state-of-the-art models on two standard datasets, namely, G1020 and ORIGA. The results obtained from our experimental result demonstrate that our best suggested approach DR2T+GJO+LS-SVM-RBF obtains better classification accuracy 93.38% and 97.31% for G1020 and ORIGA dataset with less number of features. It establishes a more concise network structure when contrasted with traditional classifiers.

This paper develops a detail image signal enhancement that makes images perceived as clearer and more resolved and so is more effective for higher resolution displays. We observe that the local variant signal enhancement makes images more vivid, and the more revealed granular signals harmonically embedded on the local variant signals make images more resolved. Based on this observation, we develop a method that not only emphasizes the local variant signals by scaling up the frequency energy in accordance with human visual perception, but also strengths up the granular signals by embedding the alpha-rooting enhanced frequency components. The proposed energy scaling method emphasizes the detail signals in texture images and rarely boosts noisy signals in plain images. In addition, to avoid the local ringing artifact, the proposed method adjusts the enhancement direction to be parallel to the underlying image signal direction. It was verified through the subjective and objective quality evaluations that the developed method makes images perceived as clearer and highly resolved.

Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

To assure the opacity, an optimal problem is to retain the occurring events sequences as many as possible. Contrary to such problem, the other optimal problem is to preserve the minimal occurring events sequences. In the paper, based on the choosing cost, an optimal opacity-enforcing model is presented to minimize the sum of discount choosing cost, which is not only to preserve the opacity, but also to retain the secret to the maximum. To solve the model, two scenarios on opacity are considered. For the two scenarios, some algorithms are presented to achieve the optimal solution for the model by using the method of dynamic programming. And then, the solutions produced by the algorithms are proved correctly by theoretical proof. Finally, some illustrations for the algorithms are given.

The accompanying mechanical behavior during the flow of ore-rock dispersion is an important factor leading to the instability and failure of the orepass in the ore storage section. It is of great significance to accurately understand the instability characteristics of the well wall in the ore section, during the ore drawing process by understanding the flow characteristics and internal mechanical transfer mechanism of ore-rock dispersion. Using the discrete element method to analyze the flow characteristics, contact compactness, stress distribution characteristics and contact force probability distribution of the ore-rock dispersion, it realizes the quantitative characterization of the damage degree of ore-rock flow, and reveals the damage mechanism of mine storage wall. The results show that: (1) The friction between ore-rock particles, between ore-rock and well wall is an important reason for the change of the macroscopic flow form of ore-rock from “one” to “V” type. (2) The compactness and stress concentration of ores are increasing with the increase of storage depth, which is shown that with the increase of storage depth, the greater the probability of well wall instability. (3) The probability distribution of contact force strength between particles decreases exponentially in the whole process of ore drawing, in which the strong chain plays a major role in the stability of the dispersion system. (4) The number of overpressure and the overpressure coefficient can be used to quantitatively characterize the wall damage degree under the action of ore-rock flow. The dynamic side pressure decreases periodically in the form of exponential fluctuations, and the dynamic load formed by the ore-rock flow mainly played a role in the lower area of the ore storage section.

This paper proposed an optimal tracking control scheme through adaptive dynamic programming(ADP) for a class of partially unknown discrete-time nonlinear systems based on radial basis function neural network(RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs, the one is used to construct the identifier, and the another is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. While the optimal feedback control and the cost function are derived via feedforward neural networks approximating, it is proposed to regulate the tracking error, the critic network and the actor network are then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation being built under the ADP framework. Simulations verify the effectiveness of the optimal tracking control technique using the neural networks.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

In today’s world face detection is the most important task. Due to the chromosomes disorder sometimes a human face suffers from different abnormalities. For example, one eye is bigger than the other, cliff face, different chin-length, variation of nose length, length or width of lips are different, etc. For computer vision currently this is a challenging task to detect normal and abnormal face and facial parts from an input image. In this research paper a method is proposed that can detect normal or abnormal faces from a frontal input image. This method used Fast Fourier Transformation (FFT) and Discrete Cosine Transformation of frequency domain and spatial domain analysis to detect those faces.

This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ⁽²⁾) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

In this article, we set up some adequate conditions for analytic functions associated with cosine hyperbolic function. We determine conditions on α such that 1+α (ϰ^(2+P(j-1) ) g^' (ϰ))/(Pg^j (ϰ)),for each j=0,1,2,3 are subordinated by Janowski function, then (g(ϰ))/ϰ^P <cosℏ⁡(ϰ),(ϰ∈C). By choosing specific values of functions g we get some adequate conditions for multivalent starlike function related with cosine hyperbolic.

We approximate the trigonometric function sine and cosine on the interval . This analysis provides two formulas to approximate sine and cosine. At first, we try to derive the formula which involves a square root, and then we derive another formula that does not require any use of a square root. Nevertheless, after deriving the procedure which requires no square root, we further try to increase its accuracy and then derive another formula that approximates trigonometric functions more accurately on the interval [0, pi/2]. So, this analysis provides mainly two types of procedures. One uses square roots, whereas the other does not. We also focus on ensuring the accuracy of these trigonometric functions in the interval [0,pi/2]. This accuracy analysis is portrayed using the graph. This graph shows the difference between the values generated by the functions defined here and the actual value of these functions. So, these graphs also indicate the error of these functions on that interval. Finally, we compare our approximation with the approximation formula of the 7th-century Indian Mathematician Bhaskara I.

We developed a novel hybrid approach for solving global optimization, computer science, bio-medical and engineering real life applications that is based on the coupling of the Whale Optimizer and Sine Cosine Algorithms via a surrogate model. We relate the whale optimizer algorithm to balance between the exploitation and the exploration process in the proposed method. There exist confirmed techniques for searching approximate best optimal solutions, but our algorithm will further guarantee that such numerical and statistical solutions satisfy physical bounds of the standard and real life functions. Our experiments with the benchmark, bio-medical, computer science and engineering real life problems have illustrated the advantages of using a newly hybrid approach based on mixing Whale Optimizer and Sine Cosine algorithms. It holds considerable potential for reducing execution time for solving standard and real life problems and at the same time improving the quality of the solution.

The goal of this paper is to propose a dual version of the direct cosine simplex algorithm (DDCA) for general linear problems. Unlike the two-phase and the big-M methods, our technique does not involve artificial variables. Our technique solves the dual Klee-Minty problem in two iterations and solves the dual Clausen’s problem in four iterations. The utility of the proposed method is evident from the extensive computational results on test problems adapted from NETLIB. Preliminary results indicate that this dual direct cosine simplex algorithm (DDCA) reduces the number of iterations of two-phase method.

Let $\mathcal{\mathcal{S}}_{\cos}^{\ast}$ denote the class of normalized analytic functions $f$ in the open unit disk $\mathbb{D}$ satisfying the subordination $\dfrac{zf^{\prime}(z)}{f(z)}\prec\cos z$. In the second section of this article we find the sharp upper bounds for the initial coefficients $a_{3}$, $a_{4}$ and $a_{5}$ and the sharp upper bound for module of the Hankel determinant $|H_{2,3}(f)|$ for the functions from the class $\mathcal{S}_{\cos}^{\ast}$. The first result of the next section deals with the sharp upper bounds of the logarithmic coefficients $\gamma_{3}$ and $\gamma_{4}$ and we found in addition the sharp upper bound for $\left|H_{2,2}\left(F_{f}/2\right)\right|$. For obtaining these results we used the very useful and appropriate Lemma 2.4 of N.E. Cho et al. [Filomat 34(6) (2020), 2061--2072], and the technique for finding the maximum value of a three variable function on a closed cuboid. All the maximum found values were checked by using MAPLE\texttrademark{} computare software, and we also found the extremal functions in each cases. All of our present results are the best ones and give sharp versions of those recently published in [Hacet. J. Math. Stat. 52, 596--618, 2023].

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

In the paper, the author finds bounds of the sine and cosine along a circle on the complex plane in terms of two double inequalities for the norms of the sine and cosine along a circle on the complex plane.

In the paper, the author discusses and computes bounds of the sine and cosine along straight lines on the complex plane.

The twisted Wang transform distribution family, defined as the composition of parameter shifted inverse CDF function with an original CDF function, is found to be most suitable for matching low shape factor distributions, characterizing hard to fit or to simulate reinsurance portfolio losses for some perils from our previous study. Among them, the best form for matching a hard-to-fit empirical loss distribution for a specific peril, is the Exponential Fractional Extra Power 0 Distribution in (0,1) with CDF:.The simplest yet still a good form of this family is the Transformed Hyperbolic Tangent Distribution with CDF:,which has analytical formulas for the moments. The twisted Wang transform distribution family is compared and confirmed to be superior to all other well-known distribution families through extensive numerical optimization practice, distribution forms guesses, and computer-aided exploration experiments.

Sentiment analysis to characterize properties of Bitcoin prices and their forecasting is here developed thanks to the capability of the Fuzzy transform to capture stylized facts and mutual connections between time series having different nature. Six years of daily Bitcoin Prices and Google Trends are analyzed in order to establish new perspectives in the management of their dynamics.

This paper studies the duration patterns of unemployment spells for immigrants and the determinants of unemployment’s completion into one of a number of studied labour market states in Finland. We estimate a duration model for unemployment with competing risks of its terminating into employment, labour market training or economic inactivity. Taking into account the wide period of observation and opportunities to analyse processes of labour market integration during various periods of economic development in Finland, in combination with the individualistic character of the labour careers of immigrants, this research is beneficial owing to the many various findings concerning labour market integration of immigrants. The approach undertaken in this research has a dualistic “descriptive-dynamic” character under which integration is understood as a never-ending process, which is conditioned by a time period of long-term existence and a context of solitary action. We find that transitions out of unemployment spells have a cyclical character; after every new “cycle” in unemployment, the probability of terminating unemployment decreases further. We also find that ascriptive factors make sense in the process of job-placement of immigrants from unemployment. Therefore, the gender, education and age of immigrants, as well as the effect of the period in which first unemployment occurred, potentially predict transitions out of unemployment and further labour market integration of immigrants.

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral.

Different variants of thinning for discrete random variables are studied. The thinning procedure allows to introduce an analog of scale parameter for positive integer-valued random variables. Sufficient and necessary conditions for the existence of such a scale are given.

In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the partition requirement, that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measuring terms: namely, this requirement can be derived from the natural desire to have all the signal values at different moments of time estimated with the same accuracy.

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the Integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense.

In view of the problem of cracking easily and partial distortion of images after encryption or decryption, a novel image encryption and decryption algorithm based on Arnod Transform and fractional chaotic is proposed. To begin with, the Arnold transform is used to encrypt. So that the spatial confidence of the original image has been comprehensively disturbed. Secondly, the XOR involving the fractional order chaotic sequence is used to encrypt. The key sequence is dynamically generated to ensure the randomness and difference of key generation. When decryption is required, the first decryption is performed using the key and XOR. Then the second decryption is carried out by using the inverse Arnold transform, and finally the decrypted image is obtained. Experimental results show that the improved algorithm has achieved better performance in encryption and decryption.

This article introduces ten similarity measures that utilize cosine and cotangent functions to compare (m,n)-rung orthopair fuzzy sets, this a super class of q-rung orthopair fuzzy sets. Further, we applied our established weighted similarity measures to medical diagnosis, pattern recognition,and building material problems and also presented the comparison between established measures with the existing cosine and cotangent measures of q-rung orthopair, pythagorean and intuitionistic fuzzy sets. Lastly, we considered a numerical example that demonstrates the effective and scientific application of these similarity measures in plant leaf disease classification. Furthermore, we present graphical interpretations to demonstrate the effectiveness of our established measures.

This article presents a new methodology for modeling and analyzing discrete dynamic systems through the construction of inverse algebraic models, giving rise to the Theory of Inverse Discrete Dynamical Systems. Key concepts such as inverse modeling, structural analysis in inverse algebraic trees, and the establishment of topological equivalences for the analytical transfer of properties between the canonical system and its inverted counterpart are introduced. Central theorems on homeomorphic invariance and topological transport are demonstrated, consolidating the validity of transferring cardinal attributes between both equivalent dynamic representations. As a concrete application, an alternative proof of the historic Collatz Conjecture is presented through the rigorous construction of the associated inverse model and the analytical transfer of properties exhibited in the inverted tree structure. Furthermore, evidence has been presented on Conway's Conjecture in the Game of Life through meticulous inverse modeling in bounded cases, overcoming initial limitations of the theory in combinatorial explosions. Although a complete proof of the conjecture is not achieved, this positively expands the modeling and analysis capacity of the methodology. The impact of properly applying this novel theory to expand understanding and solve open problems in discrete dynamical systems seems vast and profound.

Hasselmann and coauthors proposed the discrete interaction approximation (DIA) as the best tool replacing the nonlinear evolution term in a numerical wind-wave model. Much later, Polnikov and Farina radically improved the original DIA by means of location all the interacting four wave vectors, used in the DIA configuration, exactly at the nodes of the numerical frequency-angular grid. This provides nearly two-times enhancing the speed of numerical calculation for the nonlinear evolution term in a wind-wave model. For this reason, the proposed version of the DIA was called as the fast DIA (FDIA). In this paper we demonstrate all details of the FDIA concept for several frequency-angular numerical grids of high resolution, with the aim of active implementation the FDIA in modern versions of world-wide used wind-wave models.

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.

The famous singlet correlations of a composite quantum system consisting of two spatially separated components exhibit notable features of two kinds. The first kind consists of striking certainty relations: perfect correlation and perfect anti-correlation in certain settings. The second kind consists of a number of symmetries, in particular, invariance under rotation, as well as invariance under exchange of components, parity, or chirality. In this note, I investigate the class of correlation functions that can be generated by classical composite physical systems when we restrict attention to systems which reproduce the certainty relations exactly, and for which the rotational invariance of the correlation function is the manifestation of rotational invariance of the underlying classical physics. I call such correlation functions classical EPR-B correlations. It turns out that the other three (binary) symmetries can then be obtained "for free": they are exhibited by the correlation function, and can be imposed on the underlying physics by adding an underlying randomisation level. We end up with a simple probabilistic description of all possible classical EPR-B correlations in terms of a "spinning coloured disk" model, and a research programme: describe these functions in a concise analytic way.

We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of a suitable Abel-type transform of the function itself. Thus, the computation of N Legendre coefficients can be performed efficiently in O(NlogN) operations by means of a single Fast Fourier Transform of the Abel-type transform of f(x). We also show how the symmetries associated with the Abel-type transform can be exploited to further reduce the computational complexity. The dual problem of calculating the sum of Legendre expansions is also considered. We prove that a Legendre series can be written as the Abel transform of a suitable Fourier series. This fact allows us to state an efficient algorithm for the evaluation of Legendre expansions. Finally, numerical tests are presented to exemplify and confirm the theoretical results.

In this work we present a novel steganography algorithm, based on Fractal Transform domain, combined with the principles of Cryptography. The proposed method uses a private key, which will indicate which segment of the image will be taken and encoded with the Fractal Transform, to then insert the secret bits in the transformed coefficients, thus generating the stego image.

The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

This study aims to apply a Recommendation System with Content Based Filtering method with Jaccard Similarity and Cosine Similarity algorithms on the E-Learning Platform. Recommendation systems deal with how to provide personalized recommendations to users efficiently. The Content Based Filtering method with Jaccard Similarity and Cosine Similarity algorithms can be used to calculate the similarity value between E-Courses on the E-Learning Platform. Implementation for Recommendation System using Google Colaboratory with Python programming language. In the application of the Recommendation System dataset, Coursera Free Dataset consists of 975 instances. The recommendation results use the Jaccard Similarity algorithm with an average similarity value of 0.3 while the value of Cosine Similarity with the average similarity value is 0.6 where the similarity value of Cosine Similarity is higher. Based on the results of the Mean Absolute Error in the low recommendation system, the average MAE value for all iterations of Jaccard Similarity algorithm is 0.013 and for the Cosine Similarity algorithm the average MAE value for all iterations is 0.014. This shows that the Recommendation System with Jaccard Similarity and Cosine Similarity algorithms can be used on the E-Learning Platform to provide efficiency solutions for personalized recommendations.

Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time are described. ARMA type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.

The basis of the discrete-impulse energy supply (DIES) concept is the efficient use of supplied energy. The references describe in detail the general principles of DIES, examine the energy and thermodynamic aspects and the main mechanisms of intensification that can be initiated on the basis of this principle. DIES mechanisms conveniently can be divided into hard and soft ones. The former should be used to stimulate hydromechanical processes, and the latter to accelerate the processes of phase heat and mass transfer, or for the purpose of intensive mixing of multicomponent media. The authors have studied the possibility of using DIES to intensify the hydromechanical processes, in particular emulsification of milk fat (homogenization of milk, preparation of spreads), processing of cream cheese masses. Objects of research were whole non-homogenized milk, fat emulsions, cream cheese mass. In order to evaluate the efficiency of milk homogenization the homogenization coefficient change was studied, which was determined by centrifugation method as the most affordable and accurate one. Emulsions were evaluated according to the degree of destabilization, resistance and dispersion of the fat phase. The rheological characteristics of cheese masses were evaluated by the effective viscosity change.

In this paper we show how to efficiently implement parallel discrete simulations on Multi-Core and GPU architectures through a real example of application: a cellular automata model of laser dynamics. We describe the techniques employed to build and optimize the implementations using OpenMP and CUDA frameworks. We have evaluated the performance on two different hardware platforms that represent different target market segments: high-end platforms for scientific computing, using an Intel Xeon Platinum 8259CL server with48cores and also an NVIDIA Tesla6V100 GPU, both running on Amazon Web Server (AWS) Cloud, and on a consumer-oriented platform, using an Intel Core i9 9900k CPU and an NVIDIA GeForce GTX 1050 TI GPU. Performance results are compared and analysed in detail. We show that excellent performance and scalability can be obtained in both platforms, and we extract some important issues that imply a performance degradation for them. We also found that current Multi-Core CPUs with large core numbers can bring a performance very near to that of GPUs, even similar in some cases.

During routine bridge maintenance, edge detection allows the partial condition of the bridge to be viewed. However, many edge detection methods often have unsatisfactory performances when dealing with images with complex backgrounds. Moreover, the processing often involves the manual selection of thresholds, which can result in repeated testing and comparisons. To address these problems in this paper, the wavelet transform modulus maxima method is used to detect the target image, and then the threshold value of the image can be determined automatically according to the OTSU method to remove the pseudo-edges. Thus, the real image edges can be detected. The results show that the information entropy and SSIM of the detection results are the highest when compared with the commonly used Canny and Laplace algorithms, which means that the detection quality is optimal. To more fully illustrate the advantages of the algorithms, images with more complex backgrounds were detected and the processing results of the algorithms in this paper are still optimal. In addition, the automatic selection of thresholds saves the operator’s effort and improves the detection efficiency. Thanks to the combined use of the above two methods, detection quality and efficiency are significantly improved, which has a good application in engineering practice.

In this paper, we introduce two discrete degenerate random variables, namely the degenerate binomial and degenerate Poisson random variables. We deduce the expectations of the degenerate binomial random variables. We compute the generating function of the moments of the degenerate Poisson random variables, which leads us to define the new type degenerate Bell polynomials, and hence obtain explicit expressions for the moments of those random variables in terms of such polynomials. We also get the variances of the degenerate Poisson random variables. Finally, we illustrate two examples of the degenerate Poisson random variables.

Let be a power function $f_{r,M}(s)$ defined for every $s$ within the finite set $M$ as follows $$f_{r,M}(s)= \begin{cases} s^r, \ &s\in M,\\ 0, \ &\mathrm{otherwise}. \end{cases} $$ Let a discrete convolution of $f_{r,M}(s)$ be denoted as follows $\mathrm{Conv}_{r,M}[n]=(f_{r,M}*f_{r,M})[n]$. Let a real coefficients $A_{m,j}$ be given by the following recurrence $$ A_{m,j} = \begin{cases} 0, & \mathrm{if } \ j<0 \ \mathrm{or } \ j>m, \\ (2j+1)\binom{2j}{j} \sum_{d=2j+1}^{m} A_{m,d} \binom{d}{2j+1} \frac{(-1)^{d-1}}{d-j} B_{2d-2j}, & \mathrm{if } \ 0 \leq j < m, \\ (2j+1)\binom{2j}{j}, & \mathrm{if } \ j=m. \end{cases} $$ In this paper we show that for every $n>0$ the following odd-power identities involving coefficients $A_{m,j}$ and convolution transform $\mathrm{Conv}_{r,M}[n]$ hold $$ \begin{split} n^{2m+1}+1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{N}}[n],\\ n^{2m+1}-1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{Z}_{>0}}[n],\\ n^{2m+1}&=\sum_{r=0}^{m}A_{m,r}\sum_{k=1}^{n} k^r(n-k)^r\\ &=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1} k^r(n-k)^r. \end{split} $$

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals.

Abstract: The two-dimensional Fuzzy Transform was applied in image compression. The quality of the image compressed with this methodis better than that obtained using methods based on fuzzy relation equations and comparable with that of the JPEG method, with better compression execution times. In this paper we propose a variation of the method based on the two-dimensional Fuzzy Transform of image compression, in which the image is first partitioned into blocks and then each block is compressed with the higher compression rate. The advantage of this method consistsinto a greater compression of the image, guaranteeing a high quality of the reconstructed image.The results show that our method is better than the Fuzzy Transform method improving also the quality of the reconstructed image.

Malignant growth is the most widely recognized repulsive infections winning around the world, and the patients with disease are saved just when the malignant growth is distinguished at the beginning phase. Each kind of disease is interesting, with its own arrangement of development properties and hereditary changes. This paper presents the lung knob division and disease characterization by proposing an enhancement calculation. The general technique of the created approach includes four stages, such as pre-processing, division, highlight extraction, and the order. From the outset, the CT picture of the lung is taken care of to the division. When the division is done, the highlights are extricated through morphological and measurable and surface highlights like LOOP and LGP. At long last, the extricated highlights are given to the order step. Here, the characterization is done dependent on the Deep Belief Network (DBN) which is prepared by utilizing the proposed Chicken-Sine Cosine Algorithm (CSCA) which distinguish the lung tumor, giving two classes in particular, knob or non-knob. The presentation assessment of lung knob division and malignant growth grouping dependent on CSCA is figured utilizing three measurements to be specific, precision, affectability, and the explicitness.

Although Shannon mutual information has been widely used, its effective calculation is often difficult for many practical problems, including those in neural population coding. Asymptotic formulas based on Fisher information sometimes provide accurate approximations to the mutual information but this approach is restricted to continuous variables because the calculation of Fisher information requires derivatives with respect to the encoded variables. In this paper, we consider information-theoretic bounds and approximations of the mutual information based on Kullback--Leibler divergence and Rényi divergence. We propose several information metrics to approximate Shannon mutual information in the context of neural population coding. While our asymptotic formulas all work for discrete variables, one of them has consistent performance and high accuracy regardless of whether the encoded variables are discrete or continuous. We performed numerical simulations and confirmed that our approximation formulas were highly accurate for approximating the mutual information between the stimuli and the responses of a large neural population. These approximation formulas may potentially bring convenience to the applications of information theory to many practical and theoretical problems.

Advances in machine learning (ML) and artificial intelligence (AI) are transforming the way we treat patients in ways not even imagined a few years ago. Cancer research is at the forefront of this movement. Infertility, though not a life-threatening condition, affects around 15% of couples trying for a pregnancy. Increasing availability of large datasets from various sources creates an opportunity to introduce ML and AI into infertility prevention and treatment. At present in the field of assisted reproduction, very little is done in order to prevent infertility from arising, with the main focus put on treatment when often advanced maternal age and low ovarian reserve make it very difficult to conceive. A shift from this disease-centric model to a health centric model in infertility is already taking place with more emphasis on the patient as an active participator in the process. Poor quality and incomplete data as well as biological variability remain the main limitations in the widespread and reliable implementation of AI in the field of reproductive medicine. That said, one of the areas where this technology managed to find a foothold is identification of developmentally competent embryos. More work is required however to learn about ways to improve natural conception, the detection and diagnosis of infertility, and improve assisted reproduction treatments (ART) and ultimately, develop clinically useful algorithms able to adjust treatment regimens in order to assure a successful outcome of either fertility preservation or infertility treatment. Progress in genomics, digital technologies and advances in integrative biology has had a tremendousimpact on research and clinical medicine. With the rise of ‘big data’, artificial intelligence, and the advances in molecular profiling, there is an enormous potential to transform not only scientific research progress, but also clinical decision making towards predictive, preventive, and personalized medicine. In the field of reproductive health, there is now an exciting opportunity to leverage these technologies and develop more sophisticated approaches to diagnose and treat infertility disorders. In this review, we present a comprehensive analysis and interpretation of different innovation forces that are driving the emergence of a system approach to the infertility sector. Here we discuss recent influential work and explore the limitations of the use of Machine Learning models in this rapidly developing area.

We have presented a controllable and human-readable polynomial neural network (CR-PNN) that is the first human-readable neural network. One can imagine its influence on system identification. Subsequently, we developed a relation spectrum in a medical application, which is likely to stand alongside the Fourier spectrum. However, the system analysis methodology is incomplete in contrast to signal processing methodology. Here, we presented the system filters for the first time. In this paper, we used the simulation system to verify the availability of the system analysis methodology. The system analysis methodology showed great properties in system identification and filter. The contribution of this paper is the system analysis methodology: transform method (CR-PNN), relation spectrum, and system filter design.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

Abstract Using the Pauli algebra version of the Dirac equation six symmetric but non-equivalent copies of the QED Lagrangian are constructed. The group of symmetries is the group of outer automorphisms of the finite quaternion group, isomorphic to the group of permutations on three letters. Solutions to corresponding Dirac equations form six sectors of fermion fields. The intersections between different sectors can only contain massless fields, implying that the sectors are distinct. If the symmetry could be extended to the full Standard Model Lagrangian it would predict the ratio of dark matter to ordinary matter of 5 : 1 which is close to the ratio of 5.2 : 1 according to current observations.

Discrete distribution estimation is a fundamental statistical tool, which is widely used to perform data analysis tasks in various applications involving sensitive personal information. Due to privacy concerns, individuals may not always provide their raw information, which leads to unpredictable biases in the final results of estimated distribution. Local Differential Privacy (LDP) is an advanced technique for privacy protection of discrete distribution estimation. Currently, typical LDP mechanisms provide same protection for all items in the domain, which imposes unnecessary perturbation on less sensitive items and thus degrades the utility of final results. Although, several recent works try to alleviate this problem, the utility can be further improved. In this paper, we propose a novel notion called Item-Oriented Personalized LDP (IPLDP), which independently perturbs different items with different privacy budgets to achieve personalized privacy protection. Furthermore, to satisfy IPLDP, we propose the Item-Oriented Personalized Randomized Response (IPRR) based on the observation that the sensitivity of data shows an inverse relationship with the population size of respective individuals. Theoretical analysis and experimental results demonstrate that our method can provide fine-grained privacy protection and improve data utility simultaneously.

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In early days, Fishburn investigated SD from the view of distributions and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD may not be generalized directly since some properties of fractional calculus do not have a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be generalized directly from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle them.

The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with smooth particle applied mechanics by having the solid particles apply stresses expected with Hooke's law, as opposed to using a smoothing function for neighboring solid particles. This method has been tested successfully with a bar in tension, compression, and shear, as well as a disk compressed into a flat plate, and the numerical model consistently matched the analytical Hooke's law as well as Hertz contact theory for all examples. The solid modeling numerical method was then built into a 2-D model of a pressure vessel, which was tested with liquid water particles under pressure and simulated with smoothed particle hydrodynamics. This simulation was stable, and demonstrated the feasibility of Lagrangian specification modeling for fluid–solid interactions.

3D printing facilitates the straightforward construction of microchannels with complex three-dimensional architectures. Here, we demonstrate 3D-printed modular mixing components that operate on the basis of splitting and recombining fluid streams to decrease interstream diffusion length. These are compared to helical mixers that operate on the principle of chaotic advection.

In this paper we introduce a computational model for the simulation of hypervelocity impact (HVI) phenomena which is based on the Discrete Element Method (DEM). Our paper constitutes the first application of DEM to the modeling and simulating of impact events for velocities beyond 5 kms⁻¹. We present here the results of a systematic numerical study on HVI of solids. For modeling the solids, we use discrete spherical particles that interact with each other via potentials. In our numerical investigations we are particularly interested in the dynamics of material fragmentation upon impact. We model a typical HVI experiment configuration where a sphere strikes a thin plate and investigate the properties of the resulting debris cloud. We provide a quantitative computational analysis of the resulting debris cloud caused by impact and a comprehensive parameter study by varying key parameters of our model. We compare our findings from the simulations with recent HVI experiments performed at our institute. Our findings are that the DEM method leads to very stable, energy–conserving simulations of HVI scenarios that map the experimental setup where a sphere strikes a thin plate at hypervelocity speed. Our chosen interaction model works particularly well in the velocity range where the local stresses caused by impact shock waves markedly exceed the ultimate material strength.

In this paper, a technique of image watermarking using multiple images as watermarks is presented. The technique is based on transform domain functions including discrete wavelet transform (DWT), discrete cosine transform (DCT) and singular value decomposition (SVD) with an image as the host signal i.e. the watermarks will be used as proofs of the authenticity of the host image. The technique is executed by performing multilevel DWT followed by applying DCT and SVD to both the host and watermark. Multiple watermarks are used for the insurance of better security level. The scheme is immune to common image processing operations & some attacks and exhibits PSNR of 108.3781dB, normalized cross correlation (NCC) over 0.99 and normalized correlation (NC) over 0.99.

Despite the increasing popularity of liquid chromatography-mass spectrometry (LC-MS)-based lipidomics, there is a lack of accepted and validated method for lipid extract quality and quantity assessment prior to LC-MS. Fourier-Transform Infrared Spectroscopy (FTIR) has been reported for quantification of pure lipids, however, the sample complexity and purity complex lipid extract quantification in lipidomics experiments could be impact quantification accuracy. Here, we report comprehensive assessment of the sample matrix on the accuracy of lipid quantification using Attenuated Total Reflectance Fourier-Transform Infrared Spectroscopy (ATR-FTIR). Pure lipids are characterized by CH-and C=O-stretching vibrations on FTIR, with quantitative range of 40–3000 ng and a limit of detection of 12 ng. Sample extraction method and local baseline subtraction during FTIR spectral processing significantly impact lipid quantification by CH-stretching. To facilitate sample quality screening, we developed the Lipid Quality (LiQ) score from a spectral library of common contaminants, using a ratio of peak heights between CH-stretching vibrations maxima and the collective vibrations from amide/amine, CH-stretching minima and sugar moieties. We evaluated LiQ score as a rapid sample quality control method by comparing to total LC-MS intensity of targeted lipidomics of 107 human plasma lipid extracts. Exclusion of poor-quality samples based on LiQ score improved the correlation between FTIR and LC-MS quantification. Finally, the uncertainty of absolute quantification by FTIR was estimated using a 795 ng SPLASH LipidoMix standard to be &lt;10%. In summary, this study identified key parameters for accurate FTIR-based quantification of complex lipid mixture, and developed a rapid workflow requiring only 1 µL of MS-ready sample and &lt; 5 minutes for routine lipidomics sample quality and quantity assessment.

Objective:The Glioma brain tumor detection and segmentation methods are proposed in this paper using machine learning approaches. Methods:The boundary edge pixels are detected using Kirsch’s edge detectors and then contrast adaptive histogram equalization method is applied on the edge detected pixels. Then, Ridgelet transform is applied on this enhanced brain image in order to obtain the Ridgelet multi resolution coefficients. Further, features are derived from the Ridgelet transformed coefficients and the features are optimized using Principal Component Analysis (PCA) method and these optimized features are classified into Glioma or non-Glioma brain images using Co-Active Adaptive Neuro Fuzzy Expert System (CANFES) classifier.Results:The proposed method with PCA and CANFES classification approach obtains 97.6% of se, 98.56% of sp, 98.73% of Acc, 98.85% of Pr, 98.11% of FPR and 98.185 of FNR, then the proposed Glioma brain tumor detection method using CANFES classification approach only.

In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous, are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priory the accuracy.

This study advances the field of solar irradiance nowcasting by introducing a discrete-level classification approach, diverging from traditional continuous measurement methods. Grounded in a need for cost-effective and modular solutions, the research employs high-resolution computer vision coupled with a deep learning framework to predict Direct Normal Irradiance (DNI). By harnessing the capabilities of a Logitech C900 1080p HD camera and an NVIDIA Jetson module, the study achieves real-time data processing, pivotal for CSP systems' operational efficiency. The core of the methodology is the ResNet-50 convolutional neural network, refined via transfer learning on a bespoke dataset, culminating in a predictive accuracy of 85.78%. This discrete classification model contrasts with conventional, costly instruments like the MS-57, offering a novel and accessible alternative for DNI estimation. Such innovation not only demonstrates high predictive accuracy but also signifies a shift towards less resource-intensive and more adaptable solar energy forecasting tools, contributing a significant leap towards optimizing renewable energy systems.

By applying a running average (with a window-size= d), we could transform Discrete data to broad-range, Continuous values. When we have more than 2 columns and one of them is containing data about the tags of classification (Class Column), we could compare and sort the features (Non-class Columns) based on the R2 coefficient of the regression for running averages. The parameters tuning could help us to select the best features (the non-class columns which have the best correlation with the Class Column). “Window size” and “Ordering” could be tuned to achieve the goal. this optimization problem is hard and we need an Algorithm (or Heuristics) for simplifying this tuning. We demonstrate a novel heuristics, Called Simulated Distillation (SimulaD), which could help us to gain a somehow good results with this optimization problem.

Pit craters, and pit crater chains, are now recognised as being an important part of the surface morphology and structure of many planetary bodies, and are particularly remarkable on Mars. Pit craters do not possess the elevated rims, ejecta deposits, or other features that are typically associated with impact craters. They are thought to arise from the drainage/collapse of a relatively weak surficial material into an open (or widening) void in a much stronger material below. The creation of such voids has been suggested to be due to extensional fracturing/dilational faulting, shallow dike intrusion, lava tube collapse amongst other hypotheses. These craters have a very distinctive expression, often presenting funnel, cone, or bowl-shaped geometries. Analogue models of pit crater formation provide a map-view picture of their initiation and evolution but give little insight into their internal structure or geometry, but produce pits that typically have steep, nearly conical cross sections. Numerical modelling studies of their formation have been limited and have produced some quite interesting, but nonetheless puzzling, results whereby the simulated pit craters had generally convex (steepening downward) slope profiles with no distinct rim; quite unlike many of those observed on Earth or on Mars. To address these issues, I present here a high-resolution, 2D discrete element model of weak cover (regolith) collapse into either a static or a widening underlying void. I use frictional and frictional-cohesive discrete elements to represent a range of probable cover rheologies. Under Martian gravitational conditions, frictional-cohesive and frictional materials produce cone, bowl and scoop-shaped pit craters. For a given cover thickness, the specific crater shape depends on the amount of underlying void space created for drainage. When void space is small relative to cover thickness, craters have bowl or scoop-shaped geometries. In contrast, when void space is large relative to cover thickness, craters have cone-shaped geometries with essentially planar (nearing angle of repose) slope profiles. Frictional-cohesive materials exhibit more distinct rims than simple frictional materials and thus may reveal some stratigraphic layering on the pit crater walls. In the limit, when drainage from the overlying cover is insufficient to fill the underlying void, ´skylights´ into the deeper structure are created. Implications of these results for the interpretation of pit craters on Earth, Mars, other planets and moons are discussed.

In this study, we consider delta fractional Sturm--Liouville (DFSL) initial value problems in the sense of delta Caputo and delta Riemann-Liouville (R--L) operators. One of the properties of delta fractional difference operators which makes it different from nabla counterpart is to shift its domain. This feature makes it more complex than the nabla fractional operator. We obtain sum representation of solutions for DFSL initial value problems with the help of $\mathcal{Z}-$ transformation. Moreover, we get analytical solutions of homogeneous DFSL problem within Riemann-Liouville (R--L) and Caputo sense, discrete Sturm--Liouville (DSL) problem, continuous fractional Sturm--Liouville (FSL) problem in the sense of R--L and Caputo operators, and continuous Sturm--Liouville (SL) differential problem. From this point of view, we compare all the solutions with each other. Consequently, we show that all results for these four eigenvalue problems are compatible with each other and approach to each other while the orders tends to one, i.e. $\Delta^{\mu }\left( \Delta x\left( t-\mu \right) \right)\cong D_{0^{+}}^{\mu }\left( x^{\prime }\left( t\right) \right)\cong \Delta^2x(n-1) \cong x^{\prime \prime }\left( t\right) =\lambda x\left( t\right),\ \mu\rightarrow1 $ . We support our results comparatively by tables and simulations in detail.

Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp C., 2003). In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp C., 2003). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry (see Hipp C., 2016). Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility—concerning the ruin constraint—is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in (see Hipp C., 2016), Section 2.2.2 does also yield optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here. These gaps always exist in De Finetti models, see (see Hipp C., 2017).

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

This paper is concerned with the optimal linear quadratic Gaussian (LQG) control problem for discrete time-varying system with multiple input delays and multiplicative noises. The main contributions are two-fold. Firstly, when the state variables can be observed exactly, we obtain a necessary and suffcient condition for the multiple-delays system in terms of the non-homogeneous relationship between the state and costate, which is the solution to the coupled forward and backward stochastic difference equations. Secondly, when the state variables are partially observed, we derive a suboptimal linear output feedback controller for the discrete-time system based on the obtained results of the optimal LQG control. Numerical examples are shown to illustrate the proposed algorithm.

The celebrated geodesic congruence equation of Raychaudhuri, together with the resulting singularity theorems of Penrose and Hawking that it enabled, yield a highly general set of conditions under which a spacetime (or, more generically, a pseudo-Riemannian manifold) is expected to become geodesically incomplete. However, the proofs of these theorems traditionally depend upon a collection of assumptions about the continuum spacetime (and, in the physical case, the stress-energy distribution defined over it), including its global structure, its energy conditions, the existence of trapped null surfaces and the various volume/intersection properties of geodesic congruences, that are inherently difficult to translate to the case of discrete spacetime formalisms, such as causal set theory or the Wolfram model. Some, such as the discrete analog of Raychaudhuri's equation for the volumes of geodesic congruences, are subtle to formulate due to intrinsic differences in the behavior of discrete vs. continuous geodesics; for others, such as the definition of a trapped null surface, no appropriate translation is known for the general discrete case due to a lack of a priori coordinate information. It is therefore a non-trivial question to ask whether (and to what extent) there exist equivalently general conditions under which one expects discrete spacetimes to become geodesically incomplete, and how these conditions might differ from those in the continuum. This article builds upon previous work, in which the conformal and covariant Z4 (CCZ4) formulation of the Cauchy problem for the Einstein field equations, with constraint-violation damping, was defined in terms of Wolfram model evolution over discrete (spatial) hypergraphs for the case of vacuum spacetimes, and proceeds to consider a minimal extension to the non-vacuum case by introducing a massive scalar field distribution, defined in either spherical or axial symmetry. Under appropriate assumptions, this scalar field distribution admits a physical interpretation as a collapsing (and, in the axially-symmetric case, uniformly rotating) dust, and we are able to show, through a combination of rigorous mathematical analysis and explicit numerical simulation, that the resulting discrete spacetimes converge asymptotically to either non-rotating Schwarzschild black hole solutions or maximally-rotating (extremal) Kerr black hole solutions, respectively. Although the assumptions used in obtaining these preliminary results are very strong, they nevertheless offer hope that a more general, perhaps ultimately ``Penrose-like'', singularity theorem may be provable in the discrete spacetime case too.

High levels of meat consumption are increasingly being criticised for ethical, environmental, and social reasons. Plant-based meat substitutes have been identified as healthy sources of protein that, in comparison to meat, offer a number of social, environmental and health benefits and may play a role in reducing meat consumption. However, there has been a lack of research on the role they can play in the policy agenda and how specific meat substitute attributes can influence consumers to replace partially replace meat in their diets.

The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The result obtained is the approximation of the real value. There are few reports on the approximate error and the applicable condition. In this paper, according to the fractional expansions, we study the factors related to the approximate errors. Our research shows that the approximate errors relate not only to fractional order but also to time $t$ and increase rapidly with time $t$. This method can only be applied within a certain time range and the time range is relevant to fractional order and fractional expansions. Then, many obtained achievements may be incorrect if the applicable conditions are not satisfied. Some examples presented in this paper verify our analysis.

Estimating the remaining useful life (RUL) of components is a crucial task to enhance the reliability, safety, productivity, and to reduce maintenance cost. In general, predicting the RUL of a component includes constructing a health indicator ( ) to infer the current condition of the component, and modelling the degradation process, to estimate the future behavior. Although many signal processing and data-driven based methods were proposed to construct the , most of the existing methods are based on manual feature extraction techniques, and need the prior knowledge of experts, or rely on a large amount of failure data. Therefore, in this study, a new data-driven method based on the convolutional autoencoder (CAE) is presented to construct the . For this purpose, the continuous wavelet transform (CWT) technique is used to convert the raw acquired vibrational signals into a two-dimensional image; then, the CAE model is trained by the healthy operation dataset. Finally, the Mahalanobis Distance (MD) between the healthy and failure stages is measured as the . The proposed method is tested on a benchmark bearing dataset and compared with several other traditional construction models. Experimental results indicate that the constructed exhibits a monotonically increasing degradation trend and has a good performance to detect incipient faults.

Covariant integral quantization with rotational symmetry SO(3) is established for the quantum motion on this group manifold, or, alternatively, for Gabor signal analysis on this group. We revisit the action of the related (non-unitary) Weyl-Gabor operator on the Hilbert space of square integrable functions on SO(3) and disclose a set of various properties. By selecting weight functions on the corresponding discrete-continuous phase space, one derives related coherent states and Wigner transform.

The deployment of a manufacturing execution system (MES) holds promising potential in facilitating the accumulation of a substantial amount of inspection data. Low quality levels in discrete manufacturing environments are the result of multi-factor coupling and failure to find quality issues in a timely manner within manufacturing settings may trigger the propagation of defects downstream. Currently, most of the inspection quality methods are direct measurement followed by manual judgment. The integration of deep learning methods provides a feasible way to identify defects in a timely manner, thus improving the acceptance rate of factories. This paper focuses on the design of a data-driven quality prediction and control model around discrete manufacturing characteristics, and use fuzzy theory to evaluate the quality level of production stages. Building Multivariate Long and short-term memory learning hidden quality representations to extract predictions from multi-level inspection data in manufacturing systems. Finally, by validating the data of actual produced water dispensers according to three evaluation indexes, RMSE, MAE, MAPE, the results show that Multivariate Long and short-term memory has better prediction performance.

Stenting is a common method for treating atherosclerosis. A metal or polymer stent is deployed to open the stenosed artery or vein. After the stent is deployed, the blood flow dynamics influence the mechanics by compressing and expanding the structure. If the stent does not respond properly to the resulting stress, vascular wall injury or re-stenosis can occur. In this work, Discrete Multiphysics is used to study the mechanical deformation of the coronary stent and its relationship with the blood flow dynamics. The major parameters responsible for deforming the stent are sort in terms of dimensionless numbers and a relationship between the elastic forces in the stent and pressure forces in the fluid is established. The blood flow and the stiffness of the stent material contribute significantly to the stent deformation and affect the rate of deformation. The stress distribution in the stent is not uniform with the higher stresses occurring at the nodes of the structure.

We present progress in fast, high-resolution imaging, material classification, and fault detection using hyperspectral X-ray measurements. Classical X-ray CT approaches rely on data from many projection angles, resulting in long acquisition and reconstruction times. Additionally, conventional CT cannot distinguish between materials with similar densities. However, in additive manufacturing, the majority of materials used are known a priori. This knowledge allows to vastly reduce the data collected and increase the accuracy of fault detection. In this context, we propose an imaging method for non-destructive testing of materials based on the combination of spectral X-ray CT and discrete tomography. We explore the use of spectral X-ray attenuation models and measurements to recover the characteristic functions of materials in heterogeneous media with piece-wise uniform composition. We show by means of numerical simulation that using spectral measurements from a small number of angles, our approach can alleviate the typical deterioration of spatial resolution and the appearance of streaking artifacts.

In the process of image feature extraction, noise in the image will greatly affect the accuracy of edge detection. In this paper, the image is filtered to remove noise before edge detection by using the algorithm of wavelet transformation. Different wavelet functions are used to decompose image. Based on the experimental results, the best denoising wavelet function is selected. Canny algorithm is used to detect the edge of the denoised image, and the result of edge detection is evaluated according to the Pratt quality factor. It is proved that wavelet transform can improve the edge detection results.

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

In this paper, the Fourier-based synchrosqueezing transform (FSST) method is introduced into the power system to realize low frequency oscillation identification. Firstly, the modal components of low frequency oscillation signal are separated by FSST, and calculating the instantaneous parameters including magnitude, frequency and phase of every mode component with Hilbert transform. Then , calculating the damping ration of every modal component based on above parameters and derived the formulas. Thus, it realized effective identification of of modal parameters of low frequency oscillation signal. The experimental results of simulated data and 16-generator system demonstrate the validity and correctness of the FSST method. Comparing with the classical Prony method shows that the FSST method is better in the identification accuracy when the low frequency oscillation signal is polluted by noise. Finally, the effectiveness of the FSST in Actual power grid is verified based on the real data from Sichuan power grid.

In this paper, we proposed a high accurate and stable Legendre transform algorithm which can reduce the potential instability for very high order at a very small increase in the computational time. The error analysis of interpolative decomposition for Legendre transform is presented. By employing block partitioning of Legendre-Vandermonde matrix and butterfly algorithm, a new Legendre transform algorithm with computational complexity O(N(logN)^2/loglogN) in theory and less than O(N(logN)^4) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm.